多目标灰狼算法 python

### 使用Python实现多目标灰狼优化器

多目标灰狼优化(MOGWO, Multi-Objective Grey Wolf Optimizer)是一种基于群体智能的元启发式算法，用于解决具有多个相互冲突的目标函数的问题。该方法模拟了灰狼的社会等级制度及其狩猎行为来寻找最优解集。

下面是一个简单的MOGWO框架在Python中的基本实现：

import numpy as np
from pymoo.algorithms.moo.moead import MOEAD
from pymoo.optimize import minimize
from pymoo.problems.multi import get_problem
from pymoo.util.display import Display
from pymoo.visualization.scatter import Scatter


class GWO:
    def __init__(self, objective_functions, lb, ub, dimension, population_size=30, max_iter=1000):
        self.objectives = objective_functions
        self.lb = lb
        self.ub = ub
        self.dim = dimension
        self.pop_size = population_size
        self.max_iter = max_iter
        
        # 初始化种群位置向量
        self.positions = np.random.uniform(self.lb, self.ub, (self.pop_size, self.dim))
    
    def _calculate_objective_values(self, pos):
        return [obj(pos) for obj in self.objectives]

    def optimize(self):
        Alpha_pos = Beta_pos = Delta_pos = None
        Alpha_score = float('inf')
        Beta_score = float('inf')
        Delta_score = float('inf')

        Convergence_curve = []

        for l in range(0, self.max_iter):
            for i in range(0, self.pop_size):

                # 返回个体适应度值列表
                fitness = self._calculate_objective_values(self.positions[i])

                if sum(fitness) < Alpha_score:
                    Delta_score = Beta_score
                    Delta_pos = Beta_pos.copy()
                    Beta_score = Alpha_score
                    Beta_pos = Alpha_pos.copy()
                    Alpha_score = sum(fitness)
                    Alpha_pos = self.positions[i].copy()

                elif sum(fitness) < Beta_score and sum(fitness) >= Alpha_score:
                    Delta_score = Beta_score
                    Delta_pos = Beta_pos.copy()
                    Beta_score = sum(fitness)
                    Beta_pos = self.positions[i].copy()

                elif sum(fitness) < Delta_score and sum(fitness) >= Beta_score:
                    Delta_pos = self.positions[i].copy()
                    Delta_score = sum(fitness)

            a = 2 - l * ((2) / self.max_iter)

            for i in range(0, self.pop_size):
                r1 = np.random.rand(len(self.positions[i]))
                r2 = np.random.rand(len(self.positions[i]))

                A1 = 2 * a * r1 - a;
                C1 = 2 * r2;

                D_alpha = abs(C1 * Alpha_pos - self.positions[i])
                X1 = Alpha_pos - A1 * D_alpha

                r1 = np.random.rand(len(self.positions[i]))
                r2 = np.random.rand(len(self.positions[i]))

                A2 = 2 * a * r1 - a
                C2 = 2 * r2

                D_beta = abs(C2 * Beta_pos - self.positions[i])
                X2 = Beta_pos - A2 * D_beta

                r1 = np.random.rand(len(self.positions[i]))
                r2 = np.random.rand(len(self.positions[i]))

                A3 = 2 * a * r1 - a
                C3 = 2 * r2

                D_delta = abs(C3 * Delta_pos - self.positions[i])
                X3 = Delta_pos - A3 * D_delta
                
                self.positions[i] = (X1 + X2 + X3) / 3
            
            Convergence_curve.append([Alpha_score, Beta_score, Delta_score])
        
        return Alpha_pos, Convergence_curve
    
if __name__ == "__main__":
    problem = get_problem("zdt1")

    algorithm = MOEAD(
        ref_dirs=np.array([[1.0, 0.0], [0.5, 0.5], [0.0, 1.0]]),
        n_neighbors=15,
        prob_neighbor_mating=0.7,
    )

    res = minimize(problem,
                   algorithm,
                   ('n_gen', 200),
                   seed=1,
                   verbose=False)

    gwo_instance = GWO(objective_functions=[lambda x: res.F[0][0],
                                            lambda x: res.F[1][0]],
                       lb=-5,
                       ub=5,
                       dimension=res.X.shape[-1])

    best_solution, convergence_data = gwo_instance.optimize() 

print(best_solution)

此代码片段定义了一个`GWO`类，它接受几个参数作为输入：目标函数列表、下界(`lb`)、上界(`ub`)以及维度数量(`dimension`)。此外还有两个可选参数——种群大小(`population_size`)和最大迭代次数(`max_iter`)。通过调用`optimize()`成员函数执行实际寻优过程并返回找到的最佳解决方案[^1]。

为了简化示例，在主程序部分创建了一个名为`problem`的对象实例化自PyMoo库提供的测试问题之一ZDT1；接着配置好进化策略后运行最小化操作获得初步结果对象`res`；最后利用这些信息初始化我们的`gwo_instance`来进行具体求解工作[^1]。