遗传算法的优化（运筹优化5-启发式优化算法之遗传算法）

遗传算法的优化（运筹优化5-启发式优化算法之遗传算法）class GA: def __init__(self size chrom_size cp mp gen_max num): #size种群数量 #chrom_size染色体长度 #cp交叉概率 #mp变异概率 #gen_max进化最大世代数 #num变量数 self.individuals = [] self.fitness = [] self.selector_probability = [] self.new_individuals = [] self.num = num self.elitist = {'chromosome': [0] * num 'fitness': 0 'age': 0}

[雾霾]补上节划过的水...

1. 直接上问题：求解函数

待求解的目标函数

2.将目标函数定义适应度函数（刚发现可以插入代码块，这看起来更给力，抱歉之前太业余了，没发现这功能的强大）

def fitness(l): x = l[0] y = l[1] k = l[2] Z = (0.5 - (np.sin(np.sqrt(x ** 2 y ** 2)) ** 2 - 0.5) / (1 0.001 * (x ** 2 y ** 2) ** 2)) / ( 0.001 * (k ** 2 y ** 2) ** 2) return Z

如取x y k分别为1，2，3 即l = [1 2 3]

运行print('计算l=[1 2 3]的适应度值为：' fitness([1 2 3]))

得到：

适应度计算示例

3.构建GA算法

class GA: def __init__(self size chrom_size cp mp gen_max num): #size种群数量 #chrom_size染色体长度 #cp交叉概率 #mp变异概率 #gen_max进化最大世代数 #num变量数 self.individuals = [] self.fitness = [] self.selector_probability = [] self.new_individuals = [] self.num = num self.elitist = {'chromosome': [0] * num 'fitness': 0 'age': 0} self.size = size self.chromosome_size = chrom_size self.crossover_probability = cp self.mutation_probability = mp self.generation_max = gen_max self.age = 0 v = 2 ** self.chromosome_size - 1 for i in range(self.size): t = [] s = [] for j in range(num): t.append(random.randint(0 v)) s.append(0) self.individuals.append(t) self.new_individuals.append(s) self.fitness.append(0) self.selector_probability.append(0)

#==========================================以上为变量初始化

# 染色体解码 def decode(self interval chromosome): s = [] for i in range(self.num): d = interval[i][1] - interval[i][0] n = float(2 ** self.chromosome_size - 1) t = interval[i][0] chromosome[i] * d / n s.append(t) return s

例如：x y k的取值范围分别为 [[-10.0 10.0] [-10.0 10.0] [-10.0 10.0]]，则处理结果时将[69 359 3948]解码为[-9.663003663003662 -8.246642246642246 9.282051282051281]

#计算每组染色的适应度值 def fitness_func(self interval chromosome): l = self.decode(interval chromosome) func = fitness(l) return func def evaluate(self interval): sp = self.selector_probability for i in range(self.size): self.fitness[i] = self.fitness_func(interval self.individuals[i]) ft_sum = sum(self.fitness) for i in range(self.size): sp[i] = self.fitness[i] / float(ft_sum) for i in range(1 self.size): sp[i] = sp[i] sp[i - 1]

#例如初始化选择概率均为0，[0 0 0 0 0 0 ...]计算后为[0.08128979780831412 0.4931327413520626 0.05090787956742299 ...]

# 轮盘赌法选择 def select(self): (t i) = (random.random() 0) for p in self.selector_probability: if p > t: break i = i 1 return i # 交叉 def cross(self chrom1 chrom2): p = random.random() n = 2 ** self.chromosome_size - 1 if chrom1 != chrom2 and p < self.crossover_probability: t = random.randint(1 self.chromosome_size - 1) mask = n << t (r1 r2) = (chrom1 & mask chrom2 & mask) mask = n >> (self.chromosome_size - t) (l1 l2) = (chrom1 & mask chrom2 & mask) (chrom1 chrom2) = (r1 l2 r2 l1) return (chrom1 chrom2) # 变异 def mutate(self chrom): p = random.random() if p < self.mutation_probability: t = random.randint(1 self.chromosome_size) mask1 = 1 << (t - 1) mask2 = chrom & mask1 if mask2 > 0: chrom = chrom & (~mask2) else: chrom = chrom ^ mask1 return chrom # 每代中保留最佳个体 def reproduct_elitist(self): j = -1 for i in range(self.size): if self.elitist['fitness'] < self.fitness[i]: j = i self.elitist['fitness'] = self.fitness[i] if (j >= 0): self.elitist['chromosome'][0] = self.individuals[j][0] self.elitist['chromosome'][1] = self.individuals[j][1] self.elitist['age'] = self.age #每次所有个体的计算 def evolve(self interval): indvs = self.individuals new_indvs = self.new_individuals self.evaluate(interval) i = 0 while True: idv1 = self.select() idv2 = self.select() while True: t = random.randint(0 self.num - 1) s = random.randint(0 self.num - 1) if t != s: (idv1_x idv1_y) = (indvs[idv1][t] indvs[idv1][s]) (idv2_x idv2_y) = (indvs[idv2][t] indvs[idv2][s]) break (idv1_x idv2_x) = self.cross(idv1_x idv2_x) (idv1_y idv2_y) = self.cross(idv1_y idv2_y) (idv1_x idv1_y) = (self.mutate(idv1_x) self.mutate(idv1_y)) (idv2_x idv2_y) = (self.mutate(idv2_x) self.mutate(idv2_y)) (new_indvs[i][t] new_indvs[i][s]) = (idv1_x idv1_y) (new_indvs[i 1][t] new_indvs[i 1][s]) = (idv2_x idv2_y) i = i 2 if i >= self.size: break self.reproduct_elitist() for i in range(self.size): for j in range(self.num): self.individuals[i][j] = self.new_individuals[i][j] def run(self interval): for i in range(self.generation_max): self.evolve(interval) fitn = self.elitist['fitness'] x = self.elitist['chromosome'] x = self.decode(interval x) return x fitn

4. 程序运行

(1)种群数量为 10，染色体长度为 15，交叉概率为 0.7，变异概率为 0.2 进化最大世代数为 30 变量数3

if __name__ == '__main__': pop = GA (10 12 0.7 0.2 30 3) interval = [[-10.0 10.0] [-10.0 10.0] [-10.0 10.0]] t = pop.run(interval) print(t) plt.plot(range(pop.generation_max) pop.gene_fitn_best 'b') plt.show()

算法收敛结果：

收敛曲线1

输出结果：([3.7875457875457883 0.0073260073260073 -10.0] 315395913.31734186)

(2) 种群数量为 20，染色体长度为 12，交叉概率为 0.7，变异概率为 0.2 进化最大世代数为 80 变量数3

if __name__ == '__main__': pop = GA (20 12 0.7 0.2 80 3) interval = [[-10.0 10.0] [-10.0 10.0] [-10.0 10.0]] t = pop.run(interval) print(t) plt.plot(range(pop.generation_max) pop.gene_fitn_best 'r') plt.show()

收敛曲线2

输出结果：([0.0024420024420024333 -0.0024420024420024333 -10.0] 7029921141473.557)

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