nsga2算法代码python

下面是NSGA-II算法的Python实现代码：

import random
import numpy as np

# 定义问题类，问题是多目标优化问题，有两个目标
class Problem:
    def __init__(self):
        self.num_objectives = 2
        self.num_variables = 10
        self.lower_bounds = [0] * self.num_variables
        self.upper_bounds = [1] * self.num_variables

    # 计算适应度函数值
    def evaluate(self, x):
        f1 = x[0]
        g = 1 + 9 / (self.num_variables - 1) * np.sum(x[1:])
        f2 = g * (1 - np.sqrt(f1 / g))
        return [f1, f2]

# 定义个体类
class Individual:
    def __init__(self, problem):
        self.problem = problem
        self.x = [random.uniform(problem.lower_bounds[i], problem.upper_bounds[i]) for i in range(problem.num_variables)]
        self.fitness = None  # 适应度
        self.dominated_solutions = []  # 被支配的解
        self.dominating_count = 0  # 支配该解的解的数量
        self.rank = 0  # Pareto前沿等级
        self.crowding_distance = 0  # 拥挤距离

    # 计算适应度
    def evaluate_fitness(self):
        self.fitness = self.problem.evaluate(self.x)

    # 判断一个个体是否支配另一个个体
    def dominates(self, other):
        for i in range(self.problem.num_objectives):
            if self.fitness[i] > other.fitness[i]:
                return False
        return True

# 定义NSGA-II算法类
class NSGA2:
    def __init__(self, problem, population_size=100, max_generation=100):
        self.problem = problem
        self.population_size = population_size
        self.max_generation = max_generation

    # 初始化种群
    def initialize_population(self):
        self.population = [Individual(self.problem) for _ in range(self.population_size)]

    # 计算个体的被支配解集合和支配个体数量
    def calculate_dominated_solutions_and_dominating_count(self):
        for i in range(self.population_size):
            for j in range(self.population_size):
                if self.population[i].dominates(self.population[j]):
                    self.population[i].dominated_solutions.append(j)
                elif self.population[j].dominates(self.population[i]):
                    self.population[i].dominating_count += 1

    # 计算每个个体的Pareto前沿等级
    def calculate_rank(self):
        current_rank = 1
        remaining_individuals = set(range(self.population_size))
        while remaining_individuals:
            # 寻找当前Pareto前沿
            current_front = set()
            for i in remaining_individuals:
                if self.population[i].dominating_count == 0:
                    self.population[i].rank = current_rank
                    current_front.add(i)
            # 从当前Pareto前沿中减去被支配的解
            for i in current_front:
                for j in self.population[i].dominated_solutions:
                    self.population[j].dominating_count -= 1
            remaining_individuals -= current_front
            current_rank += 1

    # 计算每个个体的拥挤距离
    def calculate_crowding_distance(self, front):
        # 初始化拥挤距离
        for i in front:
            self.population[i].crowding_distance = 0
        # 对每个目标函数分别计算拥挤距离
        for objective_index in range(self.problem.num_objectives):
            # 按照目标函数值排序
            front.sort(key=lambda i: self.population[i].fitness[objective_index])
            # 设置边界的拥挤距离为无穷大
            self.population[front[0]].crowding_distance = float('inf')
            self.population[front[-1]].crowding_distance = float('inf')
            # 计算拥挤距离
            for i in range(1, len(front) - 1):
                self.population[front[i]].crowding_distance += \
                    self.population[front[i + 1]].fitness[objective_index] - self.population[front[i - 1]].fitness[objective_index]

    # 选择个体
    def select(self):
        # 选择新种群的个体数量等于原种群的个体数量
        new_population = []
        for _ in range(self.population_size):
            # 选择两个个体
            a, b = random.sample(self.population, 2)
            # 如果两个个体不在同一个Pareto前沿，则选择Pareto前沿等级高的个体
            if a.rank < b.rank:
                winner = a
            elif a.rank > b.rank:
                winner = b
            else:
                # 如果两个个体在同一个Pareto前沿，则选择拥挤距离大的个体
                if a.crowding_distance > b.crowding_distance:
                    winner = a
                else:
                    winner = b
            new_population.append(winner)
        self.population = new_population

    # 运行NSGA-II算法
    def run(self):
        self.initialize_population()
        for generation in range(self.max_generation):
            self.calculate_dominated_solutions_and_dominating_count()
            self.calculate_rank()
            fronts = [[] for _ in range(self.problem.num_objectives)]
            for individual in self.population:
                fronts[individual.rank - 1].append(individual)
            new_population = []
            i = 0
            while len(new_population) + len(fronts[i]) <= self.population_size:
                new_population += fronts[i]
                i += 1
            if len(new_population) < self.population_size:
                fronts[i].sort(key=lambda individual: individual.crowding_distance, reverse=True)
                new_population += fronts[i][:self.population_size - len(new_population)]
            self.population = new_population
            self.select()

        # 返回Pareto前沿
        pareto_front = []
        for individual in self.population:
            if individual.rank == 1:
                pareto_front.append(individual)
        return pareto_front

下面是使用示例：

problem = Problem()

nsga2 = NSGA2(problem, population_size=100, max_generation=100)
pareto_front = nsga2.run()

for individual in pareto_front:
    print(individual.fitness)

其中`Problem`类表示优化问题，`Individual`类表示一个个体，`NSGA2`类表示NSGA-II算法。在示例中，我们先创建了一个`Problem`对象表示一个多目标优化问题，然后创建了一个`NSGA2`对象表示使用NSGA-II算法求解这个问题，最后调用`run`方法运行算法并获取Pareto前沿。