速求！商品购买力最优化问题（用遗传算法求解，给出python代码）

Question

问题描述：假设有两间商店，A店有abc三种商品，B店有cdef四种商品，abcdef商品价格分别为432543元，要求每样商品必须购买，即每样商品购买数量大于0，但在A商店购买的商品总数量小于10，在B商店购买的商品总数量小于8，求最优购买力（最小值），用遗传算法怎么优化，给出Python代码

Answer 1

import numpy as np
import random

# 商品价格
prices_A = [432, 543, 432]  # A店商品abc的价格
prices_B = [543, 432, 543, 654]  # B店商品cdef的价格

# 商品数量限制
max_A = 10
max_B = 8

# 遗传算法参数
population_size = 100
generations = 200
mutation_rate = 0.1


# 适应度函数
def fitness(individual):
    quantity_A = individual[:3]  # A店的商品数量
    quantity_B = individual[3:]  # B店的商品数量

    total_A = sum(quantity_A)
    total_B = sum(quantity_B)

    if total_A > max_A or total_B > max_B:
        return float('inf')  # 不满足约束，适应度为无穷大

    total_cost = sum(quantity_A[i] * prices_A[i] for i in range(3)) + \
                 sum(quantity_B[i] * prices_B[i] for i in range(4))

    return total_cost


# 初始化种群
def initialize_population():
    return [np.random.randint(1, 10, size=7) for _ in range(population_size)]


# 选择操作
def selection(population):
    scores = np.array([fitness(ind) for ind in population])

    # 处理适应度为无穷大的个体
    scores[scores == float('inf')] = np.nan  # 将无穷大替换为NaN
    valid_indices = np.where(~np.isnan(scores))[0]  # 有效个体的索引
    valid_scores = scores[~np.isnan(scores)]  # 有效适应度

    if len(valid_scores) == 0:
        return random.sample(population, population_size // 2)  # 如果没有有效个体，随机选择

    probabilities = np.exp(-valid_scores / np.sum(valid_scores))  # 计算有效个体的概率
    probabilities /= probabilities.sum()  # 归一化

    # 确保选择的数量不超过有效个体的数量
    num_to_select = min(population_size // 2, len(valid_indices))
    selected_indices = np.random.choice(valid_indices, size=num_to_select, replace=False, p=probabilities)
    return [population[i] for i in selected_indices]


# 交叉操作
def crossover(parent1, parent2):
    crossover_point = random.randint(0, 6)
    child1 = np.concatenate((parent1[:crossover_point], parent2[crossover_point:]))
    child2 = np.concatenate((parent2[:crossover_point], parent1[crossover_point:]))
    return child1, child2


# 变异操作
def mutate(individual):
    if random.random() < mutation_rate:
        mutation_index = random.randint(0, 6)
        individual[mutation_index] = random.randint(1, 10)  # 变异为1到10之间的随机数


# 遗传算法主程序
def genetic_algorithm():
    population = initialize_population()

    for generation in range(generations):
        selected = selection(population)

        # 检查选中的个体数量
        if len(selected) < 2:
            print("有效个体不足，无法进行交叉操作。")
            break

        next_generation = []

        while len(next_generation) < population_size:
            parent1, parent2 = random.sample(selected, 2)
            child1, child2 = crossover(parent1, parent2)
            mutate(child1)
            mutate(child2)
            next_generation.extend([child1, child2])

        population = next_generation[:population_size]

    # 找到最优解
    best_individual = min(population, key=fitness)
    return best_individual, fitness(best_individual)


# 运行遗传算法
best_solution, best_cost = genetic_algorithm()
print("最优购买方案:", best_solution)
print("最小总花费:", best_cost)