算法求解车辆路径问题 python

### 使用Python实现车辆路径问题算法

#### 基于混合遗传搜索算法（HGS）求解CVRP
带能力限制的车辆路径问题是运筹学中的经典NP-Hard问题，旨在规划多辆车的路径以满足多个客户点的需求，在车辆能力限制下达到最优运输目标[^1]。

下面是一个简单的基于混合遗传搜索算法(HGS)来解决CVRP的例子：

import numpy as np
from deap import base, creator, tools, algorithms

def create_individual(size):
    individual = list(range(1, size))
    np.random.shuffle(individual)
    return individual

def evaluate(individual, distance_matrix, demand_list, vehicle_capacity):
    total_distance = 0
    current_load = 0
    num_vehicles = 1
    
    for i in range(len(individual)):
        if current_load + demand_list[individual[i]] > vehicle_capacity:
            num_vehicles += 1
            current_load = 0
        
        current_load += demand_list[individual[i]]
        
        if i != 0 and (current_load == vehicle_capacity or i == len(individual)-1):
            start_node = 0 if i==len(individual)-1 else individual[i-1]
            end_node = individual[i]
            total_distance += distance_matrix[start_node][end_node]

    return total_distance,

creator.create("FitnessMin", base.Fitness, weights=(-1.0,))
creator.create("Individual", list, fitness=creator.FitnessMin)

toolbox = base.Toolbox()
size = 10  # number of customers excluding depot
distance_matrix = [[0, 29, 37, 48], [29, 0, 16, 35], [37, 16, 0, 19], [48, 35, 19, 0]]  
demand_list = [0, 10, 20, 30]   
vehicle_capacity = 40  

toolbox.register("individual", tools.initIterate, creator.Individual, lambda: create_individual(size))
toolbox.register("population", tools.initRepeat, list, toolbox.individual)
toolbox.register("mate", tools.cxPartialyMatched)
toolbox.register("mutate", tools.mutShuffleIndexes, indpb=0.05)
toolbox.register("select", tools.selTournament, tournsize=3)
toolbox.register("evaluate", evaluate, distance_matrix=distance_matrix, demand_list=demand_list, vehicle_capacity=vehicle_capacity)

population = toolbox.population(n=50)
algorithms.eaSimple(population, toolbox, cxpb=0.5, mutpb=0.2, ngen=40, verbose=False);

best_ind = tools.selBest(population, k=1)[0]
print(f'Best solution found: {best_ind}, with a cost of {best_ind.fitness.values[0]}')

这段代码展示了如何利用DEAP库创建一个基本框架来进行进化计算。此示例仅提供了一个简化版本；实际应用可能需要更复杂的配置和调整参数设置。