1 #遗传算法特征: 自由空间, 定长编码

2 #选择: 择优选择

3 #交叉: 全空间可遍历

4 #变异: 增强全空间的搜索能力

5

6 importnumpy7 importmatplotlib.pyplot as plt8

9 #目标函数1

10 defmyfunc1(x):11 return (x ** 2 - 5 * x) * numpy.sin(x ** 2) * -1

12

13 #目标函数2

14 #def myfunc2(x1, x2):

15 #return (1 - x1) ** 2 + 100 * (x2 - x1 ** 2) ** 2

16

17

18 #遗传算法: 选择, 交叉, 变异

19 classGA(object):20

21 def __init__(self, func, lbounds, ubounds, population_size=300, maxIter=500, pm=0.01, speed=3, cf=0.1):22 self.func = func #目标函数

23 self.lbounds = lbounds #搜寻下界

24 self.ubounds = ubounds #搜寻上界

25 self.population_size = population_size #种群规模

26 self.maxIter = maxIter #最大迭代次数

27 self.pm = pm #变异概率(0, 1)

28 self.speed=speed #种群收敛速度[1, +∞)

29 self.cf = cf #交叉因子(0, 1)

30

31 self.size = len(lbounds) #搜索空间的维度

32 self.best_chrom_fitness = list() #最优染色体(染色体, 适应度)迭代记录列表

33 self.__record_fitness = list() #种群适应度迭代记录列表

34

35 defsolve(self):36 #种群随机初始化

37 population = self.__init_population()38 #记录种群最优染色体信息

39 self.__add_best(population)40

41 for i inrange(self.maxIter):42 #种群更新

43 population = self.__selection(population)44 population = self.__crossover(population)45 population = self.__mutation(population)46

47 #上一代最优个体无条件保留至下一代

48 population[0] = self.best_chrom_fitness[-1][0]49 #记录种群最优个体

50 self.__add_best(population)51

52 self.solution = self.best_chrom_fitness[-1]53

54 #选择: 轮盘赌方法

55 def __selection(self, population):56 #适应度排序

57 fitness = self.__cal_fitness(population)58 new_fitness = sorted(list((ele, idx) for idx, ele in enumerate(fitness)), key=lambda item: item[0], reverse=True)59 #轮盘区间计算 -> 采用多项式函数对收敛速度进行调整

60 roulette_interval = self.__cal_interval()61 #随机飞镖排序

62 random_dart =sorted(numpy.random.random(self.population_size))63

64 new_population =list()65 idx_interval = idx_dart =066 while idx_dart <67 if random_dart>roulette_interval[idx_interval]:68 idx_interval += 167>

69 else:70 new_population.append(population[new_fitness[idx_interval][1]])71 idx_dart += 1

72

73 #顺序打乱

74 numpy.random.shuffle(new_population)75 returnnew_population76

77 #交叉: 对称凸组合

78 def __crossover(self, population):79 #交叉随机数 -> 采用交叉因子提高计算精度

80 alpha = numpy.random.random(self.population_size - 1) *self.cf81

82 for idx in range(self.population_size - 1):83 new_chrom1 = alpha[idx] * population[idx] + (1 - alpha[idx]) * population[idx + 1]84 new_chrom2 = alpha[idx] * population[idx + 1] + (1 - alpha[idx]) *population[idx]85 population[idx] =new_chrom186 population[idx + 1] =new_chrom287

88 returnpopulation89

90 #变异: 全空间变异

91 def __mutation(self, population):92 #变异概率随机数

93 mutation_prob =numpy.random.random(self.population_size)94

95 for idx, prob inenumerate(mutation_prob):96 if prob <=self.pm:97 #变异幅度随机数

98 mutation_amplitude = numpy.random.uniform(-1, 1, self.size)99 for idx_dim, ampli inenumerate(mutation_amplitude):100 if ampli >= 0: #正向变异

101 population[idx][idx_dim] += ampli * (self.ubounds[idx_dim] -population[idx][idx_dim])102 else: #负向变异

103 population[idx][idx_dim] += ampli * (population[idx][idx_dim] -self.lbounds[idx_dim])104

105 returnpopulation106

107 #种群随机初始化

108 def __init_population(self):109 population =list()110

111 for i inrange(self.population_size):112 chrom =list()113 for j inrange(self.size):114 chrom.append(numpy.random.uniform(self.lbounds[j], self.ubounds[j]))115 population.append(numpy.array(chrom))116

117 returnpopulation118

119 #种群适应度计算

120 def __cal_fitness(self, population):121 fitness = list(self.func(*chrom) for chrom inpopulation)122 returnfitness123

124 #记录种群最优染色体信息

125 def __add_best(self, population):126 fitness = self.__cal_fitness(population)127 self.__record_fitness.append(fitness)128 min_idx =numpy.argmin(fitness)129 self.best_chrom_fitness.append((population[min_idx], fitness[min_idx]))130

131 #轮盘区间计算

132 def __cal_interval(self, speed=2):133 tmp = (numpy.arange(self.population_size) + 1) /self.population_size134 tmp_normalize = tmp / (self.population_size + 1) * 2

135

136 roulette_interval =list()137 curr_sum =0138 for item intmp_normalize:139 curr_sum +=item140 roulette_interval.append(curr_sum)141

142 roulette_interval = numpy.array(roulette_interval) **self.speed143 returnroulette_interval144

145 #求解过程可视化展示

146 defdisplay(self):147 fig = plt.figure(figsize=(8, 5))148 axes =plt.subplot()149 axes.plot(self.__record_fitness, 'g.')150 axes.plot(numpy.array(self.__record_fitness).sum(axis=1) / self.population_size, 'r-', label='$meanVal$')151 axes.set(xlim=(-1, self.maxIter+1), xlabel='$iterCnt$', ylabel='$fitness$')152 axes.set(title = 'solution = {}'.format(self.solution))153 axes.legend()154 fig.savefig('myGA.png', dpi=500)155 plt.show()156 plt.close()157

158

159 if __name__ == '__main__':160 ins = GA(myfunc1, [-9], [5], population_size=100, maxIter=1000, pm=0.01, speed=1, cf=0.1)161 #ins = GA(myfunc2, [-10, -10], [10, 10], population_size=100, maxIter=500, pm=0.3, speed=1, cf=0.1)

162 ins.solve()163 ins.display()