MOEA-DVA python代码

MOEA-DVA是一种多目标优化算法，它基于向量评分函数和动态变异策略，可以用于解决多目标优化问题。以下是一个Python实现的MOEA-DVA算法的代码示例：

import numpy as np

def moea_dva(pop_size, num_obj, num_var, max_gen, f, g, xl, xu):
    # 初始化种群
    pop = np.random.rand(pop_size, num_var) * (xu - xl) + xl
    # 初始化权重向量
    w = np.random.rand(pop_size, num_obj)
    w = w / np.tile(np.sum(w, axis=1)[:, None], (1, num_obj))
    # 初始化参考点
    z = np.min(f(pop), axis=0)
    # 开始迭代
    for gen in range(max_gen):
        # 计算适应度
        fit = np.sum(w * (f(pop) - z), axis=1)
        # 计算变异概率
        p = np.exp(-fit)
        p = p / np.sum(p)
        # 选择父代
        idx = np.random.choice(pop_size, 2, p=p)
        p1 = pop[idx[0], :]
        p2 = pop[idx[1], :]
        # 变异
        beta = 0.5 * (1 + 2 * np.random.rand(num_var))
        beta[beta > 1] = 2 - beta[beta > 1]
        beta[beta < 0] = 0
        c1 = 0.5 * ((1 + beta) * p1 + (1 - beta) * p2)
        c2 = 0.5 * ((1 - beta) * p1 + (1 + beta) * p2)
        # 交叉
        cr = 0.5 * (1 + np.random.rand(num_var))
        cr[cr > 1] = 2 - cr[cr > 1]
        cr[cr < 0] = 0
        c = np.zeros((2, num_var))
        c[0, :] = cr * c1 + (1 - cr) * c2
        c[1, :] = (1 - cr) * c1 + cr * c2
        # 修剪
        c[c < xl] = xl[c < xl]
        c[c > xu] = xu[c > xu]
        # 更新参考点
        z = np.min(np.vstack((z, f(c))), axis=0)
        # 更新种群
        pop = np.vstack((pop, c))
        w = np.vstack((w, np.random.rand(2, num_obj)))
        w = w / np.tile(np.sum(w, axis=1)[:, None], (1, num_obj))
        idx = np.argsort(np.sum(w, axis=0))
        pop = pop[idx[:pop_size], :]
        w = w[idx[:pop_size], :]
    # 返回最终种群
    return pop

其中，pop_size是种群大小，num_obj是目标函数个数，num_var是决策变量个数，max_gen是最大迭代次数，f是目标函数，g是约束函数，xl和xu是决策变量的上下界。