群体智能算法-北极熊算法(PBO)-python代码实现附详细注释

import numpy as np import random import matplotlib.pyplot as plt np.set_printoptions(suppress=False) ''' 北极熊算法 浮冰漂移:全局搜索 具体捕猎:局部搜索 author:sugarMei date:6/25 version:1.1 ''' # 全局参数设定 ''' M:种群最大容量 m:种群当前规模大小 N:目标函数解的维度 T:迭代次数 V:最大视野距离 X:解集合 P:初始化种群数量百分比 K:动态调整规模参数 B:变量限制范围 ''' # 问题1：迭代陷于局部最优 M, N, T, V, P, K, B = 100, 20, 100, 0.3, 0.75, 0.25, [-10, 10] m = int(np.floor(M * P)) X = np.zeros((M, N)) # Generate a population consisting of 75%M bears at random # 论文提出的基础的算法是random 随机生成的 def Func(x): # Rastragin f4 # return np.sum(x[:] ** 2 - 10 * np.cos(2 * np.pi * x[:]) + 10) # weierstrass # return np.sum((x + 0.5) ** 2) # Sphere f9 # return np.sum(x ** 2) # Dixon-Price f1 return (x[0] - 1) ** 2 + sum((i + 1) * (2 * x[i] ** 2 - x[i - 1]) ** 2 for i in range(1, len(x))) # Griewank f2 # return # Rosenbrock f5 # Styblinski - Tang f11 # return # Weierstrass f12 # return 0.5 * np.sum(x ** 4 - 16 * (x ** 2) + 5 * x) fits = np.zeros(M) def move(index, angle, radius, action): # print('index, angle, radius, action, N', index, angle, radius, action, N) temp = np.zeros(N) for j in range(N): # print("j:", j) result = 0 # 计算sin部分的累加值 for k in range(j): result += np.sin(angle[k]) if 'add'.__eq__(action): temp[j] = X[index][j] + radius * (result + np.cos(angle[j])) else: temp[j] = X[index][j] - radius * (result + np.cos(angle[j])) return temp res = np.zeros(50) # main loop for _ in range(1): # 初始化 m = int(np.floor(M * P)) X = np.zeros((M, N)) # 随机初始化 X[:m] = np.random.random((m, N)) * (B[1] - B[0]) + B[0] f_best = np.inf x_best = 0 for i in range(m): fits[i] = Func(X[i]) arg = np.argsort(fits[:m]) if fits[arg[0]] < f_best: f_best = fits[arg[0]] x_best = X[arg[0]] # 测试一次 迭代T次 t = 0 while t < T: # area search # 视野半径后期变大 跳出局部最优 # 对种群每一只北极熊 for i in range(m): # 局部搜索 angles = np.random.random(N) * 2 * np.pi sta = np.random.random() * V angle0 = np.random.random() * np.pi / 2 r = 4 * sta * np.cos(angle0) * np.sin(angle0) # using the sign of add tmp = move(i, angles, r, 'add') if Func(tmp) < Func(X[i]): X[i] = tmp else: tmp = move(i, angles, r, 'minus') if Func(tmp) < Func(X[i]): X[i] = tmp # 全局搜索 # 决策北极熊的位置 w = np.sqrt(np.sum((x_best - X[i]) ** 2)) alpha = np.random.random() gamma = np.random.random() * w tmp = X[i] + np.sign(w) * alpha + gamma if Func(tmp) < Func(X[i]): X[i] = tmp # 统计当前适应度值 for i in range(m): fits[i] = Func(X[i]) arg = np.argsort(fits[:m]) if fits[arg[0]] < f_best: f_best = fits[arg[0]] x_best = X[arg[0]] # 种群的动态变化 k = np.random.random() # 种群繁衍 if m < M - 1 and k > (1 - K): # 从前10%中随机抽取一个 个体与最好个体交配 生成新的个体 idx = random.randint(1, np.floor(m * 0.1) + 1) X[m] = (x_best + X[arg[idx]]) / 2 m += 1 # 最弱个体死亡 if m > M * 0.5 and k < K: # arg中排序最后的为最弱个体 # 死亡之后 后面的所有个体往前移动一个位置 X[arg[-1]:m] = X[arg[-1] + 1:m + 1] m -= 1 print(t, " 当前最小适应度值:", f_best, '个体为：', x_best, '种群数量：', m) t += 1 print("第", _, '次测试', "最小适应度值:", f_best, '个体为：', x_best) res[_] = f_best print('100个体、100次迭代、其他参数一致') print('f4 函数的测试平均结果为：', np.mean(res)) print('标准方差：', np.std(res, ddof=1))