spea2多目标优化代码

以下是spea2多目标优化的Python实现代码：

import random
import copy


class Individual:
    def __init__(self, num_objectives, chromosome_length, lower_bound, upper_bound):
        self.num_objectives = num_objectives
        self.chromosome_length = chromosome_length
        self.lower_bound = lower_bound
        self.upper_bound = upper_bound
        self.objectives = [0.0] * num_objectives
        self.dominated_by = []
        self.dominating = 0
        self.strength = 0
        self.raw_fitness = 0
        self.normalized_fitness = 0
        self.chromosome = [random.uniform(lower_bound, upper_bound) for _ in range(chromosome_length)]
    
    def evaluate(self, objectives_functions):
        for i in range(self.num_objectives):
            self.objectives[i] = objectives_functions[i](self.chromosome)
    
    def dominates(self, other):
        for i in range(self.num_objectives):
            if self.objectives[i] > other.objectives[i]:
                return False
        return True
    
    def __eq__(self, other):
        return self.chromosome == other.chromosome
    
    def __str__(self):
        return f"chromosome: {self.chromosome}, objectives: {self.objectives}"


class SPEA2:
    def __init__(self, num_objectives, chromosome_length, pop_size, archive_size, crossover_probability, mutation_probability, lower_bound, upper_bound, max_generations):
        self.num_objectives = num_objectives
        self.chromosome_length = chromosome_length
        self.pop_size = pop_size
        self.archive_size = archive_size
        self.crossover_probability = crossover_probability
        self.mutation_probability = mutation_probability
        self.lower_bound = lower_bound
        self.upper_bound = upper_bound
        self.max_generations = max_generations
        self.population = [Individual(num_objectives, chromosome_length, lower_bound, upper_bound) for _ in range(pop_size)]
        self.archive = []
    
    def environmental_selection(self):
        for ind in self.population:
            ind.dominated_by = []
            ind.dominating = 0
        
        for i in range(len(self.archive)):
            for j in range(len(self.population)):
                if self.archive[i].dominates(self.population[j]):
                    self.population[j].dominated_by.append(i)
                elif self.population[j].dominates(self.archive[i]):
                    self.archive[i].dominating += 1
        
        self.archive = [self.archive[i] for i in range(len(self.archive)) if self.archive[i].dominating < self.pop_size // 2]
        
        for ind in self.population:
            ind.strength = sum([self.archive[d].dominating for d in ind.dominated_by])
        
        for ind in self.population:
            ind.raw_fitness = 1.0 / (ind.strength + 2.0)
        
        for ind in self.archive:
            ind.raw_fitness = sum([self.population[d].strength for d in ind.dominated_by])
            ind.normalized_fitness = ind.raw_fitness / (len(self.population) + len(self.archive))
        
        self.archive.sort(key=lambda ind: ind.normalized_fitness, reverse=True)
        self.archive = self.archive[:self.archive_size]
    
    def create_offspring(self):
        offspring = []
        
        for i in range(self.pop_size):
            p1 = random.choice(self.archive)
            p2 = random.choice(self.archive)
            while p1 == p2:
                p2 = random.choice(self.archive)
            child = copy.deepcopy(p1)
            if random.random() < self.crossover_probability:
                for j in range(self.chromosome_length):
                    if random.random() < 0.5:
                        child.chromosome[j] = p2.chromosome[j]
            for j in range(self.chromosome_length):
                if random.random() < self.mutation_probability:
                    child.chromosome[j] += random.gauss(0, 0.1)
                    if child.chromosome[j] < self.lower_bound:
                        child.chromosome[j] = self.lower_bound
                    elif child.chromosome[j] > self.upper_bound:
                        child.chromosome[j] = self.upper_bound
            offspring.append(child)
        
        return offspring
    
    def run(self, objectives_functions):
        for generation in range(self.max_generations):
            print(f"Generation {generation + 1}/{self.max_generations}")
            
            for ind in self.population:
                ind.evaluate(objectives_functions)
            
            self.archive += self.population
            self.environmental_selection()
            offspring = self.create_offspring()
            self.population = offspring

这份代码实现了 SPEA2 算法，其中 `Individual` 类表示个体，包括染色体、对应的目标函数值、支配和被支配关系等信息；`SPEA2` 类则是算法的主体，包含了种群、非支配解集、交叉和变异概率、种群大小、迭代次数等参数，并实现了 SPEA2 算法的主要流程。在 `run` 方法中，我们需要传入一个目标函数列表 `objectives_functions`，它是一个长度为目标数的列表，其中每个元素是一个函数，用于计算某个个体的对应目标函数值。例如，如果我们要优化两个目标函数 $f_1(x)$ 和 $f_2(x)$，则 `objectives_functions` 可以定义为：

def f1(x):
    return x[0] ** 2

def f2(x):
    return (x[0] - 2) ** 2
objectives_functions = [f1, f2]

在实际使用 SPEA2 算法时，我们可以根据具体问题来调整各参数的值，例如种群大小、迭代次数、交叉和变异概率等。