NSGA-Ⅱpython代码

NSGA-II（Non-dominated Sorting Genetic Algorithm II）是一种经典的多目标优化算法，它基于遗传算法和非支配排序的思想。下面是一个简单的NSGA-II的Python代码示例：

import random

# 定义个体类
class Individual:
    def __init__(self, num_objectives):
        self.num_objectives = num_objectives
        self.objectives = [0] * num_objectives
        self.rank = 0
        self.crowding_distance = 0

    def evaluate(self):
        # 计算个体的目标函数值
        self.objectives[0] = random.random()
        self.objectives[1] = random.random()

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

# 定义NSGA-II算法类
class NSGA2:
    def __init__(self, num_objectives, population_size, num_generations):
        self.num_objectives = num_objectives
        self.population_size = population_size
        self.num_generations = num_generations

    def run(self):
        # 初始化种群
        population = []
        for _ in range(self.population_size):
            individual = Individual(self.num_objectives)
            individual.evaluate()
            population.append(individual)

        # 进化过程
        for generation in range(self.num_generations):
            # 快速非支配排序
            fronts = self.fast_non_dominated_sort(population)

            # 计算拥挤度距离
            for front in fronts:
                self.calculate_crowding_distance(front)

            # 生成新一代种群
            new_population = []
            front_index = 0
            while len(new_population) + len(fronts[front_index]) <= self.population_size:
                new_population.extend(fronts[front_index])
                front_index += 1

            # 按照拥挤度距离排序选择剩余个体
            fronts[front_index].sort(key=lambda x: x.crowding_distance, reverse=True)
            new_population.extend(fronts[front_index][:self.population_size - len(new_population)])

            population = new_population

        return population

    def fast_non_dominated_sort(self, population):
        # 快速非支配排序
        fronts = [[]]
        for individual in population:
            individual.domination_count = 0
            individual.dominated_solutions = []
            for other in population:
                if individual.dominates(other):
                    individual.dominated_solutions.append(other)
                elif other.dominates(individual):
                    individual.domination_count += 1
            if individual.domination_count == 0:
                individual.rank = 0
                fronts[0].append(individual)

        i = 0
        while len(fronts[i]) > 0:
            next_front = []
            for individual in fronts[i]:
                for other in individual.dominated_solutions:
                    other.domination_count -= 1
                    if other.domination_count == 0:
                        other.rank = i + 1
                        next_front.append(other)
            i += 1
            fronts.append(next_front)

        return fronts

    def calculate_crowding_distance(self, front):
        # 计算拥挤度距离
        for individual in front:
            individual.crowding_distance = 0

        for i in range(self.num_objectives):
            front.sort(key=lambda x: x.objectives[i])
            front[0].crowding_distance = float('inf')
            front[-1].crowding_distance = float('inf')
            for j in range(1, len(front) - 1):
                front[j].crowding_distance += (front[j + 1].objectives[i] - front[j - 1].objectives[i])

# 使用示例
nsga2 = NSGA2(num_objectives=2, population_size=100, num_generations=100)
population = nsga2.run()

# 输出最终种群中的个体
for individual in population:
    print(individual.objectives)

这段代码实现了一个简单的NSGA-II算法，其中包括个体类`Individual`和NSGA-II算法类`NSGA2`。个体类中定义了个体的目标函数值、支配关系等属性和方法，NSGA-II算法类中定义了快速非支配排序、拥挤度距离计算等方法，并通过遗传算法进行多目标优化。