APES算法及代码实现

APES算法是一种基于粒子群优化算法（PSO）的新型优化算法，用于解决多目标优化问题。其核心思想是维护一个帕累托最优解集合，通过对解集合中的解进行调整，寻找更好的解。下面是APES算法的代码实现：

import random

class APES:
    def __init__(self, obj_func, dim, pop_size, archive_size, max_iter):
        self.obj_func = obj_func
        self.dim = dim
        self.pop_size = pop_size
        self.archive_size = archive_size
        self.max_iter = max_iter
        self.pop = [] # 种群
        self.archive = [] # 存档
        self.gbest = None # 全局最优解
        self.gbest_fitness = None # 全局最优解对应的适应度值
        self.init_pop() # 初始化种群
    
    def init_pop(self):
        for i in range(self.pop_size):
            particle = [random.uniform(-5, 5) for j in range(self.dim)]
            self.pop.append(particle)
        self.update_archive(self.pop)
        self.gbest = self.archive[0]
        self.gbest_fitness = self.obj_func(self.gbest)
    
    def update_archive(self, solutions):
        for solution in solutions:
            fitness = self.obj_func(solution)
            if len(self.archive) < self.archive_size:
                self.archive.append((solution, fitness))
            else:
                worst_solution = max(self.archive, key=lambda x:x[1])
                if fitness < worst_solution[1]:
                    self.archive.remove(worst_solution)
                    self.archive.append((solution, fitness))
    
    def update_gbest(self):
        for solution, fitness in self.archive:
            if fitness < self.gbest_fitness:
                self.gbest = solution
                self.gbest_fitness = fitness
    
    def run(self):
        for i in range(self.max_iter):
            for j in range(self.pop_size):
                particle = self.pop[j]
                velocity = [random.uniform(-1, 1) for k in range(self.dim)]
                new_particle = [particle[k] + velocity[k] for k in range(self.dim)]
                self.pop[j] = new_particle
            self.update_archive(self.pop)
            self.update_gbest()
        return self.gbest_fitness, self.gbest

其中，`obj_func`是需要优化的目标函数，`dim`是解向量的维度，`pop_size`是种群大小，`archive_size`是存档大小，`max_iter`是最大迭代次数。`init_pop`函数用于初始化种群，`update_archive`函数用于更新存档，`update_gbest`函数用于更新全局最优解。`run`函数是算法的主函数，其中包含粒子的运动公式，以及对种群和存档的更新。