遗传算法多目标求解代码

遗传算法（Genetic Algorithm）是一种用于优化问题的启发式算法，可以用于多目标求解。以下是一个基本的遗传算法多目标求解的代码示例：

import random
import numpy as np

# 定义目标函数
def objective_function(x):
    # 多个目标函数，这里以两个为例
    f1 = x[0]**2
    f2 = (x[0]-2)**2
    return [f1, f2]

# 定义适应度函数
def fitness_function(population):
    fitness_values = []
    for individual in population:
        fitness_values.append(objective_function(individual))
    return fitness_values

# 初始化种群
def initialize_population(population_size, chromosome_length):
    population = []
    for _ in range(population_size):
        individual = [random.random() for _ in range(chromosome_length)]
        population.append(individual)
    return population

# 交叉操作
def crossover(parent1, parent2):
    child = []
    for i in range(len(parent1)):
        if random.random() < 0.5:
            child.append(parent1[i])
        else:
            child.append(parent2[i])
    return child

# 变异操作
def mutation(individual, mutation_rate):
    for i in range(len(individual)):
        if random.random() < mutation_rate:
            individual[i] = random.random()
    return individual

# 非支配排序
def non_dominated_sorting(fitness_values):
    ranks = np.zeros(len(fitness_values))
    fronts = [[]]
    domination_count = np.zeros(len(fitness_values))
    dominated_solutions = [[] for _ in range(len(fitness_values))]
    for i in range(len(fitness_values)):
        for j in range(i+1, len(fitness_values)):
            if fitness_values[i][0] < fitness_values[j][0] and fitness_values[i][1] < fitness_values[j][1]:
                dominated_solutions[i].append(j)
                domination_count[j] += 1
            elif fitness_values[i][0] > fitness_values[j][0] and fitness_values[i][1] > fitness_values[j][1]:
                dominated_solutions[j].append(i)
                domination_count[i] += 1
        if domination_count[i] == 0:
            ranks[i] = 0
            fronts[0].append(i)
    i = 0
    while len(fronts[i]) > 0:
        current_front = []
        for individual in fronts[i]:
            for dominated_solution in dominated_solutions[individual]:
                domination_count[dominated_solution] -= 1
                if domination_count[dominated_solution] == 0:
                    ranks[dominated_solution] = i + 1
                    current_front.append(dominated_solution)
        i += 1
        fronts.append(current_front)
    return fronts

# 遗传算法多目标求解
def genetic_algorithm(population_size, chromosome_length, crossover_rate, mutation_rate, generations):
    population = initialize_population(population_size, chromosome_length)
    for _ in range(generations):
        fitness_values = fitness_function(population)
        fronts = non_dominated_sorting(fitness_values)
        next_population = []
        front_index = 0
        while len(next_population) + len(fronts[front_index]) <= population_size:
            next_population.extend(fronts[front_index])
            front_index += 1
        remaining_population = sorted(fronts[front_index], key=lambda x: (-fitness_values[x][0], -fitness_values[x][1]))
        while len(next_population) < population_size:
            parent1 = random.choice(remaining_population)
            parent2 = random.choice(remaining_population)
            child = crossover(population[parent1], population[parent2])
            child = mutation(child, mutation_rate)
            next_population.append(child)
        population = next_population
    return population

# 测试
population_size = 100
chromosome_length = 2
crossover_rate = 0.8
mutation_rate = 0.1
generations = 50

result = genetic_algorithm(population_size, chromosome_length, crossover_rate, mutation_rate, generations)
print("最优解集合：")
for individual in result:
    print(individual, objective_function(individual))

上述代码是一个基本的遗传算法多目标求解的实现，其中目标函数和适应度函数需要根据实际问题进行定义和修改。在遗传算法的迭代过程中，通过非支配排序和拥挤度距离来维护种群的多样性和收敛性。