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 random
import numpy as np

# 商品价格
prices = {'a': 4, 'b': 3, 'c': 2, 'd': 5, 'e': 4, 'f': 3}

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

# 约束条件
max_items_A = 10
max_items_B = 8

# 初始化个体
def create_individual():
    # 每种商品购买数量在1到5之间
    return {
        'a': random.randint(1, 5),
        'b': random.randint(1, 5),
        'c': random.randint(1, 5),
        'd': random.randint(1, 5),
        'e': random.randint(1, 5),
        'f': random.randint(1, 5)
    }

# 适应度函数
def fitness(individual):
    total_cost = sum(individual[item] * prices[item] for item in individual)
    items_A = individual['a'] + individual['b'] + individual['c']
    items_B = individual['c'] + individual['d'] + individual['e'] + individual['f']
    
    if items_A >= max_items_A or items_B >= max_items_B:
        return float('inf')  # 不满足约束条件，惩罚

    return total_cost

# 选择
def select(population):
    population.sort(key=lambda ind: fitness(ind))
    return population[:population_size//2]

# 交叉
def crossover(parent1, parent2):
    child = parent1.copy()
    for item in child:
        if random.random() > 0.5:
            child[item] = parent2[item]
    return child

# 变异
def mutate(individual):
    if random.random() < mutation_rate:
        item = random.choice(list(individual.keys()))
        individual[item] = random.randint(1, 5)

# 主遗传算法过程
def genetic_algorithm():
    population = [create_individual() for _ in range(population_size)]
    
    for generation in range(generations):
        selected = select(population)
        offspring = []
        
        while len(offspring) < population_size:
            parent1, parent2 = random.sample(selected, 2)
            child = crossover(parent1, parent2)
            mutate(child)
            offspring.append(child)
        
        population = offspring
    
    best_individual = min(population, key=fitness)
    return best_individual, fitness(best_individual)

# 执行算法
best_solution, best_cost = genetic_algorithm()
print("最佳购买方案:", best_solution)
print("最低总成本:", best_cost)