NSGA-Ⅱ求解多目标VRP问题的python代码

以下是使用NSGA-II算法求解多目标VRP问题的Python代码：

import numpy as np
import random

# 定义车辆容量
vehicle_capacity = 10

# 定义货物数量
num_of_customers = 20

# 定义客户坐标
customers = np.random.rand(num_of_customers, 2)

# 定义距离矩阵
dist_matrix = np.zeros((num_of_customers, num_of_customers))
for i in range(num_of_customers):
    for j in range(num_of_customers):
        dist_matrix[i][j] = np.linalg.norm(customers[i] - customers[j])

# 定义NSGA-II算法参数
pop_size = 100
max_gen = 200
pc = 0.9
pm = 1.0 / num_of_customers
alpha = 1

class Individual:
    def __init__(self):
        self.chromosome = []
        self.fitness = []
        self.rank = 0
        self.distance = 0

    def __lt__(self, other):
        if self.rank != other.rank:
            return self.rank < other.rank
        else:
            return self.distance > other.distance

# 初始化种群
population = []
for i in range(pop_size):
    ind = Individual()
    ind.chromosome = [0] + random.sample(range(1, num_of_customers), num_of_customers - 1)
    population.append(ind)

# 定义快速非支配排序函数
def fast_non_dominated_sort(population):
    S = [[] for i in range(len(population))]
    front = [[]]
    n = [0 for i in range(len(population))]
    rank = [0 for i in range(len(population))]
    for p in range(len(population)):
        S[p] = []
        n[p] = 0
        for q in range(len(population)):
            if population[p].fitness[0] < population[q].fitness[0] and population[p].fitness[1] < population[q].fitness[1]:
                if q not in S[p]:
                    S[p].append(q)
            elif population[q].fitness[0] < population[p].fitness[0] and population[q].fitness[1] < population[p].fitness[1]:
                n[p] += 1
        if n[p] == 0:
            population[p].rank = 0
            if p not in front[0]:
                front[0].append(p)
    i = 0
    while front[i]:
        Q = []
        for p in front[i]:
            for q in S[p]:
                n[q] -= 1
                if n[q] == 0:
                    population[q].rank = i + 1
                    if q not in Q:
                        Q.append(q)
        i += 1
        front.append(Q)
    return front[:-1]

# 定义拥挤度计算函数
def crowding_distance(population, front):
    for i in range(len(front)):
        for ind in front[i]:
            ind.distance = 0
    for m in range(len(population[0].fitness)):
        front = sorted(front, key=lambda ind: ind.fitness[m])
        population[front[0]].distance = float('inf')
        population[front[-1]].distance = float('inf')
        for i in range(1, len(front) - 1):
            population[front[i]].distance += (population[front[i + 1]].fitness[m] - population[front[i - 1]].fitness[m])

# 定义选择函数
def selection(population):
    tournament_size = 2
    selected = []
    for i in range(pop_size):
        tournament = random.sample(population, tournament_size)
        winner = min(tournament)
        selected.append(winner)
    return selected

# 定义交叉函数
def crossover(parent1, parent2):
    child1 = Individual()
    child2 = Individual()
    child1.chromosome = [-1] * (num_of_customers + 1)
    child2.chromosome = [-1] * (num_of_customers + 1)
    r1 = random.randint(1, num_of_customers - 1)
    r2 = random.randint(r1, num_of_customers - 1)
    for i in range(r1, r2 + 1):
        child1.chromosome[i] = parent1.chromosome[i]
        child2.chromosome[i] = parent2.chromosome[i]
    j = 0
    k = 0
    for i in range(num_of_customers):
        if parent2.chromosome[i + 1] not in child1.chromosome[r1:r2 + 1]:
            child1.chromosome[j] = parent2.chromosome[i + 1]
            j += 1
        if parent1.chromosome[i + 1] not in child2.chromosome[r1:r2 + 1]:
            child2.chromosome[k] = parent1.chromosome[i + 1]
            k += 1
    for i in range(num_of_customers):
        if child1.chromosome[i] == -1:
            child1.chromosome[i] = parent2.chromosome[i + 1]
        if child2.chromosome[i] == -1:
            child2.chromosome[i] = parent1.chromosome[i + 1]
    child1.chromosome[-1] = 0
    child2.chromosome[-1] = 0
    return child1, child2

# 定义变异函数
def mutation(individual):
    for i in range(num_of_customers):
        if random.random() < pm:
            j = random.randint(0, num_of_customers - 1)
            c1 = individual.chromosome[i + 1]
            c2 = individual.chromosome[j + 1]
            individual.chromosome[i + 1] = c2
            individual.chromosome[j + 1] = c1
    return individual

# 定义求解函数
def solve():
    for i in range(max_gen):
        offsprings = []
        for j in range(int(pop_size / 2)):
            parent1, parent2 = random.sample(population, 2)
            if random.random() < pc:
                child1, child2 = crossover(parent1, parent2)
            else:
                child1 = parent1
                child2 = parent2
            child1 = mutation(child1)
            child2 = mutation(child2)
            offsprings += [child1, child2]
        population += offsprings
        for ind in population:
            ind.fitness = [0, 0]
            for i in range(len(ind.chromosome) - 1):
                ind.fitness[0] += dist_matrix[ind.chromosome[i]][ind.chromosome[i + 1]]
                ind.fitness[1] += 1
            ind.fitness[1] -= 1
        fronts = fast_non_dominated_sort(population)
        for i in range(len(fronts)):
            crowding_distance(population, fronts[i])
        population = sorted(population, reverse=True)
        population = population[:pop_size]
    return population

# 调用求解函数
population = solve()

# 输出结果
for i in range(len(population)):
    if population[i].rank == 0:
        print('Solution {}:'.format(i + 1))
        print('  Route: {}'.format(population[i].chromosome))
        print('  Distance: {}'.format(population[i].fitness[0]))
        print('  Num of vehicles: {}'.format(population[i].fitness[1]))

在代码中，先定义了车辆容量、货物数量、客户坐标和距离矩阵等参数。然后定义了Individual类来表示种群中的个体，包括染色体、适应度、排名和拥挤度等属性。接着定义了快速非支配排序和拥挤度计算函数，用于进行多目标优化。最后定义了选择、交叉、变异和求解函数，用于进行遗传算法求解。在求解函数中，使用NSGA-II算法对种群进行进化，并输出最优解的路径和距离等信息。