python实现MFOA算法

MFOA（Multi-Objective Firefly Algorithm）是一种多目标优化算法，它基于萤火虫算法（Firefly Algorithm）并进行了改进。下面是Python实现MFOA算法的示例代码：

import numpy as np
import math

# 定义目标函数
def obj_func(x):
    f1 = x[0]**2 + x[1]**2
    f2 = (x[0]-1)**2 + x[1]**2
    return [f1, f2]

# 定义MFOA算法
def mfoa(obj_func, lb, ub, dimension, n_objectives, n_fireflies, n_iterations):
    # 初始化
    alpha = 0.5  # 镜面反射系数
    gamma = 1  # 光吸收系数
    beta0 = 1  # 初始亮度
    beta_min = 0.2  # 最小亮度
    # 初始化萤火虫位置和亮度
    x = np.random.uniform(lb, ub, (n_fireflies, dimension))
    y = np.zeros((n_fireflies, n_objectives))
    for i in range(n_fireflies):
        y[i] = obj_func(x[i])
    # 迭代优化
    for t in range(n_iterations):
        # 计算亮度和吸引度
        beta = beta0 * math.exp(-gamma * t)
        for i in range(n_fireflies):
            for j in range(n_fireflies):
                if i == j:
                    continue
                dist = np.linalg.norm(x[i] - x[j])
                if y[i][0] < y[j][0] and y[i][1] < y[j][1]:
                    # 亮度越大，吸引度越强
                    y[i] += beta * math.exp(-dist**2 / alpha) * (y[j]-y[i])
                    x[i] += y[i] * np.random.uniform(0, 1, dimension)
                else:
                    y[i] += beta_min * math.exp(-dist**2 / alpha) * (y[j]-y[i])
                    x[i] += y[i] * np.random.uniform(0, 1, dimension)
        # 限制解空间
        for i in range(n_fireflies):
            for j in range(dimension):
                if x[i][j] < lb[j]:
                    x[i][j] = lb[j]
                elif x[i][j] > ub[j]:
                    x[i][j] = ub[j]
            y[i] = obj_func(x[i])
    # 返回最优解
    best_index = np.argmin(y[:, 0] + y[:, 1])
    return x[best_index], y[best_index]

# 示例
lb = [-5, -5]
ub = [5, 5]
dimension = 2
n_objectives = 2
n_fireflies = 40
n_iterations = 100
best_x, best_y = mfoa(obj_func, lb, ub, dimension, n_objectives, n_fireflies, n_iterations)
print('最优解：', best_x)
print('目标函数值：', best_y)

在示例中，定义了一个二维的目标函数，它有两个目标：f1 = x[0]**2 + x[1]**2 和 f2 = (x[0]-1)**2 + x[1]**2。然后调用mfoa函数进行优化，传入目标函数、解空间的下限和上限、维度、目标数、萤火虫数量和迭代次数等参数。最后返回最优解和目标函数值。