如何用python编写nsga-Ⅱ算法

NSGA-II（Non-dominated Sorting Genetic Algorithm II）是一种常用的多目标优化算法，它结合了遗传算法和多目标优化的思想。这里提供一个用Python编写NSGA-II算法的示例，具体实现如下：

1.导入所需的库

import random
import copy
import numpy as np

2.定义问题的目标函数

def func(x):
    """目标函数"""
    return [x[0]**2, (x[0]-2)**2]

3.定义NSGA-II算法的类

class NSGA_II():
    def __init__(self, problem_size, population_size, max_generation, crossover_prob, mutation_prob):
        """
        初始化参数
        problem_size: 问题的规模
        population_size: 种群大小
        max_generation: 最大迭代次数
        crossover_prob: 交叉概率
        mutation_prob: 变异概率
        """
        self.problem_size = problem_size
        self.population_size = population_size
        self.max_generation = max_generation
        self.crossover_prob = crossover_prob
        self.mutation_prob = mutation_prob
        self.population = []
        self.fronts = []
        self.crowd_distance = []

    def initialize_population(self):
        """初始化种群"""
        for i in range(self.population_size):
            individual = []
            for j in range(self.problem_size):
                individual.append(random.uniform(0, 1))
            self.population.append(individual)

    def fast_non_dominated_sort(self, population):
        """
        快速非支配排序
        population: 当前种群
        """
        fronts = [[]]
        S = []
        n = [0] * len(population)
        rank = [0] * len(population)
        for p in range(len(population)):
            S.append([])
            for q in range(len(population)):
                if func(population[p])[0] < func(population[q])[0] and func(population[p])[1] < func(population[q])[1]:
                    if q not in S[p]:
                        S[p].append(q)
                elif func(population[q])[0] < func(population[p])[0] and func(population[q])[1] < func(population[p])[1]:
                    n[p] += 1
            if n[p] == 0:
                rank[p] = 0
                fronts[0].append(p)
        i = 0
        while fronts[i]:
            Q = []
            for p in fronts[i]:
                for q in S[p]:
                    n[q] -= 1
                    if n[q] == 0:
                        rank[q] = i + 1
                        Q.append(q)
            i += 1
            fronts.append(Q)
        del fronts[-1]
        self.fronts = fronts

    def crowding_distance(self, front):
        """
        拥挤度计算
        front: 当前层
        """
        distance = [0] * len(front)
        for m in range(len(func([0] * self.problem_size))):
            front.sort(key=lambda x: func(x)[m])
            distance[0] = distance[-1] = float('inf')
            for i in range(1, len(front)-1):
                distance[i] += (func(front[i+1])[m] - func(front[i-1])[m]) / (func(front[-1])[m] - func(front[0])[m])
        return distance

    def selection(self, front):
        """
        选择操作
        front: 当前层
        """
        next_population = []
        front_size = len(front)
        if len(self.population) + front_size <= self.population_size:
            next_population = front
        else:
            self.crowd_distance = [0] * front_size
            front = sorted(front, key=lambda x: func(x)[0])
            for i in range(front_size):
                next_population.append(front[i])
            for m in range(len(func([0] * self.problem_size))):
                front = sorted(front, key=lambda x: func(x)[m])
                self.crowd_distance = [self.crowd_distance[i] + (func(front[i+1])[m] - func(front[i-1])[m]) / (func(front[-1])[m] - func(front[0])[m]) for i in range(1, front_size-1)]
            front = [front[i] for i in range(1, front_size-1)]
            while len(next_population) < self.population_size:
                index = self.crowd_distance.index(max(self.crowd_distance))
                next_population.append(front[index])
                del front[index]
                del self.crowd_distance[index]
        return next_population

    def crossover(self, parent1, parent2):
        """
        交叉操作
        parent1: 父代1
        parent2: 父代2
        """
        if random.random() < self.crossover_prob:
            child1 = []
            child2 = []
            alpha = random.random()
            for i in range(self.problem_size):
                child1.append(alpha * parent1[i] + (1 - alpha) * parent2[i])
                child2.append(alpha * parent2[i] + (1 - alpha) * parent1[i])
            return child1, child2
        else:
            return parent1, parent2

    def mutation(self, individual):
        """
        变异操作
        individual: 待变异个体
        """
        if random.random() < self.mutation_prob:
            mutated_individual = []
            for i in range(self.problem_size):
                mutated_individual.append(individual[i] + random.uniform(-0.1, 0.1))
            return mutated_individual
        else:
            return individual

    def evolve(self):
        """进化"""
        self.initialize_population()
        for i in range(self.max_generation):
            self.fast_non_dominated_sort(self.population)
            next_population = []
            for front in self.fronts:
                next_population += self.selection(front)
            while len(next_population) < self.population_size:
                parent1 = random.choice(self.population)
                parent2 = random.choice(self.population)
                child1, child2 = self.crossover(parent1, parent2)
                next_population.append(self.mutation(child1))
                next_population.append(self.mutation(child2))
            self.population = copy.deepcopy(next_population)

    def get_fronts(self):
        """获取非支配解集"""
        fronts = []
        self.fast_non_dominated_sort(self.population)
        for front in self.fronts:
            fronts.append([self.population[i] for i in front])
        return fronts

4.使用NSGA-II算法求解多目标优化问题

problem_size = 1
population_size = 100
max_generation = 100
crossover_prob = 0.9
mutation_prob = 0.1
nsga = NSGA_II(problem_size, population_size, max_generation, crossover_prob, mutation_prob)
nsga.evolve()
fronts = nsga.get_fronts()
for i, front in enumerate(fronts):
    print("Front {}:".format(i+1))
    for individual in front:
        print("    {}".format(individual))

注意：本示例仅针对问题规模为1的情况，如果问题规模大于1，需要将NSGA_II类中的func函数修改为问题的实际目标函数。