NSGA-II多目标优化python

NSGA-II（Non-dominated Sorting Genetic Algorithm II）是一种常用的多目标优化算法。面是一个使用Python实现NSGA-II的示例代码：

import numpy as np
from numpy.random import rand
from functools import partial
from operator import itemgetter

def nsga2(population_size, num_generations, num_objectives, num_variables, lower_bounds, upper_bounds, crossover_prob, mutation_prob):
    # 初始化种群
    population = initialize_population(population_size, num_variables, lower_bounds, upper_bounds)
    
    for generation in range(num_generations):
        # 计算个体的适应度值
        fitness_values = evaluate_population(population)
        
        # 进行非支配排序和拥挤度分配
        fronts = non_dominated_sort(fitness_values)
        crowding_distances = crowding_distance_assignment(fronts)
        
        # 创建新一代种群
        offspring = []
        while len(offspring) < population_size:
            # 选择父代个体
            parent_indices = select_parents(fronts, crowding_distances)
            parent1 = population[parent_indices[0]]
            parent2 = population[parent_indices[1]]
            
            # 交叉和变异产生子代个体
            child = crossover(parent1, parent2, crossover_prob)
            child = mutate(child, mutation_prob, lower_bounds, upper_bounds)
            
            offspring.append(child)
        
        # 合并父代和子代个体，进行环境选择
        population = environmental_selection(population, offspring, population_size)
    
    # 返回最终的非支配排序结果
    fitness_values = evaluate_population(population)
    fronts = non_dominated_sort(fitness_values)
    return population, fitness_values, fronts

def initialize_population(population_size, num_variables, lower_bounds, upper_bounds):
    population = []
    for _ in range(population_size):
        individual = lower_bounds + rand(num_variables) * (upper_bounds - lower_bounds)
        population.append(individual)
    return population

def evaluate_population(population):
    fitness_values = []
    for individual in population:
        # 根据问题定义计算个体的适应度值
        fitness = [objective1(individual), objective2(individual), ...]  # 替换成实际问题的目标函数
        fitness_values.append(fitness)
    return np.array(fitness_values)

def non_dominated_sort(fitness_values):
    # 实现非支配排序算法
    # 返回每个个体所属的前沿
    return fronts

def crowding_distance_assignment(fronts):
    # 计算每个个体的拥挤度距离
    # 返回每个个体的拥挤度距离
    return crowding_distances

def select_parents(fronts, crowding_distances):
    # 选择父代个体
    # 返回两个父代个体的索引
    return parent_indices

def crossover(parent1, parent2, crossover_prob):
    # 交叉操作
    # 返回子代个体
    return child

def mutate(child, mutation_prob, lower_bounds, upper_bounds):
    # 变异操作
    # 返回变异后的个体
    return mutated_child

def environmental_selection(population, offspring, population_size):
    # 环境选择
    # 返回新一代种群
    return new_population

# 示例问题的目标函数
def objective1(individual):
    return individual[0]**2

def objective2(individual):
    return (individual[0]-2)**2

# 示例代码的使用
population_size = 100
num_generations = 50
num_objectives = 2
num_variables = 1
lower_bounds = [0]
upper_bounds = [5]
crossover_prob = 0.8
mutation_prob = 0.1

population, fitness_values, fronts = nsga2(population_size, num_generations, num_objectives, num_variables, lower_bounds, upper_bounds, crossover_prob, mutation_prob)

# 输出最终的非支配排序结果
for i, front in enumerate(fronts):
    print("Front", i+1)
    for individual in front:
        print("Fitness:", fitness_values[individual])
        print("Solution:", population[individual])

在上述示例代码中，我们定义了一个 `nsga2` 函数来实现NSGA-II算法。该函数接受一些参数，例如种群大小、迭代代数、目标函数数量、变量数量等，并返回最终的非支配排序结果。

在算法的主要循环中，我们首先初始化种群，然后进行适应度评估、非支配排序和拥挤度分配。接下来，我们创建新一代种群，通过选择父代个体、进行交叉和变异来产生子代个体。最后，我们通过环境选择来合并父代和子代个体，并更新种群。

你需要根据你的具体问题进行相应的修改，包括目标函数的定义和问题特定的约束条件。此外，你还可以根据需要添加其他功能，例如改进的选择方法、多变量问题的处理等。

请确保替换示例代码中的目标函数、约束条件和其他问题特定的部分，以适应你的实际问题。