NSGA-II算法应用实例及python代码

NSGA-II算法是一种常用的多目标优化算法，它可以同时优化多个目标函数，并且能够得到多个不同的最优解。下面是一个NSGA-II算法的应用实例及其对应的python代码。

应用实例：多目标车辆路径规划问题

在这个问题中，我们需要规划出多个车辆的路径，使得它们能够在最短的时间内完成所有的任务，并且尽量减少它们之间的冲突。我们可以使用NSGA-II算法来解决这个问题，其中每个车辆的路径就是一个决策变量，而目标函数包括总时间和冲突数两个部分。

Python代码：

import random

# 定义决策变量的范围和目标函数
MIN_X = 0
MAX_X = 10
MIN_Y = 0
MAX_Y = 10

def f1(x):
    # 计算总时间
    total_time = sum(x)
    return total_time

def f2(x):
    # 计算冲突数
    conflicts = 0
    for i in range(len(x)):
        for j in range(i+1, len(x)):
            if x[i] == x[j]:
                conflicts += 1
    return conflicts

# 定义NSGA-II算法的主要函数
def nsga2(pop_size, n_gen, cx_prob, mut_prob):
    # 初始化种群
    pop = []
    for i in range(pop_size):
        x = [random.uniform(MIN_X, MAX_X) for j in range(10)]
        pop.append(x)

    # 进行多代进化
    for gen in range(n_gen):
        # 计算每个个体的目标函数值
        fitness = []
        for x in pop:
            fitness.append((f1(x), f2(x)))

        # 对个体按照目标函数值进行排序
        fronts = [[] for i in range(pop_size)]
        rank = [0 for i in range(pop_size)]
        dominated = [[] for i in range(pop_size)]
        n_dom = [0 for i in range(pop_size)]
        for i in range(pop_size):
            p = fitness[i]
            for j in range(pop_size):
                q = fitness[j]
                if p[0] > q[0] and p[1] > q[1]:
                    dominated[i].append(j)
                elif p[0] < q[0] and p[1] < q[1]:
                    n_dom[i] += 1
            if n_dom[i] == 0:
                rank[i] = 0
                fronts[0].append(i)

        # 对每个等级的个体进行交叉和变异
        new_pop = []
        for i in range(pop_size):
            if len(new_pop) >= pop_size:
                break
            for j in range(len(fronts[i])):
                if len(new_pop) >= pop_size:
                    break
                p = pop[fronts[i][j]]
                q = random.choice(fronts[i])
                while q == fronts[i][j]:
                    q = random.choice(fronts[i])
                r = random.choice(fronts[i])
                while r == fronts[i][j] or r == q:
                    r = random.choice(fronts[i])
                child = crossover(p, pop[q], pop[r], cx_prob)
                child = mutate(child, mut_prob)
                new_pop.append(child)

        pop = new_pop

    # 返回最终的种群
    return pop

# 定义交叉和变异操作
def crossover(p, q, r, cx_prob):
    child = []
    for i in range(len(p)):
        if random.random() < cx_prob:
            child.append(q[i])
        else:
            child.append(r[i])
    return child

def mutate(x, mut_prob):
    for i in range(len(x)):
        if random.random() < mut_prob:
            x[i] = random.uniform(MIN_X, MAX_X)
    return x

# 运行NSGA-II算法并输出结果
pop = nsga2(pop_size=100, n_gen=100, cx_prob=0.8, mut_prob=0.1)
for x in pop:
    print(f1(x), f2(x))