用遗传算法求解下列函数的最大值,设定求解精度到15位小数 f(x, y)= (0.432(X+0.125y)(cos(x)-cos(2y))3+3.226v)/(0.8+(x-4.2)3+2(y-7)') x E[0,10),y e[0,10) 用python实现
时间: 2023-10-08 10:09:43 浏览: 424
以下是使用遗传算法求解函数最大值的 Python 代码:
```python
import random
# 定义函数
def f(x, y):
return (0.432*(x+0.125*y)*(cos(x)-cos(2*y))**3+3.226)/(0.8+(x-4.2)**3+2*(y-7)**2)
# 定义遗传算法参数
POP_SIZE = 100 # 种群大小
GENERATION = 1000 # 迭代次数
MUTATION_RATE = 0.1 # 变异率
CROSSOVER_RATE = 0.8 # 交叉率
ELITISM = True # 是否保留最优个体
# 定义个体
class Individual:
def __init__(self):
self.x = random.uniform(0, 10)
self.y = random.uniform(0, 10)
self.fitness = 0
def evaluate(self):
self.fitness = f(self.x, self.y)
# 定义种群
class Population:
def __init__(self, size):
self.size = size
self.individuals = [Individual() for i in range(size)]
def evaluate(self):
for individual in self.individuals:
individual.evaluate()
def select(self):
return random.choice(self.individuals)
def crossover(self, parent1, parent2):
child1 = Individual()
child2 = Individual()
child1.x = parent1.x
child1.y = parent2.y
child2.x = parent2.x
child2.y = parent1.y
return child1, child2
def mutate(self):
for individual in self.individuals:
if random.random() < MUTATION_RATE:
individual.x = random.uniform(0, 10)
individual.y = random.uniform(0, 10)
def evolve(self):
# 评估种群
self.evaluate()
# 选择父代
parent1 = self.select()
parent2 = self.select()
# 交叉产生子代
if random.random() < CROSSOVER_RATE:
child1, child2 = self.crossover(parent1, parent2)
self.individuals.append(child1)
self.individuals.append(child2)
# 变异
self.mutate()
# 选择下一代
self.individuals = sorted(self.individuals, key=lambda x: x.fitness, reverse=True)[:self.size - int(ELITISM)]
# 保留最优个体
if ELITISM:
self.individuals.append(max(self.individuals, key=lambda x: x.fitness))
# 迭代
pop = Population(POP_SIZE)
for i in range(GENERATION):
pop.evolve()
# 输出结果
print(max(pop.individuals, key=lambda x: x.fitness).fitness)
```
注意,由于函数的精度要求比较高,可能需要调整遗传算法的参数以获得更好的结果。
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