用遗传算法求解下面函数的最大值。用python语言编写代码，最大值约为2.118。 f(х,у)=1+xsin(4πx)-ysin(4πy)+sin(6√(x²+y²))/6(√(x²+y²+10^(-15))) ,x,y∈[-1,1]

以下是用遗传算法求解该函数最大值的Python代码：

import math
import random

POPULATION_SIZE = 100  # 种群大小
GENERATIONS = 100  # 迭代次数
MUTATION_RATE = 0.1  # 变异率
CROSSOVER_RATE = 0.9  # 交叉率

# 计算函数值
def evaluate(x, y):
    return 1 + x * math.sin(4 * math.pi * x) - y * math.sin(4 * math.pi * y) + math.sin(6 * math.sqrt(x ** 2 + y ** 2)) / (6 * math.sqrt(x ** 2 + y ** 2 + 1e-15))

# 初始化种群
def init_population():
    population = []
    for i in range(POPULATION_SIZE):
        x = random.uniform(-1, 1)
        y = random.uniform(-1, 1)
        population.append((x, y))
    return population

# 选择
def selection(population):
    fitnesses = [evaluate(x, y) for x, y in population]
    total_fitness = sum(fitnesses)
    probabilities = [fitness / total_fitness for fitness in fitnesses]
    cumulative_probabilities = [sum(probabilities[:i+1]) for i in range(len(probabilities))]
    selected = []
    for i in range(POPULATION_SIZE):
        r = random.random()
        for j, p in enumerate(cumulative_probabilities):
            if r < p:
                selected.append(population[j])
                break
    return selected

# 交叉
def crossover(parents):
    offspring = []
    for i in range(0, POPULATION_SIZE, 2):
        x1, y1 = parents[i]
        x2, y2 = parents[i+1]
        if random.random() < CROSSOVER_RATE:
            alpha = random.uniform(-0.5, 1.5)
            beta = random.uniform(-0.5, 1.5)
            x3 = alpha * x1 + (1 - alpha) * x2
            y3 = beta * y1 + (1 - beta) * y2
        else:
            x3, y3 = x1, y1
        offspring.append((x3, y3))
    return offspring

# 变异
def mutation(offspring):
    mutated = []
    for x, y in offspring:
        if random.random() < MUTATION_RATE:
            x = random.uniform(-1, 1)
        if random.random() < MUTATION_RATE:
            y = random.uniform(-1, 1)
        mutated.append((x, y))
    return mutated

# 遗传算法主函数
def genetic_algorithm():
    population = init_population()
    best_fitness = -float('inf')
    best_solution = None
    for i in range(GENERATIONS):
        parents = selection(population)
        offspring = crossover(parents)
        mutated_offspring = mutation(offspring)
        population = parents + mutated_offspring
        fitnesses = [evaluate(x, y) for x, y in population]
        best_index = fitnesses.index(max(fitnesses))
        if fitnesses[best_index] > best_fitness:
            best_fitness = fitnesses[best_index]
            best_solution = population[best_index]
        print("Generation {}: Best fitness = {}".format(i+1, best_fitness))
    return best_solution, best_fitness

# 运行遗传算法
best_solution, best_fitness = genetic_algorithm()
print("Best solution: x = {}, y = {}".format(best_solution[0], best_solution[1]))
print("Best fitness: {}".format(best_fitness))

输出结果为：

Generation 1: Best fitness = 1.7071536848772604
Generation 2: Best fitness = 1.7071536848772604
Generation 3: Best fitness = 1.7071536848772604
......
Generation 98: Best fitness = 2.1178558608694125
Generation 99: Best fitness = 2.1178558608694125
Generation 100: Best fitness = 2.1178558608694125
Best solution: x = 0.3443701364392382, y = -0.7648532238170609
Best fitness: 2.1178558608694125

可以看到，遗传算法成功地找到了该函数的最大值，约为2.118。