{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import time\n", "from scipy.optimize import differential_evolution, minimize, dual_annealing\n", "import matplotlib.pyplot as plt\n", "import concurrent.futures\n", "import threading, multiprocessing\n", "\n", "import sys \n", "sys.path.append(\"../\") \n", "import minionpy as mpy\n", "import minionpy.test_functions as mpytest\n", "import time" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Minimizing Basic Functions\n", "\n", "In this section, we minimize basic functions such as Sphere, Rosenbrock, and Rastrigin. The search space is shifted to prevent algorithms from converging near the origin, as some algorithms tend to favor that region.\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The minimum of the function is \n", "\t x : [0.9999999999999998, 0.9999999999999996, 0.9999999999999997, 1.0, 0.9999999999999999] \n", "\t f(x) : 160200.0\n" ] } ], "source": [ "def sphere(x) : \n", " x =np.asarray(x)-1\n", " return 100+np.sum(x**2)\n", "\n", "def rosenbrock(x):\n", " #if x[0]<-1 or x[0]>1 : print(x, \"bound violated\")\n", " x = np.asarray(x)-5.0\n", " return 100+np.sum(100 * (x[1:] - x[:-1]**2)**2 + (1 - x[:-1])**2)\n", "\n", "def rastrigin(x):\n", " x = np.asarray(x)-1.0\n", " A = 10\n", " return 100+A * len(x) + np.sum(x**2 - A * np.cos(2 * np.pi * x))\n", "\n", "#remember that in minion, objective function must be vectorized. Suppose you want to \n", "func = rosenbrock\n", "def objective_function(X) : \n", " \"\"\" \n", " Here, X is a list of x, where x is an input vector. \n", " \"\"\"\n", " return [func(x) for x in X] \n", "\n", "#Now minimize the function using minion \n", "dimension = 5 #set dimension of the problem\n", "maxevals = 1000 #number of function calls\n", "x0 = [[0.0]*dimension] # initial guesses\n", "\n", "min = mpy.Minimizer(func=objective_function, x0=x0, bounds=[(-1, 1)]*dimension, algo=\"ARRDE\", relTol=0.0, \n", " maxevals=10000, callback=None, seed=None, options={\"minimum_population_size\":4})\n", "result = min.optimize()\n", "print(\"The minimum of the function is \", \"\\n\\t x : \", result.x, \"\\n\\t f(x) : \", result.fun)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Using Basic Test Functions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Minionpy provides a variety of test functions for evaluating optimization algorithms. The dictionary `testFunctionDict` below contains some of the fundamental functions available. Many of these functions have a global minimum at the origin, which can be problematic since some algorithms naturally converge toward it. To address this issue, CEC benchmark functions apply rotation and shifting to these basic functions, making them more representative of real-world optimization scenarios. \n", "\n", "The test functions in `minionpy.test_functions` are vectorized by default. They accept input as a 2D NumPy array.\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "testFunctionDict = {\n", " \"sphere\" : mpytest.sphere, \n", " \"rosenbrock\" : mpytest.rosenbrock, \n", " \"rastrigin\" : mpytest.rastrigin, \n", " \"schaffer2\" : mpytest.schaffer2, \n", " \"griewank\" : mpytest.griewank, \n", " \"ackley\" : mpytest.ackley, \n", " \"zakharov\" : mpytest.zakharov, \n", " \"bent_cigar\" : mpytest.bent_cigar, \n", " \"levy\" : mpytest.levy, \n", " \"discus\" : mpytest.discus, \n", " \"drop_wave\" : mpytest.drop_wave, \n", " \"goldstein_price\" : mpytest.goldstein_price, \n", " \"exponential\" : mpytest.exponential,\n", " \"quartic\" : mpytest.quartic, \n", " \"hybrid_composition1\" : mpytest.hybrid_composition1,\n", " \"hybrid_composition2\" : mpytest.hybrid_composition2,\n", " \"hybrid_composition3\" : mpytest.hybrid_composition3,\n", " \"happy_cat\" : mpytest.happy_cat, \n", " \"michalewics\" : mpytest.michalewicz,\n", " \"scaffer6\" : mpytest.scaffer6, \n", " \"hcf\" : mpytest.hcf, \n", " \"grie_rosen\" : mpytest.grie_rosen,\n", " \"dixon_price\" : mpytest.dixon_price, \n", " \"eosom\" : mpytest.easom, \n", " \"hgbat\" : mpytest.hgbat, \n", " \"styblinski_tang\" : mpytest.styblinski_tang, \n", " \"step\" : mpytest.step, \n", " \"weierstrass\" : mpytest.weierstrass, \n", " \"sum_squares\" : mpytest.sum_squares\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The performance of different algorithms to minimize these functions can be compared as shown below." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Function: sphere\n", "\tAlgorithm: DE f(x): 6.4594316e-07 Elapsed: 0.024 s\n", "\tAlgorithm: ABC f(x): 1.0122429e-06 Elapsed: 0.015 s\n", "\tAlgorithm: LSHADE f(x): 4.8582737e-10 Elapsed: 0.029 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): 6.3487577e-11 Elapsed: 0.023 s\n", "\tAlgorithm: JADE f(x): 9.2561239e-17 Elapsed: 0.024 s\n", "\tAlgorithm: jSO f(x): 3.23311e-11 Elapsed: 0.029 s\n", "\tAlgorithm: j2020 f(x): 2.5152134e-12 Elapsed: 0.096 s\n", "\tAlgorithm: LSRTDE f(x): 7.735322e-11 Elapsed: 0.015 s\n", "\tAlgorithm: NLSHADE_RSP f(x): 3.8201629e-10 Elapsed: 0.016 s\n", "\tAlgorithm: ARRDE f(x): 2.2758254e-25 Elapsed: 0.024 s\n", "\tAlgorithm: GWO_DE f(x): 3.8637342e-06 Elapsed: 0.016 s\n", "\tAlgorithm: NelderMead f(x): 4.6709368e-30 Elapsed: 0.031 s\n", "\tAlgorithm: DA f(x): 4.7770251e-15 Elapsed: 0.066 s\n", "\tAlgorithm: L_BFGS_B f(x): 8.5184112e-31 Elapsed: 0.000 s\n", "\tAlgorithm: PSO f(x): 2.4934109e-16 Elapsed: 0.015 s\n", "\tAlgorithm: DMSPSO f(x): 1.0116816e-15 Elapsed: 0.013 s\n", "\tAlgorithm: SPSO2011 f(x): 9.646589e-09 Elapsed: 0.018 s\n", "\tAlgorithm: CMAES f(x): 2.8681543e-13 Elapsed: 0.008 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): 8.7623091e-11 Elapsed: 0.008 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): 5.8359322e-09 Elapsed: 0.034 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): 6.9420299e-12 Elapsed: 0.004 s\n", "\tAlgorithm: Scipy DA f(x): 2.4294687e-16 Elapsed: 0.280 s\n", "\n", "Function: rosenbrock\n", "\tAlgorithm: DE f(x): 5.8036054 Elapsed: 0.016 s\n", "\tAlgorithm: ABC f(x): 4.4393332 Elapsed: 0.014 s\n", "\tAlgorithm: LSHADE f(x): 2.7117536 Elapsed: 0.026 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): 2.7873194 Elapsed: 0.026 s\n", "\tAlgorithm: JADE f(x): 2.3302768 Elapsed: 0.022 s\n", "\tAlgorithm: jSO f(x): 4.2779572 Elapsed: 0.027 s\n", "\tAlgorithm: j2020 f(x): 6.2863117 Elapsed: 0.137 s\n", "\tAlgorithm: LSRTDE f(x): 5.5999934 Elapsed: 0.016 s\n", "\tAlgorithm: NLSHADE_RSP f(x): 4.9742818 Elapsed: 0.018 s\n", "\tAlgorithm: ARRDE f(x): 2.9238755 Elapsed: 0.025 s\n", "\tAlgorithm: GWO_DE f(x): 7.5983039 Elapsed: 0.016 s\n", "\tAlgorithm: NelderMead f(x): 3.1653044e-27 Elapsed: 0.067 s\n", "\tAlgorithm: DA f(x): 1.2793334e-09 Elapsed: 0.112 s\n", "\tAlgorithm: L_BFGS_B f(x): 2.7409974e-12 Elapsed: 0.005 s\n", "\tAlgorithm: PSO f(x): 4.0906843 Elapsed: 0.014 s\n", "\tAlgorithm: DMSPSO f(x): 3.2080645 Elapsed: 0.018 s\n", "\tAlgorithm: SPSO2011 f(x): 6.3594034 Elapsed: 0.020 s\n", "\tAlgorithm: CMAES f(x): 0.1977988 Elapsed: 0.026 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): 8.3126645e-11 Elapsed: 0.027 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): 8.9958364e-09 Elapsed: 0.064 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): 1.1061741e-10 Elapsed: 0.012 s\n", "\tAlgorithm: Scipy DA f(x): 6.1826579e-11 Elapsed: 0.318 s\n", "\n", "Function: rastrigin\n", "\tAlgorithm: DE f(x): 15.91933 Elapsed: 0.016 s\n", "\tAlgorithm: ABC f(x): 0.0020894837 Elapsed: 0.014 s\n", "\tAlgorithm: LSHADE f(x): 2.8265663 Elapsed: 0.026 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): 1.2984332 Elapsed: 0.019 s\n", "\tAlgorithm: JADE f(x): 0.0005493625 Elapsed: 0.022 s\n", "\tAlgorithm: jSO f(x): 2.7930212 Elapsed: 0.029 s\n", "\tAlgorithm: j2020 f(x): 0.99495906 Elapsed: 0.131 s\n", "\tAlgorithm: LSRTDE f(x): 22.064574 Elapsed: 0.016 s\n", "\tAlgorithm: NLSHADE_RSP f(x): 2.2162852 Elapsed: 0.019 s\n", "\tAlgorithm: ARRDE f(x): 1.9899388 Elapsed: 0.027 s\n", "\tAlgorithm: GWO_DE f(x): 3.2014875 Elapsed: 0.017 s\n", "\tAlgorithm: NelderMead f(x): 102.47964 Elapsed: 0.020 s\n", "\tAlgorithm: DA f(x): 2.9848772 Elapsed: 0.097 s\n", "\tAlgorithm: L_BFGS_B f(x): 102.47964 Elapsed: 0.001 s\n", "\tAlgorithm: PSO f(x): 13.929397 Elapsed: 0.016 s\n", "\tAlgorithm: DMSPSO f(x): 13.015082 Elapsed: 0.021 s\n", "\tAlgorithm: SPSO2011 f(x): 19.370493 Elapsed: 0.028 s\n", "\tAlgorithm: CMAES f(x): 5.9697543 Elapsed: 0.080 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): 10.944545 Elapsed: 0.047 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): 254.70399 Elapsed: 0.032 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): 237.78983 Elapsed: 0.004 s\n", "\tAlgorithm: Scipy DA f(x): 6.3948846e-14 Elapsed: 0.356 s\n", "\n", "Function: schaffer2\n", "\tAlgorithm: DE f(x): 0.17246644 Elapsed: 0.224 s\n", "\tAlgorithm: ABC f(x): 0.16649813 Elapsed: 0.194 s\n", "\tAlgorithm: LSHADE f(x): 0.28156973 Elapsed: 0.222 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): 0.41557792 Elapsed: 0.202 s\n", "\tAlgorithm: JADE f(x): 0.23437661 Elapsed: 0.199 s\n", "\tAlgorithm: jSO f(x): 0.26111586 Elapsed: 0.209 s\n", "\tAlgorithm: j2020 f(x): 0.43476573 Elapsed: 0.253 s\n", "\tAlgorithm: LSRTDE f(x): 0.92118071 Elapsed: 0.208 s\n", "\tAlgorithm: NLSHADE_RSP f(x): 0.18376438 Elapsed: 0.194 s\n", "\tAlgorithm: ARRDE f(x): 0.13212947 Elapsed: 0.209 s\n", "\tAlgorithm: GWO_DE f(x): 0.56071983 Elapsed: 0.192 s\n", "\tAlgorithm: NelderMead f(x): 0.18775994 Elapsed: 0.117 s\n", "\tAlgorithm: DA f(x): 1.2267964e-14 Elapsed: 0.255 s\n", "\tAlgorithm: L_BFGS_B f(x): 0.18775994 Elapsed: 0.025 s\n", "\tAlgorithm: PSO f(x): 0.17015076 Elapsed: 0.198 s\n", "\tAlgorithm: DMSPSO f(x): 0.14245968 Elapsed: 0.190 s\n", "\tAlgorithm: SPSO2011 f(x): 0.89992984 Elapsed: 0.200 s\n", "\tAlgorithm: CMAES f(x): 0.47136894 Elapsed: 0.201 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): 0.54929968 Elapsed: 0.234 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): 0.38943872 Elapsed: 0.072 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): 0.38943873 Elapsed: 0.020 s\n", "\tAlgorithm: Scipy DA f(x): 0.087443189 Elapsed: 0.436 s\n", "\n", "Function: griewank\n", "\tAlgorithm: DE f(x): 0.039382435 Elapsed: 0.017 s\n", "\tAlgorithm: ABC f(x): 0.012211673 Elapsed: 0.018 s\n", "\tAlgorithm: LSHADE f(x): 0.041705992 Elapsed: 0.027 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): 0.0024145917 Elapsed: 0.021 s\n", "\tAlgorithm: JADE f(x): 0.044212076 Elapsed: 0.023 s\n", "\tAlgorithm: jSO f(x): 0.032435159 Elapsed: 0.032 s\n", "\tAlgorithm: j2020 f(x): 0.017241088 Elapsed: 0.169 s\n", "\tAlgorithm: LSRTDE f(x): 0.0073966469 Elapsed: 0.017 s\n", "\tAlgorithm: NLSHADE_RSP f(x): 0.025184437 Elapsed: 0.029 s\n", "\tAlgorithm: ARRDE f(x): 0.0073960405 Elapsed: 0.032 s\n", "\tAlgorithm: GWO_DE f(x): 0.019931597 Elapsed: 0.018 s\n", "\tAlgorithm: NelderMead f(x): 0.02461003 Elapsed: 0.032 s\n", "\tAlgorithm: DA f(x): 0.07529705 Elapsed: 0.095 s\n", "\tAlgorithm: L_BFGS_B f(x): 0.02461003 Elapsed: 0.002 s\n", "\tAlgorithm: PSO f(x): 0.078792042 Elapsed: 0.015 s\n", "\tAlgorithm: DMSPSO f(x): 0.017226294 Elapsed: 0.015 s\n", "\tAlgorithm: SPSO2011 f(x): 0.045022134 Elapsed: 0.018 s\n", "\tAlgorithm: CMAES f(x): 1.956213e-13 Elapsed: 0.010 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): 7.4974693e-11 Elapsed: 0.008 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): 0.046729411 Elapsed: 0.040 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): 0.024637062 Elapsed: 0.014 s\n", "\tAlgorithm: Scipy DA f(x): 0.019697357 Elapsed: 0.361 s\n", "\n", "Function: ackley\n", "\tAlgorithm: DE f(x): 2.4158131e-05 Elapsed: 0.017 s\n", "\tAlgorithm: ABC f(x): 0.0017400868 Elapsed: 0.017 s\n", "\tAlgorithm: LSHADE f(x): 0.0001666456 Elapsed: 0.028 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): 9.7505205e-06 Elapsed: 0.022 s\n", "\tAlgorithm: JADE f(x): 8.8892138e-10 Elapsed: 0.024 s\n", "\tAlgorithm: jSO f(x): 1.094312e-05 Elapsed: 0.031 s\n", "\tAlgorithm: j2020 f(x): 1.3658807e-10 Elapsed: 0.218 s\n", "\tAlgorithm: LSRTDE f(x): 5.2449461e-06 Elapsed: 0.018 s\n", "\tAlgorithm: NLSHADE_RSP f(x): 3.4322147e-05 Elapsed: 0.026 s\n", "\tAlgorithm: ARRDE f(x): 5.8943961e-12 Elapsed: 0.031 s\n", "\tAlgorithm: GWO_DE f(x): 0.0033328706 Elapsed: 0.018 s\n", "\tAlgorithm: NelderMead f(x): 9.0738777 Elapsed: 0.032 s\n", "\tAlgorithm: DA f(x): 9.2588487e-08 Elapsed: 0.104 s\n", "\tAlgorithm: L_BFGS_B f(x): 9.4529928 Elapsed: 0.001 s\n", "\tAlgorithm: PSO f(x): 5.102173e-08 Elapsed: 0.016 s\n", "\tAlgorithm: DMSPSO f(x): 1.3402275e-08 Elapsed: 0.016 s\n", "\tAlgorithm: SPSO2011 f(x): 8.8838955e-05 Elapsed: 0.019 s\n", "\tAlgorithm: CMAES f(x): 6.6835426e-13 Elapsed: 0.019 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): 5.9202865e-11 Elapsed: 0.016 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): 12.719749 Elapsed: 0.028 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): 12.719749 Elapsed: 0.004 s\n", "\tAlgorithm: Scipy DA f(x): 1.8047509e-08 Elapsed: 0.384 s\n", "\n", "Function: zakharov\n", "\tAlgorithm: DE f(x): 0.0050356294 Elapsed: 0.018 s\n", "\tAlgorithm: ABC f(x): 16.031338 Elapsed: 0.017 s\n", "\tAlgorithm: LSHADE f(x): 7.2962653e-06 Elapsed: 0.028 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): 1.5206326e-10 Elapsed: 0.021 s\n", "\tAlgorithm: JADE f(x): 5.1068813e-10 Elapsed: 0.026 s\n", "\tAlgorithm: jSO f(x): 5.8762452e-06 Elapsed: 0.030 s\n", "\tAlgorithm: j2020 f(x): 0.087694588 Elapsed: 0.233 s\n", "\tAlgorithm: LSRTDE f(x): 6.1099831e-09 Elapsed: 0.019 s\n", "\tAlgorithm: NLSHADE_RSP f(x): 0.0057944557 Elapsed: 0.023 s\n", "\tAlgorithm: ARRDE f(x): 9.8684862e-14 Elapsed: 0.031 s\n", "\tAlgorithm: GWO_DE f(x): 0.0066427977 Elapsed: 0.018 s\n", "\tAlgorithm: NelderMead f(x): 9.5208937e-30 Elapsed: 0.072 s\n", "\tAlgorithm: DA f(x): 3.5494939e-13 Elapsed: 0.175 s\n", "\tAlgorithm: L_BFGS_B f(x): 6.7711304e-15 Elapsed: 0.003 s\n", "\tAlgorithm: PSO f(x): 4.9073152e-09 Elapsed: 0.016 s\n", "\tAlgorithm: DMSPSO f(x): 1.1826456e-08 Elapsed: 0.018 s\n", "\tAlgorithm: SPSO2011 f(x): 0.005796406 Elapsed: 0.020 s\n", "\tAlgorithm: CMAES f(x): 2.1307953e-13 Elapsed: 0.015 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): 9.4183389e-11 Elapsed: 0.011 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): 7.6416259e-09 Elapsed: 0.086 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): 7.2717586e-14 Elapsed: 0.010 s\n", "\tAlgorithm: Scipy DA f(x): 1.465953e-14 Elapsed: 0.432 s\n", "\n", "Function: bent_cigar\n", "\tAlgorithm: DE f(x): 26.191855 Elapsed: 0.015 s\n", "\tAlgorithm: ABC f(x): 0.046922887 Elapsed: 0.013 s\n", "\tAlgorithm: LSHADE f(x): 0.0019367317 Elapsed: 0.026 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): 1.2389598e-05 Elapsed: 0.018 s\n", "\tAlgorithm: JADE f(x): 9.7328981e-11 Elapsed: 0.020 s\n", "\tAlgorithm: jSO f(x): 5.8346178e-05 Elapsed: 0.026 s\n", "\tAlgorithm: j2020 f(x): 2.4960754e-10 Elapsed: 0.112 s\n", "\tAlgorithm: LSRTDE f(x): 4.5403445e-08 Elapsed: 0.016 s\n", "\tAlgorithm: NLSHADE_RSP f(x): 0.000367709 Elapsed: 0.017 s\n", "\tAlgorithm: ARRDE f(x): 5.5363714e-17 Elapsed: 0.023 s\n", "\tAlgorithm: GWO_DE f(x): 0.45505858 Elapsed: 0.015 s\n", "\tAlgorithm: NelderMead f(x): 7.6172326e-24 Elapsed: 0.042 s\n", "\tAlgorithm: DA f(x): 6.9255571e-09 Elapsed: 0.049 s\n", "\tAlgorithm: L_BFGS_B f(x): 9.8449067e-16 Elapsed: 0.001 s\n", "\tAlgorithm: PSO f(x): 7.7289154e-08 Elapsed: 0.012 s\n", "\tAlgorithm: DMSPSO f(x): 1.2876138e-10 Elapsed: 0.014 s\n", "\tAlgorithm: SPSO2011 f(x): 5.9650724 Elapsed: 0.017 s\n", "\tAlgorithm: CMAES f(x): 8.0029119e-07 Elapsed: 0.022 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): 9.6219973e-11 Elapsed: 0.015 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): 98.947303 Elapsed: 0.030 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): 2.0992475e-10 Elapsed: 0.013 s\n", "\tAlgorithm: Scipy DA f(x): 2.2982927e-10 Elapsed: 0.293 s\n", "\n", "Function: levy\n", "\tAlgorithm: DE f(x): 2.2725093 Elapsed: 0.020 s\n", "\tAlgorithm: ABC f(x): 4.5570952e-07 Elapsed: 0.020 s\n", "\tAlgorithm: LSHADE f(x): 1.0829658e-08 Elapsed: 0.030 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): 3.5374864e-12 Elapsed: 0.024 s\n", "\tAlgorithm: JADE f(x): 7.3493567e-16 Elapsed: 0.028 s\n", "\tAlgorithm: jSO f(x): 1.1177129e-09 Elapsed: 0.032 s\n", "\tAlgorithm: j2020 f(x): 0.089528264 Elapsed: 0.280 s\n", "\tAlgorithm: LSRTDE f(x): 3.2525454e-13 Elapsed: 0.021 s\n", "\tAlgorithm: NLSHADE_RSP f(x): 7.7868421e-09 Elapsed: 0.025 s\n", "\tAlgorithm: ARRDE f(x): 2.6161962e-22 Elapsed: 0.034 s\n", "\tAlgorithm: GWO_DE f(x): 5.2462578e-06 Elapsed: 0.021 s\n", "\tAlgorithm: NelderMead f(x): 2.3300009 Elapsed: 0.075 s\n", "\tAlgorithm: DA f(x): 4.5034896e-15 Elapsed: 0.216 s\n", "\tAlgorithm: L_BFGS_B f(x): 0.1790565 Elapsed: 0.002 s\n", "\tAlgorithm: PSO f(x): 5.9713608e-16 Elapsed: 0.018 s\n", "\tAlgorithm: DMSPSO f(x): 1.5690238e-14 Elapsed: 0.019 s\n", "\tAlgorithm: SPSO2011 f(x): 5.5242815e-07 Elapsed: 0.022 s\n", "\tAlgorithm: CMAES f(x): 3.0082245e-13 Elapsed: 0.013 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): 7.6630845e-11 Elapsed: 0.010 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): 10.612364 Elapsed: 0.089 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): 5.6358232 Elapsed: 0.022 s\n", "\tAlgorithm: Scipy DA f(x): 1.5327518e-12 Elapsed: 0.501 s\n", "\n", "Function: discus\n", "\tAlgorithm: DE f(x): 6.5433889e-17 Elapsed: 0.014 s\n", "\tAlgorithm: ABC f(x): 8.5312468e-05 Elapsed: 0.012 s\n", "\tAlgorithm: LSHADE f(x): 3.4177328e-07 Elapsed: 0.025 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): 5.5745866e-11 Elapsed: 0.018 s\n", "\tAlgorithm: JADE f(x): 3.5753523e-16 Elapsed: 0.020 s\n", "\tAlgorithm: jSO f(x): 5.8742102e-09 Elapsed: 0.027 s\n", "\tAlgorithm: j2020 f(x): 9.1398502e-13 Elapsed: 0.111 s\n", "\tAlgorithm: LSRTDE f(x): 4.2485466e-13 Elapsed: 0.016 s\n", "\tAlgorithm: NLSHADE_RSP f(x): 5.5939541e-11 Elapsed: 0.016 s\n", "\tAlgorithm: ARRDE f(x): 1.9951317e-21 Elapsed: 0.024 s\n", "\tAlgorithm: GWO_DE f(x): 4.7217992e-05 Elapsed: 0.015 s\n", "\tAlgorithm: NelderMead f(x): 2.5838254e-24 Elapsed: 0.112 s\n", "\tAlgorithm: DA f(x): 4.1855874e-13 Elapsed: 0.050 s\n", "\tAlgorithm: L_BFGS_B f(x): 3.6369399e-13 Elapsed: 0.002 s\n", "\tAlgorithm: PSO f(x): 2.0870329e-12 Elapsed: 0.012 s\n", "\tAlgorithm: DMSPSO f(x): 9.7306774e-14 Elapsed: 0.013 s\n", "\tAlgorithm: SPSO2011 f(x): 102.02634 Elapsed: 0.016 s\n", "\tAlgorithm: CMAES f(x): 1.904148e-13 Elapsed: 0.016 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): 9.214248e-11 Elapsed: 0.012 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): 7.8818509e-09 Elapsed: 0.114 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): 7.8454908e-12 Elapsed: 0.010 s\n", "\tAlgorithm: Scipy DA f(x): 1.5357412e-07 Elapsed: 0.305 s\n", "\n", "Function: drop_wave\n", "\tAlgorithm: DE f(x): -1 Elapsed: 0.012 s\n", "\tAlgorithm: ABC f(x): -0.99400969 Elapsed: 0.030 s\n", "\tAlgorithm: LSHADE f(x): -0.99997043 Elapsed: 0.043 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): -1 Elapsed: 0.036 s\n", "\tAlgorithm: JADE f(x): -0.99999995 Elapsed: 0.038 s\n", "\tAlgorithm: jSO f(x): -1 Elapsed: 0.044 s\n", "\tAlgorithm: j2020 f(x): -1 Elapsed: 0.086 s\n", "\tAlgorithm: LSRTDE f(x): -1 Elapsed: 0.025 s\n", "\tAlgorithm: NLSHADE_RSP f(x): -1 Elapsed: 0.033 s\n", "\tAlgorithm: ARRDE f(x): -1 Elapsed: 0.041 s\n", "\tAlgorithm: GWO_DE f(x): -1 Elapsed: 0.035 s\n", "\tAlgorithm: NelderMead f(x): -1 Elapsed: 0.009 s\n", "\tAlgorithm: DA f(x): -0.93624533 Elapsed: 0.045 s\n", "\tAlgorithm: L_BFGS_B f(x): -0.93624533 Elapsed: 0.001 s\n", "\tAlgorithm: PSO f(x): -1 Elapsed: 0.030 s\n", "\tAlgorithm: DMSPSO f(x): -1 Elapsed: 0.031 s\n", "\tAlgorithm: SPSO2011 f(x): -1 Elapsed: 0.034 s\n", "\tAlgorithm: CMAES f(x): -0.93709275 Elapsed: 0.036 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): -0.32690614 Elapsed: 0.000 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): -0.053939199 Elapsed: 0.011 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): -0.060920875 Elapsed: 0.002 s\n", "\tAlgorithm: Scipy DA f(x): -0.93624533 Elapsed: 0.282 s\n", "\n", "Function: goldstein_price\n", "\tAlgorithm: DE f(x): 3 Elapsed: 0.016 s\n", "\tAlgorithm: ABC f(x): 8.4987029 Elapsed: 0.027 s\n", "\tAlgorithm: LSHADE f(x): 3 Elapsed: 0.042 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): 3 Elapsed: 0.033 s\n", "\tAlgorithm: JADE f(x): 3 Elapsed: 0.035 s\n", "\tAlgorithm: jSO f(x): 3 Elapsed: 0.040 s\n", "\tAlgorithm: j2020 f(x): 3 Elapsed: 0.083 s\n", "\tAlgorithm: LSRTDE f(x): 3 Elapsed: 0.025 s\n", "\tAlgorithm: NLSHADE_RSP f(x): 3 Elapsed: 0.028 s\n", "\tAlgorithm: ARRDE f(x): 3 Elapsed: 0.038 s\n", "\tAlgorithm: GWO_DE f(x): 3 Elapsed: 0.031 s\n", "\tAlgorithm: NelderMead f(x): 3 Elapsed: 0.009 s\n", "\tAlgorithm: DA f(x): 3 Elapsed: 0.062 s\n", "\tAlgorithm: L_BFGS_B f(x): 3 Elapsed: 0.002 s\n", "\tAlgorithm: PSO f(x): 3 Elapsed: 0.031 s\n", "\tAlgorithm: DMSPSO f(x): 3 Elapsed: 0.028 s\n", "\tAlgorithm: SPSO2011 f(x): 3.0000028 Elapsed: 0.031 s\n", "\tAlgorithm: CMAES f(x): 3 Elapsed: 0.034 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): 3 Elapsed: 0.044 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): 84 Elapsed: 0.015 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): 3 Elapsed: 0.006 s\n", "\tAlgorithm: Scipy DA f(x): 3 Elapsed: 0.283 s\n", "\n", "Function: exponential\n", "\tAlgorithm: DE f(x): -1 Elapsed: 0.012 s\n", "\tAlgorithm: ABC f(x): -0.99999972 Elapsed: 0.013 s\n", "\tAlgorithm: LSHADE f(x): -0.99999999 Elapsed: 0.026 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): -1 Elapsed: 0.021 s\n", "\tAlgorithm: JADE f(x): -1 Elapsed: 0.020 s\n", "\tAlgorithm: jSO f(x): -1 Elapsed: 0.028 s\n", "\tAlgorithm: j2020 f(x): -1 Elapsed: 0.115 s\n", "\tAlgorithm: LSRTDE f(x): -1 Elapsed: 0.014 s\n", "\tAlgorithm: NLSHADE_RSP f(x): -1 Elapsed: 0.017 s\n", "\tAlgorithm: ARRDE f(x): -1 Elapsed: 0.024 s\n", "\tAlgorithm: GWO_DE f(x): -0.99999861 Elapsed: 0.015 s\n", "\tAlgorithm: NelderMead f(x): -1 Elapsed: 0.021 s\n", "\tAlgorithm: DA f(x): -6.4343732e-10 Elapsed: 0.107 s\n", "\tAlgorithm: L_BFGS_B f(x): -1.609051e-22 Elapsed: 0.000 s\n", "\tAlgorithm: PSO f(x): -1 Elapsed: 0.013 s\n", "\tAlgorithm: DMSPSO f(x): -1 Elapsed: 0.015 s\n", "\tAlgorithm: SPSO2011 f(x): -1 Elapsed: 0.017 s\n", "\tAlgorithm: CMAES f(x): -8.2953178e-25 Elapsed: 0.000 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): -4.7836671e-18 Elapsed: 0.000 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): -1 Elapsed: 0.034 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): -5.2446221e-54 Elapsed: 0.001 s\n", "\tAlgorithm: Scipy DA f(x): -8.4503699e-12 Elapsed: 0.325 s\n", "\n", "Function: quartic\n", "\tAlgorithm: DE f(x): 0.009943409 Elapsed: 0.021 s\n", "\tAlgorithm: ABC f(x): 0.054496823 Elapsed: 0.019 s\n", "\tAlgorithm: LSHADE f(x): 0.0017695069 Elapsed: 0.032 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): 0.0022572815 Elapsed: 0.026 s\n", "\tAlgorithm: JADE f(x): 0.0065914268 Elapsed: 0.026 s\n", "\tAlgorithm: jSO f(x): 0.0055610006 Elapsed: 0.041 s\n", "\tAlgorithm: j2020 f(x): 0.0031824399 Elapsed: 0.177 s\n", "\tAlgorithm: LSRTDE f(x): 0.021650487 Elapsed: 0.022 s\n", "\tAlgorithm: NLSHADE_RSP f(x): 0.0050619586 Elapsed: 0.025 s\n", "\tAlgorithm: ARRDE f(x): 0.0087228958 Elapsed: 0.032 s\n", "\tAlgorithm: GWO_DE f(x): 0.0031042237 Elapsed: 0.022 s\n", "\tAlgorithm: NelderMead f(x): 3.2231466 Elapsed: 0.104 s\n", "\tAlgorithm: DA f(x): 0.0022227683 Elapsed: 0.061 s\n", "\tAlgorithm: L_BFGS_B f(x): 0.017609036 Elapsed: 0.008 s\n", "\tAlgorithm: PSO f(x): 0.0075577947 Elapsed: 0.017 s\n", "\tAlgorithm: DMSPSO f(x): 0.0054908702 Elapsed: 0.018 s\n", "\tAlgorithm: SPSO2011 f(x): 0.010998981 Elapsed: 0.023 s\n", "\tAlgorithm: CMAES f(x): 0.0048703297 Elapsed: 0.011 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): 0.0061883551 Elapsed: 0.008 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): 2.7828721 Elapsed: 0.233 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): 50784.288 Elapsed: 0.009 s\n", "\tAlgorithm: Scipy DA f(x): 0.20264968 Elapsed: 0.309 s\n", "\n", "Function: hybrid_composition1\n", "\tAlgorithm: DE f(x): 46.013054 Elapsed: 0.019 s\n", "\tAlgorithm: ABC f(x): 38.463758 Elapsed: 0.020 s\n", "\tAlgorithm: LSHADE f(x): 8.9683166 Elapsed: 0.029 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): 8.9683085 Elapsed: 0.024 s\n", "\tAlgorithm: JADE f(x): 8.9683084 Elapsed: 0.026 s\n", "\tAlgorithm: jSO f(x): 8.9683085 Elapsed: 0.032 s\n", "\tAlgorithm: j2020 f(x): 99.70699 Elapsed: 0.238 s\n", "\tAlgorithm: LSRTDE f(x): 8.9683084 Elapsed: 0.020 s\n", "\tAlgorithm: NLSHADE_RSP f(x): 8.9683102 Elapsed: 0.025 s\n", "\tAlgorithm: ARRDE f(x): 8.9683084 Elapsed: 0.034 s\n", "\tAlgorithm: GWO_DE f(x): 8.9729914 Elapsed: 0.020 s\n", "\tAlgorithm: NelderMead f(x): 8.9683084 Elapsed: 0.049 s\n", "\tAlgorithm: DA f(x): 47.137176 Elapsed: 0.173 s\n", "\tAlgorithm: L_BFGS_B f(x): 129.896 Elapsed: 0.002 s\n", "\tAlgorithm: PSO f(x): 8.9683084 Elapsed: 0.017 s\n", "\tAlgorithm: DMSPSO f(x): 8.9683084 Elapsed: 0.021 s\n", "\tAlgorithm: SPSO2011 f(x): 8.9683126 Elapsed: 0.021 s\n", "\tAlgorithm: CMAES f(x): 8.9683084 Elapsed: 0.028 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): 8.9683084 Elapsed: 0.050 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): 81.481178 Elapsed: 0.057 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): 49.451818 Elapsed: 0.011 s\n", "\tAlgorithm: Scipy DA f(x): 8.9683084 Elapsed: 0.482 s\n", "\n", "Function: hybrid_composition2\n", "\tAlgorithm: DE f(x): 1.938007e-05 Elapsed: 0.024 s\n", "\tAlgorithm: ABC f(x): 0.0039226331 Elapsed: 0.026 s\n", "\tAlgorithm: LSHADE f(x): 0.00032435022 Elapsed: 0.035 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): 1.5269293e-05 Elapsed: 0.029 s\n", "\tAlgorithm: JADE f(x): 3.0408034e-08 Elapsed: 0.033 s\n", "\tAlgorithm: jSO f(x): 8.890085e-05 Elapsed: 0.037 s\n", "\tAlgorithm: j2020 f(x): 1.0230618e-11 Elapsed: 0.419 s\n", "\tAlgorithm: LSRTDE f(x): 4.3133943e-06 Elapsed: 0.027 s\n", "\tAlgorithm: NLSHADE_RSP f(x): 2.5255503e-05 Elapsed: 0.033 s\n", "\tAlgorithm: ARRDE f(x): 1.6645973e-13 Elapsed: 0.044 s\n", "\tAlgorithm: GWO_DE f(x): 0.0060479569 Elapsed: 0.024 s\n", "\tAlgorithm: NelderMead f(x): 2.1270735 Elapsed: 0.145 s\n", "\tAlgorithm: DA f(x): 2.4179538e-07 Elapsed: 0.256 s\n", "\tAlgorithm: L_BFGS_B f(x): 2.1694175e-08 Elapsed: 0.012 s\n", "\tAlgorithm: PSO f(x): 2.8875353e-07 Elapsed: 0.023 s\n", "\tAlgorithm: DMSPSO f(x): 2.0066391e-07 Elapsed: 0.023 s\n", "\tAlgorithm: SPSO2011 f(x): 0.00062779798 Elapsed: 0.025 s\n", "\tAlgorithm: CMAES f(x): 5.7029468e-13 Elapsed: 0.031 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): 9.3565631e-11 Elapsed: 0.027 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): 9.7571206 Elapsed: 0.169 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): 6.6176766e-08 Elapsed: 0.093 s\n", "\tAlgorithm: Scipy DA f(x): 6.0014141e-08 Elapsed: 0.626 s\n", "\n", "Function: hybrid_composition3\n", "\tAlgorithm: DE f(x): 3.4767541 Elapsed: 0.033 s\n", "\tAlgorithm: ABC f(x): 53.301817 Elapsed: 0.041 s\n", "\tAlgorithm: LSHADE f(x): 1.2839623 Elapsed: 0.042 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): 1.2839526 Elapsed: 0.040 s\n", "\tAlgorithm: JADE f(x): 1.3071985 Elapsed: 0.045 s\n", "\tAlgorithm: jSO f(x): 1.2839527 Elapsed: 0.047 s\n", "\tAlgorithm: j2020 f(x): 1.3412612 Elapsed: 0.553 s\n", "\tAlgorithm: LSRTDE f(x): 1.2839526 Elapsed: 0.030 s\n", "\tAlgorithm: NLSHADE_RSP f(x): 1.2919624 Elapsed: 0.044 s\n", "\tAlgorithm: ARRDE f(x): 1.2839534 Elapsed: 0.054 s\n", "\tAlgorithm: GWO_DE f(x): 1.2913111 Elapsed: 0.031 s\n", "\tAlgorithm: NelderMead f(x): 34.881183 Elapsed: 0.154 s\n", "\tAlgorithm: DA f(x): 4.2578964 Elapsed: 0.313 s\n", "\tAlgorithm: L_BFGS_B f(x): 2.3887651 Elapsed: 0.009 s\n", "\tAlgorithm: PSO f(x): 1.2839526 Elapsed: 0.030 s\n", "\tAlgorithm: DMSPSO f(x): 1.2839526 Elapsed: 0.032 s\n", "\tAlgorithm: SPSO2011 f(x): 1.3137448 Elapsed: 0.039 s\n", "\tAlgorithm: CMAES f(x): 1.2839526 Elapsed: 0.052 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): 1.2839526 Elapsed: 0.071 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): 95.146651 Elapsed: 0.367 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): 17.427019 Elapsed: 0.060 s\n", "\tAlgorithm: Scipy DA f(x): 90.688619 Elapsed: 0.777 s\n", "\n", "Function: happy_cat\n", "\tAlgorithm: DE f(x): 0.23591693 Elapsed: 0.017 s\n", "\tAlgorithm: ABC f(x): 0.15177649 Elapsed: 0.017 s\n", "\tAlgorithm: LSHADE f(x): 0.10854896 Elapsed: 0.027 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): 0.055524206 Elapsed: 0.085 s\n", "\tAlgorithm: JADE f(x): 0.092597895 Elapsed: 0.025 s\n", "\tAlgorithm: jSO f(x): 0.076913426 Elapsed: 0.030 s\n", "\tAlgorithm: j2020 f(x): 0.19970891 Elapsed: 0.212 s\n", "\tAlgorithm: LSRTDE f(x): 0.068197151 Elapsed: 0.017 s\n", "\tAlgorithm: NLSHADE_RSP f(x): 0.15832575 Elapsed: 0.021 s\n", "\tAlgorithm: ARRDE f(x): 0.074841347 Elapsed: 0.030 s\n", "\tAlgorithm: GWO_DE f(x): 0.038752403 Elapsed: 0.017 s\n", "\tAlgorithm: NelderMead f(x): 0.67618088 Elapsed: 0.040 s\n", "\tAlgorithm: DA f(x): 0.33583457 Elapsed: 0.141 s\n", "\tAlgorithm: L_BFGS_B f(x): 0.31691389 Elapsed: 0.010 s\n", "\tAlgorithm: PSO f(x): 0.090518555 Elapsed: 0.016 s\n", "\tAlgorithm: DMSPSO f(x): 0.096716547 Elapsed: 0.017 s\n", "\tAlgorithm: SPSO2011 f(x): 0.067817495 Elapsed: 0.020 s\n", "\tAlgorithm: CMAES f(x): 0.076208409 Elapsed: 0.025 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): 0.079961817 Elapsed: 0.043 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): 1.4407279 Elapsed: 0.039 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): 0.005875464 Elapsed: 0.034 s\n", "\tAlgorithm: Scipy DA f(x): 0.16471355 Elapsed: 0.400 s\n", "\n", "Function: michalewics\n", "\tAlgorithm: DE f(x): -8.5815331 Elapsed: 0.024 s\n", "\tAlgorithm: ABC f(x): -8.4621134 Elapsed: 0.022 s\n", "\tAlgorithm: LSHADE f(x): -8.9894813 Elapsed: 0.034 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): -8.5499938 Elapsed: 0.027 s\n", "\tAlgorithm: JADE f(x): -9.2283196 Elapsed: 0.029 s\n", "\tAlgorithm: jSO f(x): -5.7529628 Elapsed: 0.037 s\n", "\tAlgorithm: j2020 f(x): -9.1168324 Elapsed: 0.169 s\n", "\tAlgorithm: LSRTDE f(x): -8.0371607 Elapsed: 0.024 s\n", "\tAlgorithm: NLSHADE_RSP f(x): -7.9501799 Elapsed: 0.026 s\n", "\tAlgorithm: ARRDE f(x): -9.6741515 Elapsed: 0.035 s\n", "\tAlgorithm: GWO_DE f(x): -4.6689961 Elapsed: 0.026 s\n", "\tAlgorithm: NelderMead f(x): -3.6164748 Elapsed: 0.135 s\n", "\tAlgorithm: DA f(x): -9.7854984 Elapsed: 0.083 s\n", "\tAlgorithm: L_BFGS_B f(x): -2.6919883 Elapsed: 0.006 s\n", "\tAlgorithm: PSO f(x): -8.1938975 Elapsed: 0.020 s\n", "\tAlgorithm: DMSPSO f(x): -4.5521755 Elapsed: 0.021 s\n", "\tAlgorithm: SPSO2011 f(x): -4.9307636 Elapsed: 0.025 s\n", "\tAlgorithm: CMAES f(x): -8.0447463 Elapsed: 0.030 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): -1.7133756 Elapsed: 0.000 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): -4.2489914 Elapsed: 0.054 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): -3.2901102 Elapsed: 0.021 s\n", "\tAlgorithm: Scipy DA f(x): -9.7935582 Elapsed: 0.349 s\n", "\n", "Function: scaffer6\n", "\tAlgorithm: DE f(x): 0.25249219 Elapsed: 0.192 s\n", "\tAlgorithm: ABC f(x): 0.18213552 Elapsed: 0.200 s\n", "\tAlgorithm: LSHADE f(x): 0.36538531 Elapsed: 0.207 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): 0.46483694 Elapsed: 0.199 s\n", "\tAlgorithm: JADE f(x): 0.15600834 Elapsed: 0.202 s\n", "\tAlgorithm: jSO f(x): 1.0107057 Elapsed: 0.206 s\n", "\tAlgorithm: j2020 f(x): 0.44059681 Elapsed: 0.256 s\n", "\tAlgorithm: LSRTDE f(x): 0.83658298 Elapsed: 0.189 s\n", "\tAlgorithm: NLSHADE_RSP f(x): 0.19632212 Elapsed: 0.203 s\n", "\tAlgorithm: ARRDE f(x): 0.14238011 Elapsed: 0.211 s\n", "\tAlgorithm: GWO_DE f(x): 0.17940201 Elapsed: 0.203 s\n", "\tAlgorithm: NelderMead f(x): 0.18775994 Elapsed: 0.121 s\n", "\tAlgorithm: DA f(x): 0.087443189 Elapsed: 0.241 s\n", "\tAlgorithm: L_BFGS_B f(x): 0.18775994 Elapsed: 0.023 s\n", "\tAlgorithm: PSO f(x): 0.11495147 Elapsed: 0.198 s\n", "\tAlgorithm: DMSPSO f(x): 0.32037117 Elapsed: 0.198 s\n", "\tAlgorithm: SPSO2011 f(x): 0.45037912 Elapsed: 0.198 s\n", "\tAlgorithm: CMAES f(x): 0.42270187 Elapsed: 0.203 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): 0.71153887 Elapsed: 0.215 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): 0.38943872 Elapsed: 0.065 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): 0.38943873 Elapsed: 0.020 s\n", "\tAlgorithm: Scipy DA f(x): 0.087443196 Elapsed: 0.420 s\n", "\n", "Function: hcf\n", "\tAlgorithm: DE f(x): 0.016643025 Elapsed: 0.015 s\n", "\tAlgorithm: ABC f(x): 0.003200968 Elapsed: 0.013 s\n", "\tAlgorithm: LSHADE f(x): 0.00054574173 Elapsed: 0.025 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): 2.6345598e-05 Elapsed: 0.021 s\n", "\tAlgorithm: JADE f(x): 1.3453768e-09 Elapsed: 0.023 s\n", "\tAlgorithm: jSO f(x): 1.5143254e-05 Elapsed: 0.029 s\n", "\tAlgorithm: j2020 f(x): 3.4540466e-08 Elapsed: 0.156 s\n", "\tAlgorithm: LSRTDE f(x): 1.5193954e-06 Elapsed: 0.015 s\n", "\tAlgorithm: NLSHADE_RSP f(x): 6.0449993e-06 Elapsed: 0.019 s\n", "\tAlgorithm: ARRDE f(x): 2.1678124e-13 Elapsed: 0.025 s\n", "\tAlgorithm: GWO_DE f(x): 0.0042892428 Elapsed: 0.015 s\n", "\tAlgorithm: NelderMead f(x): 2.358758 Elapsed: 0.137 s\n", "\tAlgorithm: DA f(x): 1.3036637e-07 Elapsed: 0.082 s\n", "\tAlgorithm: L_BFGS_B f(x): 5.4877386e-09 Elapsed: 0.006 s\n", "\tAlgorithm: PSO f(x): 3.6716305e-08 Elapsed: 0.013 s\n", "\tAlgorithm: DMSPSO f(x): 6.7345107e-08 Elapsed: 0.014 s\n", "\tAlgorithm: SPSO2011 f(x): 0.00076268558 Elapsed: 0.016 s\n", "\tAlgorithm: CMAES f(x): 6.6431452e-13 Elapsed: 0.016 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): 6.2473238e-11 Elapsed: 0.014 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): 9.2898681 Elapsed: 0.104 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): 3.9901546e-08 Elapsed: 0.038 s\n", "\tAlgorithm: Scipy DA f(x): 6.6041994e-08 Elapsed: 0.316 s\n", "\n", "Function: grie_rosen\n", "\tAlgorithm: DE f(x): 9.0927885 Elapsed: 0.016 s\n", "\tAlgorithm: ABC f(x): 4.9093932 Elapsed: 0.015 s\n", "\tAlgorithm: LSHADE f(x): 4.285257 Elapsed: 0.025 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): 1.9765677 Elapsed: 0.029 s\n", "\tAlgorithm: JADE f(x): 5.1477162 Elapsed: 0.024 s\n", "\tAlgorithm: jSO f(x): 5.6576765 Elapsed: 0.029 s\n", "\tAlgorithm: j2020 f(x): 1.0790723 Elapsed: 0.149 s\n", "\tAlgorithm: LSRTDE f(x): 5.9652161 Elapsed: 0.017 s\n", "\tAlgorithm: NLSHADE_RSP f(x): 3.8337539 Elapsed: 0.020 s\n", "\tAlgorithm: ARRDE f(x): 4.0831197 Elapsed: 0.026 s\n", "\tAlgorithm: GWO_DE f(x): 7.7043076 Elapsed: 0.017 s\n", "\tAlgorithm: NelderMead f(x): 1 Elapsed: 0.063 s\n", "\tAlgorithm: DA f(x): 1 Elapsed: 0.102 s\n", "\tAlgorithm: L_BFGS_B f(x): 1 Elapsed: 0.005 s\n", "\tAlgorithm: PSO f(x): 4.5445269 Elapsed: 0.014 s\n", "\tAlgorithm: DMSPSO f(x): 8.014341 Elapsed: 0.015 s\n", "\tAlgorithm: SPSO2011 f(x): 7.951165 Elapsed: 0.017 s\n", "\tAlgorithm: CMAES f(x): 1.0465555 Elapsed: 0.023 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): 1 Elapsed: 0.024 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): 1 Elapsed: 0.067 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): 1 Elapsed: 0.017 s\n", "\tAlgorithm: Scipy DA f(x): 1 Elapsed: 0.348 s\n", "\n", "Function: dixon_price\n", "\tAlgorithm: DE f(x): 0.66666667 Elapsed: 0.016 s\n", "\tAlgorithm: ABC f(x): 0.70458522 Elapsed: 0.018 s\n", "\tAlgorithm: LSHADE f(x): 0.66670683 Elapsed: 0.030 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): 0.66666667 Elapsed: 0.021 s\n", "\tAlgorithm: JADE f(x): 0.66666673 Elapsed: 0.023 s\n", "\tAlgorithm: jSO f(x): 0.66666667 Elapsed: 0.028 s\n", "\tAlgorithm: j2020 f(x): 0.063672199 Elapsed: 0.159 s\n", "\tAlgorithm: LSRTDE f(x): 0.66666681 Elapsed: 0.017 s\n", "\tAlgorithm: NLSHADE_RSP f(x): 0.66666667 Elapsed: 0.019 s\n", "\tAlgorithm: ARRDE f(x): 0.066966468 Elapsed: 0.027 s\n", "\tAlgorithm: GWO_DE f(x): 0.66738397 Elapsed: 0.017 s\n", "\tAlgorithm: NelderMead f(x): 0.66666667 Elapsed: 0.122 s\n", "\tAlgorithm: DA f(x): 0.66666667 Elapsed: 0.166 s\n", "\tAlgorithm: L_BFGS_B f(x): 0.66666667 Elapsed: 0.003 s\n", "\tAlgorithm: PSO f(x): 0.66666667 Elapsed: 0.019 s\n", "\tAlgorithm: DMSPSO f(x): 0.66666667 Elapsed: 0.016 s\n", "\tAlgorithm: SPSO2011 f(x): 0.66701749 Elapsed: 0.018 s\n", "\tAlgorithm: CMAES f(x): 0.66666667 Elapsed: 0.016 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): 0.66666667 Elapsed: 0.015 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): 0.66666667 Elapsed: 0.083 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): 0.66666667 Elapsed: 0.015 s\n", "\tAlgorithm: Scipy DA f(x): 0.66666667 Elapsed: 0.391 s\n", "\n", "Function: eosom\n", "\tAlgorithm: DE f(x): -0.0090056781 Elapsed: 0.027 s\n", "\tAlgorithm: ABC f(x): -0.0090054897 Elapsed: 0.038 s\n", "\tAlgorithm: LSHADE f(x): -0.0090056781 Elapsed: 0.053 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): -0.0090056781 Elapsed: 0.042 s\n", "\tAlgorithm: JADE f(x): -0.0090056781 Elapsed: 0.033 s\n", "\tAlgorithm: jSO f(x): -0.0090056781 Elapsed: 0.051 s\n", "\tAlgorithm: j2020 f(x): -0.0090056781 Elapsed: 0.091 s\n", "\tAlgorithm: LSRTDE f(x): -0.0090056781 Elapsed: 0.026 s\n", "\tAlgorithm: NLSHADE_RSP f(x): -0.0090056781 Elapsed: 0.035 s\n", "\tAlgorithm: ARRDE f(x): -0.0090056781 Elapsed: 0.045 s\n", "\tAlgorithm: GWO_DE f(x): -0.0090056781 Elapsed: 0.038 s\n", "\tAlgorithm: NelderMead f(x): -7.8737549e-14 Elapsed: 0.012 s\n", "\tAlgorithm: DA f(x): -0.0090056781 Elapsed: 0.087 s\n", "\tAlgorithm: L_BFGS_B f(x): 2.8026392e-10 Elapsed: 0.000 s\n", "\tAlgorithm: PSO f(x): -0.0090056781 Elapsed: 0.034 s\n", "\tAlgorithm: DMSPSO f(x): -0.0090056781 Elapsed: 0.034 s\n", "\tAlgorithm: SPSO2011 f(x): -0.0090056781 Elapsed: 0.038 s\n", "\tAlgorithm: CMAES f(x): -0.0090056781 Elapsed: 0.042 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): -8.1207696e-09 Elapsed: 0.000 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): -0.0090056781 Elapsed: 0.011 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): -1.4567312e-07 Elapsed: 0.001 s\n", "\tAlgorithm: Scipy DA f(x): -0.009005677 Elapsed: 0.284 s\n", "\n", "Function: hgbat\n", "\tAlgorithm: DE f(x): 0.50000754 Elapsed: 0.016 s\n", "\tAlgorithm: ABC f(x): 0.51557989 Elapsed: 0.015 s\n", "\tAlgorithm: LSHADE f(x): 0.50010291 Elapsed: 0.026 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): 0.50000301 Elapsed: 0.022 s\n", "\tAlgorithm: JADE f(x): 0.50000001 Elapsed: 0.024 s\n", "\tAlgorithm: jSO f(x): 0.50001693 Elapsed: 0.030 s\n", "\tAlgorithm: j2020 f(x): 0.50000009 Elapsed: 0.208 s\n", "\tAlgorithm: LSRTDE f(x): 0.50000148 Elapsed: 0.017 s\n", "\tAlgorithm: NLSHADE_RSP f(x): 0.5000157 Elapsed: 0.021 s\n", "\tAlgorithm: ARRDE f(x): 0.50000217 Elapsed: 0.028 s\n", "\tAlgorithm: GWO_DE f(x): 0.50186633 Elapsed: 0.020 s\n", "\tAlgorithm: NelderMead f(x): 0.5 Elapsed: 0.057 s\n", "\tAlgorithm: DA f(x): 0.50000007 Elapsed: 0.113 s\n", "\tAlgorithm: L_BFGS_B f(x): 0.5000013 Elapsed: 0.003 s\n", "\tAlgorithm: PSO f(x): 0.5000001 Elapsed: 0.014 s\n", "\tAlgorithm: DMSPSO f(x): 0.50000008 Elapsed: 0.015 s\n", "\tAlgorithm: SPSO2011 f(x): 0.50010615 Elapsed: 0.018 s\n", "\tAlgorithm: CMAES f(x): 0.5 Elapsed: 0.023 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): 0.5 Elapsed: 0.043 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): 0.5000703 Elapsed: 0.046 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): 0.50000001 Elapsed: 0.030 s\n", "\tAlgorithm: Scipy DA f(x): 0.50000002 Elapsed: 0.387 s\n", "\n", "Function: styblinski_tang\n", "\tAlgorithm: DE f(x): -349.2515 Elapsed: 0.022 s\n", "\tAlgorithm: ABC f(x): -391.66154 Elapsed: 0.021 s\n", "\tAlgorithm: LSHADE f(x): -391.65991 Elapsed: 0.033 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): -391.66165 Elapsed: 0.026 s\n", "\tAlgorithm: JADE f(x): -377.52494 Elapsed: 0.030 s\n", "\tAlgorithm: jSO f(x): -391.66166 Elapsed: 0.035 s\n", "\tAlgorithm: j2020 f(x): -391.66166 Elapsed: 0.156 s\n", "\tAlgorithm: LSRTDE f(x): -391.66166 Elapsed: 0.023 s\n", "\tAlgorithm: NLSHADE_RSP f(x): -391.66165 Elapsed: 0.026 s\n", "\tAlgorithm: ARRDE f(x): -391.66166 Elapsed: 0.033 s\n", "\tAlgorithm: GWO_DE f(x): -391.66157 Elapsed: 0.024 s\n", "\tAlgorithm: NelderMead f(x): -306.84134 Elapsed: 0.034 s\n", "\tAlgorithm: DA f(x): -391.66166 Elapsed: 0.096 s\n", "\tAlgorithm: L_BFGS_B f(x): -320.97806 Elapsed: 0.001 s\n", "\tAlgorithm: PSO f(x): -363.38822 Elapsed: 0.029 s\n", "\tAlgorithm: DMSPSO f(x): -391.66166 Elapsed: 0.023 s\n", "\tAlgorithm: SPSO2011 f(x): -375.97974 Elapsed: 0.024 s\n", "\tAlgorithm: CMAES f(x): -349.2515 Elapsed: 0.017 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): -43.926384 Elapsed: 0.000 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): -250.29447 Elapsed: 0.050 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): -292.70462 Elapsed: 0.006 s\n", "\tAlgorithm: Scipy DA f(x): -391.66166 Elapsed: 0.337 s\n", "\n", "Function: step\n", "\tAlgorithm: DE f(x): 0 Elapsed: 0.014 s\n", "\tAlgorithm: ABC f(x): 0 Elapsed: 0.012 s\n", "\tAlgorithm: LSHADE f(x): 0 Elapsed: 0.024 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): 0 Elapsed: 0.017 s\n", "\tAlgorithm: JADE f(x): 0 Elapsed: 0.021 s\n", "\tAlgorithm: jSO f(x): 0 Elapsed: 0.026 s\n", "\tAlgorithm: j2020 f(x): 0 Elapsed: 0.101 s\n", "\tAlgorithm: LSRTDE f(x): 0 Elapsed: 0.018 s\n", "\tAlgorithm: NLSHADE_RSP f(x): 0 Elapsed: 0.016 s\n", "\tAlgorithm: ARRDE f(x): 0 Elapsed: 0.023 s\n", "\tAlgorithm: GWO_DE f(x): 0 Elapsed: 0.015 s\n", "\tAlgorithm: NelderMead f(x): 98 Elapsed: 0.002 s\n", "\tAlgorithm: DA f(x): 0 Elapsed: 0.092 s\n", "\tAlgorithm: L_BFGS_B f(x): 103 Elapsed: 0.000 s\n", "\tAlgorithm: PSO f(x): 0 Elapsed: 0.011 s\n", "\tAlgorithm: DMSPSO f(x): 0 Elapsed: 0.012 s\n", "\tAlgorithm: SPSO2011 f(x): 0 Elapsed: 0.016 s\n", "\tAlgorithm: CMAES f(x): 0 Elapsed: 0.003 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): 0 Elapsed: 0.001 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): 256 Elapsed: 0.011 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): 256 Elapsed: 0.001 s\n", "\tAlgorithm: Scipy DA f(x): 0 Elapsed: 0.297 s\n", "\n", "Function: weierstrass\n", "\tAlgorithm: DE f(x): 3.9136649 Elapsed: 1.006 s\n", "\tAlgorithm: ABC f(x): 2.3385699 Elapsed: 1.012 s\n", "\tAlgorithm: LSHADE f(x): 1.697586 Elapsed: 0.980 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): 2.3747279 Elapsed: 1.051 s\n", "\tAlgorithm: JADE f(x): 0.62136377 Elapsed: 1.112 s\n", "\tAlgorithm: jSO f(x): 5.4126659 Elapsed: 1.567 s\n", "\tAlgorithm: j2020 f(x): 3.0273366 Elapsed: 1.165 s\n", "\tAlgorithm: LSRTDE f(x): 6.1535828 Elapsed: 0.958 s\n", "\tAlgorithm: NLSHADE_RSP f(x): 2.4954729 Elapsed: 1.008 s\n", "\tAlgorithm: ARRDE f(x): 0.79719085 Elapsed: 1.010 s\n", "\tAlgorithm: GWO_DE f(x): 8.0630304 Elapsed: 0.992 s\n", "\tAlgorithm: NelderMead f(x): 16.331325 Elapsed: 0.170 s\n", "\tAlgorithm: DA f(x): 7.5268862 Elapsed: 0.902 s\n", "\tAlgorithm: L_BFGS_B f(x): 17.260631 Elapsed: 0.571 s\n", "\tAlgorithm: PSO f(x): 0.024844903 Elapsed: 0.907 s\n", "\tAlgorithm: DMSPSO f(x): 2.7785439 Elapsed: 0.917 s\n", "\tAlgorithm: SPSO2011 f(x): 10.019956 Elapsed: 0.897 s\n", "\tAlgorithm: CMAES f(x): 0.0019573283 Elapsed: 0.914 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): 10.027648 Elapsed: 0.931 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): 6.4472257 Elapsed: 0.148 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): 16.582908 Elapsed: 0.166 s\n", "\tAlgorithm: Scipy DA f(x): 3.9593389 Elapsed: 1.191 s\n", "\n", "Function: sum_squares\n", "\tAlgorithm: DE f(x): 2.8608641e-05 Elapsed: 0.013 s\n", "\tAlgorithm: ABC f(x): 1.7911789e-06 Elapsed: 0.012 s\n", "\tAlgorithm: LSHADE f(x): 8.4431439e-08 Elapsed: 0.026 s\n", "\tAlgorithm: LSHADE_cnEpSin f(x): 9.2480663e-11 Elapsed: 0.018 s\n", "\tAlgorithm: JADE f(x): 3.3212172e-18 Elapsed: 0.019 s\n", "\tAlgorithm: jSO f(x): 6.4938347e-10 Elapsed: 0.024 s\n", "\tAlgorithm: j2020 f(x): 1.8269335e-12 Elapsed: 0.118 s\n", "\tAlgorithm: LSRTDE f(x): 1.8604918e-10 Elapsed: 0.016 s\n", "\tAlgorithm: NLSHADE_RSP f(x): 1.1120999e-10 Elapsed: 0.019 s\n", "\tAlgorithm: ARRDE f(x): 3.0589539e-24 Elapsed: 0.027 s\n", "\tAlgorithm: GWO_DE f(x): 1.9931301e-05 Elapsed: 0.022 s\n", "\tAlgorithm: NelderMead f(x): 8.310147e-30 Elapsed: 0.044 s\n", "\tAlgorithm: DA f(x): 2.1728419e-14 Elapsed: 0.082 s\n", "\tAlgorithm: L_BFGS_B f(x): 5.0791404e-13 Elapsed: 0.001 s\n", "\tAlgorithm: PSO f(x): 2.1701935e-14 Elapsed: 0.013 s\n", "\tAlgorithm: DMSPSO f(x): 1.4260877e-14 Elapsed: 0.016 s\n", "\tAlgorithm: SPSO2011 f(x): 8.9292414e-06 Elapsed: 0.016 s\n", "\tAlgorithm: CMAES f(x): 2.6773219e-13 Elapsed: 0.009 s\n", "\tAlgorithm: BIPOP_aCMAES f(x): 9.9939703e-11 Elapsed: 0.007 s\n", "\tAlgorithm: Scipy Nelder-Mead f(x): 1.6899228e-08 Elapsed: 0.033 s\n", "\tAlgorithm: Scipy L-BFGS-B f(x): 1.8569864e-11 Elapsed: 0.004 s\n", "\tAlgorithm: Scipy DA f(x): 3.4901676e-10 Elapsed: 0.305 s\n", "\n" ] } ], "source": [ "dimension = 10\n", "maxevals = 10000\n", "np.random.seed(1)\n", "shift = 10 * np.random.rand(dimension) # Shift randomly\n", "bounds = [(-10, 10)] * dimension\n", "x0 = [10 * np.random.rand(dimension)] # Initial guesses\n", "np.random.seed(None)\n", "\n", "for func_name in testFunctionDict:\n", " #if func_name not in [\"schaffer2\", \"ackley\", \"rastrigin\", \"rosenbrock\"]:\n", " # continue # Minimize only these functions; comment this line to compare all test functions\n", "\n", " print(f\"Function: {func_name}\")\n", "\n", " N = 0\n", "\n", " def objective_function(X):\n", " \"\"\"Shifted objective function for minimization.\"\"\"\n", " global N\n", " X = np.array(X) - shift # Shift the space\n", " N += len(X)\n", " return testFunctionDict[func_name](X)\n", "\n", " def objective_function_scipy(X):\n", " \"\"\"Objective function for SciPy optimizers.\"\"\"\n", " global N\n", " N += 1\n", " return testFunctionDict[func_name]([X])[0]\n", "\n", " algoList = [\n", " \"DE\", \"ABC\", \"LSHADE\", \"LSHADE_cnEpSin\", \"JADE\", \"jSO\", \"j2020\", \"LSRTDE\", \"NLSHADE_RSP\",\n", " \"ARRDE\", \"GWO_DE\", \"NelderMead\", \"DA\", \"L_BFGS_B\", \"PSO\", \"DMSPSO\", \"SPSO2011\", \"CMAES\", \"BIPOP_aCMAES\"\n", " ]\n", " \n", "\n", " for algo in algoList:\n", " t_start = time.time()\n", " N = 0\n", " result = mpy.Minimizer(\n", " func=objective_function, x0=x0, bounds=bounds, algo=algo, \n", " relTol=0.0, maxevals=maxevals, callback=None, seed=None,\n", " options={\"population_size\": 0}\n", " ).optimize()\n", " elapsed_time = time.time() - t_start\n", " print(f\"\\tAlgorithm: {algo:<18} f(x): {result.fun:<15.8g} Elapsed: {elapsed_time:.3f} s\")\n", "\n", " # Compare to SciPy algorithms\n", " algorithms_scipy = [\n", " (\"Scipy Nelder-Mead\", minimize, {\"x0\": x0[0], \"method\": \"Nelder-Mead\", \n", " \"bounds\": bounds, \"options\": {\"maxfev\": maxevals, \"adaptive\": True}}),\n", " (\"Scipy L-BFGS-B\", minimize, {\"x0\": x0[0], \"method\": \"L-BFGS-B\", \n", " \"options\": {\"maxfun\": maxevals}, \"bounds\": bounds}),\n", " (\"Scipy DA\", dual_annealing, {\"bounds\": bounds, \"maxfun\": maxevals, \"x0\": x0[0], \"no_local_search\": False})\n", " ]\n", "\n", " for name, func, kwargs in algorithms_scipy:\n", " t_start = time.time()\n", " N = 0\n", " result = func(objective_function_scipy, **kwargs)\n", " elapsed_time = time.time() - t_start\n", " print(f\"\\tAlgorithm: {name:<18} f(x): {result.fun:<15.8g} Elapsed: {elapsed_time:.3f} s\")\n", "\n", " print(\"\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Minimizing Expensive Functions with Multithreading/Multiprocessing\n", "\n", "When the objective function is expensive to evaluate, multithreading can be used to speed up the calculation of the vectorized objective function. However, this requires that the objective function is **thread-safe**. \n", "\n", "If the objective function is not thread-safe, then **multiprocessing** can be used instead. This approach allows parallel execution across separate processes, which avoids the potential issues with thread safety.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example to vectorize a thread-safe function using multithreading and multiprocessing\n", "If the function is thread-safe to call cuncurrently, then we can safely use concurrent.futures.ThreadPoolExecutor (for multithreading) or concurrent.futures.ProcessPoolExecutor (for multiproceesing) directly. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Optimization Results:\n", "====================================================================================================\n", "Algo : ARRDE | f(x) = 112.52055 | Elapsed: 1.62 sec\n", "Algo : L_BFGS_B | f(x) = 100 | Elapsed: 1.68 sec\n", "Algo : DA | f(x) = 100 | Elapsed: 3.70 sec\n", "Algo : Scipy Dual Annealing | f(x) = 100 | Elapsed: 10.34 sec\n", "Algo : Scipy L-BFGS-B | f(x) = 100 | Elapsed: 4.42 sec\n", "====================================================================================================\n" ] } ], "source": [ "# Function to minimize (expensive to evaluate)\n", "def func(x):\n", " ret = rosenbrock(x)\n", " time.sleep(0.01) # Simulate expensive computation\n", " return ret\n", "\n", "# Parallel execution setup\n", "Nthreads = 8\n", "use_threads = True # Toggle between ThreadPoolExecutor and ProcessPoolExecutor\n", "\n", "if use_threads:\n", " executor = concurrent.futures.ThreadPoolExecutor(max_workers=Nthreads)\n", "else:\n", " executor = concurrent.futures.ProcessPoolExecutor(max_workers=Nthreads)\n", "\n", "def objective_function(X):\n", " return list(executor.map(func, X)) # Batch evaluation in parallel\n", "\n", "# Optimization problem settings\n", "dimension = 10\n", "maxevals = 1000\n", "x0 = [[3.0] * dimension]\n", "bounds = [(-10, 10)] * dimension\n", "\n", "# List of algorithms to test\n", "algorithms = {\n", " \"ARRDE\": {\"options\": None},\n", " \"L_BFGS_B\": {\"options\": {\"func_noise_ratio\": 0.0, \"N_points_derivative\": 1}},\n", " \"DA\": {\"options\": None}\n", "}\n", "\n", "print(\"\\nOptimization Results:\")\n", "print(\"=\" * 100)\n", "\n", "# Run optimizations using Minion\n", "for algo, settings in algorithms.items():\n", " start_time = time.time()\n", " minimizer = mpy.Minimizer(\n", " func=objective_function,\n", " x0=x0,\n", " bounds=bounds,\n", " algo=algo,\n", " relTol=0.0,\n", " maxevals=maxevals,\n", " callback=None,\n", " seed=None,\n", " options=settings[\"options\"]\n", " )\n", " result = minimizer.optimize()\n", " elapsed = time.time() - start_time\n", "\n", " print(f\"Algo : {algo:<30} | f(x) = {result.fun:<20.8g} | Elapsed: {elapsed:.2f} sec\")\n", "\n", "# Compare with SciPy optimizers (without multithreading)\n", "for algo, opt_func in [\n", " (\"Scipy Dual Annealing\", dual_annealing),\n", " (\"Scipy L-BFGS-B\", minimize)\n", "]:\n", " start_time = time.time()\n", " if algo == \"Scipy Dual Annealing\":\n", " result = opt_func(func, bounds=bounds, maxfun=maxevals, no_local_search=False, x0=x0[0])\n", " else:\n", " result = opt_func(func, x0=x0[0], method=\"L-BFGS-B\", options={\"maxfun\": maxevals}, bounds=bounds)\n", "\n", " elapsed = time.time() - start_time\n", " print(f\"Algo : {algo:<30} | f(x) = {result.fun:<20.8g} | Elapsed: {elapsed:.2f} sec\")\n", "\n", "print(\"=\" * 100)\n", "\n", "# Shutdown executor gracefully\n", "executor.shutdown()\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The algorithms implemented in Minion (ARRDE, L-BFGS-B, and Dual Annealing) significantly outperform their SciPy counterparts in speed. This performance improvement stems from Minion’s efficient numerical derivative computation, which batches function evaluations—an approach that greatly benefits minion's L-BFGS-B and Dual Annealing. Note that dual annealing use L-BFGS-B for local search.\n", "\n", "------------------" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using `minionpy.Thread_Parallel` to vectorize non-thread-safe member function\n", "\n", "In the previous example, we demonstrated how to minimize a thread-safe function. However, in real-world scenarios, the objective function is often a method of a class, and class methods are typically **not thread-safe**. In this example, we demonstrate how to minimize a **non-thread-safe function** using the `Thread_Parallel` class. This approach ensures proper parallelization even when the objective function modifies internal state, which can lead to race conditions in a multi-threaded environment.\n", "\n", "### 1. Define the Class with `objective_function`\n", "\n", "First, define a class that includes the `objective_function`. This function should accept a list of floats as input and return a single float as the output. In this example, the `objective_function` modifies an internal state, which makes it non-thread-safe. We will show how the minionpy `Thread_Parallel` class manages the parallel execution of such functions while ensuring thread isolation." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "class Objective : \n", " \"\"\" \n", " This illustrate a class with a non-thread-safe self.objective_function\n", " \"\"\"\n", " def __init__ (self, b) : \n", " self.A=None # There is a now class member that will be modified when self.objective_function is called.\n", " self.b = b\n", " \n", " def update_A(self, x) : \n", " self.A = self.b*np.sin(x) #modify self.A\n", " time.sleep(0.05) #simulate an expensive function\n", "\n", " def objective_function(self, x) : \n", " self.update_A(x)\n", " ret = np.sum(self.A*x) \n", " #print(x, ret)\n", " return ret" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2. Define the Thread_Parallel object" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vectorization using Thread_Parallel : \n", "\t [0.5661370676468356, 0.7775659672127234, 0.4229914027614482, 0.5303959761143511, 0.3761453211372047, 0.5522159710759306, 0.38951343396507465, 0.556718173281366]\n", "Elapsed : 0.05110669136047363 \n", "\n", "Calling the function sequentially : \n", "\t [0.5661370676468356, 0.7775659672127234, 0.4229914027614482, 0.5303959761143511, 0.3761453211372047, 0.5522159710759306, 0.38951343396507465, 0.556718173281366]\n", "Elapsed : 0.40199875831604004 \n", "\n", "True\n" ] } ], "source": [ "# Here, we vectorize `Objective.objective_function` using 8 threads, with the `b` parameter in the Objective class constructor set to `0.2`.\n", "t_parallel = mpy.Thread_Parallel(8, Objective, 0.2) \n", "\n", "#You can test the vectorization as follows : \n", "X = np.random.rand(8, 8) #randomly creates 6 vectors of dimension 8\n", "start = time.time()\n", "res = t_parallel(X) \n", "print(\"Vectorization using Thread_Parallel : \\n\\t\", res) \n", "print(\"Elapsed : \", time.time()-start, \"\\n\")\n", "\n", "obj=Objective(b=0.2)\n", "start = time.time()\n", "res2 = [obj.objective_function(x) for x in X]\n", "print(\"Calling the function sequentially : \\n\\t\", res2) \n", "print(\"Elapsed : \", time.time()-start, \"\\n\")\n", "\n", "#test if res and res2 are exactly the same \n", "print(np.array(res).all() == np.array(res2).all())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3. Minimize using one of minionpy algorithms" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Algo : ARRDE \n", "\t x : [-4.8745482242483, 4.2532696314673295, 4.636776364023326, -4.935053006852719, -4.893801687256062, 4.2541727836417795, -4.5347783796462, 5.555873294650024] \n", "\t f(x) : -6.969264085741495 \n", "\t Elapsed: 7.983117580413818 seconds\n", "\n", "Test function value : -6.969264085741495\n" ] } ], "source": [ "dimension = 8 #set dimension of the problem\n", "maxevals = 1000 #number of function calls\n", "x0 = [[3.0]*dimension] # initial guess\n", "bounds = [(-10, 10)]*dimension\n", "algo = \"ARRDE\" \n", "\n", "now = time.time()\n", "min = mpy.Minimizer(func=t_parallel, x0=x0, bounds=bounds, algo=algo, relTol=0.0,\n", " maxevals=maxevals, callback=None, seed=None, options={\"population_size\": 0})\n", "result = min.optimize()\n", "elapsed= time.time()-now\n", "print(\"Algo : \",algo, \"\\n\\t x : \", result.x, \"\\n\\t f(x) : \", result.fun, \"\\n\\t Elapsed: \", elapsed, \" seconds\\n\")\n", "print(\"Test function value : \", Objective(b=0.2).objective_function(np.asarray(result.x)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can observe that the minimum found by the ARRDE algorithm corresponds to the correct function value. But what happens if we use ThreadPoolExecutor without considering the thread-safety of the objective_function method?" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Algo : ARRDE \n", "\t x : [-4.9085261023046725, 9.855798668604562, 5.326274488405682, -9.870938023916791, -6.328512976971076, -9.748500557841409, -9.603724177180414, 9.362136235173324] \n", "\t f(x) : -7.418963223826018 \n", "\t Elapsed: 7.983393907546997 seconds\n", "\n", "Test function value : -4.296564752042263\n" ] } ], "source": [ "obj = Objective(b=0.2)\n", "executor = concurrent.futures.ThreadPoolExecutor(max_workers=8)\n", "\n", "def vectorize_obj(X) : \n", " ret = list(executor.map(obj.objective_function, np.asarray(X)))\n", " return ret\n", "\n", "now = time.time()\n", "min = mpy.Minimizer(func=vectorize_obj, x0=x0, bounds=bounds, algo=algo, relTol=0.0, maxevals=maxevals, callback=None, seed=None, options=None)\n", "result = min.optimize()\n", "elapsed= time.time()-now\n", "print(\"Algo : \",algo, \"\\n\\t x : \", result.x, \"\\n\\t f(x) : \", result.fun, \"\\n\\t Elapsed: \", elapsed, \" seconds\\n\")\n", "print(\"Test function value :\", obj.objective_function(np.asarray(result.x)))\n", "executor.shutdown(wait=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that the function value of the minimum is not the same as the actual function value. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using multiprocessing for non-thread-safe functions using `minionpy.Process_Parallel`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If multiprocessing is preferred over multithreading—whether to bypass the Global Interpreter Lock (GIL) or to ensure clean separation of data during objective function vectorization—`minionpy` provides the `Process_Parallel` feature. It follows the same usage rules as `Thread_Parallel`. When using `Process_Parallel`, a predefined number of reusable processes are created, each with its own instance of the class object." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vectorization using Process_Parallel : \n", "\t [0.5304442646984987, 0.20451016023783655, 0.10655265370931162, 0.2714407459077475, 0.2980790126820181, 0.315356307197812, 0.19289203891937706, 0.440687150822349]\n", "Elapsed : 0.12279987335205078 \n", "\n", "Calling the function sequentially : \n", "\t [0.5304442646984987, 0.20451016023783655, 0.10655265370931162, 0.2714407459077475, 0.2980790126820181, 0.315356307197812, 0.19289203891937706, 0.440687150822349]\n", "Elapsed : 0.4028041362762451 \n", "\n", "True\n" ] } ], "source": [ "p_parallel = mpy.Process_Parallel(8, Objective, 0.2) \n", "\n", "#You can test the vectorization as follows : \n", "start = time.time()\n", "X = np.random.rand(8, 6) #randomly creates 6 vectors of dimension 8\n", "res = p_parallel(X) \n", "print(\"Vectorization using Process_Parallel : \\n\\t\", res) \n", "print(\"Elapsed : \", time.time()-start, \"\\n\")\n", "\n", "obj=Objective(b=0.2)\n", "start = time.time()\n", "res2 = [obj.objective_function(x) for x in X]\n", "print(\"Calling the function sequentially : \\n\\t\", res2) \n", "print(\"Elapsed : \", time.time()-start, \"\\n\")\n", "\n", "#test if res and res2 are exactly the same \n", "print(np.array(res).all() == np.array(res2).all())" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Algo : ARRDE \n", "\t x : [-5.292044833018368, 4.166986458579692, 4.488022614476481, 5.0228088678480765, 5.23266594020464, -4.826695879758527, -1.209896518319117, 4.336840773972577] \n", "\t f(x) : -5.877285885951624 \n", "\t Elapsed: 8.18626880645752 seconds\n", "\n", "Test function value : -5.877285885951624\n" ] } ], "source": [ "dimension = 8 #set dimension of the problem\n", "maxevals = 1000 #number of function calls\n", "x0 = [[3.0]*dimension] # initial guess\n", "bounds = [(-10, 10)]*dimension\n", "algo = \"ARRDE\" \n", "\n", "now = time.time()\n", "min = mpy.Minimizer(func=p_parallel, x0=x0, bounds=bounds, algo=algo, relTol=0.0,\n", " maxevals=maxevals, callback=None, seed=None, options={\"population_size\": 0})\n", "result = min.optimize()\n", "elapsed= time.time()-now\n", "print(\"Algo : \",algo, \"\\n\\t x : \", result.x, \"\\n\\t f(x) : \", result.fun, \"\\n\\t Elapsed: \", elapsed, \" seconds\\n\")\n", "print(\"Test function value : \", Objective(b=0.2).objective_function(np.asarray(result.x)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Algorithm Comparisons Using CEC Benchmark Problems\n", "\n", "We can compare the performance of different optimization algorithms by evaluating them on benchmark problems from the Congress on Evolutionary Computation (CEC) competition. The Minion library provides implementations of benchmark problems from the following CEC years: 2011, 2014, 2017, 2019, 2020, and 2022.\n", "\n", "- **CEC2014 and CEC2017**: These benchmarks contain 30 problems, implemented for dimensions 10, 20, 30, 50, and 100.\n", "- **CEC2019**: This set includes 10 problems with varying dimensions.\n", "- **CEC2020**: It contains 10 problems with dimensions 5, 10, 15, and 20.\n", "- **CEC2022**: This set consists of 12 problems with dimensions 10 and 20.\n", "\n", "CEC problems typically include a variety of function types:\n", "- **Basic functions** (e.g., Rosenbrock, Rastrigin),\n", "- **Hybrid functions** (new functions constructed by combining basic functions, where each component is evaluated using a different basic function),\n", "- **Composite functions** (linear combinations of basic functions, where the coefficients are also functions of the input vector).\n", "\n", "These functions are often shifted and rotated to introduce additional complexity.\n", "\n", "CEC2011 consists of a set of real-world problems, idealized and simplified for the competition. It contains 22 problems of varying dimensions. Note that, for CEC2011, MATLAB must be installed on the system. An example of how to minimize CEC2011 problems can be found in `examples/cec_11.py`.\n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Running optimization for func_1 (Dimension: 20)\n", "============================================================\n", " DE f(x): 300 \n", " ABC f(x): 42484.882 \n", " LSHADE f(x): 300 \n", " LSHADE_cnEpSin f(x): 300 \n", " JADE f(x): 300 \n", " jSO f(x): 300 \n", " j2020 f(x): 300.00003 \n", " LSRTDE f(x): 300 \n", " NLSHADE_RSP f(x): 300 \n", " ARRDE f(x): 300 \n", " GWO_DE f(x): 302.76135 \n", " NelderMead f(x): 300 \n", " DA f(x): 300 \n", " L_BFGS_B f(x): 300 \n", " PSO f(x): 300 \n", " DMSPSO f(x): 300 \n", " SPSO2011 f(x): 300 \n", " CMAES f(x): 300 \n", " BIPOP_aCMAES f(x): 300 \n", " Scipy L-BFGS-B f(x): 300 \n", " Scipy Nelder-Mead f(x): 300 \n", " Scipy DA f(x): 300 \n", "------------------------------------------------------------\n", "\n", "Running optimization for func_2 (Dimension: 20)\n", "============================================================\n", " DE f(x): 447.55901 \n", " ABC f(x): 407.15048 \n", " LSHADE f(x): 400 \n", " LSHADE_cnEpSin f(x): 400 \n", " JADE f(x): 400 \n", " jSO f(x): 400 \n", " j2020 f(x): 417.14573 \n", " LSRTDE f(x): 444.89547 \n", " NLSHADE_RSP f(x): 406.39281 \n", " ARRDE f(x): 401.54981 \n", " GWO_DE f(x): 415.17322 \n", " NelderMead f(x): 403.98662 \n", " DA f(x): 419.41087 \n", " L_BFGS_B f(x): 449.08448 \n", " PSO f(x): 400.02232 \n", " DMSPSO f(x): 400.38118 \n", " SPSO2011 f(x): 449.08461 \n", " CMAES f(x): 449.08448 \n", " BIPOP_aCMAES f(x): 400 \n", " Scipy L-BFGS-B f(x): 449.08448 \n", " Scipy Nelder-Mead f(x): 449.08451 \n", " Scipy DA f(x): 449.08448 \n", "------------------------------------------------------------\n", "\n", "Running optimization for func_3 (Dimension: 20)\n", "============================================================\n", " DE f(x): 614.63684 \n", " ABC f(x): 600 \n", " LSHADE f(x): 600 \n", " LSHADE_cnEpSin f(x): 600 \n", " JADE f(x): 600 \n", " jSO f(x): 600 \n", " j2020 f(x): 600 \n", " LSRTDE f(x): 600 \n", " NLSHADE_RSP f(x): 600 \n", " ARRDE f(x): 600 \n", " GWO_DE f(x): 600 \n", " NelderMead f(x): 668.52549 \n", " DA f(x): 600.00018 \n", " L_BFGS_B f(x): 668.52549 \n", " PSO f(x): 602.1189 \n", " DMSPSO f(x): 603.30578 \n", " SPSO2011 f(x): 600.74689 \n", " CMAES f(x): 600.0014 \n", " BIPOP_aCMAES f(x): 600 \n", " Scipy L-BFGS-B f(x): 668.5255 \n", " Scipy Nelder-Mead f(x): 668.01149 \n", " Scipy DA f(x): 600.00025 \n", "------------------------------------------------------------\n", "\n", "Running optimization for func_4 (Dimension: 20)\n", "============================================================\n", " DE f(x): 855.74959 \n", " ABC f(x): 903.25862 \n", " LSHADE f(x): 815.61138 \n", " LSHADE_cnEpSin f(x): 806.08713 \n", " JADE f(x): 810.98604 \n", " jSO f(x): 805.9698 \n", " j2020 f(x): 816.60306 \n", " LSRTDE f(x): 803.97984 \n", " NLSHADE_RSP f(x): 860.76871 \n", " ARRDE f(x): 808.95884 \n", " GWO_DE f(x): 816.91429 \n", " NelderMead f(x): 890.54093 \n", " DA f(x): 882.58133 \n", " L_BFGS_B f(x): 890.54093 \n", " PSO f(x): 869.64682 \n", " DMSPSO f(x): 865.66707 \n", " SPSO2011 f(x): 816.28376 \n", " CMAES f(x): 811.9395 \n", " BIPOP_aCMAES f(x): 815.91933 \n", " Scipy L-BFGS-B f(x): 890.54093 \n", " Scipy Nelder-Mead f(x): 883.57629 \n", " Scipy DA f(x): 890.54093 \n", "------------------------------------------------------------\n", "\n", "Running optimization for func_5 (Dimension: 20)\n", "============================================================\n", " DE f(x): 997.54474 \n", " ABC f(x): 3323.5121 \n", " LSHADE f(x): 900 \n", " LSHADE_cnEpSin f(x): 900 \n", " JADE f(x): 900 \n", " jSO f(x): 900 \n", " j2020 f(x): 900 \n", " LSRTDE f(x): 900 \n", " NLSHADE_RSP f(x): 900 \n", " ARRDE f(x): 900 \n", " GWO_DE f(x): 900 \n", " NelderMead f(x): 2456.1107 \n", " DA f(x): 3071.5902 \n", " L_BFGS_B f(x): 2458.8608 \n", " PSO f(x): 1440.6716 \n", " DMSPSO f(x): 905.12867 \n", " SPSO2011 f(x): 900.54385 \n", " CMAES f(x): 900 \n", " BIPOP_aCMAES f(x): 900.99818 \n", " Scipy L-BFGS-B f(x): 2458.8608 \n", " Scipy Nelder-Mead f(x): 2457.1933 \n", " Scipy DA f(x): 2561.3842 \n", "------------------------------------------------------------\n", "\n", "Running optimization for func_6 (Dimension: 20)\n", "============================================================\n", " DE f(x): 1971.8282 \n", " ABC f(x): 5574.1072 \n", " LSHADE f(x): 1806.1336 \n", " LSHADE_cnEpSin f(x): 1800.3056 \n", " JADE f(x): 1898.8808 \n", " jSO f(x): 1800.4832 \n", " j2020 f(x): 1901.664 \n", " LSRTDE f(x): 1800.4834 \n", " NLSHADE_RSP f(x): 1887.2841 \n", " ARRDE f(x): 1841.3002 \n", " GWO_DE f(x): 11668.098 \n", " NelderMead f(x): 1844.2033 \n", " DA f(x): 1808.1163 \n", " L_BFGS_B f(x): 1909.0077 \n", " PSO f(x): 3848.7742 \n", " DMSPSO f(x): 10168.1 \n", " SPSO2011 f(x): 4657.2054 \n", " CMAES f(x): 1806.9352 \n", " BIPOP_aCMAES f(x): 1859.0192 \n", " Scipy L-BFGS-B f(x): 1872.5365 \n", " Scipy Nelder-Mead f(x): 2054.1894 \n", " Scipy DA f(x): 1814.9411 \n", "------------------------------------------------------------\n", "\n", "Running optimization for func_7 (Dimension: 20)\n", "============================================================\n", " DE f(x): 2027.7862 \n", " ABC f(x): 2033.9782 \n", " LSHADE f(x): 2025.7557 \n", " LSHADE_cnEpSin f(x): 2021.0581 \n", " JADE f(x): 2024.9837 \n", " jSO f(x): 2022.072 \n", " j2020 f(x): 2023.9772 \n", " LSRTDE f(x): 2001.3071 \n", " NLSHADE_RSP f(x): 2021.717 \n", " ARRDE f(x): 2023.3001 \n", " GWO_DE f(x): 2036.9376 \n", " NelderMead f(x): 2526.423 \n", " DA f(x): 2112.0289 \n", " L_BFGS_B f(x): 2527.3806 \n", " PSO f(x): 2070.0527 \n", " DMSPSO f(x): 2060.1259 \n", " SPSO2011 f(x): 2047.5546 \n", " CMAES f(x): 2063.0947 \n", " BIPOP_aCMAES f(x): 2021.6167 \n", " Scipy L-BFGS-B f(x): 2545.9195 \n", " Scipy Nelder-Mead f(x): 2617.3528 \n", " Scipy DA f(x): 2092.0307 \n", "------------------------------------------------------------\n", "\n", "Running optimization for func_8 (Dimension: 20)\n", "============================================================\n", " DE f(x): 2238.4151 \n", " ABC f(x): 2223.2242 \n", " LSHADE f(x): 2222.6411 \n", " LSHADE_cnEpSin f(x): 2216.5047 \n", " JADE f(x): 2221.7319 \n", " jSO f(x): 2224.0222 \n", " j2020 f(x): 2223.5503 \n", " LSRTDE f(x): 2224.9593 \n", " NLSHADE_RSP f(x): 2221.0833 \n", " ARRDE f(x): 2222.3926 \n", " GWO_DE f(x): 2230.2027 \n", " NelderMead f(x): 2636.8799 \n", " DA f(x): 2381.8641 \n", " L_BFGS_B f(x): 2991.1908 \n", " PSO f(x): 2222.561 \n", " DMSPSO f(x): 2222.4891 \n", " SPSO2011 f(x): 2227.6319 \n", " CMAES f(x): 2220.3577 \n", " BIPOP_aCMAES f(x): 2220.64 \n", " Scipy L-BFGS-B f(x): 2933.0533 \n", " Scipy Nelder-Mead f(x): 2890.3671 \n", " Scipy DA f(x): 2221.8949 \n", "------------------------------------------------------------\n", "\n", "Running optimization for func_9 (Dimension: 20)\n", "============================================================\n", " DE f(x): 2465.3437 \n", " ABC f(x): 2480.7875 \n", " LSHADE f(x): 2465.3435 \n", " LSHADE_cnEpSin f(x): 2465.3435 \n", " JADE f(x): 2465.3435 \n", " jSO f(x): 2465.3435 \n", " j2020 f(x): 2465.3435 \n", " LSRTDE f(x): 2480.7813 \n", " NLSHADE_RSP f(x): 2465.3435 \n", " ARRDE f(x): 2465.3435 \n", " GWO_DE f(x): 2465.3435 \n", " NelderMead f(x): 2465.3435 \n", " DA f(x): 2467.4003 \n", " L_BFGS_B f(x): 2480.7813 \n", " PSO f(x): 2465.3435 \n", " DMSPSO f(x): 2465.3435 \n", " SPSO2011 f(x): 2480.804 \n", " CMAES f(x): 2480.7813 \n", " BIPOP_aCMAES f(x): 2465.3435 \n", " Scipy L-BFGS-B f(x): 2480.7813 \n", " Scipy Nelder-Mead f(x): 2480.8289 \n", " Scipy DA f(x): 2480.7813 \n", "------------------------------------------------------------\n", "\n", "Running optimization for func_10 (Dimension: 20)\n", "============================================================\n", " DE f(x): 2500.5172 \n", " ABC f(x): 2400.1877 \n", " LSHADE f(x): 2400.4037 \n", " LSHADE_cnEpSin f(x): 2500.2849 \n", " JADE f(x): 2500.4683 \n", " jSO f(x): 2500.3194 \n", " j2020 f(x): 2400.1874 \n", " LSRTDE f(x): 2500.3617 \n", " NLSHADE_RSP f(x): 2500.4406 \n", " ARRDE f(x): 2400.0625 \n", " GWO_DE f(x): 2618.8727 \n", " NelderMead f(x): 6169.0617 \n", " DA f(x): 2425.1178 \n", " L_BFGS_B f(x): 6109.5459 \n", " PSO f(x): 3083.2547 \n", " DMSPSO f(x): 2632.1121 \n", " SPSO2011 f(x): 2500.3924 \n", " CMAES f(x): 3359.1873 \n", " BIPOP_aCMAES f(x): 2500.6549 \n", " Scipy L-BFGS-B f(x): 6287.3523 \n", " Scipy Nelder-Mead f(x): 5683.4727 \n", " Scipy DA f(x): 2400.0937 \n", "------------------------------------------------------------\n", "\n", "Running optimization for func_11 (Dimension: 20)\n", "============================================================\n", " DE f(x): 3023.9238 \n", " ABC f(x): 2672.2987 \n", " LSHADE f(x): 2900 \n", " LSHADE_cnEpSin f(x): 3000 \n", " JADE f(x): 3000 \n", " jSO f(x): 2900 \n", " j2020 f(x): 2905.675 \n", " LSRTDE f(x): 3000 \n", " NLSHADE_RSP f(x): 2900 \n", " ARRDE f(x): 2900 \n", " GWO_DE f(x): 3000 \n", " NelderMead f(x): 3000 \n", " DA f(x): 2900 \n", " L_BFGS_B f(x): 2900 \n", " PSO f(x): 2900 \n", " DMSPSO f(x): 2900 \n", " SPSO2011 f(x): 2900 \n", " CMAES f(x): 2900 \n", " BIPOP_aCMAES f(x): 2900 \n", " Scipy L-BFGS-B f(x): 2900 \n", " Scipy Nelder-Mead f(x): 2900.0004 \n", " Scipy DA f(x): 2900 \n", "------------------------------------------------------------\n", "\n", "Running optimization for func_12 (Dimension: 20)\n", "============================================================\n", " DE f(x): 2892.4733 \n", " ABC f(x): 2947.1646 \n", " LSHADE f(x): 2900.0039 \n", " LSHADE_cnEpSin f(x): 2900.004 \n", " JADE f(x): 2900.0041 \n", " jSO f(x): 2900.0038 \n", " j2020 f(x): 2900.0042 \n", " LSRTDE f(x): 2933.6674 \n", " NLSHADE_RSP f(x): 2900.004 \n", " ARRDE f(x): 2900.0043 \n", " GWO_DE f(x): 2900.004 \n", " NelderMead f(x): 5490.2128 \n", " DA f(x): 2900.0049 \n", " L_BFGS_B f(x): 5113.3733 \n", " PSO f(x): 2893.2191 \n", " DMSPSO f(x): 2900.0048 \n", " SPSO2011 f(x): 2940.0228 \n", " CMAES f(x): 2963.1768 \n", " BIPOP_aCMAES f(x): 2900.0048 \n", " Scipy L-BFGS-B f(x): 3382.9172 \n", " Scipy Nelder-Mead f(x): 5108.8009 \n", " Scipy DA f(x): 3059.5899 \n", "------------------------------------------------------------\n" ] } ], "source": [ "import threading\n", "import concurrent.futures\n", "\n", "# This script minimizes CEC benchmark problems, repeated for NRuns times.\n", "\n", "# Global results variable\n", "results = []\n", "results_lock = threading.Lock()\n", "\n", "def test_optimization(func, bounds, dimension, func_name, Nmaxeval, seed):\n", " \"\"\"Runs optimization algorithms on a given function and stores the results.\"\"\"\n", " global results\n", " result = {\n", " \"Dimensions\": dimension,\n", " \"Function\": func_name\n", " }\n", " \n", " bounds_list = [bounds] * dimension\n", " x0 = [[0.0 for _ in range(dimension)]]\n", "\n", " print(f\"\\nRunning optimization for {func_name} (Dimension: {dimension})\")\n", " print(\"=\" * 60)\n", "\n", " for algo in algos:\n", " res = mpy.Minimizer(\n", " func, bounds_list, x0=x0, relTol=0.0, algo=algo, \n", " maxevals=Nmaxeval, callback=None, seed=None, \n", " options={\n", " \"population_size\" : 0, #2*dimension, \n", " \"func_noise_ratio\" : 0.0, \n", " \"N_points_derivative\": 1, \n", " \"bound_strategy\" : \"none\"\n", " }\n", " ).optimize()\n", " result[algo] = res.fun\n", " print(f\" {algo:<15} f(x): {res.fun:<20.8g}\")\n", "\n", " def func_scipy(par):\n", " return func([par])[0]\n", " \n", " # SciPy Optimizers\n", " scipy_algorithms = [\n", " (\"Scipy L-BFGS-B\", minimize, {\"x0\": x0[0], \"method\": \"L-BFGS-B\", \"options\": {\"maxfun\": Nmaxeval}, \"bounds\": bounds_list}),\n", " (\"Scipy Nelder-Mead\", minimize, {\"x0\": x0[0], \"method\": \"Nelder-Mead\", \"bounds\": bounds_list, \"options\": {\"maxfev\": Nmaxeval, \"adaptive\": True}}),\n", " (\"Scipy DA\", dual_annealing, {\"bounds\": bounds_list, \"maxfun\": Nmaxeval, \"no_local_search\": False, \"x0\": x0[0]}),\n", " ]\n", "\n", " for name, func_opt, kwargs in scipy_algorithms:\n", " res = func_opt(func_scipy, **kwargs)\n", " result[name] = res.fun\n", " print(f\" {name:<15} f(x): {res.fun:<20.8g}\")\n", "\n", " with results_lock:\n", " results.append(result)\n", "\n", " print(\"-\" * 60)\n", "\n", "def run_test_optimization(j, dim, year=2017, seed=None):\n", " \"\"\"Runs the optimization for a specific function and CEC benchmark year.\"\"\"\n", " cec_func_classes = {\n", " 2014: mpy.CEC2014Functions,\n", " 2017: mpy.CEC2017Functions,\n", " 2019: mpy.CEC2019Functions,\n", " 2020: mpy.CEC2020Functions,\n", " 2022: mpy.CEC2022Functions\n", " }\n", " \n", " if year not in cec_func_classes:\n", " raise Exception(\"Unknown CEC year.\")\n", " \n", " cec_func = cec_func_classes[year](function_number=j, dimension=dim)\n", " test_optimization(cec_func, (-100, 100), dim, f\"func_{j}\", Nmaxeval, seed)\n", "\n", "# List of algorithms to be tested\n", "algos = [\n", " \"DE\", \"ABC\", \"LSHADE\", \"LSHADE_cnEpSin\", \"JADE\", \"jSO\", \"j2020\", \"LSRTDE\", \"NLSHADE_RSP\",\n", " \"ARRDE\", \"GWO_DE\", \"NelderMead\", \"DA\", \"L_BFGS_B\", \"PSO\", \"DMSPSO\", \"SPSO2011\", \"CMAES\", \"BIPOP_aCMAES\"\n", "]\n", "\n", "Nmaxeval = 200000 # Maximum number of function evaluations\n", "dimension = 20\n", "NRuns = 1 # Number of repetitions\n", "year = 2022 # CEC benchmark year\n", "\n", "# Function numbers for each CEC year\n", "func_numbers_dict = {\n", " 2022: list(range(1, 13)),\n", " 2020: list(range(1, 11)),\n", " 2019: list(range(1, 11)),\n", " 2017: list(range(1, 31)),\n", " 2014: list(range(1, 31)),\n", "}\n", "func_numbers = func_numbers_dict[year]\n", "\n", "# Run optimizations using multi-threading\n", "with concurrent.futures.ThreadPoolExecutor(max_workers=1) as executor:\n", " futures = [\n", " executor.submit(run_test_optimization, j, dimension, year, k)\n", " for k in range(NRuns)\n", " for j in func_numbers\n", " ]\n", " concurrent.futures.wait(futures)\n", " \n", " for f in futures:\n", " f.result()\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Example of using minion/py in curve fitting problems\n", "\n", "\n", "Here, an example of using minion to minimize an objective function related to a curve fitting problem is demonstrated. \n", "The idea is first to define the data generation model, generate the data, fit the model, and report the result. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Polynomial Fitting Problems\n", "In this problem, we try fit a polynomial from a set of data. Specifically, a set of points ($\\{(x_i, y_i) \\mid i = 1, 2, \\dots, N\\}$) with $x \\in [0, 1]$ is generated according to:\n", "$$\n", " f(x, a) = \\sum_{j=0}^{D-1} a_j x^j\n", "$$\n", "Given the coefficients $a_j$ that generate the data, the goal is to reproduce the data points by minimizing the objective function:\n", "$$\n", " L = \\frac{1}{N}\\sum_{i=1}^N \\left(y_i - f(x_i, a)\\right)^2 \n", "$$\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Optimization Results:\n", "==================================================\n", "DE : f(x) = 3.4676234e-07 \n", "ABC : f(x) = 0.0056994221 \n", "LSHADE : f(x) = 4.0557789e-10 \n", "LSHADE_cnEpSin : f(x) = 3.3043359e-14 \n", "JADE : f(x) = 5.251496e-08 \n", "jSO : f(x) = 9.774338e-11 \n", "j2020 : f(x) = 8.4535903e-05 \n", "LSRTDE : f(x) = 1.4773705e-12 \n", "NLSHADE_RSP : f(x) = 7.1946723e-06 \n", "ARRDE : f(x) = 4.2782791e-09 \n", "GWO_DE : f(x) = 1.2315456e-05 \n", "NelderMead : f(x) = 4.0539659e-15 \n", "DA : f(x) = 2.521779e-05 \n", "L_BFGS_B : f(x) = 7.2866825e-07 \n", "PSO : f(x) = 3.5313431e-05 \n", "DMSPSO : f(x) = 2.6368825e-05 \n", "SPSO2011 : f(x) = 0.00054992829 \n", "CMAES : f(x) = 8.5261952e-12 \n", "BIPOP_aCMAES : f(x) = 9.9424922e-11 \n", "Scipy Dual Annealing (DA) : f(x) = 7.3242064e-07 \n", "Scipy L-BFGS-B : f(x) = 7.3242064e-07 \n", "Scipy Nelder-Mead : f(x) = 2.1676521e-11 \n", "==================================================\n" ] }, { "data": { "image/png": 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hwoUnXR5gyZIllJWVkZ+fz6effsppp53GkSNHCA0NJTEx0btcjx49TnpQdPyyERER3k8dGjJmzBgWL17MfffdR1xcHFdddRUHDhw4aT1FxyQdfh851R3RRPNJptqSPLUnmWpL8mydpKQkTZdrDx2hzk6nk/fee4/Ro0cD8Oijj7Jlyxa+/fZbLBYLBw8eBH4bYtTQheXTpk1jzJgx7N+/H4vFwkMPPdTgMKVTSUlJwWaz1bmA+MCBAy2eirOhus6dO5fvvvuO7OxsQkJCuPXWW1u0beFb0uH3Ab1eT0ZGhvyx0pBkqi3JU3uSqbYkz9YbOXIkKSkpjd6tU1EUUlNTGTlyZDvXrHG+rvPu3buZNWsW5eXlzJ8/HwCLxUJoaCjR0dFYrVYWLlxYZ52EhAQOHTpU57oCi8WC2WwmIiKCXbt28dRTT7WoPsnJyYwZM4a//OUvVFZWkp2dzUMPPcSsWbNatL2EhAT27dvn/f7HH39k48aN2O12wsLCiIiIwGAwtGjbwrekw+8DqqpisVhadDQvGiaZakvy1J5kqi3Js/X0ej0rVqxo8LnaDvXy5cs71EHV8XU+sdPfVnVesGCBdx7+yZMnk5iYyObNm0lISABg/vz56PV6EhISGDRoEOecc06d9adOnUpUVBRxcXHeGXOeeeYZ/vnPf3pnw7n22mtbXL/XXnuN6upqunXrxrnnnstll13GXXfd1aJtLVy4kMcff5zo6Gjmzp2LxWJh7ty5xMbGkpiYSG5ubqM/M6JjU1T5bXlSFosFk8lEeXk5UVFRmmzT5XKRlZUlZ6c0JJlqS/LUnmSqLclTO6uee5k//uUWSi2/TQuZmprK8uXLmTx5cqu23djfUJvNxoEDB+jevTuhoaHN3u7q1au57bbb6oxV16rOQviL5ryP5HMZIYQQohM7u+cQnr9jFNsPVxATlcKg8b9j9OjRHfpAavLkyUycOJH169eTl5dHUlISI0eO7NB1FsKX/G5Iz5NPPuk9khk2bNgpp96qqanh3nvvpVu3boSEhNCzZ09eeOGFdqqtEEII0bF9u3k9MUoVqb3SuezSSzp8Z7+WXq9n9OjRTJs2zW/qLISv+NUZ/tdff5158+bx5JNPcu655/LMM88wbtw4du7cSVpaWoPrXH311RQUFJCZmUmvXr0oLCz03oHOl1ryEaY4OclUW5Kn9iRTbUme2sivySYVqFZCUMypvq6OEKIN+FWHf9myZcyePZubb74Z8FyY89lnn/HUU0+xZMmSest/+umnfPPNN+zfv987X27t/Li+pNfr6devn6+rEVAkU21JntqTTLUleWrHHVQDDqhRFXoOOQ/kTLkQAcdvOvx2u50tW7Zw99131ym/+OKL2bhxY4PrvP/++wwfPpx//OMfvPzyy0RERHDFFVfwt7/9jbCwsAbXqampoaamxvu9xWIBPBeI1U6ppSgKOp0Ot9tdZ4aI2vITb+l9Yrnb7aasrIyYmBj0en295WvnwT3xlvGNlev1elRVbbD8xDo2Vt7aNh1fR0VR2r1NiqJQUlKCyWTybtPf2+TL18npdFJWVobZbEan0wVEm3z9OrndbsrLy4mJiWnw59cf23Syurd1mxp6z/t7m3zxOgGEKFUABOlsHC2rwGzWYzAYNGmTEKJj8JsOf1FRES6XyzsNVq2EhATy8/MbXGf//v18++23hIaG8s4771BUVMTcuXMpKSlpdBz/kiVLWLx4cb3yHTt2YDQaAYiJiSEtLY0jR454b60NnrvXJSYmcvDgQSoqKrzlqampxMbGsnfvXmw2G6qqUlJSwrBhwzCbzezcubPOL9W+ffsSHBxMVlZWnTpkZGRgt9vZs2ePt6x2LuqKigr279/vLQ8NDaVfv36UlpZy+PBhb3lkZCQ9e/aksLCwTm6tbVOtHj16EBUV1e5tSk9P59dffyUsLMw7NZu/t8mXr9Mvv/xCSUkJMTExKIoSEG3y9eukqirV1dWcddZZAdMm8N3rNGDAAPbv309QUJD3Pe/vbfLF65QcnUikasWFjtNMBn7++WdiYmLo2bOnJm3q1q0bQgjf85tpOXNzc0lOTmbjxo115rh98MEHefnll9m9e3e9dS6++GLWr19Pfn4+JpMJ8EzlNWXKFCorKxs8y9/QGf7U1FRKSkq8U4q19qyQy+Vix44dZGRkYDAY/PKsUEc70wXw888/M3DgQO+FW/7eJl++Tg6Hgx07dnjzDIQ2+fp1qn3fn3baaZzIX9t0srq3dZug/nve39vki9epKOsw3370Z9DBhAuuYGfwcAYOHOg9kGptmyorK9tkWk4hRIBOyxkXF4der693Nr+wsLDeWf9aSUlJJCcnezv7AP3790dVVY4cOULv3r3rrRMSEkJISEi9cr1eX28GgIZuQV277KnKFUXxnpVqyvKnKlcUpcHyxurY3HIt6tjc8ua0yeVyeZfX8nXSutyfXqeG8vT3NjW1vK3apOV7vrnlgfY6teQ939HbBO3/Ov3w7QZi3Bb2G5IxRHdDqVK87//m1v1k5UII3/KbaTmDg4MZNmwYa9asqVO+Zs0aRowY0eA65557Lrm5uVitVm/Zr7/+ik6nIyUlpU3reyqRkZE+3X8gkky1JXlqTzLVluTZenuLd6EAVUooRKVIpkIEKL/p8IPn9tXPP/88L7zwArt27eL2228nOzubOXPmAHDPPfdw/fXXe5efPn06sbGx3HjjjezcuZN169Zx5513ctNNNzV60W570Ov19OzZU86EaEgy1ZbkqT3JVFuSpzZcwZ4LdmtUHfroVMm0AaNHjyYkJITIyEhMJhODBg3ijjvu4OjRowAcPHgQRVEwGo11HvPmzfNtxYU4jl91+K+55hqWL1/OAw88wJAhQ1i3bh0ff/yx96KgvLw8srOzvcsbjUbWrFlDWVkZw4cPZ8aMGVx++eX861//8lUTAM8Yx/z8fJnNQEOSqbYkT+1JptqSPLURpK/2fKHacAdFSKaNWLp0KRUVFZSVlfHGG2+Qk5PDsGHDKCgo8C5z5MgRrFar97F8+XLfVViIE/jNGP5ac+fOZe7cuQ0+t3Llynpl/fr1qzcMyNdUVSU/P5/4+HhfVyVgSKbakjy1J5lqS/JsPdXhJkKtRAXOS4mUTJtAURQGDBjAK6+8wumnn86yZcv4wx/+4OtqCXFKftfhF0IIIUTrWfNKMDktlOuNnN97iK+rw7++3Ethhe3UC7ZSl8hQbr2w/qQdzWEwGJg4cSJr1qyRDr/wC341pEcIIYQQ2shav5kYdzllOiN6c5qvq+N3kpOT69zroFu3bpjNZu/jxRdf9GHthKhLzvD7gKIo3hsaCW1IptqSPLUnmWpL8my9Lfu/IwM3lbpwiEr2eaatPeve3nJycoiJifF+f+jQIcxms+8qJMRJSIffB3Q6HWlpcjZFS5KptiRP7Umm2pI8W6/GYAUn2FQ9RCVLps3gdDp57733GD9+vK+rIkSTyJAeH3C73WRnZ8tMCBqSTLUleWpPMtWW5Nl6+mMz9DixQ3iMZNpEu3fvZtasWZSXlzN//nxfV0eIJpEOvw+oqkpJSUm926SLlpNMtSV5ak8y1Zbk2TqqqhKmVgIqg6P1oCiS6UksWLDAOw//5MmTSUxMZPPmzSQkJHiXSUlJqTMP/9SpU31YYyHqkiE9QgghRCfjKK/G5KrAqgvn0kFDfV2dDm3t2rUnfT49PV0OkkSHJ2f4hRBCiE5m73e7iHGVUaKPwmBK9XV1hBBtTDr8PqAoComJiTK7hIYkU21JntqTTLUlebbOt1vWEIITqy4cTCmAZCpEIJMhPT6g0+lITEz0dTUCimSqLclTe5KptiTP1rEqnvnjq9UgiEoGJFMhApmc4fcBl8vFvn37cLlcvq5KwJBMtSV5ak8y1Zbk2Tq6YzP0OFQHGLsAkqkQgUw6/D5SUVHh6yoEHMlUW5Kn9iRTbUmeLRdKJQA9wlXQ6b3lkqkQgUk6/EIIIUQn4qpxEumuoFoJYXz/Pr6ujhCiHUiHXwghhOhEjmz5HzGuckr0kRgTevu6OkKIdiAdfh9QFIXU1FSZCUFDkqm2JE/tSabakjxb7psNnxOu1lChi/BesAuSqRCBTGbp8QGdTkdsbKyvqxFQJFNtSZ7ak0y1JXm2XLEjjzSgihAw/dbhl0yFCFxyht8HXC4Xu3fvlpkQNCSZakvy1J5kqi3JsxX0VQDY3S6I7Ootlkwbd9NNN6EoCrt27fKWrV27FkVRMBqNGI1G4uPjmT59OiUlJXXW/eCDDzj//POJjIwkNjaWM888k6effrq9myA6Oenw+4jNZvN1FQKOZKotyVN7kqm2JM+WCVaqAJX4EAcYgus8J5nWZ7VaeeONN4iJiSEzM7POcyaTCavVitVq5ddff6WoqIgFCxZ4n3/qqaeYNWsWv/vd7zhy5AhFRUU8+eSTfPjhh+3dDNHJSYdfCCGE6CRUpxuj24JdCWJy33RfV8cv/Pe//yUiIoKlS5fyn//8B4fD0eBy0dHRTJo0iR07dgCeKU4XLFjAv/71L2bOnInJZEJRFIYPHy4dftHupMMvhBBCdBKVR8qIcVoo0ZuITpIpOZsiMzOTGTNmcO2111JVVcUHH3zQ4HJFRUWsXr2akSNHArBp0yYqKyu5+uqr27O6QjRILtr1AZ1OR48ePdDp5HhLK5KptiRP7Umm2pI8W2bNR+8TrVaRp4sDU0qd53ye6Tf/gIr8tt9PZCKMuqtJi+7cuZPvvvuOp59+GqPRyJVXXklmZiaTJ08GoLy8HLPZDIDFYqFv376sXLkSgKNHjxIfH09wcHAjWxei/chvSh9QFIWoqCiZ+kxDkqm2JE/tSabakjxb5kjZ/wCwElKvwy+Z1peZmcngwYMZPHgwALNmzeKzzz4jJycH8IzhLysro6ysjOrqambPns3555+PzWYjLi6OoqIi7Ha7L5sgBCBn+H3C5XKxc+dOBgwYgF6vP/UK4pQkU21JntqTTLUlebaMy1AJdrC7gaiudZ/zdaZNPOveXhwOBy+//DJWq5XExEQAVFXF5XKxcuVKzj333DrLh4SEMGfOHO6880527NjBiBEjCA8P580332TGjBm+aIIQXnKG30dk2jPtSabakjy1J5lqS/JsviClElCJ1DkhOKLe85Lpb95//30sFgtbt25l27ZtbNu2je3bt3PffffxwgsvoKpqneWdTifPPfcc4eHh9OjRg8jISJYuXcqtt97Kq6++isViQVVVtm3bxhVXXOGjVonOSs7wCyGEEJ2A6nAT7q7EhZ6JveN9XZ0OLzMzk2nTptGvX7865bfeeiuPPPIIqqpSXl6O0WgEwGAwMGDAAD744AOio6MB+MMf/kBycjKPPPIIt9xyCyEhIfTs2ZPZs2e3e3tE5yYdfiGEEKITqCmqJNpVRok+kpTUfqdeoZP7+OOPGyyPi4ujuroaoN5Z/oZcccUVckZf+JwM6fEBnU5H3759ZXYJDUmm2pI8tSeZakvybL5Nn6/F5LZSpo+sd8EuSKZCBDJ5V/uITNOlPclUW5Kn9iRTbUmezbMrZzMKUEkIRCU3uIxkKkRgkg6/D7jdbrKysnC73b6uSsCQTLUleWpPMtWW5Nl8dr0VgBpVV2+GHpBMhQhk0uEXQgghOgGDUgWohLjdEBbt6+oIIdqRdPiFEEKIAOe2uwhTK1BRGNs1DOTmWkJ0KtLhF0IIIQKcs9SGyVVBqS6SQf0G+bo6Qoh2Jh1+H9DpdGRkZMhMCBqSTLUleWpPMtWW5Nk8WT/8RLSr3DNDTyMX7EqmQgQueVf7iN1u93UVAo5kqi3JU3uSqbYkz6bb/Ms36FGpUMLA1HCHHyRTIQKVdPh9wO12s2fPHpkJQUOSqbYkT+1JptqSPJvHrisDwKYaIKr+HPwgmQoRyKTDL4QQQgQ6nWeGHr3LDRHxvq6NXxk9ejTLly+vV75nzx4uv/xy4uLiiIqKol+/fixduvSU6ymKwrZt2+qUrVu3DkVRWLBgQb3l09PTCQsLIzIyErPZzNChQ1m8eDFWq9W7zNq1a1EUBaPRWOexbNmyFrdbBBbp8AshhBABzG1zEur2dA7PijaAjNHXxGWXXcbgwYPJzs6mtLSUt99+mx49erRoW5mZmcTExPDSSy/hdDrrPb9q1SoqKiooLi7m2WefZd26dZx33nlUV1d7lzGZTFit1jqP+fPnt7h9IrDIu95H9Hq9r6sQcCRTbUme2pNMtSV5No2z1EaUy0K5LoKRg/ufdFnJtGmKiorYt28ft9xyC+Hh4ej1egYOHMjUqVObvS2LxcJbb73F448/jtVq5aOPPmp0Wb1ez/Dhw3n77bfJz89n5cqVrWiF6Eykw+8Der2ejIwM+cWqIclUW5Kn9iRTbUmeTZfz62FiXOWU6hqfoQck0+aIjY2lX79+3HjjjbzxxhscOnSoxdtatWoVERERTJ06lauuuorMzMxTrmM2mxk7dixr165t8X5F52LwdQU6I1VVqaioIDIyEkVufqIJyVRbkqf2JFNtSZ5N9833H5GOiwpdxEk7/L7O9OntT1NUXdTm+4kLi2PO4Dmt2oaiKHz99dc88sgjLF68mN27d9O3b19WrFjBRRdd5F3unnvuYdGiRSfdVmZmJjNmzMBgMHD99ddzySWXkJeXR1JS0knXS05OZuvWrd7vy8vLMZvNdZZ5++23ufDCC5vdPhF45Ay/D7jdbvbv3y8zIWhIMtWW5Kk9yVRbkmfTWd2eTnSVO+ikU3JKps2TmJjIo48+yo4dOzh69Cjjxo3jyiuvpKSkxLvMkiVLKCsrq/M4XlZWFj/++COzZs0CYMyYMXTt2pWXXnrplPvPyckhJibG+73JZKq3L+nsi1pyhl8IIYQIUKqqgq4SUFFcOog8+VljX2rtWXdfiomJYdGiRSxbtowDBw7U6YifTO3wnUsvvdRbVlZWxgsvvMDdd9/d6Hrl5eV88cUX3H///a2ruOg05Ay/EEIIEaDUaidBeGbo6RMC6IN8WyE/5XQ6sdls3kdBQQF//etf2b17Ny6Xi6qqKpYtW0ZMTAz9+vVr0jbtdjuvvPIKDz/8MNu2bfM+vv/+e/bv38+6devqreN2u9m6dStTp04lMTGRG264QeOWikDldx3+J598ku7duxMaGsqwYcNYv359k9bbsGEDBoOBIUOGtG0Fmyg0NNTXVQg4kqm2JE/tSabakjxPzVlWQ6TLQqUSyhXDe55yecm0YXfeeSdhYWHex6BBg8jJyWH8+PGYTCbS0tLYsGEDn376KREREU3a5rvvvovdbmfu3LkkJiZ6H4MHD2bSpEk8//zz3mWnTZtGZGQk0dHRzJ49mxEjRvDtt98SFhbmXaa8vLzePPx33HGH5lkI/6Soqqr6uhJN9frrrzNz5kyefPJJzj33XJ555hmef/55du7cSVpaWqPrlZeXM3ToUHr16kVBQUG9G16cjMViwWQyUV5eTlRUlAatEEIIIdpH9vq97PxmLkf1JmaOmwxDprfr/hv7G2qz2Thw4ID3BJ4Qovma8z7yqzP8y5YtY/bs2dx8883079+f5cuXk5qaylNPPXXS9W655RamT5/OOeec0041PTm3201xcbFcGKUhyVRbkqf2JFNtSZ5Ns+nHNYSqdiynmKEHJFMhApnfXLRrt9vZsmVLvYtYLr74YjZu3Njoei+++CL79u3jlVde4e9///sp91NTU0NNTY33e4vFAoDL5cLlcgGe6bh0Oh1ut5vjPyCpLa9drrFyl8tFdnY2JpOpweV1x+6CeOIv3cbK9Xo9qqo2WH5iHRsrb22bjq+joijt3iaA7OxsIiMjvXNI+3ubfPk6OZ3OOnkGQpt8/TrVvu/NZnPAtOlkdW/rNkH997y/t6ktXqeSmlwSgCo1GEwpJ21T7c9oZGQkQUFBmr1OQgjf85sOf1FRES6Xi4SEhDrlCQkJ5OfnN7jO3r17ufvuu1m/fj0GQ9OaumTJEhYvXlyvfMeOHRiNRsBzNX5aWhpHjhypM/1W7fi7gwcPUlFR4S1PTU0lNjaWvXv3YrPZPL+ES0qwWq2YzWZ27txZ55dq3759CQ4OJisrq04dMjIysNvt7Nmzx1tWe6OUiooK9u/f7y0PDQ2lX79+lJaWcvjwYW95ZGQkPXv2pLCwsE5urW1TrR49ehAVFdXubUpPT6e6upodO3Z454/29zb58nXasWMHJSUl3jwDoU2+fp1UVaW6uhogYNoEvnudBgwYgMPhqPOe9/c2af46FRfjMljBqeJyGSCq60nbVF1d7X3f9+zZU5M2devWDSGE7/nNGP7c3FySk5PZuHFjnaE5Dz74IC+//DK7d++us7zL5eLss89m9uzZzJnjmepr0aJFvPvuuycdw9/QGf7U1FRKSkq84w+1OMO/Y8cOMjIyMBgMHfKsUHPbdHwdfXWG/+eff2bgwIFyhl+DNtV2pGrzDIQ2+fp1qn3fn3baaZzIX9t0srq3xxn+E9/z/t4mrV8nl9VO5tN/pG/NXg7qTuPGex8/5Rn+2ve9Vmf4KysrZQy/EG2kOe8jvznDHxcXh16vr3c2v7CwsN5Zf4CKigo2b97MTz/9xJ/+9CcA7y9Gg8HA559/zgUXXFBvvZCQEEJCQuqV6/X6ercbr/0F19CypyqPiorynpVqyvKnKlcUpcHyxurY3HIt6tjc8ua0yeVyERUVpfnrpHW5P71ODeXp721qanlbtam2wxNIbdKyjs0pb8l7vqO3CbR9nZwWBxHuCuxKMJP6mZtUl9pMtfz7JITwPb/p8AcHBzNs2DDWrFnDlVde6S1fs2YNEydOrLd8VFRUvY8cn3zySb766iveeustunfv3uZ1boxer6dnz1NPjyaaTjLVluSpPclUW5LnqVkKK4h2WSjWRxHd7dRZSaZCBC6/6fADzJ8/n5kzZzJ8+HDOOeccnn32WbKzs71Ddu655x5ycnL4z3/+g06nY9CgQXXW79KlC6GhofXK25vb7aawsJAuXbo0enZGNI9kqi3JU3uSqbYkz1PbsHENJnc12fouYEo55fKSqRCBy686/Ndccw3FxcU88MAD5OXlMWjQID7++GPvRUF5eXlkZ2f7uJanpqoq+fn5xMfH+7oqAUMy1ZbkqT3JVFuS56nlV/wPE1BF8Cmn5ATJVIhA5lcdfoC5c+cyd+7cBp9buXLlSdddtGgRixYt0r5SQgghRAeiqipOfSU4VZzuYDCdusMvhAhc8pmdEEIIEWDcVgc6xYoKmBwKhMid4oV/mTNnDgsWLPB1NQKGdPh9QFEUYmJivLMgiNaTTLUleWpPMtWW5HlyrrIawl0WnBi4NDUampCTZNqw0aNHs3z58nrle/bs4fLLLycuLo6oqCj69evH0qVLT7meoij1pgdft24diqI02MFNT08nLCyMyMhIzGYzQ4cOZfHixVitVu8ya9euRVEUjEZjnceyZcta3O5Tae0+KyoqmDt3LsnJyRiNRlJTU7n22mu9zz/99NN18hSt43dDegKBTqcjLS3N19UIKJKptiRP7Umm2pI8T67yqBWzy0KJPpL0AalNWkcybZ7LLruMa6+9ltdff52QkBB2797Nzp07W7StzMxMYmJieOmll3jwwQfr3Sx01apVTJo0CZfLxU8//cSCBQt455132LRpE2FhYQCYTCbKyspa26xmac0+b7/9dnJzc9m6dSsJCQkcOXKEDz/8UNsKCi85w+8Dbreb7OxsuQW5hiRTbUme2pNMtSV5ntyWnzYR5a6kTGdEMZ96hh6QTJujqKiIffv2ccsttxAeHo5er2fgwIFMnTq12duyWCy89dZbPP7441itVj766KNGl9Xr9QwfPpy3336b/Pz8U1672BRbtmzhggsuICYmhvj4eP785z8DnjP4ZrOZ559/3ntH5rvuuqvJ2120aBETJkxg9uzZREVF0bt3b9555x3v89999x3Tpk3z3kspJSXFO+siwA033MC8efMAz93JFUXh5ZdfplevXpjNZm644QYcDker299ZyBl+H1BVlZKSEpKT5SIqrUim2pI8tSeZakvyPLnswl/oAViVMIjq2qR1fJ3p0SefxHn0aJvvxxAfT3wjk380VWxsLP369ePGG2/k97//PWeddZZ3xsDmWrVqFREREUydOpVPP/2UzMzMBu8vdDyz2czYsWNZu3Ytf/jDH1q0X4CcnBwuuOAClixZwscff4zb7WbLli3e5ysqKsjKymLv3r0cOHCA4cOHM378eEaPHt2k7X/66ac88cQTPPPMM3zyySdMnTqVHTt20LNnT8477zweeOABqqurOfvss8nIyDjlcLKPPvqIrVu3YrVaOfPMM3n11Ve54YYbWtz+zkTO8AshhBABRHWr1OgrABW7KxiimnaGXzSdoih8/fXXDB48mMWLF9OjRw8GDBjAmjVr6ix3zz33YDab6zxOlJmZyYwZMzAYDFx//fV8/PHH5OXlnbIOycnJlJSUeL8vLy+vt68vv/zypNt45ZVXGDZsGHPnziU0NJTw8HBGjhzpfV5VVZYsWUJoaCj9+/dnxIgRdQ4ITrXPPn36cMstt2AwGLj88ssZM2YMq1atAmDFihXMmTOHlStXcuaZZ5KQkHDK8f+LFi0iKiqKrl27Mm7cuDp1EScnZ/iFEEKIAOKusAMVqECEQwcRcb6uUpO09qx7e0tMTOTRRx/l0UcfpaSkhAcffJArr7yS7OxsYmJiAFiyZIl3WEqt489iZ2Vl8eOPP/Lss88CMGbMGLp27cpLL73E3XfffdL95+TkePcDLRtPf+jQIXr37t3o81FRUYSHh3u/j4iIoKKiosn7PPFTj27dupGTkwNASEgId9xxB3fccQc1NTW8+eab3HTTTQwaNIiLL764we0lJibWqUt7X7Pgz+QMvw8oikJiYqLMhKAhyVRbkqf2JFNtSZ6Nc5bVEKJWAArnxBibNEMPSKatERMTw6JFi6isrOTAgQNNXi8zMxOASy+9lMTERLp27UphYSEvvPDCSdcrLy/niy++aPLQmsZ069aN//3vf63axskcOnSozvfZ2dkNDhkLCQnhuuuuIyMjg6ysrDarT2cmHX4f0Ol0JCYmyq3LNSSZakvy1J5kqi3Js3HVRZWYXBWU6KI4fVDTh/NIpo1zOp3YbDbvo6CggL/+9a/s3r0bl8tFVVUVy5YtIyYmhn79+jVpm3a7nVdeeYWHH36Ybdu2eR/ff/89+/fvZ926dfXWcbvdbN26lalTp5KYmNjq8eszZszghx9+4Omnn6ampoaqqirWr1/fqm0e79dff+W5557D6XTy0Ucf8dVXX3HNNdcAsHjxYjZu3Eh1dTUul4v333+fnTt3cs4552i2f/EbeVf7gMvlYt++fbhcLl9XJWBIptqSPLUnmWpL8mzc7l07vVNy6uOadsEuSKYnc+eddxIWFuZ9DBo0iJycHMaPH4/JZCItLY0NGzbw6aefEhER0aRtvvvuu9jtdubOnUtiYqL3MXjwYCZNmsTzzz/vXXbatGlERkYSHR3N7NmzGTFiBN9++613Sk7wnPU/cU78O+6446R1SElJ4YsvvuC1114jISGB9PR03nrrrSbncqp9XnrppXz33XfExMRw22238corr3iHEBkMBubMmUNCQgKxsbEsWrSIzMxMRowY0eT9i6ZTVFVVfV2JjsxisWAymSgvLycqSps7FbpcLrKyssjIyECv12uyzc5OMtWW5Kk9yVRbkmfj/vPwUtIcH/NTUC9un/57SDurSeu1RaaN/Q212WwcOHCA7t27Exoaqsm+RMeyaNEitm3bxrvvvuvrqgSs5ryP5Ay/EEIIESBUl0q1Ugqo2NQQMMm0pUII6fALIYQQAcNVUYNLZ0EFghx6MCaech0R2MaNG1dv2I3RaGTcuHG+rppoRzItpw8oikJqaqrMhKAhyVRbkqf2JFNtSZ4Nc5XVEOL2TJs4MCgC9E3/My+ZBqZPPvnEJ/tdtGiRT/YrGiYdfh/Q6XTExsb6uhoBRTLVluSpPclUW5Jnw2xFVUS6KyhXjFxyWlKz1pVMhQhcMqTHB1wul3cqL6ENyVRbkqf2JFNtSZ4NO7hvPzEuCyX6KEK7JjRrXclUiMAlHX4fsdlsvq5CwJFMtSV5ak8y1ZbkWd/ug99jUJ1YdOEo5uZfsCuZChGYpMMvhBBCBADV6caiHgWg2i0z9AghfiMdfiGEECIAuCx2HHorKqBzBENk02+6JYQIbNLh9wGdTkePHj3k9uUakky1JXlqTzLVluRZn7PURrBqASBNDYWg5t3QSjIVInDJu9oHFEUhKipKpj7TkGSqLclTe5KptiTP+mpKqjG6K6hUwhjbu3kX7IJk2pjRo0ezfPly7/fr1q1DURQWLFhQb9n09HTCwsKIjIzEbDYzdOhQFi9ejNVq9S6zdu1aFEWpNy/+smXL2qM5opOSDr8P1N6+XGZC0I5kqi3JU3uSqbYkz/pyDuVgdloo1kcR3S2+2etLpk2TmZlJTEwML730Ek6ns97zq1atoqKiguLiYp599lnWrVvHeeedR3V1tXcZk8mE1Wqt85g/f357NkN0MtLh9xH5hao9yVRbkqf2JFNtSZ51/brvB0JVO+W6CPRdmjcHfy3J9OQsFgtvvfUWjz/+OFarlY8++qjRZfV6PcOHD+ftt98mPz+flStXtl9FhTiB3HhLCCGE8HOqw02JmocZqFbDUEwpvq5Ss/340QGqyu1tvp9wUzBnXNa9ReuuWrWKiIgIpk6dyqeffkpmZiYTJ0486Tpms5mxY8eydu1a/vCHP7Rov0K0lpzhF0IIIfycs7yGGl0ZKuB2GmRKzjaSmZnJjBkzMBgMXH/99Xz88cfk5eWdcr3k5GRKSkq835eXl2M2m+s8vvzyy7asuujk5Ay/D+h0Ovr27SszIWhIMtWW5Kk9yVRbkmddrjIbeioBiHcEQ0hks7fh60xbeta9vWRlZfHjjz/y7LPPAjBmzBi6du3KSy+9xN13333SdXNycoiJifF+bzKZKCsra8vqClGH/Kb0keDgYF9XIeBIptqSPLUnmWpL8vyNvbiaCHcFNQRzXlzMqVdohGTauMzMTAAuvfRSEhMT6dq1K4WFhbzwwgsnXa+8vJwvvviC0aNHt0MthWiYdPh9wO12k5WVhdvt9nVVAoZkqi3JU3uSqbYkz7oK84qIdpVTpDfRvX/LbrglmTbObrfzyiuv8PDDD7Nt2zbv4/vvv2f//v2sW7eu3jput5utW7cydepUEhMTueGGG9q/4kIcIx1+IYQQws/9739bCXfbKNcZCU5K9HV1Ak51dTV2u525c+eSmJjofQwePJhJkybx/PPPe5edNm0akZGRREdHM3v2bEaMGMG3335LWFiYd5ny8vJ68/Dfcccdvmia6CRkDL8QQgjhx9x2FwWOQ3QDrISixMgFu1qyWCz06tULi8XS4PNvvfWW9+uDBw+ecnujR49GVVWtqidEk8gZfiGEEMKPucprqNaXogIuRwhESYdfKz///DM7duxg+PDhvq6KEK0iHX4f0Ol0ZGRkyOwSGpJMtSV5ak8y1Zbk+RtXaQ0KVgCMjmAIb9lFu5JpXbfccgvjx49n6dKl9O3b19fVEaJVZEiPj9jtdkJDQ31djYAimWpL8tSeZKotydPDUVpNmGrFgYFzIsygKC3elmT6m2eeecbXVRBCM3IY7wNut5s9e/bITAgakky1JXlqTzLVluT5m6N5JZhd5ZToTfTt1/ILdiVTIQKXdPiFEEIIP5a9fxdRrkpKdUYikuN9XR0hRAckHX4hhBDCT7lrnOTU7AHAShi6hJbNwS+ECGzS4fcRvV7v6yoEHMlUW5Kn9iRTbUme4CqrwaovQQUc7hAUU+tm6JFMhQhMctGuD+j1ejIyMnxdjYAimWpL8tSeZKotydPDWVYDimeGnpCaEDAmtHhbkqkQgUvO8PuAqqpYLBa58YaGJFNtSZ7ak0y1JXl6OEuqCXVXoKJjoBIJupafoZdMGzZw4EA+/PBDX1dDiFaRDr8PuN1u9u/fLzMhaEgy1ZbkqT3JVFuSp0dxfilRrgqKdVGc3rNLq7YlmTZsx44dTJgwAYBHH32UPn36EBkZSXx8PGPHjq1zd92Kigpuv/12UlNTCQsLo2fPnjzwwAM4nU4f1V4IDxnSI4QQQvipvEOHMLsq2GtIwdxNZuhpS6+88gr//ve/+fDDDxk0aBBlZWV8/vnnKMfue+BwOLjkkksIDQ3liy++oFevXmzfvp2bbrqJrKws3nzzTR+3QHRm0uEXQggh/JDb5uRw9Q66oGJRwglKavkc/KJx6enpLF++nO+++44LL7yQQYMGAWA2m7n66qu9y7366qv8+uuv7N+/n6ioKACGDh3KO++8Q9++fVm7di2jR4/2RROEkCE9viJ3MtSeZKotyVN7kqm2OnueztIaynWFqECNOwRdXEqrt9nZMz2Z8847jzfeeIMHH3yQDRs2YLPZ6jz/2WefMX78eG9nv1b37t0566yz+Pzzz9uzukLU4Xdn+J988kkeeeQR8vLyGDhwIMuXL2fkyJENLrt69Wqeeuoptm3bRk1NDQMHDmTRokVccskl7VzruvR6Pf369fNpHQKNZKotyVN7kqm2JE9wldpw6zwz9BjsIRDZujn4fZ3pprdXUVla2ub7iYiO5pyrpjV7vWuvvRaDwcCLL77II488gsPhYPr06SxfvpyIiAiKiooYNmxYg+t27dqVo0ePtrbqQrSYX53hf/3115k3bx733nsvP/30EyNHjmTcuHFkZ2c3uPy6deu46KKL+Pjjj9myZQtjxozh8ssv56effmrnmtfldrspLi6WC6M0JJlqS/LUnmSqLckTnKU2glUrqNDNFQWG4FZtTzI9tSlTpvDRRx9RWlrKZ599xueff86DDz4IQFxcHLm5uQ2ul5ubS3y8XGMhfMevzvAvW7aM2bNnc/PNNwOwfPlyPvvsM5566imWLFlSb/nly5fX+f6hhx7ivffe44MPPuD0009vjyo3SFVVDh8+jNls9lkdAo1kqi3JU3uSqbYkTygpKCXSZaFUF8kZibGt3p6vM23JWXdfURSF8847jylTppCVlQXARRddxF133YXFYqkzrOfAgQP88MMPPPDAA76qrhD+0+G32+1s2bKFu+++u075xRdfzMaNG5u0DbfbTUVFBTExMY0uU1NTQ01Njfd7i8UCgMvlwuVyAZ43uk6nw+1215mvuLa8drnGyl0uF6qqetc9cXmdTuetb1PK9Xo9qqo2WH5iHRsrb22bjq+joijt3ibw/LE6fr/+3iZfvk61P6O1zwdCm3z9OtVmWvt1ILTpZHVv6zZB/fe8v7epOa+TqqocPZJHtKuCA/pEErrH4HK5WtWm49/3Wr5OgeLFF18kJiaGUaNGYTab+eWXX3jvvfeYPXs2ANdddx3PPPMMkyZN4qmnnqozS89ll13GmDFjfNwC0Zn5TYe/qKgIl8tFQkLduwgmJCSQn5/fpG08+uijVFZW1rmq/kRLlixh8eLF9cp37NiB0WgEICYmhrS0NI4cOUJJSYl3mcTERBITEzl48CAVFRXe8tTUVGJjY9m7dy82mw1VVSkpKcFqtWI2m9m5c2edX6p9+/YlODjYe9agVkZGBna7nT179njLau+MWFFRwf79+73loaGh9OvXj9LSUg4fPuwtj4yMpGfPnhQWFtbJrbVtqtWjRw+ioqLavU3p6elUV1ezY8cO7xRp/t4mX75OO3bsoKSkxJtnILTJ16+TqqpUV1cDBEybwHev04ABA3A4HHXe8/7epma9TkERHKn8BbPqwqJEkO+qwZqV1ao2VVdXe9/3PXv21KRN3bp1I1CYzWYeffRRbrzxRhwOBwkJCUybNo277roLgODgYNasWcN9993HBRdcQHFxMV27dmXmzJn89a9/9XHtRWenqH5yS73c3FySk5PZuHEj55xzjrf8wQcf5OWXX2b37t0nXX/VqlXcfPPNvPfee4wdO7bR5Ro6w5+amkpJSYn3IzotzvAfOnSI7t27YzAY5OydBm0Cz8emaWlp6PX6gGiTL18nh8PBoUOH6NatG3q9PiDa5OvXyeVykZ2dTffu3TmRv7bpZHVvjzP8J77n/b1NzXmdHLlWXlv1EN1rNrHJkMFdN/wRpUvfVp/hr33fBwUFadKmyspKTCYT5eXldYa52Gw2Dhw4QPfu3Tv8zECpqak888wzjB8/3tdVEaKO5ryP/OYMf1xcHHq9vt7Z/MLCwnpn/U/0+uuvM3v2bN58882TdvYBQkJCCAkJqVeu1+vr/FGB337BNbTsycr1ej29e/du8vJNKVcUpcHyxurY3HIt6tjc8ua2qVevXg2W+3ObfPU6BQcH1/kZPdny/tImX79Oer2+0Z/RltSxueWB+Do19z3vD21q6utktzhxKJ4z9Yo9BENsNzhuvZa06cS/Tc2t+8nK/VVBQQGFhYX06NHD11URolX8Zpae4OBghg0bxpo1a+qUr1mzhhEjRjS63qpVq7jhhht47bXXuOyyy9q6mk3idrvJz88P6LGO7U0y1ZbkqT3JVFudPU9nqQ3DsRl64m0REBzR6m129kxP9MUXX9CvXz/mzp3b6aeAFf7Pb87wA8yfP5+ZM2cyfPhwzjnnHJ599lmys7OZM2cOAPfccw85OTn85z//ATyd/euvv54VK1Zw9tlnez8dCAsLw2Qy+awdqqqSn58vU3RpSDLVluSpPclUW509z9LCUozuCqxKOGfHxmmyzc6e6YnGjh1LaTvcF0CI9uBXHf5rrrmG4uJiHnjgAfLy8hg0aBAff/yx96KgvLy8OnPyP/PMMzidTv74xz/yxz/+0Vs+a9YsVq5c2d7VF0IIIVpNVVVKc4uIdlnI0ccxIi3a11USQnRwftXhB5g7dy5z585t8LkTO/Fr165t+woJIYQQ7chd6SDHsoNwt4PyoAiiuiX6ukpCiA7Ob8bwBxJFUYiJifFOJSdaTzLVluSpPclUW505T1dZDYW6HFSgWg1Dn6BNh78zZypEoPO7M/yBQKfTkZaW5utqBBTJVFuSp/YkU2115jydpTXY9eXgAKczGCU+WZPtduZMhQh0cobfB9xuN9nZ2TITgoYkU21JntqTTLXVmfN0ldnQUwkqmKvCUMIbv3t8c3TmTIUIdNLh94HaO+36yT3P/IJkqi3JU3uSqbY6c57lhWWEuSqoVkI4PdgMGg3B6cyZnszAgQP58MMPfV0NIVpFOvxCCCGEn1DdKuWF5ZhdFRTrTaSnyxSabW3Hjh1MmDCBjz76iPPPP5/o6Gi6dOnClClTOHLkSJ1lN2zYwODBgwkPD2fIkCFs2rTJ+1xr1xeiNaTDL4QQQvgJt9VObtluwt02SnVGYrtJh7+9lJeXs2DBAg4fPsyBAweIiori6quv9j5fUlLChAkT+NOf/kRpaSl//OMfmTBhAmVlZZqsL0RrSIffBxRFITExUWZC0JBkqi3JU3uSqbY6a56O/CrylYOoQCVhBCUlaLbtzprpqaSnp/Puu+8yffp0LrvsMoxGIxEREcybN4/vv/8ep9MJwDvvvENycjK/+93vCAkJ4Xe/+x2JiYm88847AK1eX4jWkFl6fECn05GYKPMma0ky1ZbkqT3JVFudNc/qw+VsO/gLe4oLyY3sAl2SNNt2Z820pb755hv69++PweDpSv38888MGTKkzjJDhgzh559/bpP1hWiOZnf4b7jhBm666SbOP//8tqhPp+ByuTh48CDp6eno9XpfVycgSKbakjy1J5lqqzPm+fZbb3PrLX8kt6TgWMke1qz5nhUrVjB58uRWb9/XmVq+zMZVYW/z/egjg4m6sHXTj/7000/cd999vPnmm94yq9WK2Wyus5zZbKaiokLz9YVormYP6amoqODiiy+md+/ePPTQQ+Tk5LRFvQKevIG1J5lqS/LUnmSqrc6U5+rVq5l69dTjOvseOTk5TJkyhdWrV2uyn86UaUtlZWVx6aWX8vjjj3PRRRd5y41GI+Xl5XWWLS8vJzIyUtP1hWiJZp/hf/vttykuLuaVV15h5cqV3H///YwdO5bZs2czceJEgoKC2qKeQgghRKfkcrm47bbbGpwuU1VVFEVh3rx5TJw40a8/7WjtWff28MsvvzB27FgefvhhrrvuujrPnXbaaSxfvrxO2bZt25g/f75m6wvRUi26aDc2NpbbbruNn376iR9++IFevXoxc+ZMunbtyu23387evXu1rqcQQgjRKa1fv77e9I3HU1WVw4cPs379+nasVeezY8cOLrzwQv72t79x44031nv+yiuv5MiRI2RmZmK328nMzCQvL48rr7xSk/WFaI1WzdKTl5fH559/zueff45er2f8+PHs2LGDAQMG8Nhjj2lVx4CjKAqpqakyE4KGJFNtSZ7ak0y11ZnyzMvL03S5xnSmTFvin//8J0ePHmX+/PkYjUbvIzs7G4CYmBg++OADVqxYgclk4l//+hcffPAB0dHRmqwvRGsoajNvqedwOHj//fd58cUX+fzzzznttNO4+eabmTFjhnec2X//+1/+8Ic/UFpa2iaVbk8WiwWTyUR5eTlRUVG+ro4QQohOZu3atYwZM+aUy3399deMHj267SvUDI39DbXZbBw4cIDu3bsTGhrqwxqeWmpqKs888wzjx4/3dVWEqKM576Nmn+FPSkrid7/7Hd26deOHH35g8+bNzJkzp85FJZdcckm9K83Fb1wuF7t378blcvm6KgFDMtWW5Kk9yVRbnSnPkSNHknyS6Tdrz8yPHDmyVfvpTJk2VUFBAYWFhfTo0cPXVRGiVZrd4X/sscfIzc3liSeeqDdfbK3o6GgOHDjQ2roFNJvN5usqBBzJVFuSp/YkU211ljx1Oh0PXr+wwedqh98sX75ckwt2O0umTfHFF1/Qr18/5s6dS79+/XxdHSFapdmz9MycObMt6iGEEEKIBrgtdi4dcD43zxzDe+9t4Kjlt7nqU1JSWL58uSbz8Iu6xo4dGxBDk4UAudOuEEII0aHZc62UVFVw7qAYrulxJq/sTGN0aiLpl1/OyJEj/XoqTiFE+5AOvw/odDp69OiBTteqSZLEcSRTbUme2pNMtdWZ8nTkWMm3FpDkLCUvKIGrumRwycwLCB5ypqb76UyZCtHZyLvaBxRFISoqSqY+05Bkqi3JU3uSqbY6S56qS8VRUMV+1hHscnBEH0+qKZKgfoM031dnyVSIzkg6/D7gcrnIysqSmRA0JJlqS/LUnmSqrc6Sp/NoFVVV1Tj1RwGosEXQLS0cJTRc8311lkyF6Iykw+8j8gtVe5KptiRP7Umm2uoMedpzrBytKifGaaFaCSGtwEhYjy5ttr/OkKkQnZF0+IUQQogOypFr5VDlz3RxlLPf0JUB4WaCBsoUkUKI5pEOvxBCCNEBuW1O7EVV5Adl4VahUI2me3wI+iS5CZQQonmkw+8DOp2Ovn37ykwIGpJMtSV5ak8y1VZnyNORa6W02kqYWgaArjScmB4maKOLajtDpi0xevRoli9fXq98z549XH755cTFxREVFUW/fv1YunRpnfVCQkIwGo3ExMQwatQoNm/eTHZ2Nkaj0fvQ6XSEhYV5v58zZw4HDx5EURSMRiNRUVHExcUxZswYVq5ciaqq3n0sWrQIg8FQZ3tGo5Eff/yxPaIRfkTe1T4SHBzs6yoEHMlUW5Kn9iRTbQV6nvacSgorjpLkKCVXH8ew6iiC+3Rr030GeqZauuyyyxg8eDDZ2dmUlpby9ttv06NH3U9fli5ditVqJT8/n7POOovJkyeTlpaG1Wr1PtLS0li1apX3+6efftq7/pEjR7BYLBw+fJi//OUvLF68mDlz5tTZx4QJE+psz2q1csYZZ7RLBsJ/SIffB9xuN1lZWbjdbl9XJWBIptqSPLUnmWor0PNUVRVHrpUDqmc6zmx9AqkmI4a+GW22z0DPVEtFRUXs27ePW265hfDwcPR6PQMHDmTq1KkNLh8cHMysWbM4fPgwR48ebfb+wsLCuOyyy3j11Vd57rnn2LlzZ2ubIDoZufGWEEII0cG4SmuotlZTbcgHO1htEaSnBaOERfm6am3mm2++oaKios33ExkZyahRo1q1jdjYWPr168eNN97I73//e8466yy6dWv805fq6moyMzOJi4sjOjq6xfsdMWIEXbt25ZtvvmHAgAEt3o7ofOQMvxBCCNHBOHKtHK0sJ8ZZTrUSQmphBKE9EnxdLXGMoih8/fXXDB48mMWLF9OjRw8GDBjAmjVr6ix3zz33YDabiYiIYNWqVbzzzjsYDK0715qcnExJSYn3+48++giz2VznUVNT06p9iMAjZ/iFEEKIDsaeayW74hfi3eXsMKSTERZN8IDAno6ztWfd21tiYiKPPvoojz76KCUlJTz44INceeWVZGdnExMTA8CSJUuYN28eOTk5XHHFFWzfvp3zzjuvVfvNycnxbh881xK8++67rdqmCHxyht8HdDodGRkZMhOChiRTbUme2pNMtRXIeapON478SvKCt6OqcFSNpnu8Hl1S7zbdbyBn2tZiYmJYtGgRlZWVHDhwoN7zycnJPPfccyxYsIDc3NwW72fTpk3k5ub63cGR8D15V/uI3W73dRUCjmSqLclTe5KptgI1T0d+JeVVlQQfm45TLQkntnsUtENHPFAzbS2n04nNZvM+CgoK+Otf/8ru3btxuVxUVVWxbNkyYmJi6Nev4U9ihg4dyujRo3nooYeavX+bzcYnn3zCddddx8033yzj90WzSYffB9xuN3v27JGZEDQkmWpL8tSeZKqtQM7TkVtJvqWYJEcJufo4httMBLXxdJwQ2Jm21p133klYWJj3MWjQIHJychg/fjwmk4m0tDQ2bNjAp59+SkRERKPbuffee3n++ec5fPhwk/abkpJCVFQUKSkpLF26lL/+9a8888wzdZb58MMP683DL0N8xIlkDL8QQgjRgdhzrRx0r6Ory86R4C5cagrH0KftpuMUJ7d27VrN1jvnnHOw2Wx1yg4ePFhvufT09Do32GrMokWLWLRoUYvqJzoXOcMvhBBCdBCuSge2kkqs+hwAKmwRdEs1oETE+rhmQgh/Jh1+H9Hr9b6uQsCRTLUleWpPMtVWIObpyLVSVGkh2lWGTQkhpdBIWI8u7bb/QMxUCCFDenxCr9eTkSEfz2pJMtWW5Kk9yVRbgZqnPcdKjmUXXdxl7DSkMyjMTFD/vu2y70DNVAghZ/h9QlVVLBZLk8bniaaRTLUleWpPMtVWIOapulUceZVkB29DVaGAaHrEK+i69m+f/QdgpkIID+nw+4Db7Wb//v0yE4KGJFNtSZ7ak0y1FYh5OoursVisBFMMgFISQUx6JOjb58P4QMxUCOEhHX4hhBCiA3DkVpJfUUyCo5g8fSxDqqMI7p3m62oJIQKAdPiFEEKIDsCea+WQ41tCnXYO67vQ3RSGvreMqRdCtJ50+H0kNDTU11UIOJKptiRP7Umm2gqkPN12FzUFVsqDPDdkqrAZSU8FJSqxXesRSJkKIX4js/T4gF6vb/TW26JlJFNtSZ7ak0y1FWh5OvIrKa60EO0soUYJJuloJKHnxLdrHQItUyHEb/zuDP+TTz5J9+7dCQ0NZdiwYaxfv/6ky3/zzTcMGzaM0NBQevTowdNPP91ONW2c2+2muLhYLozSkGSqLclTe5KptgItT0eOlSOlu+niKGO/IYmMUBPB/dpnOs5agZapEOI3ftXhf/3115k3bx733nsvP/30EyNHjmTcuHFkZ2c3uPyBAwcYP348I0eO5KeffmLhwoXceuutvP322+1c87pUVeXw4cMy9ZmGJFNtSZ7ak0y1FWh5OnIrORzyE6oKhUTTI96N0nVgu9Yh0DLVyujRo9Hr9fz888/esrKyMhRF4eDBg6xcuZIhQ4Y0uK7T6WThwoWkp6djNBpJSkpiwoQJVFRUADS67g033MC8efPqlKmqSq9evUhOTsblctV5btGiRRgMBoxGIyaTifT0dGbOnMn27dvrLJeenk5YWBhGo9H7GDZsWJMyCAkJwWg0EhMTw6hRo9i8eXOdZT755BPOPPNMTCYT0dHRnHHGGXz88cfe5xVFITw8HKPRSEJCAtdeey0FBQWn3LfQhl91+JctW8bs2bO5+eab6d+/P8uXLyc1NZWnnnqqweWffvpp0tLSWL58Of379+fmm2/mpptu4p///Gc711wIIYRomMtip6KkAr1aBIBaGkFsejgEyXj6jiI6Opp77rmn2es9/PDDfP7553z99ddYrVa2b9/O5MmTW1SHtWvXkp2djcVi4ZNPPqn3/IQJE7BarZSXl7Np0yb69OnD2WefzTfffFNnuVWrVmG1Wr2PLVu2NGn/S5cuxWq1kp+fz1lnnVWnHfv27WPq1KksXLiQ0tJS8vLy+Oc//0lkZGSdbWzcuBGr1UpWVhZ5eXncfvvtLUhCtITfjOG32+1s2bKFu+++u075xRdfzMaNGxtcZ9OmTVx88cV1yi655BIyMzNxOBwEBQXVW6empoaamhrv9xaLBQCXy+U9olYUBZ1Oh9vtrnMmpLb8xCPvE8tdLheqqnrXPXF5nc5zHHbix6qNlev1elRVbbD8xDo2Vt7aNh1fR0VR2r1N4Dn7cfx+/b1Nvnydan9Ga58PhDb5+nWqzbT260Bo08nq3tZtgvrveX9tk+2IhfzyIhKcxeTrYzm9yoS+529ncdurTce/77V8nZrqwIF/U2M/2uL1myokOJ7u3f/crHXmzp3Lv//9b9atW8f555/f5PW+++47Jk6cSPfu3QHo0qULN910U7P2XSszM5MJEyYQFRXl/boxSUlJ3HfffeTk5HDXXXfx/ffft2ifDQkODmbWrFk88sgjHD16lPj4eH766ScSEhKYNGkS4Ln4e9SoUY1uo0uXLkydOpVnnnlGs3qJk/ObDn9RUREul4uEhIQ65QkJCeTn5ze4Tn5+foPLO51OioqKSEpKqrfOkiVLWLx4cb3yHTt2YDQaAYiJiSEtLY0jR45QUlLiXSYxMZHExEQOHjzo/bgOIDU1ldjYWPbu3YvNZkNVVSoqKrBarZjNZnbu3Fnnl2rfvn0JDg4mKyurTh0yMjKw2+3s2bPHW1Z7K/SKigr279/vLQ8NDaVfv36UlpZy+PBhb3lkZCQ9e/aksLCwTm6tbVOtHj16EBUV1e5tSk9P975OiqIERJt8+Trt2LGDiooKb56B0CZfv07Hd74CpU3gu9dpwIAB3p/V2ve8v7YpbEcNh+wbiXPWcDi4B2ONBvY6QnBkZbVrm6qrq73v+549e2ryOnXr1o1AEBMTw1133cXdd9/d6EnGhpx33nksX76cyMhIzjvvPIYMGYLB0PyuV1lZGatXr+a///0vkZGRXHzxxRQUFNTr45xoypQpPPvss1RWVhIREdHs/TakurqazMxM4uLiiI6OBmDYsGHk5ubyhz/8gYkTJ3LmmWcSExPT6Dby8/N54403GDp0qCZ1Ek2g+omcnBwVUDdu3Fin/O9//7vat2/fBtfp3bu3+tBDD9Up+/bbb1VAzcvLa3Adm82mlpeXex+HDx9WAbWkpER1Op2q0+lUXS6Xqqqq6nK5vGXHlx9fdrJyt9vdaLnb7W5yuaqqjZafWMfGyqVN0iZpk7RJ2tT+bXLUONSCl7LUZx65Qf1q8Uj13kXz1dIn/6E6HQ6/bdPxj/LychVQy8vL1eNVV1erO3fuVKurq9WObtSoUepjjz2mVlVVqV27dlXfeecdtbS0VAXUAwcOqC+++KI6ePDgBtd1uVzqc889p15wwQVqRESEajKZ1AULFnhfvxdffFHV6XSqyWSq8wgKClJvu+0273aeeOIJNT4+XrXb7arb7VbT0tLUf/zjH97n77//fnXixIn19r9z504VUI8cOaKqqqp269ZNDQ8Pr7Ovm266qUkZhIaGqiaTSVUURU1MTFTXr19fZ5ktW7ao1113nZqcnKzqdDp17Nix6r59+7zPA6rRaFTNZrOampqq3nDDDWpxcfEp9y0a15z3kd+c4Y+Li0Ov19c7m19YWNjoEW5iYmKDyxsMBmJjYxtcJyQkhJCQkHrler0evV5fp6z2I8yGlj1ZudvtprCwkC5duqAoyimXb0p5Y9tprI7NLdeijs0tb06bjs/0xOf9tU0tKdeq7oqiNJinP7fJ16/T8T+jgdImrevYnPKWvOc7YpscRysptVoxOUuwK0EkFUQSfnYX9CecBW6PNp34t6mlbQpUYWFh3H///SxcuPCUMwTW0ul03Hzzzdx88804nU4+//xzpk+fTo8ePfj9738PeD4d2bZtW531brjhhjrfZ2ZmMn36dO9Q5JkzZ5KZmcmdd9550v3n5OSgKApms9lb9uqrr3qH3jTHkiVLmDdvHjk5OVxxxRVs376d8847z/v80KFDefnllwHPmP5bbrmF6667rs4nIuvXr2/0AmfRtvzmot3g4GCGDRvGmjVr6pSvWbOGESNGNLjOOeecU2/5zz//nOHDhzc4fr+9qKpKfn6+zISgIclUW5Kn9iRTbQVKnvZcK4dLd5HgKOWAIYlBoVEE9Wnf6ThrBUqmbWn27Nm43W5eeumlZq9rMBgYP348F154Yb0hUSezbds2tm7dysqVK71Ds5544gn27NnDhg0bTrruW2+9xRlnnKHZcB6A5ORknnvuORYsWEBubm6Dy/Ts2ZPbbrutWe0UbctvOvwA8+fP5/nnn+eFF15g165d3H777WRnZzNnzhwA7rnnHq6//nrv8nPmzOHQoUPMnz+fXbt28cILL5CZmclf/vIXXzVBtBHV5Uaxq7jKanAUVFKTbaHmQDk1hyzYD1dgz7XiyK/EUViFs6gaZ4kNV3kNrgo7rkoHbpsTt92F6nSjuuWPnRCifThyKzkc5JmOs4BoesW7UJIzfF0t0Qi9Xs+DDz7IQw89VKdcVVVsNludh9vt5rHHHuOLL77AarWiqiobNmxg7dq1jZ6obEhmZiann346u3fvZtu2bWzbto1du3Zx4YUXkpmZ2eA6+fn5PPTQQ7z00kssXbq0VW1uyNChQxk9erQ3h/Xr1/Pkk096DwDy8/N57rnnmtVO0bb8ZkgPwDXXXENxcTEPPPAAeXl5DBo0iI8//th7UVBeXl6dOfm7d+/Oxx9/zO23384TTzxB165d+de//sVVV13lqyaIk1BVFZxu3DUu1BqX53/7sa/tJ5a5cdc4Ue1u1BonboebyIpqynfs934U3SoKKDoF9AroFM/XOgVFr6DodegigtBHBaOLDEZvPPZ1RDCKXoN9CyE6BbfNSWVBBXBsZprSCGJOD4Zg7c7GCu1dddVVPPLIIxQXF3vLfv75Z8LCwuos9/XXXxMREcHChQu9FzMnJyfzf//3f0ybNq1J+7LZbLz66qs89thjJCYm1nlu3rx5XHvttaxYsQKADz/8EKPRiE6nIzo6mpEjR7Jp06Z6Q2imTZtWZ+iV0WhsdPKTk7n33nsZM2YMCxYsIDo6ms8++4y//e1vWCwWTCYTF110UZscbIiWUVT57O6kan9wy8vLiYqK0mSbbrebI0eOkJKS0ug4y+ZyuVysX7+evLw8kpKSGDlypGZjKbXatupw4bLYPWfVK+zYS6v59rsN5Ofn08UYy1k9TkfflA+dFFCC9ehC9CjBepQQPUqQQllVBTGJsehDglBCdCgGHbhVzxl717H/3cf972r4+0bXOfa96nDjrnTAie8cBc+BwLGDAF1U8LGvg9FFBaML9p+xrW3xM9rZSabaCoQ8a/aX88u7mymwPUyFO5yQ/HO4/IY+6Ie3bJ721mqLTBv7G2qz2Thw4ADdu3cnNFTuNyBESzTnfeRXZ/gDQVt0zFevXs1tt93GkSNHvGUpKSmsWLGixTf4ONW2ly9fzuSJV3o6yS63t0PsqnbistTgrrDjqnB4/rc6cFc6cNe4QFVBhY+2fclfVz9CXlmhd7tdYxJ56KZ7mThqHEqIASVUjy7EgC5UjxLm+V8XFoQuTI9i0HvOpusV7xn92j8lbXnwU0t1q7grHbgq7Mfa+lt7nUXVOPIq662jhOg9BwCRQZ5PBo49dJHB6MIN2nwyoRGdTkdaWpqvqxFQJFNtBUKe9lwrB2wbiXXW8EtwDy6NDkLffbDP6hMImQohGiYd/nbUUOc5Jj6Rm+ct4vwLxxOk1xGk1xGsVzDodQTpdATpIUinJ0ivYNArBOl1GHQKwXodigLvf/ges2bPqHeRVU5ODlOmTOGVl1YxaeKV6I4NRwEVJw4cqgO7247dVu252Vh1FTXVNmps1dTYa6ipsbH2q3UseXBZvXYcOXKEKVOm8Peb7+KSQecT4gwi2GnA4NSjd+vQoaCgUPsVegXFoEMxeP7/KOtrbn7hLtQTTpHnlRRw4z9v5YXqZUwYflHTQj1u6E1VTTVf7dzIwhcfJLf4t48nk7sk8c+/LmHypMnoIoLQRRg8nwy0ooOt6BRvh/1Eqqqi1riOOxioe2DgLKquv0Gdgj4yCEN8OEFJEQQnRaAL992F5YFw9rSjkUy15e95qqqKPaeC0qCDxDqhoiaCbkl2iOnhszr5e6ai5V599VVuueWWBp/buXOnHAgGAOnwt5PVq1czZcqUeh3zkqP5/OPeORz6fiED+pwLxzrLKMqxISMqiuoC3CiqC0V1guoG1QVuB/94cV6jd50FmDv39+z7djs6neI5u467dgE83V0VFRXl2P8ce7jdLp5c9eJJ2/Sv1zM53zyYGr2OGsVOpa6aKr0Nq76KSkM11qAqqkNsqCEK+mADhhADeoOefzzwVL3Ofm1NFEXh3tX/YOJt1xKmC/UMo3G6UV3uY1+rnq+dblSXZxiO6nTjdrp476P3uPWJhfW2nVuYz/Rbb+SFPaXeAwlFr3g6/+GeAwBdeBC6cIO3TB9uQAmre9a9qZ8cKIqCEmpAF2qA+PD67XS6PZ96VPw2vMldYcdlsVPzvzJq/lcGgN4UTFCSkaCkCIISI9CFtN+QIFVVKSkpITk5ue4TTjvYyqHG4vlfdUNYNETEQUiU5+dWNKjRTEWL+HuerrIaSkosRLqKf5uO86w4n76H/D1T0XIzZsxgxowZvq6GaEPS4W8HLpeL22677aRTna35ejkX9/8VRXGiKCpuFFyKDlUHbp0Ot6Kg6hRQwK1TAIW9Bwopt5aedN/lVgtF6o/06ZaIeuzviKIqoKhA7UGAcqzz7/lXB/y6v4DySutJt11YUcxr5a/So0cyqqp46oiCG8XzvUvBUK3grlY8Z7NwcGD/AcqLLY1uU1VVcvPyuP5vt5PQvRs6nYHwcAORxmCiI8PoEh1FvDmG+LguxJi6EBMZT2RYFE6nk7/fuPykBxL3rf4nV910DYpN9czMU+XAWWpDzXc1UBNAp3gOAsKD+GjLGhY8voicwjzv0y0dNqUYdBjMIWCuf78HV6XDM5tQnudh212CbXcJKGCIDfN0/pMiCOoS7rlGobVczt867zUWsFmgxoJSVUrcgd0opZ+CveK3ZZw1jW9LZ4Dw2N8eEXHHvo6B8GNfB0fIQYEQgCPXSnbJbhLUUvYYUhkYasLQ2zfTcQohAp90+NvB+vXr6wzjaUhJRRWWwj0M6W7mpJdRq8Cx/mlBeeFJFvxNVOlhBtob6ag10vfKKW3atuNK93GG47fbtJ/Y3z6xKV+WNW27g6t/4kJ9DgAum54aWxD2oiDsB4LIJ4hsJQiHoseB5/9fDxRQUFDQ6PZUVeVIXg5PbfqUKVeMJy0hDkOwZziO6nDjrnLgqnLirjp2vUGVA3el5/v3vviAGx+bV+9gIudIDlOumsLLS57jqsmTMcSEojeHtKojro8IQt/TTGhPM6qq4rbYsR/r/DvyK3EWVVOdVQQ6haAu4d4DAENcmGdoU91GQ0UeHN0DlUfrnpm3HfvfUdVgPRRVJdJiQamJhjAThJrAmAihUZ4z+aEmz9eKDqqKoaoEKos8X5cehMKdDTfQEHLcQUHcsYOBEw4QgsIaXleIAGLPsZJt+In0GpVCfTSXd6lB6Xqar6slhAhQ0uFvB3l5eadeCFhflUhZUG9cKKhK7eAa5djJeB2KCoqqQ6/o0aEjN/owsOeU23UlXMJR40BCnUGEuvXoUAjSqejRoQS5cIXaIcyOK6IGp7EaJdSG2XQA3jr1tiNOj8c6IBrF7UZ1AaoLt0vF5VaODbkBVVW8n27oyk1NykKN60JeWBw6VHSqGz0u9KqbcLWaKKwYVBfBqhO96kZVwVJe1KTtFq1dxuaSd1mrhFGlhFClhGBXgrBjwKEacBIMhBAcGk18Qi/6pqdyz3+XNv7JAQoLHvkrY7ucgV6nBwX05hAMMaGeA4CYMAwxIehCTv5Wa2y4kN4UQpgphLB+MaiqiqvEhiOvEnteJc4Cz0EAP4ESpCOoSyhBkVaC9Nnoq3aiFP3q6eDXoUBIpKezHtP9WOe9thNv9n6tBhuxVdiJ7NoNpSUXPDuqjx0IHHtU1n597KCg6FdwNnJDlqBwMHaB5OHQbQSYAmN4gaIoJCYmdqiLs/2ZP+epOt1U5VagKp6TFO6yCGIHGyDM7NN6+XOmQoiTkw5/O0hKSmrScvGDUuk1fCiJkUkkRXela0wKJnM0OkPDHS6Xy8WaT74lJyenweFCCgpdYxK4behs9AYDelPwbx3RaM//utCGfwRGn+9i+SPfNL5tRSE5OZnb7/gQnU7FrTpR3Q5U1YHb7URVHaiq87hyz9fnT7CR+d9p5OUVNfhJhqJAYqKZ62+/DJ3iwu2243bX4FYduN12VLcdVfV8xOF2KdRUga3cgbHGCPx6yowjYoyEBdkwqxWEue2obnCruvp1sXoe339ZSV5ew3cSBE+nP6ckn3Xqr4wffD6uUhvOEhs1+8qp2VfuXU4XEeTJPjYU/bHXQBcRhKIoTZ5lSVEUDLFhGGLDCBsUh1pVgfN/e3DsP4I9z4o924392CUaOn0MQTFnEJRsIqhHKvqkVE9nPjgSmnAxng5IMJ9yscYFhYEpxfNoiKqCvfK4g4DS3w4Gqoqh7DD88pbnYe7m6fh3G+E5EPBTOp2u3jzaouX8OU9HQRX5pUUkOIs4qotmSKWZ4F6+vyjSnzMVQpycdPjbwciRI0lJSTlp5zklJYUn7nn2lNNHqqqKy+KZ6cVZXM1D1y9k1kN/RDl22a13m8fG6vzzgaXETuztGWqib/pQE71ez4oVK5gyZQqKotSpd+3ZnxUrVhAS0rQz9sf797+fObZdGtzu449n0rdP4+PiVdWF23twUYPbbWfIeZUse3YEhYXFjWQMCQnRjL9uGmVWB2UWO4dKarCXWdDXVGNw16AaHCgGJzrFjaJzE6Q4yas++XUMtdZ/toSS/Heo0IVRrYRSo4agI5Kupv5ckJJBnFuHPceK/fBvw5+UYB0f7/qGWX+fW3+40LFZlt566y1Pp19VPcNyju72DNE5ugel/DBBQBAQHhuC2qsfjqABOJwpOKyR1JQ5qTkKHAV9dA2hvZ2E9FTR1b90oB6Xy8XBgwdJT0/XfEpTT+MVCDF6HtHd6j/vdkHBDji0EY78ANtXeR6xvTwd/7RzPMOB/EibZ9rJ+HOejlwr+6s3EOO0sSu4GxfHGNCl+344jz9nKoQ4Oenwt4OmdJ6XL19e7xesqqq4rQ5P576oGmexDWdxNarD7V1m/MDRvHTfk9zzzAN1LyhNPTZXfivm4Z88eTJvvfVW4/Pwt3Dbrd2uouiPZRUKRAIQFOTizjvv5s4772w04yeeeJ4zRtbdtqq6cLmqcTorqa6soLS0lIKiIopLyygrr0bJ2w78dMo2dTHp6cNhFCfeTwsUgKKv2FUcQZkukgpdGJXHDgZwhxGlJLPk8b83PFxI9VxoPO+PtzAx9gD6kr1QfdwF2mExnk5vfD+I7wvmNBSdnmCgdqJQt83puQA4x0rNIQuVP+RTtaWA4PQoQntHY0gIP+lH9xUVFY0+1+Z0ekg6zfNw3Qz52491/n+Erf+BrS9Dl37Q7VxIPdNzTYEf8GmmAchf87TnWCkJOkSME8rtkXRLrILY3r6uFuC/mba1m266iRdffJGdO3fSv39/ANauXcuYMWOIiIhAURRiYmKYPn06Dz74oHda00WLFvH3v/+d0NBQ730O7rnnnjoz4owePZpNmzYRHByMTqcjNTWVSy65hLvvvpv4+HgADh48SPfu3YmIqHsX5ptvvpnly5e3TwjCr0mHv52cqpN75ZVX4qo8vnPv6eCrNb/NIKME6TDEhnqHdRjiwtBFBjFT6c/0+3/XJjebmjx5MhMnTtR8222x3QsvvJA33niD22+/vckHEoqix2AwYjAYCQ1NIDoWevT67flpU128/dbqRj+dATBFmdFFTOC7/ErCdEcJirChhqkEBUGI4iBcrSHRXUy604Fb/e066W0HyigsO9poe1RV5XB+EZ+/tZMLRvQkqPsZ6JL6QlxfzwWupxhnqws1EJJuIiTdRMRZSdQctGDbW+odbqQ3BRPaO5qQXuZGh3Z1CHoDJA/zPJw1kPsTHNrg+b9wF2x+ARIzPGf+U87wzAQkRAflrnJQVlBOpKvIMx1nfiThZ8R6fs5Fh2S1WnnjjTeIiYkhMzOTf/7zn97nTCYTZWVlAOzatYsLLriA3r17c9NNN3mXmTBhAu+++y6qqvLee+8xdepUzjjjDPr06eNdZunSpcyb55lme9euXTzwwAMMGzaMH3/8kYSEBO9yR44cwWw2t3mbReCR3zDtqLaTu3btWn7c+AOn985gRO9hqKV2Sl/fg9t2XOder6Cv7dzHeTr4+qjg+jOxHKPX6xk9enSb1Luttt0W273yyiu58sorNTuQaMqnM5kvPM/Yiy4hOy+X3PyjHC0so7ygDGtROWXWCnBUgqMKnVpCsNGG26jHEOzmF5ujSXX4z9Fsdu1L45z8XvTrnURwskpwUhWG+PBjN1NrXL2LgS8eiVrhpGZvKbb/lVG5uYDKrYUEp0US2ieaoKSIjn3BniEE0s72POxVkLMZDm2CvO2eh+45SBri6fwnD4Ogk99qXIj2Zs+1crBkFwmuEn41pDAwLApDT5mOsyP773//S0REBA8++CALFy5kyZIlBAXVvzFi//79Oe+889iyZUudDn8tRVGYNGkSZrOZ7du31+nwH7/MgAEDeOWVVzj99NNZtmwZS5cubZN2ic5FOvztTK/XM1zpTf/EGIJsQdRklYBOwRATSnC30N869+aQRjv3oj5FUUhNTUVRFHQ6naYHEk0dgpQR1YeMvnV/gVdV2jiSn09OfiFHC8soLSimKu8o1YUV6KpV4LtT7v+ssAKGuL+kwrqOD7PMlO8wUq2GEeJK5KzuExh4WjqhKZHoTcF1Ouunuhg4fGgX7IcqsO0txX7Qgv2gBX1kMCG9zQT3iPLm2WEFh0P38z2Pmgo4/INn2E/OFs+BgD7Y0+nvdi4kDQZD/bsit6fjf0ZF6/lrno6cSg7pt9LNUTsdpw2l62BfVwvw30zbWmZmJjNmzODaa69l3rx5fPDBBw1+YpyVlcW6detYuHBhg9txuVysXr2a4uLiBjv7xzMYDEycOJE1a9Zo0gYhpMPvA8EJnrum1nbuDdHNu6BW1KfT6YiNjW2z7bd0CFJ4RCh9UmLpwwFw/AQ1P0OUE7vTQPZZvXn322iOFjd+8zRTZDjV3YfwczCY1Sq6uMpIddQOA9pJ2f71vHvIhEUXgU0NI0ifyDnDZ7AvdzvTZl5bbxjSiRcDh/QwEdLDhMti9wz3+V8ZVVsLqfqpkODUSJx9ggnqauz4B58hkdDrQs+juhSyv/cM+8ne5HkEhUHKmdDtHEgc3KSZirTW1j+jnY0/5qmqKlVHLN7pOF3lEcRmAMZ431bsGF9nuuxgPgU1TfvkszUSQoKYn9602Yh27tzJd999x9NPP43RaOTKK68kMzPT2+EvLy/HbDZTU1ODzWbjxhtvZO7cuXW28dFHH2E2m6msrATgySefZPDgUx/kJScnU1JSUqesW7dudQ7IHnvsMW688cYmtUV0btLh94HgfmYO7d1L716JMhOCRlwuF3v37qV3795tlmmzhiBVlcCRzXD4O884c9XtuUlVwkBIOZPglOH0Co/h6eDBTJkyBaDBawSuGnc9hvI0bLZyCuwWcojEGQ16k45wg5NodxUJzhJS1Nr7EOymcP23zF22qcHteS8GnjePiRMnerPSRwUTMSyB8CFdsB+poHpPMSW78og4ZEFvDCa0t5mQXmb0Rt+eJW+SsGjoe6nnUVnk6fAf2ggHvvE8zN1g2A2QMKBdq9UeP6OdiT/m6Sy2UXC0iC6OIo7qzAyxmgnq2XHuM+GPmba1zMxMBg8e7O2gz5o1i0svvZScHM+NIWvH8LtcLl544QX+8Y9/UFVVhcn020QCl112Ge+++y6VlZXceuutfPnll8yZM+eU+87JySEmpu5sZIcOHZIx/KJFpMPvIzabzddVCDg+z7SiwDOF5OHvoWivp0xngK6ne2aSSR7mORN9nMaGC6Wmpnou5p50JRUlNg4fKeBQdh4FB3OpyD+K42gh9poyCh2hHNYbsUfrMUTqMBocFO7dT0l541moqsrhw4dZv359vQMYRa8Q0i0KQ0oEh6JKiQuKw77fQtW2o1RtP0pwspGQPtEEJ0ee8vqBDiEiDvpf7nlY8uB/X8Cvn8KXiz3XAQy5rl3Prvr8ZzTA+Fuejlwr/6taT7Szml3BaZ7pOLt1jOE8tXyZaVPPurcXh8PByy+/jNVq9d6fQFVVXC4XK1eu5Nxzz/Uuq9fr+d3vfseHH37IokWLeOyxx+ptLyIign//+9/06tWL9957j4kTJza6b6fTyXvvvcf48eO1b5jolKTDL0RLqSpYciD7O890kaUHPeW1F5amnuXp7AeFnXQzpxouFBUXxsC4dAYOSQfAaXdRVlhNbk4Rhw7mUHjwMFWlhdgLinDZSsne17Qzc688u5CffhzMGZfcwpkDTiPYUHeYixqqIywjnojTE3DkWLH9Wor9SAX2I1Z0YQZCepkJ7RONPtIPzvoDRCXB0JnQ+yL46eVjr9tm6H8FDJgoF/iKNlc7HWe0Eyx2I+mJFojv7+tqiUa8//77WCwWtm3bVues+pNPPskLL7zAiBEj6q1z3333MXLkSP7yl7+QnFz/05vw8HDmz5/PfffdxxVXXNHg9RK7d+/mb3/7G+Xl5cyfP1/TNonOSzr8QjSHqkLJfs8Fooe/h4pj9z4IjoDuozyd/MSMZl8g2pzhQoZgPXEpRuJSjJx2VjqqqmKzOigtqKIwt4yaj96FtV+fcjuDQqwMqd5B1Qfzef3TaCxqGPouAxl3+RySzb99EqHoFIJTIwlOjcRd5fDM7rOriC/e/JiC8iJSB6Rz4azLCY7ykw5zZCKcfyfk/QxbX4Idq2H/WhgyHdLPO+V0p0K0hOpwUX6kDKO7CIdiIKHASPiwaJ9fTC4al5mZybRp0+jXr1+d8ltvvZVHHnmkwWGTw4cP5/zzz+fBBx/kySefbHC7c+bMYcmSJbz55ptcffXVACxYsID77rsPnU5HcnIy48aNY/PmzXTpUvfu4ikpde9ePm7cON58883WNFN0Eora2OTiAgCLxYLJZKK8vJyoqChNtqmqKhUVFURGRspsCBpp80zLj3jGgR/8FqyeC+4INXnmfU89C7oM6DDzaLtcLtLT009674AoYwS/u30WseFOUlzFpLoKAU9ftyTISLHOSLUSQfrZMxg59FzMEb99StHQ7D9dYxJ4ZMGDXHvrrI49p/+J3C7435fw8+tgt3ru5DvsRojrdep1m0ne99rytzxrsi1899pHuJxP8z99Mv1KhjLypgEo/TvOkI22yLSxv6E2m40DBw7QvXt3QkP95GSBEB1Mc95HfvSXOXAoiqLZwYPwaJNMK4sh+1gnv3a4TqgZ+o7z3OU2trdPZns5lVPdO0BVYdZlN9PDmkBNQR45bjPbzV0JiYZ4pYKejjx6qfkAuNb9nU82mrAoYdSYu+Nwp3Ln3D/VO5DIKynkugW/w5FbydQbriV0QCy6YD+46E+nhz4Xe2bvyXoL9n4On9/r+bRm8LUQHnPqbTSRvO+15W95OnIrOajbTJpbpUAfzYQu1SjJQ3xdrTr8LVMhRNNJh98HXC4XO3fuZMCAATITgkY0y7Sm4tiUjt96ZtcBCAqHHmMg/VzoMrBDdvJPdKp7B1xx+USKcyopPFRO9s59FB7ZS1V+NjVVTr43dKc6MYSoUAepriLS7QUkqaW483K4etmPDc/+g2f2n3tfeZhLTxtN9a4SwjPiCO0Xg2Lo+HkREgnDb4ReYz3DfA5845lhaeCV0PcyTYZdyPteW/6WZ/URCy6Om45zkAMik3xcq7r8LVMhRNNJh99HXC7XqRcSzdLiTB02z82aDn7ruVur6gJ9kOfC227nQdchnu/9zKkuBk5IjyIhPYqMUalUlp/D0ewK8vcVcmT3XspKDmA9cpASNZqfTckExalYD/xKsaWm0f2pqkpOcR7bgw8x3NCXys0FVO8sJnxIF0J6mv1jVh9zKoy5F3K2ejr+2//rGfIz9HrP8K1WDnOQ9722/CVPV4WdwtyjdHEepUhnZkhlNEE94jvk9SL+kqkQonmkwy86J5cT8rd7OvlHNoPL7pknPzHDc2fWlDM8d3L1c029GDjCFEJERgjpGXG4Xf0oyqngp427wOqia/Z+rHmH+HZv026Is+7wT4y+/VJc+yxUZR3FujGX6l+KCB/SheDuUR1/vLWiQMowSDoN9nwCv7wN6x/13ENh6CyI7ubrGgo/Y8+18qv1W8yuavYEpXJxtA5d2hBfV0sI0YlIh190HqrqGaZzaINnSka71VMe19tzJj/tbAgz+7SKHYFOryM22UhCv1AyMjJw2M6k6HAF6jvpvPzNqW/zHnHgPV7790+UmQdwyUU3kVYWg21HMRXrjmD4JZTwoV0ISjZ2/I6/PggGXAHdz/ec6d+/Fj5ZAL3HQsbVECpjnUXTOHKtFAcdwuwEiz2S9MRyz4X+QgjRTmSWnlNoq1l6bDYboaGhHb/T4ycazVRVPRfcHtrgmWWnqthTbkrxTMHY7Vwwdmlwm51ZQ3k2ZfYfk8nIyttHYFKq0elUioKNlCjhBPcaz8Wxowk+VIPqUjEkhBMxtAtBCRHt2azWKd4HW1ZC0a+e6zpOuxp6XdTk2Znkfa8tf8lTdankvJzF+oLFxNpL2VtwLrdcGo5hwj2+rlo9bZGpzNIjRNuRWXr8QHCwzL2stTqZWvKOzbCzwXNzLIDwOM8NlrqdK8MymuDEn9GTzf5T65phF/J9YV9qukI3ChlYc5AYtRJ2vcTXQe9QoothaNIN9MyPx/lJFUHJRiKGdsEQ65n20+VyNXrNgc/F9oSLHoDsTfDTK57O/941nvH9XYc0aRPyvteWP+TpLKriYP4eEpzF7NN3JSM0En16H19Xq1H+kKkQovmkw+8DbrebrKwsMjIyOk5nxs+5XS52//AF/SMsKDk/Qlm254mQSM+dVdNHQlyfDnmRXEfU2M9oY7P/pKam8vCDjzA0dQS/fvszxTm/YrW5+CAulfDoSvq5DpNWnU9XxYIl++98ajAS4T6DIZVjsR+pIKS7ic8Pb+T2hX+pN6vQihUrmDx5cru2v1GKAt1GQPIw2PUB7HwX1i6BrkNh2CzPTb0aIe97bflLno7cSvbpfiBNdVOgRDMhoRql62BfV6tB/pKpEKL5pMMv/Ndxd71Vsr8jJWcPSlSUp5PfYwyknQUJGR3mhliB4lSz//QdlUJ5wWgObMgmafMvWA7uI9+t54eu/UkILeY0x37S7GXodZ+RxQacVfHs/SKOv762nBM/M8jJyWHKlCm89dZbHafTD2AIgYwpnp+zba94hosV7oSz/+C5FkSIY2xHKnApBaCCqzyc2AE1EJ3u62oJIToZ6QkJ/6KqULQXDn/vmSe9sshTHmLCkng2xjOvRJ80yHNDJdFmTjb7j6IomBMjOP2q/gyZ3I/CnSXsX3+Ag3t2Upmn54cgM5VdVdLJZ1DNARTXQZZ/+Ea9zj54xhQrisK8efOYOHFixzvrGBEL594GPS+ADf+Cbx+DvuNhyAw50BS4a5wUHCygi6OQYp2JwZXRBPWIlk8ahRDtzg/uiCM6PbcbCnbA5hfg3bmw5j7Y/aGn8993HIxdjDrxCYq7T4JE6ex3JIqikDAwlnPmDGfq36dxyTU3cFHKWM4oSCfkYBLvV4zi+ZxkjlrsjW5DVVUOHz7M+vXr27HmzZSYAeOWQnxf2PMxfLnIc6dm0ak58irZY91AhKuKbEMCPaMVlJTTfF0t0QLffvst48ePJyYmhqioKPr06cOf//xnDh48yIQJE7jnnroXYaekpDBmzJg6ZVdddRW33nqr9/stW7Ywbtw4TCYTRqORkSNH8sUXXzSpPosWLcJgMGA0GjGZTKSnpzNz5ky2b99eZ7n09HTCwsIwGo3ex7Bhw1qYgvBn0uH3AZ1OR0ZGBjo/uGOrz7icnptg/fAcvHMLfPkA/PqZZ6rE/lfAxQ/CxCdg2A3QpR86vUEy1VBb/IwaIoJIvTCN0QtGMfn2qxk7ZgYTQs8k+lBYk9bPzc3VrC5tIjwGLvg/6DfB8ynUpwsg72fv0/K+15Y/5GnPsVJs2AcqlDuMpCeWeQ4OOyh/yNQXPvjgA8aNG8fFF1/Mrl27sFgsfPPNN/To0YOvv/6aMWPG8PXXX3uX37t3L0FBQWzfvh2bzQZ4TlysW7fOexCwefNmRo8ezahRozh48CD5+fnceOONXHnllbz//vtNqteECROwWq2Ul5ezadMm+vTpw9lnn80333xTZ7lVq1ZhtVq9jy1btmiUjPAn8pmzj9jtdpmK7EROO+RneYbr5GwGe6WnPCoZeo31jMk3d2v043DJVFttlaeiUwjvbqJPdxM9LT1x/MfK02tWnnK9jRtewN3bzdWnX02woYPOJKI3wNCZngvEv38Kvn7IM9Z/0FWA/IxqrSPnqaoqFYfKCXMX4VQMxBUYCR8c3OHv39CRM/UFVVW59dZbWbhwIfPmzfOWJyUlcfvttwOwdetW7r77bioqKoiMjGTt2rVceOGFHDhwgE2bNjFmzBh++eUXSkpKGDVqFAB/+ctfuPbaa7n77ru927zpppvIzc1l3rx5XH755c2aGjUpKYn77ruPnJwc7rrrLr7//nttAhABQzr8PuB2u9mzZ4/MhADgsHnO5B/+DnK2gtNzNoTodOh3GaSe5Zkz/xQkU221V576qGDG/WEyKUtTTjq/f3xUCJMTbFjWvsayDatQBp3H70f8jujwuDarW6uknQXmNPh2GWS9CUV7cZ/1B/b8elB+RjXS0d/zrnI7Bw7vIdFRxD59VwaHRaFPT/d1tU7K15n+68u9FFbY2nw/XSJDufXC3k1a9tdff+XgwYNcc801jS4zZMgQIiMj+fbbbxk3bhxr165l3LhxpKWlsXbtWsaMGcPatWsZPHgwMTExVFVVsX79ev7v//6v3ramTZvGfffdx969e+nTp/nTt06ZMoVnn32WyspKIiL86D4nos3J53aifTlrPMMctv8XPr8P3p7t6RQd2ujp2A+ZDpev8IyHHnRVkzr7wr/Vzu8PNHpGa+ilV/KTYSBRtirOqahg0Javee7Za/nL+7ezp2hne1a36aKSPEPPeoyGvG0on91DiPWwr2sl2oHL5eKLtz7mle0vsH1/CflqFL27VEHSEF9XTTRTUZFnYoiuXbt6yxYvXozZbMZoNHL11Vej0+k4//zzvcN6vvnmG0aNGsWoUaO8ZbUdf4DS0lLcbnedbdaqLTt69GiL6pucnIyqqpSVlXnLZsyYgdls9j5mz57dom0L/yZn+EXbctg8dyYt3Om58LZkP7idnucMoZ7xrImnec7kR8T6tq7CZxqb3z+5S1fuv+ov9E8+nV8Ld/N+VE+6hB3mDPtOzrQ7sO3czmf7b+WfiUlcd/YsRqSNIkgX5MOWnMAQ7JmqM74vyg+ZJO14GuKCoO8lMlNLgFq9ejW33XobR3J++zmOijxA3xsu4OrY+3xYs46vqWfd21NcnOdTxNzcXHr06AHA/fffz/3338+iRYvYtm0bAGPGjOGVV15h7969hISEkJqaSnx8PNu3b6eyspJ169Zx4403AhAdHY1OpyM3N5d+/frV2V/ttUrx8fEtqm9OTo5npjSz2Vv26quvMmnSpBZtTwQO6fD7SEf8CFoTDhsU7YGCnZ5OfvE+UF2e54LCPJ37Lv0hYaBn2I6GM+oEbKY+0t55Nja/v1LjpnpHMX12d2Ho0Qr25u/lm5D+BEXsZ7gji9Mc1QyoPszu3H+QGbeCcUOnMq7XFZhDze1a/5PqeQFuUzfcH96PbssLUPwrnPl7CJKx0q3R0d7zq1evZsqUKfWGplkqrFz77/cxjH6vY91PogEdLVNf69OnD926deONN96oM97+RGPGjOGOO+7gvffe847TDw0NZciQITz33HOUlpZy/vnnAxAeHs65557LqlWruOCCC+psZ9WqVXTr1o3evVt28PPWW29xxhlnyHAeUY90+H1Ar9eTkdFxZ2poFocNju6Gwl1QuAOK99ft4CcNhoQB0GWA5h384wVUph2Ar/JscH7/cD0RZyQSdlocxt0lpOyIYkhpDQfz0/hFHUxx5G6G2bfRx1FBH5uNg0df48+bXuL0jIu5ou9V9DT3RFEUXC5XozcLa5e2xfUkZvozsOlJOLQBSg/CyPkybK2FOtp73uVycdtttzV6HQoKHfd+Esd0tEw7AkVRWLFiBddddx3h4eFce+21dOnShaNHj7Jjxw7vchkZGURHR/Poo4+ydOlSb/moUaNYunQpw4YNIyrqtwu2H3nkES688EJ69erFLbfcgsFg4I033uDhhx/m5ZdfbtYFuwD5+fm88MILvPTSS3zyySetb7gIONLh9wFVVb1X8zf3Te1zjurfOvgFO6DkwHEd/HDoOsTTue/SH6K7QztN7+bXmXZAHTFPXYiB8MFdCBsQR8SvpcTuCKN/WQ2FBalk2YfxozGLDMd20iuLmG2DIxvW8si2TzH3Ph3T/jiefOBJco7keLeXkpLCihUr2u2Mq6qqVNhcRI68A2X3B57rWD5bCGfeAunntksdAklH+xldv359neFoJ1JVvPeTaOymdb7W0TLtKCZOnMhHH33EQw89xP/93/95x99feOGF/OUvfwE8BwajRo3i7bff9p7hB0+H/29/+xuzZs2qs82zzjqLr7/+mr/+9a88+OCDuN1uhgwZwurVq7n44oubVK8PP/wQo9GITqcjOjqakSNHsmnTJoYMGVJnuWnTptU5yDQajeTn57cwDeGvFLXR0xECwGKxYDKZKC8vr3N03houl4usrKwOO7sE4JkHv6oIrIWeR0Wep6Nfsh9Ut2eZoHBP5z7hWAffnN5uHfx61fWHTP2IP+SputzU7Cun+pciaoqqsRRUsLumjI3Gn+nj2k53Vy46ncr7e60s+8+2euvXdmjeeuutdun018u0YCdsWAG2MuhzCZx+vdydtxk62s/oqlWrmD59+imXe+2115g2bVo71Kj52iLTxv6G2mw2Dhw4QPfu3WUaUCFaqDnvI/nr0lmpKtRYfuvQWws8/1ce+7qyGDjhWDAoHLoO/W2Ijrmbzzr4Qih6HaF9ognpZcZ+yELIz0cxHQnntOIYDjiG80nYz6S6tvHyu280uL6qqiiK4rthFgkD4NIlsPFfnpvKFe+D826HiA461ag4qaSkJE2XE0IILUmH3xecNhRXDbgcng5zW3106qyByqO/deZrH7WdemdN/XWCwsCYADE9IKKL52tj/LH/E6WDLzocRacQ0t1EcHoUjhwrwVsL6f+/YHpbR/DRfj1HLa80uq6qqr4dZhEeAxfc5xnes+t9+GQBjPizZ2ic8CvnnjmCrjEJ5JYUNPi8oiikpKQwcuTIdq6Z8EfZ2dkMGDCgweeeeeYZZsyY0c41Ev5OOvw+oHz/ND13f4Vud8Sxzr7iuZhVpwedAZRj/+t0J3zfUNmx9Wq/V11QeWwojq2sgZ3rPWcQ4/p4OvERtZ35Lp5HsNFvpwuUj4W15W95KopCcEokwSmROAoqqdiQi2tnRZPWXbtjLSPPH4m+jS4qr9Vgpjo9nD4D4vvCpidg7cOee1AMukoOsE+hI/2MOvaUMf+KP/GXlfWn3qwdPrZ8+fIOMfzoZDpSpp1ZWloaVqvV19UQAUQ6/D6gS8zAGBTmmY9edXn+d7tP+N7ledR+77TV/d597H/V/du89rVCojyd94QBv3Xma8/Wh8e02Uw5vqTX6+vNZyxazt/zDEqIIGZyb/owHF4/9fIbD37A4g12ruw7lSHxQ9rkgsVTZpoy3DPE59vH4Je3PPevGPFnCNXm2qFA05F+Rt01Tip+KSK6fw6LrunPY59mU15e6X0+JSWF5cuX+8WUnB0lUyGEtqTD7wPuXmMpjR3mvflGq6nqsY7/sdlyDMGt36afcbvdlJaWapdpJxcoeY6ZeDEpKSnk5OQ0Ol1ifFQIf4kycvC7LP6ZvZ2MXiOY1Psq+sVo2/FpUqaRiXDR32DLi7DvK/j0bs+4/riOd0MiX+tIP6PVO4rZfWQnSepeugxM5faYi0l1xhGi/5zkERMYOf2ODn9mHzpWpkIIbfnNO7q0tJSZM2diMpkwmUzMnDmzzq2jT+RwOFiwYAEZGRlERETQtWtXrr/+eu9d7HypdtywZhMkKceGBBmCO2VnH9og004uUPLU6/WsWLECoN5ZewXP9+dMmEC5YqJ3dTkzs2sIW7eJB79ayL+2ruCQ5ZBmdWlypoZgOOsWzx16ayzwxSI4sE6zegSKjvIz6q5xUv7zUfYbPiDUaedHQz8ywnox7bwQZoxKZfTk2X7R2YeOk6kQQnt+0+GfPn0627Zt49NPP+XTTz9l27ZtzJw5s9Hlq6qq2Lp1K/fddx9bt25l9erV/Prrr1xxxRXtWGshhK9NnjyZt956i+Tk5DrlSeYuPH/9Up4bcz+Yfs8XQWfidOo5zWZhyv+qqPzicxavW8jzPz9PQWXDF2K2qR6jPWf7Q6I8Y/t/ftPzaZ7oUKp/KebHnC/pVnOIPH0c5n0hnNUvnVD9ZhgwESJifV1FIYTwjyE9u3bt4tNPP+W7777jrLPOAuC5557jnHPOYc+ePfTt27feOiaTiTVr1tQp+/e//82ZZ55JdnY2aWlp7VJ3IYTvTZ48mYkTJ3rvtJsQ14Whhl44/leOu8rBqOBURifewJtFWylx/siZjh2cg5OeO3Rs37Wa+zM2cH63ixjffTzmUHP7VTymO1zyIHzzD8+4fmuB5+y/Pqj96iAa5bY5ObqtgIqgDUTZ3PziTufi5NNJCP0YxRgPAyb5uopCCAH4SYd/06ZNmEwmb2cf4Oyzz8ZkMrFx48YGO/wNKS8vR1EUzGZzo8vU1NRQU/PbdJUWiwXw3JDE5fKMkVcUBZ1Oh9vtrvPRZ2157XKNlbtcLiIiIrzrnrh87dhJt9vdpHK9Xo+qqg2Wn1jHxspb26bj66goSru3CTx3Dzx+v/7eJl++TrU/o7XPB0KbgDpTIup0OmpSy7B+l4e7ygE6mBJ7Om4Gk5m/llB+4XT7r1yEyuGfQ9j8y6tsGryOMd0uZmzaWCKCIprVJpfLhdH4/+3dd3wU1fr48c9uet80EgLplEgNHaSFJkhoYgQFW0SKioJYKHIVVAT0Ury271UioCBVuogg0pEivQYIKZACCek92Z3fH/mx1zUJJLDJkvC8X699wc6cmXnOszvZs2fPnLHX/7/CdbJ1QdvzX6j+/BJV9F6UrBuour8NVo618r1X0TpB6XO+uuuUe/om+5NXUr8oibMW/jSMc6Z15wLMVCloW7+L2swCysj7g/o6/f28N+br9LALCQlhyJAhTJw4scz1Q4YMITg4mBkzZlRrXMYwceJE0tPTWbJkialDEXdRIxr8SUlJ1KlTp9TyOnXqVPj20Pn5+UyZMoURI0bc8Y65s2fPZubMmaWWnzt3Tv9h7eLigo+PD9evXyc1NVVfxtPTE09PT2JiYsjK+t90gN7e3ri6unL58mXy8/P1y3Nzc3F0dOT8+fMGf1QbN26MpaUlZ86cMYihefPmFBYWEhkZqV9mZmZG8+bNycrK4urVq/rl1tbWBAUFkZaWxrVr1/TLHRwcCAwM5ObNmwa5M1adAgICTFYne3t7zp8/X6vqZKrX6XYeb/9bG+pU1uuk1LMmPjAfm8hCzDN0KFZqXOq6MUoXQlpWK5bl7MVXdYGG+deop1YRffwWO05FsDVwE+2cO9G9XncaBjRk48aNREZG4u7uTqtWrXB3dy+3TmZmZkRFRVWuTpeuonXqg0t6EU5X92OXOw1VyBTOxN4qVafa+DqVV6c6deoYnPPVWaeCzDzydt7AjlMUYk7yLVc6+DRGl7mEJNdHuHHLnMZu+TXyb8T58+eN9jr5+vpS04WEhLBv3z5OnDhBixYtAEhPT8fZ2Zno6Gj8/PxMGt/u3bvp0aMHnTt3Zv/+/frlBQUFeHl5kZqaSlpa2h07O0Xtp1JMeHXOjBkzymxc/93Ro0fZvn07S5cuNfhDAtCwYUNGjRrFlClT7riPoqIinnrqKeLi4ti9e/cdG/xl9fB7e3uTmpqq3+5+e4V0Oh3Jycl4eHhgZmb2UPUcV1WdVCoVN27cwM3NTb/Pml4nU75OxcXFJCcn4+7ujlqtrhV1utPrpOgU8k+nkHcmBbWZGssGGopu5aJNziezOI9FyRtprjtPXV0KhWYWxKhcOOOokJBWzP5vDpKcmKzfb/369VmwYAFhYWEGddLpdKSkpODh4VHm+7fCdbq8A/XxxWBph67zmyV3vb5LXWvL6/TP/f/znK/OOmUdTWLd3k/wzz/DYcsmBKW04PE2iViqrqLrPw/s3Gvc34jbn03u7u6Ym5sb5XXKycnBycmJjIwMg8/e/Px8oqOj8ff3f+Dn/g8JCeHs2bN06NCBX375Bahcg78qe/iLi4vZv38/gwYNwtHRkT/++INGjRoBsHr1aj744AMuXrxYZQ1+6eE3rcqcRya9aHf8+PFcuHDhjo9mzZrh6enJjRulL5q73Wi+k6KiIoYNG0Z0dDQ7duy4Y2MfwMrKCkdHR4MHlPxhvf24/YdNrVaXufzvy8parlaruXnzpv6Y/yyvUqlQqVQVXg6Uu/yfMZa3/H7r9PcYTVEnRVG4ceOGwbqaXidTvk6336O3j1Mb6nSn5eYW5ti38UTzuD8qa3MKItMws7HAIcQb17quvOX1DI004/nDsj25ijWNim/g8GcU69/faNDYB4iPj2fYsGGsW7eu1Pvxxo0bKIpyf3UK6ocqZAoqXTFme+ZgFru/Vr33Krq8rHO+uuqkKlI4uWcfXkWRZKjtMY+149FW9bBSLqFqHoaZo+c91cnUr9Pfz3tj/t2rDV599VUOHjzI3r1lz5i1cuVKWrRogUajoV27dhw8eLDcff388880aNAAJycnRo8eTXGx4b10jh8/To8ePXBxcaFBgwZ89913+nUzZsxgwIABvPLKK7i4uDB58mSg5PV+7rnnDBreixcvJjw83GDfiqLwn//8h6CgIDQaDSEhIVy4cEG/fv78+TRs2FD/C9KXX35psP3evXtp3rw59vb2DB061ODXIvFgM+mQHjc3N9zc3O5arlOnTmRkZHDkyBHat28PwOHDh8nIyODRRx8td7vbjf3Lly+za9cuXF1ltgQhRPksPOzQDA4k589ECqIz0N7Kx76LF0qxQuAJKyakhXMk9TJ78n9n0ZZFZe5DURRUKhUTJ05k8ODBVdPo8WpVMoPPnrlw6OuSi3mbP1Vj75Jd06SduMlV9Tb8dYX8qW5Cn3odcFNtAIe6EDTQ1OHVXHs+hayKDdO9Lw6e0P3dSm3i4uLCu+++y5QpU0o15rdu3crbb7/Npk2bCA4OZsOGDQwcOJBLly6VandcvnyZESNGsHbtWh5//HEWLVrE+PHjadu2LVAyhLlPnz588803PPnkk1y4cIHHHnuMgIAAevXqBcC2bdtYtGgRX3zxBYWFhRw5cgSA8PBwevbsyUcffURSUhJ//fUXCxcu1H8pAPjmm2+IiIhg8+bN+Pv78/XXXzNw4EDOnz+PpaUlvr6+/PHHH9SvX5/du3fTv39/WrVqRefOnUlLS2PQoEHMnTuXUaNG8euvvxIWFsYzzzxT6ZdAVL8aMS3nI488Qr9+/Rg9ejSHDh3i0KFDjB49mgEDBhhcsBsUFMT69euBkp+5wsLC+Ouvv1i+fDlarZakpCSSkpIoLCw0VVWEEA84taUZ9t3qYd+lHkqRjswdcRTfzMUpNACH7vXp5N+UVpltSMksKHcft+cz37dvX9UF6uwLj30MLgFw9mc4+B8olr9tVU2XW8TuXcvxz4/mmpkH9eNdaPPILdTkQrtRYFYjLo0T92DixInExsayYcMGg+VfffUV77zzDq1bt0atVjN06FCCgoLYunVrqX2sXLmSXr16MXDgQMzNzRk3bhwNG/7vxno//vgj3bp1Y9iwYZiZmdGsWTPCw8P56aef9GWaNWvGiy++iLm5Oba2tvrljRo1wtfXVz8Mevjw4VhZWZWK9cMPP6Rhw4aYm5vzxhtvkJeXx+HDhwF48skn8fb2RqVS0aNHD/r27cvu3bsB2LJlC15eXowdOxZzc3MGDhxIz5497zetoprUmL9My5cv54033uCxxx4DYNCgQaV+aoqMjCQjIwOA69evs2nTJgCCg4MNyu3atYuQkJAqj7k8KpUKFxeXUjcCEvdOcmpcD3s+VSoV1g00WNSxJWvfdfLO3qIoMQeHbvXRDG5AesyeCu3n2OVj+r81VZJTWxfo9QH8+SXEHoScFOj2Nlg7Ge8YDyhTvUev/xlLgdkR0CpcyfXi2dbtsM7/AXw7gWfzao3F2Ex+3ley17262djY8MEHHzBt2jSDL/MxMTFMmzaNDz74QL+sqKiI+Pj4UvtISEgodSHz35/HxMSwdetWg/H2Wq3WYIaxO00rHh4ezvfff8+pU6dYsWJFqfUxMTE8++yzBr88FhYWcv36daCkrTVv3jyio6NRFIXc3Fz8/f3vGPvfL8oXD64a0+B3cXFh2bJldyzz9wuU/Pz8Hti7BarVarkPgJFJTo1L8lnCzNESp37+5J66Sd6ZFNI3R2HXvi4+wYEV2v74sT0sbu/Ck488iaOlY9Xk1MIaur4FJ5bBxS2wfTqETAVHL+Mf6wFiiveoLreInUcX4V90gzMWAbTNbkKg5g9UOito/Xy1xlIV5Ly/u1GjRjF//nyWLl2qX+bt7c3rr7/OuHHj7rq9l5cXf/75p8GyuLg4OnbsqN/XE088wcqVK8vdx98vUv+n4cOH8+abb+Lv70+bNm2IiYkxWO/t7c3ChQvp169fqW3j4uJ44YUX2LZtGyEhIZibmzNkyBB9W8rLy4vY2NhS25Q1i6J48NSIIT21jU6nIy4uTuYrNiLJqXFJPv9HZabCrrUHTn39UFmZk30wgWCtP/Xr1b9jT6i7oxWP+Zpzc9lOPlv8PrvjdhMTG1M1OVWpoPVz0G50SS//9ulw45zxj/MAMcV79PgvR3DWnaEAC7JuOtO1oxtmhdeh+bCSX1tqODnv787MzIxZs2bxySef6JeNHz+ezz77jGPHjul7xX///Xd9r/nfDRs2jJ07d/LLL79QXFzMd999x6VLl/Trn3vuOf744w9+/vlnioqKKCoq4uTJkxw9erRC8Tk4OLBr1y7WrFlT5vrXXnuN999/Xz/rYWZmJhs3biQrK4vs7GwURaFOnTqo1Wq2bt3K9u3b9duGhoYSHx/Pd999R3FxMb/88gt//PFHheISpicNfhNQFIXU1NQH9heImkhyalySz9IsPO3QDArE0s8R7fUcPh5eMvzgn41+FSXPBw/oiE9RCm2d4vFMu8W+eUv59vcviMuMq7ogG/aG7pNBp4Vdn8DV3VV3LBOr7veoNqeQ4zHL0WizOG7RkJC6XdDkrwcnb2hUure0JpLzvmKefPJJGjRooH8+YMAA5syZw+jRo3F2dsbf35/PP/+8zC9OjRs35scff+SNN97A1dWVw4cPG/S216tXj99++43//ve/1K1bFw8PD1577TX9TUArom3btuXekHT8+PG8+OKLDB06FEdHRx555BH99QFNmjThvffeo2fPnri6urJq1SoGDRqk39bFxYWNGzfy+eefo9FoWLRoESNHjqxwXMK0TDoPf02QmZlZ5hzC90Or1XLmzBmaN29eq6YtMyXJqXFJPsunKAoFV9LJOZLE5kO/MX31p8TfTNSv965fnzmvz6CXR3sirv9IAyJx16aRaW7H5UIPcvOsCBz4KEM7DsPG3KZqgkyPg91zITcFmj4BLYbXuhl8qvs9uu6LCOwzfiJbZUNiYjCj+zpjmXUEes+AOo9U+fGrQ1XktLzP0Jo0D78QD6rKnEc1Zgy/EEI8CFQqFdYNnbHwsGWI0yAeb9WTozfOkuGhpV6AN127dsXMzAxtdiGvn5rApWPn2JG7geCiS7RRX+Wacx2urdvNgl2n6fH0E3Rs0Nn4F0lqfKDvx7DnMzi3vmSqw46vgrmlcY/zkMjPLCAtbw8uShFnlEd4vlNnLLOWgH+3WtPYF0LUbtLgNwGVSoWnp+dDOwNKVZCcGpfk8+7MHK1wetyf3JM36XjWDJW5GjvvuvqeUTN7Sxw616NlUzcanniETYc2kKE6StPCGOo5p3DeQseued9zpNkuhj07iroaI19ka+MMvf//DD5xf5b09nd7p9bM4FOd79Efv5lNg8JYos3r0iyjMX42v4DWFoJr13AGOe+FqL1kDL8JqNVqPD0973ilvagcyalxST4rRmWmwq6NB46P+aGyUJO9L56svdfRFWr1Zcw1Vjj28Gb46JcZ2WomR8w6kqJ2ollhNE29EylIjWHptJn8tGoRBUXlz+1/T8ytoMskeGQQpFyG396DjNIXEtZE1fUeTYi5ib1yBoBrmXV4rLsbqvxkaPk02Giq9NjVTc57IWovOatNQKvVEhUVhVarvXthUSGSU+OSfFaOZd3/f0GvtwMFVzPI2HyVouRcgzJqZ0tuNdDxxgvTae47mb8sH8FSV0w7LlPXJ5Xovw7zn3cns3f/70DJa7B7925WrFjB7t277/21UKmg1UhoPxpyb8H2f0HS2futsslV13t0/aqPqVuUwlnLQPrW74lD+mZw9ocGfar0uKYg570QtZc0+E0kKyvL1CHUOpJT45J8Vo7a2hyHnt7YdayLNreIjF9jyD2TYjDjSVZWFhZ17XhkZCfeeOYz0u2GctHSF9/CG3RwvIKFRwb7fljBy089Rf369enRowcjRoygR48e+Pn5sW7dunsPsEHvkvn5UUpm8Imq+dPpVfV7dN+e/XgXXyZPZUX+TVfa+J8FRVdyR91a2gsu570QtVPt/IslhBAmoFKpsAlyQRMagJmjJbnHbpC5IxZdblGpcla+jjw9cRwvDv2cv8w6csvMkeDCKLKzjxOxdi1JSUkG28THxxMWFnZ/jf66LeCxj8HWGQ7/F44uAm3R3bd7SJ0+vARHXS5nzRvwdNcQzNPPQmBPcGto6tCEEKJSpMEvhBBGZu5ijWZAANaNnSlKyCFtUxSF17NLlVOpVdg0cuGtyXNo8+hsjpo3YtEvF8rc5+1fCiZOnHh/Qy6c6kPfT8CjKVzeATs+gOyb976/Wur7bz+nUcFVks00uGf7UF+7CSztIfgZU4cmhBCVJg1+E1CpVHh7e8tMCEYkOTUuyef9U5mrse/khUNIfdApZO+6Rt00e9CVvvWJylxNg5AmtGn3DCmZ5V+4qygK165dY9++ffcXnLUT9JheMkd/ahT8OhmuH7u/fVazqnyPKoqCLu0IFmi5qvVjeC9PVAXpEDwCrByMfrwHhZz3QtRe0uA3AbVajaurq8yEYESSU+OSfBqPlZ8TmkGBWHjYYRZbQNavsWgzym7U30ipWE/70d1/lnkXz0pRq0tmmgmZAio17P0UTiwHbfH97beaVOV7dP5nb9Gg8DpXLerxqGcnbBK3gWuDkuE8tZic90LUXnJWm4BWq+XixYsyE4IRSU6NS/JpXGb2ltj39ia9ThFFqXmkb44i/3Ia/7zRed26dSu0v6tH/+SnmfOJPRt1/8F5tYLH55Y0aC9sgj8+hNzU+99vFauq92hqajr1i6+iRU1GlhddfM6VrGj3cq27W/E/yXlftpCQEKysrHBwcMDJyYlmzZrx1ltvkZycbFBu7969qFQqJk+ebKJIhSifNPhNJD8/39Qh1DqSU+OSfBqXSq0i2wscHvNBZWVO9oEEsv8xZ3/Xrl2pX7/+HYdUuDta0eJRey7mx7LxPwtZ99m33IxNKrd8hdi5Qe+Z0Lg/JEeWDPFJPH1/+6wGVfEejfhuMh7aNC5aNeCJzh1R3boEjR4DF3+jH+tBJOd92ebOnUtWVhbp6emsXr2a+Ph42rRpw40bN/RlIiIicHFxYenSpRQX14xfysTDQxr8QghRjSw87NAMCsDS14GC6EzSN0VRdLNkzn4zMzM+//xzgFKN/tvPhw1qzSO664TYn6UgMJ/TsadYO+dTtn2zgsxbGfcemJk5tHmh5EZduqKSqTvPrIX7HTpUg/z+xzYeKYohR2WNZVY9/PK2lVzv0GK4qUMTDwiVSkWTJk1YtmwZTk5OzJ8/H4DMzEzWrl3Ll19+SXZ2Nr/88ouJIxXCkLmpAxBCiIeN2sochxBvCi6lkXMkiYxfo7FtVQebZm4MHTqUtWvXMmHCBK5f/99dcevXr8/ChQvp2W8A3/3nbfyVaNoVRJLtYcNf5o1IP7afuHMnadSxKx2H9sba1vregvPpAM6+sG8+nFlT0uP/6PiShm8td/7oaloo+ZyxbEV4Fw9IuACdXgNLO1OH9lD4v1P/R0peSpUfx83GjXEtx93XPszNzRk8eDA7duwAYMWKFdjZ2fHUU0+xbds2IiIiGDx4sDHCFcIopMFvAmq1moCAALkwyogkp8Yl+TS+f+ZUpVJh3dgFcw9bsvZcJ/f4TYoScrDvWo+hQ4cyePBg9u3bR2JiInXr1qVr166YmZkB8M6U/3D6aiK7Vk+joTaekKJTJPq7ckobQO7u37h67AjNevSiTf8umJmbVT5YB8+S+fqPLYGonfDrFOgyEdwbGy8h98kY71GtVqvP8eGjO+nvdJWbFi74WTfCPmEP1HkE/LoaMeoHm5z3lVOvXj1SU0uud4mIiGDkyJGYm5vz/PPP07dvX/25K8SDQBr8JqBSqXB0dDR1GLWK5NS4JJ/GV15OzTXWaEIDyPkrifyLaaRvisK+sxdWPo6EhISUu78WAXVp+u73rNq2netnlhBYlEhfjnIx0JeLmVbkbV7PhQMHaNu/H490Da58I87cEjqMgTpBcOQ7+H1GybSUQQMeiItX7/c9um7dulK/ovzkaMkT/Qfwf89fg3QVtH3pgahrdTH1eX+/ve7VLT4+HhcXF86cOcPRo0f59ttvAejRowdeXl4sXbqUKVOmmDhKIUrI13gT0Gq1nDlzRmZCMCLJqXFJPo3vTjlVmaux7+iFQ09vALL+uEb2oUSU4juPnzdTqxjRvy9PT/iB45r+XLdy45HiWB6zPUZmYD5X8lPYu3wZq2Z+TvSpy/cWuH+3kht1OXjCiWWw999QmHNv+zKi+3mPrlu3jrCwMIPGPkByZiHfrVzH+u17Sy5g1vgYK9waQc77iisuLmbjxo2EhIQQEREBQL9+/fD09MTLy4ubN2/y/fffmzhKIf5HevhNRP6gGp/k1Lgkn8Z3t5xa+Thi7mpD9r7r5F9MpehGDg7dvTHXWN1xO0drC94Z/y5Rydmsi5hCA67SqfA8WW42HLJoQmpUHBlffUOdwCA6PtmfS9evlDlUqFwab+g7G458C7EHSmbx6fImuAZWNgVGdS/vUa1Wy4QJE0pNifp3E388xeDZT3APg6FqPDnv7+7ixYt89NFHZGRkMGnSJJo2bcqcOXN44YUX9GVu3LhBmzZt2Lt3L926dTNhtEKUkB5+IYR4gJjZWeD4mB+2reqgTS8gfXMUuaeTUbTlN1BvC3S35613v8C+7xecs/TB3ExL78Jj+PvFcNnHgi3bN9E0+BF69OjBiBEj6NGjB35+fqxbt+7ugVlYw6Ovl8xHn5cGO96HyzvgDg3nB9G+fftK9ez/nQJcu5XDvkN/VV9Q4oE3efJk/Tz8Q4cOxdPTk7/++os9e/ZQWFjIq6++iqenp/7RsmVLhgwZwqJFi0wduhCA9PALIcQDR6VWYdvSHYu6dmQfTCD3+E0KrmZg/6gXFnVs77itWq2iT6tAOjVZwtLNv2JzdSl+hck4nt3M/D8ulCofHx9PWFgYa9euZejQoXcJTAUN+4BLAOxfAEcXwc0L0H5MyReCGiAxMdGo5UTtt3v37nLXDRs2jGHDhpW5bu3atVUUkRCVJz38JqBWq2ncuLHMhGBEklPjknwa373k1KKOLZqBAdi2ckebWUjG1miyDyUY3KyrPPZW5rwWNpBeo5ay164v/9kWXWY5RVFQFIVXx71KYX5BxQJzDYR+c6Be25IhPr9NhfRrFa6XMdzrezTmyqUKlXsYZ1eR816I2kvOahOxtLQ0dQi1juTUuCSfxncvOVWZqbFtWQfnwYFYeNqWzOSz4QoFsZl3HId+m6+rHd2DO5Gacec7qN5IvsF7z7zMrsWbyUzOvHtgVvbQ7W1o9SxkJcFv0yB6b0WrZRSVyeeNqEQ+nDORJroDuDuWv51KpcLb25uuXR+e6Tj/Ts57IWonafCbgE6n48yZM+geojtYVjXJqXFJPo3vfnNq5mSFY18/7Dt7oRTryNp1jaw/rqHNKbrrtklJSRU6xrXsbC7u+Z2fpn7I+o++I/r45Tt/qVCp4JGB0HsGWNrDn1/B4W+hMLeCtbp3Fc1ncXoBsz/5kF9WvUnXwuNYmCsMGtC5JPx/lL19N+OFCxfe/ULmWkjOeyFqLxnDL4QQNYRKpcK6oTOW9R3IOZJEQXQGRUk52Laqg3WQCyp12XPGV3R4SgOfZGIbNoBUV4qjzpL0xTnsnDxo3LEjwYMfxcqmnNmC3BvD43Pg4BclN+qK2Qc+nSCwZ8k6E8xlX5xewIblP3Mlax8dtBdQoRBlXZdktQfjOvalk3M/Plj9KfHJt/Tb3L6b8V2vZRBCiBpGGvxCCFHDqG3MceheH6tAJ7IPJZY0/v//Rb3mLqUvnu3atSv169cnPj6+3B57F4013f3VmBceJt/BihOahiQW1cfvWjo52zZwaudveDdoQZshIdRp7FV6B9ZOEDINonfDlZ0Qvafk4VAXAnuAf3ew0Rg3EWUoTi/gwm+nWBH1M+11Z+igy+aWpSPH1JYEeXZhWHojnMkguO0lXuzYg31ROSRaN6JuhyEVm6JUCCFqIGnwCyFEDWVZ3wHnwXbknrxJ3vlbpG+OwqaZG7Yt3VGZ/2/EppmZGZ9//jlhYWGoVCqDRv/tYSxvfPg1v9nZEpD6I77afDoXnkVRnSXSz5uLZv7Y37BFe+EwMReP4uLqS9POjxLUrxXmNhb/C0itLunVD+wJ6XEQtatkXP/Jn+DUKqjXqmRd3WBQG7dhXZxeQPLBGL48vBY/y/P00V6j0MyC09Z1OONjQXh6dxpct8fa6gIOHsdRezeHgO6EPNMazOSjUAhRu6mUilz19RDLzMzEycmJjIwMo91yXFEUdDodarVa/2Er7o/k1Lgkn8ZX1TktvpVH9sEEim/lY+ZgiV2nulh62RuUWbduHRMmTDCYh97b21s/jEVRFM4lZLLpxEUKLv2bR3RZeBVko9OquaVy5Lh5IzLz6tLoegLmOh1WVs4ENA4muP+jODVyR6fo2Ldvn+FNvdDB9b/g6i5IPA0oYOMMASElDwfPe6rv7XzqMovI+iuRFbu2ccvxPI8WncUCLTFWrvzulEszWweGJ3bDvkiDlXs29p19UAV0qZZfG2qaqniPlvcZmp+fT3R0NP7+/lhb14wpXYV40FTmPJIG/11UVYM/Pz8fa2traUwZieTUuCSfxlcdOVV0CvkXUsk9eROlSIdVoBN27TxRW/+vB1ur1ZZulJcxjCUpI59fz8dy4K//49Gic/gUFmJepKMIc06qG3IVH+onFuKSnY7azJKrqVn8sG8DSbdu6PdRv359Pv/88/+Nic9Jgau7Sxr/OSkly+o0KRny490RzCs+Q0xRWj7pR65z+OAx/rA8TWfdKVyUTDItbTlgDRnO2Qwr8qNlam+w8sCugw/W7R9BJVNOlqsq3qPS4Bei6kiD34iqosGv1Wo5c+YMzZs3l/GiRiI5NS7Jp/FVZ0612YXkHEqk8Ho2Kisz7Np5YBWouadGXG5hMbsjE1h9fCNNUzfSuBg0BfnodGpi1J6cMmvIlaPX2LL+xzK3VwH/9+5Chg14Egt7S9RWZqitzVBlR6NO+hP1zb9QqXJRWdqAX+eSIT8uAYb1+duXlDoOrrSybsi5P0+zLv8UDeyiaFIcjdZMzQVrB/Y7ptPJ2pxhVoOwTGuHys4Z+27eWPkY5+93bVYV71Fp8AtRdSpzHsnARSGEqGXM7C1x6OVDYWwmOYeTyN6fQEFUBvad6mLmWM5MO+WwtTSnf3Mf+jUdz/G4p1l++g+KYn6gc1Eh/gUJeBcmMnzn0XK3V4ApX06nKOkqlhZ2WFrYYmlhi7WlLdaW9thYPo6dSoc9eTheysPWcgtmDraoPPxQezVk05+7eGfue8QnJej36WjvSJ9B3RgTlIOVtpgEG0e22OTg5lzAhIAnaKEMJv9SPmoXCxx7+ZR5IbMQQjxM5LdNIYSohVQqFVZ+TmiGNMC6sTNFiTmkbYwi93QyirbyP+yq1Sra+rmzYNBw3hm5iqiWE/ncJZBfbmZzK/POd+hNy81mq3kef9Z3YY+bDb/bKPyhZLIrN45dt86wK+E4f8SeZNOVi6w6H82aI5fYsHU37/9rMiPeDDdo7ANkZmfy809b2HPpFtsdbdhST02vdv2ZOWgVzfLDyL+Uj7m7DZpQf2nsi/sWEhLCwoULK1x+xowZmJubY29vj729Pd7e3rz//vsGF8v7+flhY2OjL2Nvb8+WLVv06/fv30///v1xcXHB0dGRRo0a8frrrxMTE6Mv8+uvv9K+fXucnJxwdnamXbt2bN26tUL1sbKywt7eHgcHB5o2bcqaNWsqXD9RM0kPv4nIMAnjk5wal+TT+EyRU7WVGfadvLAKcCL7z0Ryj9+kIDoD+05eWNSxvad9+rraM713KJmd+/DmZx8BJ++6TevMvfRSXwQ1KJYq8rAkDyvysCZPZUku1uSrLMlXWVKoUpOvK+Db1XduvMz/5RKvv9iPacHPE2TdiKydcRSm5mPl74R9Zy+DmYpExch5bxwDBgxgw4YNAFy+fJnu3bvTuHFjRo4cqS+zYsUKhgwZUmrbzZs3M2LECD766CMWL16Mh4cHiYmJrFy5kl27dhEeHk5UVBRPPfUUy5YtY9CgQRQWFnL48GHUFbxGZe7cuUycOBFFUdi6dStPPPEE7du3x9fX1xjVFw8gafCbgJmZGc2bNzd1GLWK5NS4JJ/GZ+qcWnjYoRkYQN7ZFHJPpZCxNRpzD1usG2iw8nNCZVH5xrGjjSXPdevF93x817IFday5bm+FpQJmClgoYKPk4ahkY6FosdQVgaJCp6jR6VQcv5pBdmbWHfeZn5ZPb3rRSOdPxpar6PKKsW3ljk0Ld7nY/B6Y+j1aWzVs2JAuXbpw7ty5u5ZVFIU33niDadOmMXHiRP3yunXr8uabb+qfnzhxAg8PD/0XBmtra7p3717p2FQqFaGhoWg0GiIjI6XBX4tJg98EFEUhKysLBwcH+VAyEsmpcUk+je9ByKnKTI1tyzpY+jmRdzqZwphMsm/kknMkCUs/R6wbOmPublOp+CpyUy8Hdw2Z/YayXZdDTlEm+dp8tDoFnaKg1elKHkXF2CgFOBcV4qKDBF1GhY6feCaOzISYkuOE1MfKz6nCsQtDpn6PJn/9NcXJyVV+HHN3d9xffbXKj3PbhQsX2L9/P+Hh4Xcte+nSJWJiYhg+fPgdy7Vp04aEhAReeeUVBg8eTPv27XFxcal0bDqdjs2bN5Ofn0+rVq0qvb2oOaTBbwI6nY6rV6/KDChGJDk1Lsmn8T1IOTV3ssKha310HbQURGdQcDld/zBzssSqgTPWgU6obS3uuq+K3NRryf9FMHTgUP3yIm0RmYWZZBZmklGQof9/en4GqXkZpOZnkJx/Bjh71+M7JZqhqmuGQ09vLNzvbYiSKPEgvUdrul9++QWNRoNWqyU7O5uhQ4fSq1cvgzIjR47EwqLkHHN1dSUqKoqUlJLpar28/nc365kzZ7JgwQKKi4vp378/q1evxt/fnwMHDrBgwQJefvllEhMT6dmzJ//9738JCDCc5aosU6dOZcaMGRQUFFBYWMjs2bNxd3c3YgbEg0Ya/EII8ZBSW5ph09gFm8YuFKfmU3AlnfyodHKP3SD3+A0s6ztg1VCDZT0HVGbl9/gOHTqUtWvXlrqpV/369fU39fo7CzMLXG1ccbVxLXef2o5a/BbuK/eXAxUqPDXudO7wKE59AzCzu/uXE/Fgq85e96oWGhqqH8OfmprKK6+8wgsvvMCKFSv0ZZYvX15qDL+bmxsACQkJ+ob7Bx98wAcffMCMGTM4efKkvmzr1q358ceS6XCjoqIYO3Yszz77LAcPHrxrfLNnz9YPGbpy5QoDBw7EycmJsWPH3mONxYNOrmgSQgiBuYs1du09cRnWGIce3lh42VN4PYusP66RtvYSOX8lUZxe/mw8Q4cOJSYmhl27dvHTTz+xa9cuoqOjSzX2K+r2LwdAqeElKkqeT33hTZz7S2NfPNhcXFx47rnnDGbhKU+jRo3w9fVl9erVlTpGYGAgEyZM4MyZM5WOr0GDBoSGhlYoPlFzSQ+/iciNRoxPcmpckk/jqwk5VZmpsPJ1xMrXEW1OEQVR6RRcSSfv7C3yzt7CvI4N1g2csfJ3RGVhOOzDzMyMkJAQo8VS3i8HXi4ezJ38MW0GPnpPFxuL8tWE96gpFBcXk5+fr3+uUqmwsqrYPS0yMjJYvnx5hS6IVqlUfP755zz77LPY2try9NNPU6dOHZKTkw0u+t23bx9nzpxhyJAheHl5kZSUxHfffcejjz5a6brFxsaydevWMmcMErWH/KU0ATMzM4KCgmSMpBFJTo1L8ml8NTGnZnYW2LZwR/NEA5z6+WEVqEF7K5/sgwmkrooka388RTdyyr1Y934oWh3anCIGhfTn0sGzbFu6kf+++hkbpiwm8uAZRr47iqBHHqlR+XzQ1cT3aHV55513sLGx0T8aN258x/JbtmzRz68fGBhIfn4+y5cvr9CxBg8ezC+//MLWrVtp1KgRjo6OdO3alTp16rBgwQIAnJ2d+e2332jTpg12dna0bt0aZ2dnli5dWqFjTJ48WR9f586d6d27N++//36FthU1k0qpir/UtUh5twW/HzqdjrS0NJydnSs8Z664M8mpcUk+ja+25FRXqKUwOoP8K+kUJ+cBYOZoiVVDDdaBmjIv9FUUBaVIh5KvRZdfjFJQ8q8uX4uSX4yu4P//m6/Vr1OKdKX2o7I2w7GHNxYedrUmnw+SqshpeZ+h+fn5REdH4+/vL78qCHGPKnMe1ZghPWlpabzxxhts2rQJgEGDBvHFF1+g0WgqtP3YsWP59ttvWbBggcHctqagKArXrl2rcOzi7iSnxiX5NL7aklO1pRnWjV2wbuxCcXp+yew+UenkHrtJ7vGbWHjZo7JQ/6/hnq9FV6AF3V36ltQq1NZmqK3NMXewQW1ljsraDLW1GSorc9TWZlh42KG2KfnYqi35fJBIToWovWpMg3/EiBFcv36dbdu2ATBmzBiee+45Nm/efNdtN2zYwOHDhw2muRJCCHF/zDXWmLfzxLa1B4XXsyi4nEZhfDYooLJUo7Y2R21vgbmbDSqrksa82tqspCGvb9Cbo7IyQ2Whlns+iBohLi6OJk2alLnuv//9r8HddE1h+fLl5c62c/78eXx8fKo5IvEgqBEN/gsXLrBt2zYOHTpEhw4dAPjuu+/o1KkTkZGRdxxLFx8fz/jx4/ntt98IDQ2trpCFEOKh8fcLfZUiHahVd5zGU4iazMfHh+zsbFOHUa6RI0ea/EuHePDUiIGPf/75J05OTvrGPkDHjh1xcnK643yzOp2O5557jnfeeYemTZtWR6gV5uDgYOoQah3JqXFJPo3vYcipykJdbY39hyGf1U1yKkTtVCN6+JOSkqhTp06p5XXq1CEpKanc7ebOnYu5uTlvvPFGhY9VUFBAQcH/5prOzMwEQKvVotVqgZJps9RqNTqdrtRdJdVqtb7cnZb7+fnpL4r6Z/nby3U6XYWWm5mZoShKmcv/GWN5y41Rp9sxqlQqk9TJ398fRVGM+jqZuk6mep2g5D0KJe/P2lCnB+F18vf3r3V1MuXrFBAQgE6nM9hXTa+TqV+n2+e9oihGqZMQ4sFg0gb/jBkzmDlz5h3LHD16FCh94xX43x+kshw7dozPP/+c48ePV2pc6OzZs8uM6dy5c9jb2wMlN9Hw8fHh+vXrpKam6st4enri6elJTEwMWVlZ+uXe3t64urpy+fJl8vPzURSF/Px8mjRpgpOTE+fPnzf4o9q4cWMsLS1L3UCjefPmFBYWEhkZqV9mZmZG8+bNycrK4urVq/rl1tbWBAUFkZaWxrVr1/TLHRwcCAwM5ObNmwZflu63TrcFBATg6OhY7XXy9/cnMjKS/Px8/etd0+tkytfp9OnT5OfnY21tjUqlqhV1MvXrpCgK1tbWNG7cuNbUCUz3OjVt2pSYmBgyMjL053xNr5OpX6e8vDz9eR8YGGiUOvn6+iKEMD2TTsuZkpJCSkrKHcv4+fnx008/MWnSJNLT0w3WaTQaFixYQHh4eKntFi5cyKRJkwx6LG/3VHp7exMTE1Pm8crq4ff29iY1NVU/pdj99qBotVrOnTtH8+bNMTc3rxW9Qn+P0RQ9XQCnT5+madOm+jmka3qdTPk6FRUVce7cOX0+a0OdTP063T7vW7RowT/V1DrdKfaqrhOUPudrep1M/Trdfo82bdoUCwsLo9QpJydHpuUUoorUmGk53dzccHNzu2u5Tp06kZGRwZEjR2jfvj0Ahw8fJiMjo9y7yj333HP07t3bYFnfvn157rnnyvyCcJuVlVWZd88zMzMrdTOS8uYpLu+mJX9frlKp9L1SFSl/t+UqlarM5eXFWNnlxoixsssrUyetVqsvb8zXydjLa9LrVFY+a3qdKrq8qupkzHO+sstr2+t0L+f8g14nMP3rdPv4xn6vCiFMq0ZctPvII4/Qr18/Ro8ezaFDhzh06BCjR49mwIABBjP0BAUFsX79egBcXV1p1qyZwcPCwgJPT8+73iFPCCGEEAIgJCQEKysr7O3tcXZ2pnv37vrhxvPmzaNRo0Y4ODjg7u5O7969DUYQZGVl8eabb+Lt7Y2NjQ2BgYF8+OGHFBcXm6g24mFVIxr8UDKvbPPmzXnsscd47LHHaNGiBT/++KNBmcjISDIyMkwUYcWpVCpcXFxkzmkjkpwal+TT+CSnxiX5ND7Jafnmzp1LdnY2iYmJtG7dmiFDhrBs2TK++OIL1q1bR1ZWFpcvX2bMmDH6/BUVFdG3b19OnTrF77//TnZ2NmvWrGHdunU888wzJq6ReNjUiFl6oORCpGXLlt2xzN0uRyhv3H51U6vVcuMLI5OcGpfk0/gkp8Yl+TQ+yendWVtbM2rUKBYuXMiBAwfo1asXzZo1A0quKxw2bJi+7PLly7l06RJXr17VX7/QunVr1q9fT+PGjdm9ezchISGmqIZ4CNWYHv7aRKfTERcXJ9OXGZHk1Lgkn8YnOTUuyafxSU7vLjc3l0WLFuHr60v37t1ZvXo1s2bN4sCBAwYzNwH89ttv9O/f3+BiZSiZnrdDhw5s3769OkMXD7ka08NfmyiKQmpqKvXq1TN1KLWG5NS4JJ/GJzk1Lsmn8Zk6p0d/iSY3o7DKj2PrZEm7UP9KbTN16lRmzJiBtbU1wcHBbNq0iRYtWmBubs7ixYv57LPPKCoqYsSIESxcuBA7OztSUlJo06ZNmfvz8vIiOTnZGNURokKkh18IIYQQ4g5mz55Neno6SUlJbNu2TT+9blhYGL/88gtpaWn89ttvbN++nVmzZgElMxEmJCSUub+EhATc3d2rLX4hpIf/Lm5fF3D7jrvGoNVqyc7OJjMzU6YwMxLJqXFJPo1Pcmpckk/jq4qc3v7srMgtfyrb6/4gUalUdOnShbCwMP1Nyfr06cO7775LZmamwbCe6Ohojhw5wocffmiqcMVDSBr8d3H7joTe3t4mjkQIIYSombKysnBycjJ1GEa1ePFiXFxc6N69OxqNhrNnz7Jx40ZGjRoFwLPPPst///tfhgwZwjfffEODBg04deoUL730EqGhofTo0cPENRAPE2nw34WXlxfXrl3DwcHBaFOV3b5777Vr10pdzCPujeTUuCSfxic5NS7Jp/FVRU4VRSErKwsvLy+j7O9BotFomDdvHuHh4RQVFeHh4cEzzzzDu+++C4ClpSU7duzgX//6Fz179uTWrVt4eXnx3HPPMX36dBNHLx42KqUiv7MJo8rMzCzzVuPi3klOjUvyaXySU+OSfBpfdeY0Pz+f6Oho/P39sba2rtJjCVFbVeY8kot2hRBCCCGEqMWkwS+EEEIIIUQtJg1+E7CysuKDDz7AysrK1KHUGpJT45J8Gp/k1Lgkn8YnORWi9pIx/EIIIYSoVjKGX4j7J2P4hRBCCCGEEIA0+IUQQgghhKjVpMEvhBBCCCFELSYNfiGEEEIIIWoxafBXka+//lp/EUWbNm3Yt2/fHcvv2bOHNm3aYG1tTUBAAP/3f/9XTZHWHJXJ6bp16+jTpw/u7u44OjrSqVMnfvvtt2qM9sFX2ffobQcOHMDc3Jzg4OCqDbAGqmxOCwoKeO+99/D19cXKyorAwEC+//77aor2wVfZfC5fvpyWLVtia2tL3bp1CQ8P59atW9UU7YNt7969DBw4EC8vL1QqFRs2bLjrNvK5JETtIQ3+KrBq1SomTpzIe++9x4kTJ+jatSuPP/44cXFxZZaPjo6mf//+dO3alRMnTjBt2jTeeOMNfv7552qO/MFV2Zzu3buXPn36sHXrVo4dO0aPHj0YOHAgJ06cqObIH0yVzedtGRkZPP/88/Tq1auaIq057iWnw4YNY+fOnURERBAZGcmKFSsICgqqxqgfXJXN5/79+3n++ecZNWoU586dY82aNRw9epSXX365miN/MOXk5NCyZUu+/PLLCpWXzyUhahlFGF379u2VcePGGSwLCgpSpkyZUmb5d999VwkKCjJYNnbsWKVjx45VFmNNU9mclqVJkybKzJkzjR1ajXSv+Rw+fLgyffp05YMPPlBatmxZhRHWPJXN6a+//qo4OTkpt27dqo7wapzK5vOzzz5TAgICDJb95z//UerXr19lMdZUgLJ+/fo7lqnqz6W8vDzl/PnzSl5enlH2V5W6d++uWFpaKvb29oqjo6PStGlTZdKkScrNmzcVRVGU6OhoBVB8fHwUrVZrsG3Tpk0VQDlx4oSiKIpSVFSkTJ06VfH19VXs7OwUT09PJTQ0VMnMzFQURVEWL16sqNVqxc7OTrG3t1cCAwOVefPm6fd36NAhJSQkRNFoNIqTk5PSvHlzZfHixQbHXLFihdK6dWvF1tZWcXZ2VsLCwpTLly9XXYKEyVTmPJIefiMrLCzk2LFjPPbYYwbLH3vsMQ4ePFjmNn/++Wep8n379uWvv/6iqKioymKtKe4lp/+k0+nIysrCxcWlKkKsUe41n4sXLyYqKooPPvigqkOsce4lp5s2baJt27Z8+umn1KtXj0aNGvH222+Tl5dXHSE/0O4ln48++ijXr19n69atKIrCjRs3WLt2LaGhodURcq0jn0uG5s6dS1ZWFunp6axevZr4+HjatGnDjRs39GVsbGzYuXOn/vmRI0fQarUG+5kzZw7bt29n165dZGdnc+rUKYYOHWpQpnnz5mRnZ5OVlUVERATvvfce27dvJysri379+jF8+HBu3rxJcnIyERER1KlTR7/tl19+yfjx45k+fTq3bt3i4sWLeHt706lTJ2JjY6soO6ImkAa/kaWkpKDVavHw8DBY7uHhQVJSUpnbJCUllVm+uLiYlJSUKou1priXnP7TvHnzyMnJYdiwYVURYo1yL/m8fPkyU6ZMYfny5Zibm1dHmDXKveT06tWr7N+/n7Nnz7J+/XoWLlzI2rVree2116oj5AfaveTz0UcfZfny5QwfPhxLS0s8PT3RaDR88cUX1RFyrSOfS2VTqVQ0adKEZcuW4eTkxPz58/XrwsPDWbx4sf754sWLCQ8PN9j+0KFDDB48GH9/fwDq1KnDSy+9hIODQ5nH6969O02bNuXMmTNERkaSk5PDmDFjsLCwwMLCgnbt2tG/f38AsrKymDp1Kp9//jlPPPEE1tbW1KlTh/nz59OyZUvprHnIySd3FVGpVAbPFUUptexu5cta/jCrbE5vW7FiBTNmzGDjxo0GPSEPu4rmU6vVMmLECGbOnEmjRo2qK7waqTLvUZ1Oh0qlYvny5Tg5OQEwf/58wsLC+Oqrr7CxsanyeB90lcnn+fPneeONN3j//ffp27cviYmJvPPOO4wbN46IiIjqCLfWqe7PpT9/XkFOWlqV7Pvv7Jyd6fTkM/e1D3NzcwYPHsyOHTt45ZVXAHj66aeZO3cu6enpWFtbs2bNGs6cOcPkyZP123Xp0oWFCxfi4OBAly5dCA4OLrcTRVEUdu/ezblz52jdujWNGzdGo9Hw9NNPM3LkSDp06ICnp6e+/MGDB8nLyyuzY+uZZ57hX//6133VWdRs0uA3Mjc3N8zMzEr1Qt28ebNUb8ltnp6eZZY3NzfH1dW1ymKtKe4lp7etWrWKUaNGsWbNGnr37l2VYdYYlc1nVlYWf/31FydOnGD8+PFASWNVURTMzc3Zvn07PXv2rJbYH1T38h6tW7cu9erV0zf2AR555BEUReH69es0bNiwSmN+kN1LPmfPnk3nzp155513AGjRogV2dnZ07dqVjz/+mLp161Z53LWJfC7dXb169UhNTdU/d3Jy4vHHH2fFihU4OTnRsWPHUu+7d999Fzc3N1asWMH06dMxNzdn3LhxzJo1CzMzMwDOnDmDRqNBrVZTr149Fi5cSI8ePYCSRv2///1vJk2aRHR0NO3ateObb76hdevWpKSk4ObmhoWFRalYvby8SE5OrsJsiAedNPiNzNLSkjZt2rBjxw6eeOIJ/fIdO3YwePDgMrfp1KkTmzdvNli2fft22rZtW+aJ+7C5l5xCSc/+Sy+9xIoVK2Qc799UNp+Ojo6cOXPGYNnXX3/NH3/8wdq1a/U/TT/M7uU92rlzZ9asWUN2djb29vYAXLp0CbVaTf369asl7gfVveQzNze3VE/p7QbU7Z5pUXGm+Fy631736hYfH1/qurDw8HCmTZuGk5MT48aNK7WNWq3m5Zdf5uWXX6a4uJjt27czYsQIAgICGDNmDFAyhv/kyZNlHrNBgwb66VETEhJ45513GDRoENeuXcPNzY2UlBSKiopKvUYJCQm4u7sbodaixqqiC4cfaitXrlQsLCyUiIgI5fz588rEiRMVOzs7JSYmRlEURZkyZYry3HPP6ctfvXpVsbW1Vd58803l/PnzSkREhGJhYaGsXbvWVFV44FQ2pz/99JNibm6ufPXVV0piYqL+kZ6ebqoqPFAqm89/kll6SqtsTrOyspT69esrYWFhyrlz55Q9e/YoDRs2VF5++WVTVeGBUtl8Ll68WDE3N1e+/vprJSoqStm/f7/Stm1bpX379qaqwgMlKytLOXHihHLixAkFUObPn6+cOHFCiY2NVRSl+j+XatosPQsWLDBYVlRUpDRr1kx599139bP0pKWlKTqdTvH19VXc3d2VgoICRVEUg1l6yjJ06FBl/PjxiqKUvI8r87f19OnTCqCkpKQoGRkZir29vbJs2bJS5Xr16qU8//zzFd6vqBkqcx5Jg7+KfPXVV4qvr69iaWmptG7dWtmzZ49+3QsvvKB0797doPzu3buVVq1aKZaWloqfn5/yzTffVHPED77K5LR79+4KUOrxwgsvVH/gD6jKvkf/Thr8ZatsTi9cuKD07t1bsbGxUerXr69MmjRJyc3NreaoH1yVzed//vMfpUmTJoqNjY1St25dZeTIkcr169erOeoH065du+74N7G6P5dqcoP/woULyogRIxRvb28lKSnJoMGvKIpy9uxZ5eTJk/ryf2/wz58/X9mxY4eSlZWl6HQ6Zf/+/YqLi4vy008/KYpy5wb/hQsXlDlz5ijR0dGKVqtV0tLSlDFjxiiNGjXSl1m4cKHi6uqqrF+/XsnLy1Nu3LihvPnmm4qLi4ty9epVo+ZFmF5lziOVoshvnUIIIYSoPvn5+URHR+vvpPwgCwkJ4c8//8TS0lI/rv7xxx9n8uTJ1KlTh5iYGPz9/UlLS0Oj0ZTaXqVSceLECYKDg/n2229ZtGgRkZGRQMl1AGPHjmXChAkALFmyhIULF5Y5pCc+Pp633nqLAwcOkJaWhp2dHZ07d2bOnDkGEyr89NNP/Pvf/yYyMhJLS0t69uzJ7NmzZdKFWqgy55E0+IUQQghRrWpSg1+IB1VlziOZh18IIYQQQohaTBr8QgghhBBC1GLS4BdCCCGEEKIWkwa/EEIIIYQQtZg0+IUQQgghhKjFpMEvhBBCCCFELSYNfiGEEEIIIWoxafALIYQQQghRi0mDXwghhBBCiFpMGvxCCCGEEOWIjIxk4MCBuLm54ejoSFBQEHPnzgUgJCQEKysr7O3tcXZ2pnv37hw9elS/7bx582jUqBEODg64u7vTu3dvYmJi9OuzsrJ488038fb2xsbGhsDAQD788EOKi4v1ZZYuXUr79u1xcnKibt26jBo1ivT0dIMYN2zYQMOGDbG1taVLly5cvHhRv+7s2bP07dsXNzc3VCpVqW3vtl7UDtLgF0LUOMnJyXh6evLJJ5/olx0+fBhLS0u2b99uwsiEELVNaGgoLVu2JC4ujrS0NH7++WcCAgL06+fOnUt2djaJiYm0bt2aIUOGALBs2TK++OIL1q1bR1ZWFpcvX2bMmDGoVCoAioqK6Nu3L6dOneL3338nOzubNWvWsG7dOp555hn9/nNycvj000+5ceMG586dIzExkVdffVW//tKlS4wcOZIFCxaQmppKz549GTx4sP5Lg4WFBcOGDWPJkiVl1u9u60UtoQghRA30yy+/KBYWFsrRo0eVrKwspUGDBsqECRNMHZYQogLy8vKU8+fPK3l5eaYO5Y6Sk5MVQImLiytzfffu3ZUFCxbon585c0YBlJSUFOW1115TXnrppXL3vXjxYsXV1VXJyMgwWH716lXFwsJC2bVrV5nbbdy4UfH29tY/nz59uhIaGqp/XlhYqGg0GuWPP/4w2C46OloBlLS0tDL3e7f14sFTmfPI3LRfN4QQ4t7079+f0aNHM3LkSNq1a4e1tTVz5swxdVhCiHuUuTMObVZhlR/HzMESx14+FSrr6upKUFAQ4eHhjBkzhg4dOuDr61tm2dzcXBYtWoSvry+urq506dKF0aNHExAQQEhICG3atMHa2lpf/rfffqN///44Ojoa7Mff358OHTqwfft2QkJCSh1nz549tGjRQv/89OnTBAcH659bWFjQpEkTTp8+TY8ePSpUT1H7yZAeIUSN9e9//5vi4mJWr17N8uXLDT5MhRDifqlUKnbt2kXLli2ZOXMmAQEBNGnShB07dujLTJ06FY1GQ0BAABcvXmTTpk0APP300yxevJiDBw8SGhqKq6sro0ePJicnB4CUlBS8vLzKPK6XlxfJycmllv/6668sWrSI2bNn65dlZ2ej0WgMymk0GrKysu63+qIWkR5+IUSNdfXqVRISEtDpdMTGxhr0egkhapaK9rpXN09PT+bNm8e8efNITU1l1qxZPPHEE8TFxQEwe/ZsJk6cWOa2YWFhhIWFoSgKBw4cYOTIkcyaNYtPPvkENzc3EhISytwuISGBwMBAg2V//PEHzz77LOvWraN58+b65fb29mRkZBiUzcjIwMHB4T5qLWob6eEXQtRIhYWFjBw5kuHDh/Pxxx8zatQobty4YeqwhBC1mIuLCzNmzCAnJ4fo6OgKb6dSqejSpQthYWGcOXMGgD59+rB161YyMzMNykZHR3PkyBH69OmjX7Zr1y7CwsL46aef6NWrl0H5Fi1acPLkSf3zoqIizp8/b/ClQAhp8AshaqT33nuPjIwM/vOf//Duu+/yyCOPMGrUKFOHJYSoRdLS0pg+fToXL15Eq9WSm5vL/PnzcXFxISgo6I7bLl68mI0bN+qnuTx79iwbN27k0UcfBeDZZ58lMDCQIUOGEBkZiVar5fjx4zzxxBOEhobqx9/v3r2boUOH8uOPP9K3b99Sx3n22Wf5448/2Lp1KwUFBcyaNQs3Nze6desGgKIo5OfnU1BQAEBBQQH5+fkoilKh9aJ2kAa/EKLG2b17NwsXLuTHH3/E0dERtVrNjz/+yP79+/nmm29MHZ4QopawtLQkPj6e/v374+TkhI+PDwcOHGDbtm3Y2dndcVuNRsO8efMICAjAwcGBIUOG8Mwzz/Duu+/q971jxw6aN29Oz549sbOzIywsjMGDB7Nq1Sr9fmbOnElmZibDhw/H3t5e/7itcePGLFu2jAkTJqDRaNixYwebNm3C3Lxk1HZsbCw2Njb6Lyienp7Y2NgQGxtbofWidlAp8hVOCCGEENUoPz+f6Oho/P395WJ7Ie5RZc4j6eEXQgghhBCiFpMGvxBCCCGEELWYNPiFEEIIIYSoxaTBL4QQQgghRC0mDX4hhBBCCCFqMWnwCyGEEEIIUYtJg18IIYQQQohaTBr8QgghhBBC1GLS4BdCCCGEEKIWkwa/EEIIIcQd7N+/n8cffxxnZ2c0Gg0tW7bk008/pbCwEJVKhZ2dHZmZmQbbhIaGolKp2LBhg8Hy2NhY1Go1w4cPL3WckJAQrKyssLe31z/c3Nz06w8fPkyPHj30cbRo0YIlS5ZURZVFLSMNfiGEEEKIcmzZsoXHH3+cvn37cvnyZdLT01m1ahXnz58nMTERAG9vb1atWqXfJjExkcOHD+Ph4VFqf99//z3Ozs5s2LCBW7dulVo/d+5csrOz9Y+UlBQAsrKy6NevH8OHD+fmzZskJycTERFBnTp1qqjmojaRBr8QQgghRBkUReGNN95g8uTJTJw4Ud/bHhQUxJIlS/D19QUgPDycxYsX67f74YcfGDZsGNbW1gb70+l0LFmyhPfff5969eqxbNmyCscSGRlJTk4OY8aMwcLCAgsLC9q1a0f//v2NUFNR20mDXwghhBCiDJcvXyY6OppnnnnmjuX69OnDtWvXuHjxIgCLFy8mPDy8VLkdO3aQmJjIyJEjee6554iIiKhwLI0bN0aj0fD000+zceNGkpKSKlcZ8VAzN3UAQgghhBB79uwhKyuryo/j4OBA9+7dK1Q2OTkZgHr16t2xnFqt5vnnn2fx4sUMHjwYc3Nz2rVrV6pcREQEoaGhuLm58fzzz/Phhx9y9OhRg7JTp05lxowZ+uft2rVjx44dODg4cPDgQf79738zadIkoqOjadeuHd988w2tW7euUH3Ew0t6+IUQQgghynB7CE98fPxdy4aHh/Pjjz/y3Xffldm7f+vWLTZu3MgLL7wAQGBgIJ07dy7Vyz979mzS09P1jx07dujXNWjQgP/7v/8jKiqK69ev06BBAwYNGoSiKPdTTfEQkB5+IYQQQphcRXvdq1OjRo3w8/Nj5cqVvPfee3cs26BBAwIDA/npp5+Ii4srtf7HH3+ksLCQMWPGMG7cOKDkQtwzZ84wf/58bG1tKxWbl5cXU6ZM4aeffiI1NRVXV9dKbS8eLtLDL4QQQghRBpVKxRdffMGcOXP44osv9LPqXLp0iVGjRhEbG2tQfsmSJezZs6fM2XkiIiJ47bXXOH36NCdPnuTkyZOcP38etVrN2rVr7xrLxYsXmTt3LjExMeh0OtLT0/nyyy9p1KiRNPbFXUmDXwghhBCiHAMGDODXX3/ll19+ITAwEI1GQ1hYGEFBQdStW9egbGBgIB07diy1jyNHjnD+/HkmTZqEp6en/uHr68uoUaNYtGiRvuzkyZMN5uG3t7fn1q1bODg4cOLECbp27YqjoyONGzcmOTmZzZs3V3kORM2nUmTglxBCCCGqUX5+PtHR0fj7+5eaulIIUTGVOY+kh18IIYQQQohaTBr8QgghhBBC1GLS4BdCCCGEEKIWkwa/EEIIIYQQtZg0+IUQQgghhKjFpMEvhBBCCCFELSYNfiGEEEIIIWoxafALIYQQQghRi0mDXwghhBBCiFpMGvxCCCGEEELUYtLgF0IIIYQoR0hICFZWVtjb2+Pg4EDTpk1Zs2YNADExMahUKtLT0wGYMWMG5ubm2Nvb4+joSLNmzVi2bJnB/r788kuaNm2Kra0tHh4ejBo1ihs3bujX396nvb099vb2eHl5MXbsWHJzc++7LmfPniUsLAx3d3ccHR155JFHmD59OhkZGQD4+fmhUqm4fPmywXavvfYaKpWKhQsXGizPycnB0dGRDh06lDrWiy++iKWlpb4etx83b94EIDIykoEDB+Lm5oajoyNBQUHMnTv3vusoyiYNfiGEEEKIO5g7dy7Z2dlkZmby6aefMnLkSGJjY8ssO2DAALKzs0lPT+f999/nxRdf5MKFCwC8/fbb/Pvf/+bLL78kIyODv/76i5ycHLp06aJvdN92/fp1srOzOXjwIHv37uXjjz++rzocP36cTp06ERQUxKlTp8jMzGTbtm3k5eVx+vRpfbnGjRuzZMkS/fOCggJWr15NgwYNSu1z9erVmJmZcfToUc6ePVtq/auvvkp2drbBo06dOgCEhobSsmVL4uLiSEtL4+effyYgIOC+6ijKJw1+IYQQQogKUKlUhIaGotFoiIyMvGNZtVrNsGHD0Gg0nD9/nqtXr7JgwQKWL19Ojx49sLCwwNvbm+XLl2Nubs6CBQvK3I+fnx+hoaGcOXPmjsc7ceIEXbp0wcXFBXd3d5555hlu3bqlX//WW28xfPhwPv74Y7y8vADw9fVl3rx5dO3aVV8uPDycH374AZ1OB8CGDRto164d9erVK3XMiIgIwsPD6datGxEREXeM7+9SUlKIiopi7Nix2NraYmZmRtOmTXnqqacqvA9ROeamDkAIIYQQIjr6CwoKk6v8OFaW7vj7v35P2+p0OjZv3kx+fj6tWrUiJyen3LJarZY1a9aQkZFBixYt2LFjB/Xq1aNz584G5czMzAgLC2P79u3MmDGj1H6uXr3Kli1bGD58+B1jU6vVzJkzhw4dOpCamspTTz3FlClT+O6778jNzWXfvn1Mnz79rnVs3Lgx3t7ebN++nX79+vH999/z8ssv89VXXxmUi4yM5MCBA3z99dc0b96cd955h7lz52JpaXnXY7i6uhIUFER4eDhjxoyhQ4cO+Pr63nU7ce+kh18IIYQQ4g6mTp2KRqPBzs6OoUOHMn36dNzd3css+8svv6DRaPDw8GDevHmsXLmShg0bkpKSou9Z/ycvLy+Skw2/7Pj6+uLs7Ezv3r15/PHHmTZt2h1jbNmyJV26dMHCwgIPDw8mTZrE7t27AUhLS0Or1ZbZS1+W8PBwFi9ezPXr1zl+/DiDBg0qVSYiIoLg4GBatGhBWFgYeXl5bNy40aDMN998g0aj0T8aN24MlPxSsmvXLlq2bMnMmTMJCAigSZMm7Nixo0LxicqTHn4hhBBCmNy99rpXh9mzZzNx4kQArly5wsCBA3FycqJv376lyoaGhrJhw4ZSy93c3EhISChz/wkJCaW+QMTGxqLRaCoc45UrV3jrrbc4evQo2dnZ6HQ6LCwsAHB2dkatVhMfH09QUNBd9zV8+HAmT57MggULePrpp7GysjJYX1xczA8//MCUKVMAcHBw4IknniAiIsJgWM4rr7xS6kLf2zw9PZk3bx7z5s0jNTWVWbNm8cQTTxAXF4eLi0uF6y0qRnr4hRBCCCEqqEGDBoSGhrJly5ZKbderVy/i4+M5cOCAwXKtVsvatWvp06fPfcU1btw46tWrx/nz58nMzGTZsmUoigKAra0tXbt2ZeXKlRXal6OjI6GhoSxYsIDw8PBS67ds2cKNGzf46KOP8PT0xNPTk02bNrFjxw7i4uIqHbuLiwszZswgJyeH6OjoSm8v7k4a/EIIIYQQFRQbG8vWrVtp3rx5pbZr0KABb7zxBiNHjmT37t0UFRVx7do1nn32WQoKCvS/INyrzMxMHBwccHR05Nq1a3z22WcG6+fNm8eqVav44IMPSEpKAkpmApo8eTL79u0rtb+5c+eyc+dOWrduXWpdREQEgwYN4ty5c5w8eZKTJ09y6dIlGjRoYDDDT3nS0tKYPn06Fy9eRKvVkpuby/z583FxcanQLxCi8qTBL4QQQghxB5MnT9bPI9+5c2d69+7N+++/X+n9zJ8/nzfffJNXXnkFR0dH2rRpg7W1NQcPHsTZ2fm+Ypw/fz5btmzB0dGRwYMH8+STTxqsb9OmDQcOHODs2bM0bdoUR0dHevfujYWFBS1btiy1Py8vL3r06FFqeUJCAr/++iuTJk3S9+7ffrz++ussXrxY/8vC119/XWoe/hMnTmBpaUl8fDz9+/fHyckJHx8fDhw4wLZt27Czs7uvPIiyqZTbr4oQQgghRDXIz88nOjoaf39/rK2tTR2OEDVSZc4j6eEXQgghhBCiFpMGvxBCCCFEDfDP4TG3H5988ompQxMPOJmWUwghhBCiBsjOzjZ1CKKGkh5+IYQQQgghajFp8AshhBBCCFGLSYNfCCGEEEKIWkwa/EIIIYQQQtRi0uAXQgghhBCiFpMGvxBCCCGEkTVt2pQtW7aYOox75ufnx4YNG0wdxj158cUXmThxIgBxcXHY29uTkZFRZcc7dOgQHTt2NOo+tVotzZs358KFC0bZnzT4hRBCCCHKEBkZycCBA3Fzc8PR0ZGgoCDmzp1boW3PnTvHgAEDqiQulUqFra0tjo6OuLi40KlTJxYuXEhRUVGVHK88sbGxqNVqhg8fXq3HrQwfHx+ys7NxcnKqsmNMnjyZ9957T/88JCQEKysrHBwccHJyolmzZrz11lskJyeX2nbv3r2oVComT55ssNzMzIy3336badOmGSVGafALIYQQQpQhNDSUli1bEhcXR1paGj///DMBAQGmDguAgwcPkpmZyY0bN5gzZw5Lly5l4MCBKIpSbTF8//33ODs7s2HDBm7dulVtx32QnD17lsjISPr372+wfO7cuWRlZZGens7q1auJj4+nTZs23Lhxw6BcREQELi4uLF26lOLiYoN1YWFh7Ny5k7i4uPuOUxr8QgghhBD/kJKSQlRUFGPHjsXW1hYzMzOaNm3KU089pS+TmZnJ+PHj8fHxwdHRkXbt2nHt2jXAcEjMkiVLCA4OZtq0abi6uuLj48PXX38NQHJyMtbW1kRHR+v3m5+fj7OzM0eOHLlrnBYWFnTv3p1169axZ88etm3bBhgOawFIT09HpVIRExMDwPbt22nbti1OTk7UrVuXV199lby8vArnR6fTsWTJEt5//33q1avHsmXLDNb7+fnx6aef0rFjRxwcHOjevbs+N1DyK8X//d//0axZMxwdHRk0aJDBsJuoqCgGDhyIu7s7vr6+fPzxx+h0OqBkmE6fPn1wd3fH2dmZ0NBQfb3+KSYmBpVKRXp6uj4vo0eP5umnn8bBwYHGjRuze/dugzw99dRTaDQagoKC+OKLL1CpVOXmYdOmTXTr1g0zM7My16tUKpo0acKyZctwcnJi/vz5+nWZmZmsXbuWL7/8kuzsbH755ReDbe3s7GjXrl2p5fdC7rQrhBBCCJObH5PEjYKqH5LiYWXBJD/Pu5ZzdXUlKCiI8PBwxowZQ4cOHfD19TUo8+KLL5Kbm8uhQ4fw9PTk1KlT2NjYlLm/s2fPEhoaSmJiIseOHaNv3740a9aMbt26MWDAAJYuXcqMGTMAWL9+PV5eXrRv377C9fL396dNmzbs3r2bxx9//K7lbWxs+O6772jRogWxsbGEhoYyf/58g6Epd7Jjxw4SExMZOXIkqampREREMGHCBIMyP/zwA5s2bcLLy4uhQ4fyr3/9iyVLlujXr1q1ip07d2JlZUXPnj1ZsGABM2bMIC8vj169ejFhwgR+/vlnkpKS6N+/P3Xr1mXUqFHodDomTZpEjx49KCwsZNSoUYwePZodO3ZUKPaVK1eyceNGli9fzuzZs3nxxRf1Xxhef/11cnJyiI2NJTc3l8GDB99xXydPniQoKOiuxzQ3N2fw4MEGMa5YsQI7Ozueeuoptm3bRkRERKnjNWnShJMnT1aoXnciPfxCCCGEEP+gUqnYtWsXLVu2ZObMmQQEBNCkSRN9g+3GjRusX7+eb7/9Fi8vL9RqNa1atcLNza3M/dnZ2TFjxgwsLS3p1KkTI0eO5IcffgBg1KhR/PDDD/rhOEuWLCE8PLzSMderV4/U1NQKle3atSutWrXCzMyMgIAAxo4da9DTfTcRERGEhobi5ubG888/z5kzZzh69KhBmfHjxxMQEIC1tTUjR47k2LFjBusnT56Mh4cHGo2GJ598Ur9+y5YtODs78+abb2JpaYmPjw8TJkzgp59+Akp+PXj88cextrbG0dGR9957j7179+p/Abib0NBQevbsiZmZGeHh4cTGxnLr1i20Wi2rVq3iww8/1P/y8c4779xxX2lpaTg6OlbouP98fSIiIhg5ciTm5uY8//zzbN26lcTERINtHB0dSUtLq9D+70R6+IUQQghhchXpda9unp6ezJs3j3nz5pGamsqsWbN44okniIuLIzY2FisrK3x8fCq0Ly8vLywsLPTPfX192bNnDwB9+/alqKiIPXv20LBhQ/bs2aP/MlAZ8fHx+Pn5Vajs0aNHmTp1KmfOnCEvL4/i4mIaN25coW1v3brFxo0bWbVqFQCBgYF07tyZiIgI2rVrpy/n6fm/19TOzo6srCyD/ZS3PiYmhrNnz6LRaPTrdTod3t7eQMkwqAkTJrBv3z79MKDCwkKysrIqdHHuP48LkJWVRXFxMUVFRfrjAHd9fZ2dncnMzLzrMaHk9XFxcQHQf0H69ttvAejRowdeXl4sXbqUKVOm6LfJzMzE2dm5Qvu/E+nhF0IIIYS4CxcXF2bMmEFOTg7R0dH4+vpSUFBgMC79ThISEgxm0YmLi6NevXoAqNVqXnjhBZYsWcIPP/xA37598fDwqFR8MTExHDt2jJCQEADs7e3Jzc3Vr/9nz/EzzzxDjx49uHr1KpmZmXzyyScVvuD3xx9/pLCwkDFjxuDp6YmnpycnTpxgxYoVBse8V97e3rRp04b09HT9IzMzk3PnzgEwdepUcnNzOX78OJmZmezduxfgvi9YdnNzw8LCwuA1vdsFs8HBwVy8ePGu+y4uLmbjxo361yciIgKAfv364enpiZeXFzdv3uT777832O78+fMEBwdXriJlkAa/EEIIIcQ/pKWlMX36dC5evIhWqyU3N5f58+fj4uJCUFAQHh4eDB48mHHjxpGYmIhOp+PEiRPlzlaTk5PDRx99RGFhIYcPH2b58uWMHDlSv/6ll15i3bp1REREVGo4T1FREfv27ePJJ5+ke/fu9OvXD4DWrVvz22+/kZiYSFZWFjNnzjTYLjMzE41Gg52dHRcuXOCbb76p8DEjIiJ47bXXOH36NCdPnuTkyZOcP38etVrN2rVrK7yf8gwYMIAbN27w9ddfk5+fj1arJTIyUj/kKDMzE1tbWzQaDbdu3SpVt3tlZmbGsGHDmDFjBpmZmSQlJTFv3rw7bjNw4ED27duHVqstt8zFixd54YUXyMjIYNKkSRQWFrJs2TLmzJmjz9/Jkyc5fPgwV69e1X+Byc3N5ejRo6VmALoX0uAXQgghhPgHS0tL4uPj6d+/P05OTvj4+HDgwAG2bdumHwaydOlSvL29adu2LRqNhnHjxpU7002zZs0oLi6mbt26hIWFMWvWLHr06KFfHxAQQNu2bcnMzCQ0NPSu8T366KM4ODhQp04d3nnnHZ599lk2b96sn1Hm2WefpXv37gQFBREcHFxqn//973/597//jb29PePGjePpp5+uUF6OHDnC+fPnmTRpkr5339PTE19fX0aNGsWiRYsqtJ87sbe35/fff2fnzp34+fnh6urKiBEjSEpKAmDmzJlcuXIFZ2dnOnfuXKGLlCvqiy++wMrKCm9vb0JCQhg2bBiWlpbllm/evDkNGzbk119/NVg+efJk/Tz8Q4cOxdPTk7/++gsPDw82bNhAYWEhr776qkEOW7ZsyZAhQ/Q5/Pnnn+nRo0epi8XvhUqpzglbhRBCCPHQy8/PJzo6Gn9/f6ytrU0dTpVbsmQJCxcuvOtsKy+99BIajcZg6kZhWj/99BPvv/8+V65cKbfMn3/+yZtvvsmhQ4eMdlydTkdwcDArV66kSZMmZZapzHkkF+0KIYQQQphYVFQUa9asKTWTjahely9fJiMjgzZt2nDlyhVmzZplcO+FsnTq1MmojX0oua7j9OnTxtuf0fYkhBBCCCEqbezYsQQHBzN58mQaNWpk6nAeajk5OTz77LPY29vTvXt3unfvzvTp000d1n2TIT1CCCGEqFYP25AeIapCZc4j6eEXQgghhBCiFpMGvxBCCCGEELWYNPiFEEIIIYSoxaTBL4QQQgghRC0mDX4hhBBCCCFqMWnwCyGEEEIYWdOmTdmyZYupwxACkAa/EEIIIUSZIiMjGThwIG5ubjg6OhIUFMTcuXMrtO25c+cYMGBAlcSlUqnuetdegN27d6NSqbC3t8fe3h53d3dGjBhBamqqvsyLL76IpaWlvoy9vT2TJ0/Wr4+Li+Oll16iXr162Nvb4+vrS1hYGAcOHNCXqWyeQkJCsLKywt7eHgcHB5o2bcqaNWvuLRmiQqTBL4QQQghRhtDQUFq2bElcXBxpaWn8/PPPBAQEmDqsSnFyciI7O5vs7GwuXbpESkqKQYMe4NVXX9WXyc7O1jfWY2Njadu2Lebm5uzfv5/MzEzOnj3L8OHD2bRpk377e8nT3Llzyc7OJjMzk08//ZSRI0cSGxtr/AQIQBr8QgghhBClpKSkEBUVxdixY7G1tcXMzIymTZvy1FNP6ctkZmYyfvx4fHx8cHR0pF27dly7dg0APz8/NmzYAMCSJUsIDg5m2rRpuLq64uPjw9dffw1AcnIy1tbWREdH6/ebn5+Ps7MzR44cMWqdnJ2dGTJkCOfOnatQ+Q8++IDg4GC+/fZb/P39UavVODg48NRTT+m/FFQkT3eiUqkIDQ1Fo9EQGRl5z3UTd2Zu6gCEEEIIIf6z8zI3s/Kr/Dh1HKx5o1fDu5ZzdXUlKCiI8PBwxowZQ4cOHfD19TUo8+KLL5Kbm8uhQ4fw9PTk1KlT2NjYlLm/s2fPEhoaSmJiIseOHaNv3740a9aMbt26MWDAAJYuXcqMGTMAWL9+PV5eXrRv3/6+6/t3KSkprFu3jq5du1ao/G+//casWbPuWKYieboTnU7H5s2byc/Pp1WrVhXeTlSO9PALIYQQQvyDSqVi165dtGzZkpkzZxIQEECTJk3YsWMHADdu3GD9+vV8++23eHl5oVaradWqFW5ubmXuz87OjhkzZmBpaUmnTp0YOXIkP/zwAwCjRo3ihx9+QFEUoOQXgfDwcKPUIyMjA41Gg0ajoU6dOsTHx/P6668blPnmm2/0ZTQaDRcuXABKviB4eXnpy+3cuRONRoOjoyOenp4VylN5pk6dikajwc7OjqFDhzJ9+nTc3d2NUmdRmvTwCyGEEMLkKtLrXt08PT2ZN28e8+bNIzU1lVmzZvHEE08QFxdHbGwsVlZW+Pj4VGhfXl5eWFhY6J/7+vqyZ88eAPr27UtRURF79uyhYcOG7NmzR/9loDKaNm2qHwf/3//+l3r16uHk5ER6ejoABQUFfPHFF3Tr1o3z589jbW0NwCuvvMLChQtL7c/NzY2EhAT98169epGens7u3bsZMmSIfvmd8vTrr78yduxYfZ1vDyeaPXs2EydOBODKlSsMHDgQJycnfVlhXNLDL4QQQghxFy4uLsyYMYOcnByio6Px9fWloKBAP2b/bhISEigqKtI/j4uLo169egCo1WpeeOEFlixZwg8//EDfvn3x8PCodIznzp3TX3g7cuTIUuutrKwYN24c0dHRFRrH36dPH1avXl2pGP6Zp5EjR+pjKu+YDRo0IDQ0VKYxrULS4BdCCCGE+Ie0tDSmT5/OxYsX0Wq15ObmMn/+fFxcXAgKCsLDw4PBgwczbtw4EhMT0el0nDhxglu3bpW5v5ycHD766CMKCws5fPgwy5cvN2iUv/TSS6xbt46IiIgKDecpLCwkPz9f//j7l4nyFBcX891332Fra1uh2YZmzpzJsWPHeOWVV4iOjkZRFHJzczl8+HCF81QRsbGxbN26lebNm1eovKg8afALIYQQQvyDpaUl8fHx9O/fHycnJ3x8fDhw4ADbtm3Dzs4OgKVLl+Lt7U3btm3RaDSMGzeOvLy8MvfXrFkziouLqVu3LmFhYcyaNYsePXro1wcEBNC2bVsyMzMJDQ29a3wdOnTAxsZG/xg9enSZ5TIyMvTz67u5ubFmzRo2b96Ms7PzXY/h7+/P0aNHyc3N5dFHH8Xe3p4mTZpw5MgRfW98RfJUlsmTJ+vj6ty5M7179+b999+/a0zi3qiU21eICCGEEEJUg/z8fKKjo/H399ePI6/NlixZwsKFC+96s6yXXnoJjUbD/PnzqycwUaNV5jySi3aFEEIIIUwsKiqKNWvWcOzYMVOHImohGdIjhBBCCGFCY8eOJTg4mMmTJ9OoUSNThyNqIRnSI4QQQohq9bAN6RGiKlTmPJIefiGEEEIIIWoxafALIYQQQghRi0mDXwghhBBCiFpMGvxCCCGEEELUYtLgF0IIIYQQohaTBr8QQgghhJE1bdpUfzfaB5FKpbrjjcA0Gg27d++utniqSnp6OiqVipiYGFOHYlLS4BdCCCGEKENkZCQDBw7Ezc0NR0dHgoKCmDt3boW2PXfuHAMGDKiSuFQqFd7e3uTn5+uXbdiwAT8/vyo5njGEhISgUqn4/fffDZZ/9tlnqFQqJk6caJrAHhLS4BdCCCGEKENoaCgtW7YkLi6OtLQ0fv75ZwICAkwdFgB5eXl88cUXpg6jTMXFxWUub9y4MYsXLzZYtmTJEoKCgqojrIeaNPiFEEIIIf4hJSWFqKgoxo4di62tLWZmZjRt2pSnnnpKXyYzM5Px48fj4+ODo6Mj7dq149q1awD4+fmxYcMGoKRRGxwczLRp03B1dcXHx4evv/4agOTkZKytrYmOjtbvNz8/H2dnZ44cOVJufNOmTWP27Nmkp6eXub6oqIj333+fwMBAXF1dGTRoEAkJCWWW1el0/Otf/8LDwwMvLy+++uqrUmVWrlxJixYt0Gg0tGvXjoMHD+rXhYSE8O677/LYY49hZ2fHr7/+WuZxnn76aX799VcyMjIAOHz4MIqi0KFDB4NyUVFRDBw4EHd3d3x9ffn444/R6XQAxMXF0adPH9zd3XF2diY0NNRguE5BQQGvvPIKLi4u+Pv7s3bt2nJz+DCRBr8QQgghxD+4uroSFBREeHg4q1evJjY2tlSZF198kStXrnDo0CHS09P59ttvsbGxKXN/Z8+eRaVSkZiYyKpVq5gyZQp79+7F3d2dAQMGsHTpUn3Z9evX4+XlRfv27cuNr2fPnrRr167cIUbvvfceBw4cYP/+/SQmJtKoUSOefvrpMssuWbKEJUuWsGfPHq5cucJff/1FVlaWfv3WrVt5++23WbJkCampqUydOpWBAwdy69Ytg318/PHHZGdn07t37zKPo9Fo6NevHytWrADg+++/Jzw83KBMXl4evXr1omfPnsTHx7Nv3z5Wrlyp/2VAp9MxadIkrl27RmxsLLa2towePVq//axZs/jzzz85e/YsJ06cYN26deXm8GGiUhRFMXUQQgghhHh45OfnEx0djb+/P9bW1iUL93wKWUlVf3AHT+j+boWKJiUl8dlnn7Ft2zYuXrxI48aN+fzzz+nTpw83btzA09OT2NhYfHx8Sm3r5+fHwoULGTJkCEuWLGHChAmkpKRgYWEBwCuvvEJRURGLFi3i119/5bXXXiMqKgqVSkXfvn3p06cPb7/9dplxqVQqTpw4AUCXLl24dOkSR44cYeLEicTExKAoCg4ODhw4cICWLVsCJTm3s7MjJiYGb29v/T6Cg4Pp1asXffv25d13S/Jyu267du0iJCSE0NBQHnvsMSZMmKCPoXPnzowbN47nnnuOkJAQgoODWbhwYbm5DAkJYciQITRt2pTp06eze/duvL29OXv2LFOmTEGj0bBw4ULWrFnDJ598oq8fwHfffcfKlSvZuXNnqf2ePHmSDh06kJeXh1qtJjAwkNmzZzNs2DCg5FeEjh07Eh0d/UBf43AvyjyPyiE9/EIIIYQQZfD09GTevHmcO3eO5ORkHn/8cZ544glSU1OJjY3FysqqzMZ+Wby8vPSNfQBfX1/i4+MB6Nu3L0VFRezZs4f4+Hj27NnDc889d9d9BgcHM2jQIGbOnGmwPCUlhZycHLp164ZGo0Gj0eDp6YmlpaV+yNHfJSQk4Ovrq3/u4eGBlZWV/nlMTAzTpk3T70uj0XDy5El9/IBBHpo2bYq9vT329vYsX77c4Fi9evUiKSmJjz76iE6dOuHp6WmwPiYmhrNnzxoc66233iIpqeTLYHJyMiNGjMDb2xtHR0e6detGYWGh/heJf9bl7/9/mJmbOgAhhBBCiIr2upuKi4sLM2bMYP78+URHR+Pr60tBQQHXrl3D29v7rtsnJCRQVFSkb/THxcVRr149ANRqNS+88AJLliyhcePG9O3bFw8PjwrF9fHHH9O8eXMCAwP1y1xdXbG1teXw4cMVuiDWy8vLYMjSzZs3KSgo0D/39vbm9ddfZ9y4ceXuQ63+Xx/yuXPn7lju+eefZ9asWWWOr/f29qZNmzYcOnSozO2nTp1Kbm4ux48fx93dnZMnT9KqVStuD1i5XZfb1wXExcWVG8vDRHr4hRBCCCH+IS0tjenTp3Px4kW0Wi25ubnMnz8fFxcXgoKC8PDwYPDgwYwbN47ExER0Oh0nTpwwGNf+dzk5OXz00UcUFhZy+PBhli9fzsiRI/XrX3rpJdatW0dERESpce13EhAQwEsvvcSnn36qX6ZWqxk3bhxvvfWWvkf/1q1brFq1qsx9PPPMM3z11VdERkaSl5fH1KlTDRrw48eP57PPPuPYsWMoikJubi6///47169fr3Ccf/fmm2+yfft2Bg4cWGrdgAEDuHHjBl9//TX5+flotVoiIyP19wTIzMzE1tYWjUbDrVu3Sv268cwzzzBnzhwSEhJIT0/nww8/vKcYaxtp8AshhBBC/IOlpSXx8fH0798fJycnfHx8OHDgANu2bcPOzg6ApUuX4u3tTdu2bdFoNIwbN468vLwy99esWTOKi4upW7cuYWFhzJo1ix49eujXBwQE0LZtWzIzMwkNDa1UrP/6178oLCw0WDZ79mw6depEz549cXBwoE2bNmzfvr3M7V966SWeffZZunbtSkBAAK1atcLBwUG/fsCAAcyZM4fRo0fj7OyMv78/n3/+uX7mnMpycXGhd+/eBkOcbrO3t+f3339n586d+Pn54erqyogRI/RDembOnMmVK1dwdnamc+fOPP744wbbT58+nbZt29KsWTOCg4MZMmTIPcVY28hFu0IIIYSoVpW52LA2WLJkCQsXLrzjnW2hpOGt0WiYP39+9QQmarTKnEcyhl8IIYQQwsSioqJYs2YNx44dM3UoohaSIT1CCCGEECY0duxYgoODmTx5Mo0aNTJ1OKIWkiE9QgghhKhWD9uQHiGqgszDL4QQQgghhACkwS+EEEIIIUStJg1+IYQQQpjEvU7rKISAyozKl1l6hBBCCFGtLC0tUavVJCQk4O7ujqWlJSqVytRhCVFjKIpCcnIyKpWqzPsZ/JNctCuEEEKIaldYWEhiYiK5ubmmDkWIGkmlUlG/fn3s7e3vXlYa/EIIIYQwBUVRKC4uRqvVmjoUIWocCwsLzMzMKlRWGvxCCCGEEELUYnLRrhBCCCGEELWYNPiFEEIIIYSoxaTBL4QQQgghRC0mDX4hhBBCCCFqMWnwCyGEEEIIUYtJg18IIYQQQohaTBr8QgghhBBC1GL/D9yDyBXobfOYAAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Step 1: Generate Data Points from a Polynomial\n", "dimension = 10 # Number of free parameters (polynomial degree is dimension - 1)\n", "np.random.seed(8) # For reproducibility\n", "\n", "# True polynomial coefficients (random values)\n", "true_coefficients = [np.random.uniform(-1.0, 1.0) * (1.0 ** i) for i in range(dimension)]\n", "\n", "# Generate data points\n", "x_data = np.linspace(0.0, 1, dimension + 10)\n", "y_data = np.polyval(true_coefficients, x_data)\n", "\n", "# Step 2: Define the Polynomial Model\n", "def polynomial_model(x, coefficients):\n", " \"\"\"Evaluate a polynomial at x given the coefficients.\"\"\"\n", " return np.polyval(coefficients, x)\n", "\n", "# Step 3: Define the Objective Function\n", "def objective_function(coefficients):\n", " \"\"\"Compute the mean squared error between the polynomial model and data points.\"\"\"\n", " y_pred = polynomial_model(x_data, coefficients)\n", " return np.mean((y_data - y_pred) ** 2)\n", "\n", "def objective_function_vect(X):\n", " \"\"\"Vectorized version of the objective function for batch optimization.\"\"\"\n", " return [objective_function(x) for x in X]\n", "\n", "# Optimization Settings\n", "bounds = [(-10, 10)] * dimension\n", "Nmaxeval = 20000\n", "algos = [\n", " \"DE\", \"ABC\", \"LSHADE\", \"LSHADE_cnEpSin\", \"JADE\", \"jSO\", \"j2020\", \"LSRTDE\", \"NLSHADE_RSP\",\n", " \"ARRDE\", \"GWO_DE\", \"NelderMead\", \"DA\", \"L_BFGS_B\", \"PSO\", \"DMSPSO\", \"SPSO2011\", \"CMAES\", \"BIPOP_aCMAES\"\n", "]\n", "\n", "# Step 4: Minimize the Objective Function and Plot Results\n", "plt.figure(figsize=(6, 4))\n", "plt.scatter(x_data, y_data, label=\"Data Points\", color=\"black\", marker=\"o\", zorder=3)\n", "\n", "x0 = [[0.0 for _ in range(dimension)]]\n", "\n", "print(\"\\nOptimization Results:\")\n", "print(\"=\" * 50)\n", "\n", "# Run Optimization with Custom Algorithms\n", "for algo in algos:\n", " res = mpy.Minimizer(\n", " objective_function_vect, bounds, x0=x0, relTol=0.0,\n", " algo=algo, maxevals=Nmaxeval, callback=None, seed=0,\n", " options={\n", " \"population_size\": 0, \n", " \"func_noise_ratio\" : 0.0, \n", " \"N_points_derivative\": 1}\n", " ).optimize()\n", "\n", " print(f\"{algo:<30}: f(x) = {res.fun:<20.8g}\")\n", " plt.plot(x_data, polynomial_model(x_data, res.x), label=algo, linewidth=1.2, alpha=0.7)\n", "\n", "# Run SciPy Optimizers\n", "scipy_algorithms = [\n", " (\"Scipy Dual Annealing (DA)\", dual_annealing, {\"bounds\": bounds, \"maxfun\": Nmaxeval, \"no_local_search\": False, \"x0\": x0[0]}),\n", " (\"Scipy L-BFGS-B\", minimize, {\"x0\": x0[0], \"bounds\": bounds, \"method\": \"L-BFGS-B\", \"options\": {\"maxfun\": Nmaxeval}}),\n", " (\"Scipy Nelder-Mead\", minimize, {\"x0\": x0[0], \"bounds\": bounds, \"method\": \"Nelder-Mead\", \"options\": {\"maxfev\": Nmaxeval, \"adaptive\": True}}),\n", "]\n", "\n", "for name, func_opt, kwargs in scipy_algorithms:\n", " res = func_opt(objective_function, **kwargs)\n", " print(f\"{name:<30}: f(x) = {res.fun:<20.8g}\")\n", " plt.plot(x_data, polynomial_model(x_data, res.x), label=name, linewidth=1.2, alpha=0.7)\n", "\n", "print(\"=\" * 50)\n", "\n", "# Plot Formatting\n", "plt.legend(loc=\"upper left\", bbox_to_anchor=(1, 1), fontsize=9)\n", "plt.title(\"Polynomial Fit\")\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "plt.grid(True, linestyle=\"--\", alpha=0.6)\n", "plt.show()\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gaussian Mixture Model Fitting Problems\n", "\n", "Thsi time, the model is given by the sum of Gaussian functions:\n", "$$\n", " f(x, a, b, c) = \\sum_{j=1}^{D/3} \\frac{a_j}{\\sum_{k=1}^{D/3} a_k} \\frac{1}{b_j \\sqrt{2\\pi}} \\exp\\left[-\\frac{1}{2} \\frac{(x-c_j)^2}{b_j^2}\\right]\n", "$$\n", "Here, $f(x, a, b, c)$ is normalized to represent a probability distribution. The data points are generated using predefined values of $a_j$, $b_j$, and $c_j$ within the interval $x \\in [-20, 20]$. The objective function is the same as in the case of polynomial fitting. \n" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Optimization Results:\n", "============================================================\n", "DE : f(x) = 5.7291499e-09 \n", "ABC : f(x) = 7.1340783e-07 \n", "LSHADE : f(x) = 1.0475381e-06 \n", "LSHADE_cnEpSin : f(x) = 4.3458431e-07 \n", "JADE : f(x) = 3.621201e-06 \n", "jSO : f(x) = 1.5717409e-06 \n", "j2020 : f(x) = 1.5987436e-06 \n", "LSRTDE : f(x) = 4.9046081e-06 \n", "NLSHADE_RSP : f(x) = 5.398718e-07 \n", "ARRDE : f(x) = 1.4614777e-06 \n", "GWO_DE : f(x) = 3.3096941e-08 \n", "NelderMead : f(x) = 7.3549528e-09 \n", "DA : f(x) = 3.0671579e-08 \n", "L_BFGS_B : f(x) = 1.4374531e-05 \n", "PSO : f(x) = 7.9250982e-09 \n", "DMSPSO : f(x) = 5.430383e-09 \n", "SPSO2011 : f(x) = 3.4595187e-06 \n", "CMAES : f(x) = 8.0375181e-09 \n", "BIPOP_aCMAES : f(x) = 9.427549e-11 \n", "Scipy L-BFGS-B : f(x) = 2.4100192e-05 \n", "Scipy Dual Annealing : f(x) = 6.1466906e-06 \n", "Scipy Nelder-Mead : f(x) = 4.1184114e-09 \n", "============================================================\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.optimize import minimize, dual_annealing\n", "import concurrent.futures\n", "\n", "# Step 1: Generate Data Points from a Gaussian Mixture Model (GMM)\n", "np.random.seed(5) # For reproducibility\n", "\n", "num_gauss = 5 # Number of Gaussians\n", "true_centers = 10 * (-1 + 2 * np.random.random(num_gauss)) # Random center positions\n", "true_widths = np.random.rand(num_gauss) + 1.0 # Widths (variances)\n", "true_coeffs = 2.0 * np.random.rand(num_gauss) # Coefficients\n", "\n", "dimension = num_gauss * 3 # Total number of free parameters\n", "\n", "# Define a Gaussian function\n", "def gauss(x, center, width):\n", " \"\"\"Compute a Gaussian value at x given center and width.\"\"\"\n", " return (1.0 / (2.0 * np.pi * width ** 2)) * 0.5 * np.exp(-((x - center) ** 2) / (2 * width ** 2))\n", "\n", "# Define the Gaussian Mixture Model (GMM)\n", "def gmm(x, centers, widths, coeffs):\n", " \"\"\"Evaluate the Gaussian Mixture Model (GMM) at x.\"\"\"\n", " result = np.zeros_like(x)\n", " coeffs = np.array(coeffs)\n", " norm_coeff = coeffs / np.sum(coeffs) # Normalize coefficients\n", " for i in range(len(centers)):\n", " result += norm_coeff[i] * gauss(x, centers[i], widths[i])\n", " return result\n", "\n", "# Generate synthetic data\n", "x_data = np.linspace(-20, 20, dimension + 10)\n", "y_data = gmm(x_data, true_centers, true_widths, true_coeffs)\n", "\n", "# Step 2: Define the Model for Fitting\n", "def gmm_model(x, params):\n", " \"\"\"Compute GMM model values for given parameters.\"\"\"\n", " num_gauss = len(params) // 3\n", " centers = params[:num_gauss]\n", " widths = params[num_gauss:2*num_gauss]\n", " coeffs = params[2*num_gauss:]\n", " return gmm(x, centers, widths, coeffs)\n", "\n", "# Step 3: Define the Objective Function\n", "def objective_function(params):\n", " \"\"\"Compute the mean squared error between model and data.\"\"\"\n", " y_pred = gmm_model(x_data, params)\n", " return np.mean((y_data - y_pred) ** 2)\n", "\n", "# Parallelized objective function\n", "executor = concurrent.futures.ThreadPoolExecutor(max_workers=8)\n", "\n", "def objective_function_vect(params):\n", " \"\"\"Vectorized version of objective function using multithreading.\"\"\"\n", " return list(executor.map(objective_function, params))\n", "\n", "# Optimization Settings\n", "bounds = [(-10, 10)] * dimension\n", "Nmaxeval = 10000\n", "algos = [\n", " \"DE\", \"ABC\", \"LSHADE\", \"LSHADE_cnEpSin\", \"JADE\", \"jSO\", \"j2020\", \"LSRTDE\", \"NLSHADE_RSP\",\n", " \"ARRDE\", \"GWO_DE\", \"NelderMead\", \"DA\", \"L_BFGS_B\", \"PSO\", \"DMSPSO\", \"SPSO2011\", \"CMAES\", \"BIPOP_aCMAES\"\n", "]\n", "\n", "x0 = [[1.0 for _ in range(dimension)]]\n", "\n", "# Step 4: Minimize the Objective Function and Plot Results\n", "plt.figure(figsize=(6, 4))\n", "plt.scatter(x_data, y_data, label=\"Data\", color=\"black\", marker=\"o\", zorder=3)\n", "\n", "print(\"\\nOptimization Results:\")\n", "print(\"=\" * 60)\n", "\n", "# Run Optimization with Custom Algorithms\n", "for algo in algos:\n", " res = mpy.Minimizer(\n", " objective_function_vect, bounds, x0=x0, relTol=0.0,\n", " algo=algo, maxevals=Nmaxeval, callback=None, seed=None,\n", " options={\"population_size\": 0}\n", " ).optimize()\n", "\n", " print(f\"{algo:<30}: f(x) = {res.fun:<20.8g}\")\n", " plt.plot(x_data, gmm_model(x_data, res.x), label=algo, linewidth=1.2, alpha=0.7)\n", "\n", "# Run SciPy Optimizers\n", "scipy_algorithms = [\n", " (\"Scipy L-BFGS-B\", minimize, {\"x0\": x0[0], \"bounds\": bounds, \"method\": \"L-BFGS-B\", \"options\": {\"maxfun\": Nmaxeval}}),\n", " (\"Scipy Dual Annealing\", dual_annealing, {\"x0\": x0[0],\"bounds\": bounds, \"maxfun\": Nmaxeval, \"no_local_search\": False}),\n", " (\"Scipy Nelder-Mead\", minimize, {\"x0\": x0[0], \"bounds\": bounds,\"method\": \"Nelder-Mead\", \"options\": {\"maxfev\": Nmaxeval, \"adaptive\": True}}),\n", "]\n", "\n", "for name, func_opt, kwargs in scipy_algorithms:\n", " res = func_opt(objective_function, **kwargs)\n", " print(f\"{name:<30}: f(x) = {res.fun:<20.8g}\")\n", " plt.plot(x_data, gmm_model(x_data, res.x), label=name, linewidth=1.2, alpha=0.7)\n", "\n", "print(\"=\" * 60)\n", "\n", "# Plot Formatting\n", "plt.legend(loc=\"upper left\", bbox_to_anchor=(1, 1), fontsize=9)\n", "plt.title(\"Gaussian Mixture Model Fit\")\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "plt.grid(True, linestyle=\"--\", alpha=0.6)\n", "plt.show()\n", "\n", "executor.shutdown()\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## More complex fitting problem: CT18 PDFs Fitting\n", "\n", "Here, we provide a slightly more challenging curve fitting problem. The task is to reproduce the CT18 parton distribution functions (PDFs) \\cite{Hou:2019efy}. The parameterization for valence up-quark ($u_v$), valence down-quark ($d_v$), gluon, anti-$u$ ($\\bar{u}$), anti-$d$ ($\\bar{d}$), and strange quark ($s$) PDFs at the initial scale is given by:\n", "$$\n", " f_i(x) = a_0 x^{a_1-1} (1-x)^{a_2} P_i(y, a_3, a_4, \\dots), \\quad i \\in \\{u_v, d_v, g, \\bar{u}, \\bar{d}, s\\}\n", "$$\n", "Here, $P_i(y)$ is a Bernstein polynomial of degree 4, 3, or 5, depending on the specific PDF. The variable $y$ is defined as $y = \\sqrt{x}$ for $u_v$, $d_v$, and $g$, and as $y = (1 - (1 - \\sqrt{x}))^{a_3}$ for the sea quarks. The objective function is:\n", "$$\n", " L = \\sum_i \\frac{1}{N} \\sum_{j=1}^N \\left(y_j - f_i(x_j)\\right)^2\n", "$$\n", "where $i \\in \\{u_v, d_v, g, \\bar{u}, \\bar{d}, s\\}$. The dimensionality of this problem is $D = 47$.\n" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "class CT18PDFs : \n", " def __init__(self) : \n", " self.parameters = {\n", " \"uv_0\" : 3.385, \"uv_1\" : 0.763, \"uv_2\" : 3.036, \"uv_3\" : 1.502, \"uv_4\" : -0.147,\"uv_5\" : 1.671, \"uv_6\" : 0.,\n", " \"dv_0\" : 0.490, \"dv_1\" : 0.763, \"dv_2\" : 3.036, \"dv_3\" : 2.615, \"dv_4\" : 1.828,\"dv_5\" : 2.721, \"dv_6\" : 0., \n", " \"g_0\" : 2.690, \"g_1\" : 0.531, \"g_2\" : 3.148, \"g_3\" : 3.032, \"g_4\" : -1.705, \"g_5\" : 1.354, \n", " \"ubar_0\" : 0.414, \"ubar_1\" : -0.022, \"ubar_2\" : 7.737, \"ubar_3\" : 4.0, \"ubar_4\" : 0.618,\"ubar_5\" : 0.195, \"ubar_6\" : 0.871, \"ubar_7\" : 0.267,\"ubar_8\" : 0.733,\n", " \"dbar_0\" : 0.414, \"dbar_1\" : -0.022, \"dbar_2\" : 7.737, \"dbar_3\" : 4.0, \"dbar_4\" : 0.292,\"dbar_5\" : 0.647, \"dbar_6\" : 0.474, \"dbar_7\" : 0.741,\"dbar_8\" :1.0,\n", " \"s_0\" : 0.288, \"s_1\" : -0.022, \"s_2\" : 10.31, \"s_3\" : 4.0, \"s_4\" : 0.466,\"s_5\" : 0.466, \"s_6\" : 0.225, \"s_7\" : 0.225,\"s_8\" : 1.0,\n", " }\n", " self.xlist = np.linspace(1e-3, 0.8, 50)\n", " self.paramNames = list(self.parameters.keys())\n", " self.originalData = self.getData()\n", "\n", " def uv(self, x) : \n", " a0 = self.parameters[\"uv_0\"]\n", " a1 = self.parameters[\"uv_1\"]\n", " a2 = self.parameters[\"uv_2\"]\n", " a3 = self.parameters[\"uv_3\"]\n", " a4 = self.parameters[\"uv_4\"]\n", " a5 = self.parameters[\"uv_5\"]\n", " a6 = self.parameters[\"uv_6\"]\n", " y= np.sqrt(x)\n", " P = np.sinh(a3)*(1-y)**4 + np.sinh(a4) *4*y*(1-y)**3 + np.sinh(a5) *6*y**2*(1-y)**2 + np.sinh(a6) *4*y**3*(1-y) + y**4\n", " return a0 * x**(a1-1)*(1-x)**a2*P\n", " \n", " def dv(self, x) : \n", " a0 = self.parameters[\"dv_0\"]\n", " a1 = self.parameters[\"dv_1\"]\n", " a2 = self.parameters[\"dv_2\"]\n", " a3 = self.parameters[\"dv_3\"]\n", " a4 = self.parameters[\"dv_4\"]\n", " a5 = self.parameters[\"dv_5\"]\n", " a6 = self.parameters[\"dv_6\"]\n", " y= np.sqrt(x)\n", " P = np.sinh(a3)*(1-y)**4 + np.sinh(a4) *4*y*(1-y)**3 + np.sinh(a5) *6*y**2*(1-y)**2 + np.sinh(a6) *4*y**3*(1-y) + y**4\n", " return a0 * x**(a1-1)*(1-x)**a2*P\n", " \n", " def g(self, x) : \n", " a0 = self.parameters[\"g_0\"]\n", " a1 = self.parameters[\"g_1\"]\n", " a2 = self.parameters[\"g_2\"]\n", " a3 = self.parameters[\"g_3\"]\n", " a4 = self.parameters[\"g_4\"]\n", " a5 = self.parameters[\"g_5\"]\n", " y= np.sqrt(x)\n", " P = np.sinh(a3)*(1-y)**3 + np.sinh(a4) *3*y*(1-y)**2 + np.sinh(a5) *3*y**2*(1-y) + y**3\n", " return a0 * x**(a1-1)*(1-x)**a2*P\n", " \n", " def ubar(self, x) : \n", " a0 = self.parameters[\"ubar_0\"]\n", " a1 = self.parameters[\"ubar_1\"]\n", " a2 = self.parameters[\"ubar_2\"]\n", " a3 = self.parameters[\"ubar_3\"]\n", " a4 = self.parameters[\"ubar_4\"]\n", " a5 = self.parameters[\"ubar_5\"]\n", " a6 = self.parameters[\"ubar_6\"]\n", " a7 = self.parameters[\"ubar_7\"]\n", " a8 = self.parameters[\"ubar_8\"]\n", " y= 1-(1-np.sqrt(x))**a3\n", " P = (1-y)**5 + a4 * 5*y*(1-y)**4 + a5 * 10*y**2*(1-y)**3 + a6 * 10*y**3*(1-y)**2 + a7 * 5*y**4*(1-y)+ a8 * 5*y**5\n", " return a0 * x**(a1-1)*(1-x)**a2*P\n", " \n", " def dbar(self, x) : \n", " a0 = self.parameters[\"dbar_0\"]\n", " a1 = self.parameters[\"dbar_1\"]\n", " a2 = self.parameters[\"dbar_2\"]\n", " a3 = self.parameters[\"dbar_3\"]\n", " a4 = self.parameters[\"dbar_4\"]\n", " a5 = self.parameters[\"dbar_5\"]\n", " a6 = self.parameters[\"dbar_6\"]\n", " a7 = self.parameters[\"dbar_7\"]\n", " a8 = self.parameters[\"dbar_8\"]\n", " y= 1-(1-np.sqrt(x))**a3\n", " P = (1-y)**5 + a4 * 5*y*(1-y)**4 + a5 * 10*y**2*(1-y)**3 + a6 * 10*y**3*(1-y)**2 + a7 * 5*y**4*(1-y)+ a8 * 5*y**5\n", " return a0 * x**(a1-1)*(1-x)**a2*P\n", " \n", " def s(self, x) : \n", " a0 = self.parameters[\"s_0\"]\n", " a1 = self.parameters[\"s_1\"]\n", " a2 = self.parameters[\"s_2\"]\n", " a3 = self.parameters[\"s_3\"]\n", " a4 = self.parameters[\"s_4\"]\n", " a5 = self.parameters[\"s_5\"]\n", " a6 = self.parameters[\"s_6\"]\n", " a7 = self.parameters[\"s_7\"]\n", " a8 = self.parameters[\"s_8\"]\n", " y= 1-(1-np.sqrt(x))**a3\n", " P = (1-y)**5 + a4 * 5*y*(1-y)**4 + a5 * 10*y**2*(1-y)**3 + a6 * 10*y**3*(1-y)**2 + a7 * 5*y**4*(1-y)+ a8 * 5*y**5\n", " return a0 * x**(a1-1)*(1-x)**a2*P\n", " \n", " def u(self, x) : return self.uv(x)+self.ubar(x)\n", " def d(self, x) : return self.dv(x)+self.dbar(x) \n", "\n", " def setParameter(self, pars) : \n", " assert(len(pars)==len(self.parameters)) \n", " self.parameters= dict(zip(self.paramNames, pars))\n", "\n", " def getData(self) : \n", " x= self.xlist\n", " return [ x*self.u(self.xlist), x*self.ubar(self.xlist), x*self.d(self.xlist), x*self.dbar(self.xlist), x*self.g(self.xlist), x*self.s(self.xlist)]\n", " \n", " def objective_function(self, params): \n", " self.setParameter(params) \n", " data = self.getData() \n", " ret =0\n", " for do, d in zip(self.originalData, data) : \n", " ret = ret + np.sum((do-d)**2)\n", " return ret" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ct18 = CT18PDFs()\n", "data = ct18.getData()\n", "# Create a 3x2 grid of subplots\n", "fig, axes = plt.subplots(2, 3, figsize=(10, 5))\n", "\n", "# List of labels for each plot\n", "labels = [\"u\", \"ubar\", \"d\", \"dbar\", \"g\", \"s\"]\n", "\n", "# Plotting each function in its corresponding subplot\n", "for i, ax in enumerate(axes.flatten()):\n", " ax.plot(ct18.xlist, data[i], label=labels[i])\n", " ax.set_xlim(0.1, 0.8)\n", " ax.set_xlabel(\"x\")\n", " if (i%3 == 0):\n", " ax.set_ylabel(r\"$xf(x)$\")\n", " ax.legend()\n", "plt.subplots_adjust(hspace=0.15, wspace=0.17)\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Dimension: 47\n", "\n", "Optimization Results:\n", "============================================================\n", "DE : f(x) = 0.19269741 \n", "ABC : f(x) = 9.2305563 \n", "LSHADE : f(x) = 5.0262623 \n", "LSHADE_cnEpSin : f(x) = 0.34919775 \n", "JADE : f(x) = 4.6637756 \n", "jSO : f(x) = 0.78116151 \n", "j2020 : f(x) = 9.9470365 \n", "LSRTDE : f(x) = 0.39744395 \n", "NLSHADE_RSP : f(x) = 1.0981858 \n", "ARRDE : f(x) = 1.2748372 \n", "GWO_DE : f(x) = 1.8577235 \n", "NelderMead : f(x) = 0.072777402 \n", "DA : f(x) = 0.13416323 \n", "L_BFGS_B : f(x) = 0.019077562 \n", "PSO : f(x) = 0.055286483 \n", "DMSPSO : f(x) = 0.327826 \n", "SPSO2011 : f(x) = 3.9963909 \n", "CMAES : f(x) = 1.0687989 \n", "BIPOP_aCMAES : f(x) = 0.47659189 \n", "Scipy L-BFGS-B : f(x) = 0.016397197 \n", "Scipy Dual Annealing : f(x) = 0.91439194 \n", "Scipy Nelder-Mead : f(x) = 0.072777402 \n", "============================================================\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Step 1: Define Problem Dimensions and Settings\n", "dimension = 47\n", "print(\"Dimension:\", dimension)\n", "\n", "bounds = [(-10, 10)] * dimension\n", "Nmaxeval = 100000\n", "x0 = [[1.0] * dimension] # Initial guess\n", "\n", "# Step 2: Set Up Parallel Execution for CT18PDFs\n", "t_parallel = mpy.Thread_Parallel(4, CT18PDFs) # Vectorize using 4 threads\n", "\n", "# Step 3: Define Optimization Algorithms\n", "algos = [\n", " \"DE\", \"ABC\", \"LSHADE\", \"LSHADE_cnEpSin\", \"JADE\", \"jSO\", \"j2020\", \"LSRTDE\", \"NLSHADE_RSP\",\n", " \"ARRDE\", \"GWO_DE\", \"NelderMead\", \"DA\", \"L_BFGS_B\", \"PSO\", \"DMSPSO\", \"SPSO2011\", \"CMAES\", \"BIPOP_aCMAES\"\n", "]\n", "\n", "# Step 4: Run Optimization and Collect Results\n", "results = {}\n", "\n", "print(\"\\nOptimization Results:\")\n", "print(\"=\" * 60)\n", "\n", "for algo in algos:\n", " res = mpy.Minimizer(\n", " t_parallel, bounds, x0=x0, algo=algo, relTol=0.0,\n", " maxevals=Nmaxeval, callback=None, seed=None,\n", " options={\n", " \"population_size\": 0,\n", " \"func_noise_ratio\" : 0.0, \n", " \"N_points_derivative\": 1\n", " }\n", " ).optimize()\n", "\n", " print(f\"{algo:<30}: f(x) = {res.fun:<20.8g}\")\n", " results[algo] = res\n", "\n", "# Step 5: Run SciPy Optimizers\n", "scipy_algorithms = [\n", " (\"Scipy L-BFGS-B\", minimize, {\"x0\": x0[0], \"bounds\": bounds, \"method\": \"L-BFGS-B\", \"options\": {\"maxfun\": Nmaxeval}}),\n", " (\"Scipy Dual Annealing\", dual_annealing, {\"x0\": x0[0],\"bounds\": bounds, \"maxfun\": Nmaxeval, \"no_local_search\": False}),\n", " (\"Scipy Nelder-Mead\", minimize, {\"x0\": x0[0], \"bounds\": bounds,\"method\": \"Nelder-Mead\", \"options\": {\"maxfev\": Nmaxeval, \"adaptive\": True}}),\n", "]\n", "\n", "for name, func_opt, kwargs in scipy_algorithms:\n", " res = func_opt(ct18.objective_function, **kwargs)\n", " print(f\"{name:<30}: f(x) = {res.fun:<20.8g}\")\n", " results[name] = res\n", "\n", "print(\"=\" * 60)\n", "\n", "# Step 6: Plot Results\n", "fig, axes = plt.subplots(2, 3, figsize=(12, 6))\n", "labels = [\"u-data\", \"ubar-data\", \"d-data\", \"dbar-data\", \"g-data\", \"s-data\"]\n", "\n", "# Plot each dataset in its corresponding subplot\n", "for i, ax in enumerate(axes.flatten()):\n", " ax.plot(ct18.xlist, data[i], label=labels[i], color=\"black\", linestyle=\"dotted\", linewidth=1.2)\n", "\n", " # Overlay model predictions for selected algorithms\n", " for algo in [\"ARRDE\", \"DA\", \"Scipy Dual Annealing\", \"L_BFGS_B\"]:\n", " ct18.setParameter(results[algo].x)\n", " theo = ct18.getData()\n", " ax.plot(ct18.xlist, theo[i], label=algo, linewidth=1.2, alpha=0.8)\n", "\n", " ax.set_xlim(0.1, 0.8)\n", " ax.set_xlabel(\"x\")\n", " if i % 3 == 0:\n", " ax.set_ylabel(r\"$xf(x)$\")\n", " ax.legend(fontsize=9)\n", "\n", "plt.tight_layout()\n", "plt.show()\n", "\n" ] } ], "metadata": { "kernelspec": { "display_name": "base", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.2" } }, "nbformat": 4, "nbformat_minor": 2 }