人工智能遗传算法f(x,y)=(6.452(x+0.125y)(cos(x)-cos(2y))^2)/(0.8+(x-4.2)^2+2(y-7)^2)+3.226y代码
时间: 2023-10-17 19:05:18 浏览: 245
以下是一个简单的Python代码实现,用遗传算法求解f(x,y)的最大值:
```python
import random
import math
# 目标函数
def f(x, y):
return (6.452 * (x + 0.125 * y) * (math.cos(x) - math.cos(2 * y)) ** 2) / \
(0.8 + (x - 4.2) ** 2 + 2 * (y - 7) ** 2) + 3.226 * y
# 遗传算法
def genetic_algorithm():
# 参数设置
pop_size = 100 # 种群大小
chrom_len = 20 # 染色体长度
p_crossover = 0.8 # 交叉概率
p_mutation = 0.1 # 变异概率
max_iter = 100 # 最大迭代次数
# 初始化种群
pop = [[random.randint(0, 1) for _ in range(chrom_len)] for _ in range(pop_size)]
# 迭代寻优
for i in range(max_iter):
# 计算适应度
fits = [f(x, y) for x, y in decode(pop)]
# 选择操作
new_pop = []
for j in range(pop_size):
parent1 = select(pop, fits)
parent2 = select(pop, fits)
child = crossover(parent1, parent2, p_crossover)
child = mutation(child, p_mutation)
new_pop.append(child)
# 更新种群
pop = new_pop
# 返回最优解
return max(decode(pop), key=lambda x: f(x[0], x[1]))
# 解码
def decode(pop):
return [(x, y) for chrom in pop for x, y in [(chrom[:10], chrom[10:])]]
# 选择操作
def select(pop, fits):
return pop[roulette(fits)]
# 轮盘赌选择
def roulette(fits):
total_fit = sum(fits)
r = random.uniform(0, total_fit)
cum_fit = 0
for i in range(len(fits)):
cum_fit += fits[i]
if cum_fit > r:
return i
# 交叉操作
def crossover(parent1, parent2, p_crossover):
child = parent1[:]
if random.random() < p_crossover:
index = random.randint(1, len(parent1) - 1)
child = parent1[:index] + parent2[index:]
return child
# 变异操作
def mutation(chrom, p_mutation):
for i in range(len(chrom)):
if random.random() < p_mutation:
chrom[i] = 1 - chrom[i]
return chrom
# 测试
print(genetic_algorithm())
```
上述代码中,首先定义了目标函数f(x,y),然后实现了遗传算法的主要操作,包括初始化种群、计算适应度、选择操作、交叉操作、变异操作等。最后通过调用genetic_algorithm()函数来求解目标函数f(x,y)的最大值。注意,由于目标函数是非凸函数,因此求解结果受初始种群和参数设置的影响较大,可能会得到不同的结果。
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