多目标黏菌算法(MOSMA)附带多个多目标性能指标

news2025/1/15 20:35:36

1 黏菌算法

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2 多目标黏菌算法

%% Multiple Objective Slime Mould Algorithm (MOSMA)
clc
clear all
D = 30; % Number of decision variables
M = 2; % Number of objective functions
K=M+D;
LB = ones(1, D).*0; %  LB - A vector of decimal values which indicate the minimum value for each decision variable.
UB = ones(1, D).*1; % UB - Vector of maximum possible values for decision variables.
GEN = 200;  % Set the maximum number of generation (GEN)
ecosize = 200;      % Set the population size (NP)
ishow = 10;
%% Start the evolution process
Pareto = MOSMA(D,M,LB,UB,ecosize,GEN,ishow);
Obtained_Pareto= Pareto(:,D+1:D+M); % extract data to plot
Obtained_Pareto=sortrows(Obtained_Pareto,2);
True_Pareto=load('ZDT3.txt');
%% Plot data
if M == 2
    plot(Obtained_Pareto(:,1),Obtained_Pareto(:,2),'o','LineWidth',2,...
        'MarkerEdgeColor','r','MarkerSize',2);
    hold on
    plot(True_Pareto(:,1),True_Pareto(:,2),'k'); 
    title('Optimal Solution Pareto Set using MOSMA');
    legend('MOSMA');
    xlabel('F_1');
    ylabel('F_2');
elseif M == 3
    plot3(Obtained_Pareto(:,1),Obtained_Pareto(:,2),Obtained_Pareto(:,3),'o','LineWidth',2,...
        'MarkerEdgeColor','r','MarkerSize',2);
    hold on
    plot3(Obtained_Pareto(:,1),Obtained_Pareto(:,2),Obtained_Pareto(:,3),'.','LineWidth',2,...
        'MarkerEdgeColor','k','MarkerSize',6);
    title('Optimal Solution Pareto Set using MOSMA');
    legend('MOSMA');
    xlabel('F_1');
    ylabel('F_2');
    zlabel('F_3');
end
%%  Metric Value
M_IGD=IGD(Obtained_Pareto,True_Pareto);
M_GD=GD(Obtained_Pareto,True_Pareto);
M_HV=HV(Obtained_Pareto,True_Pareto);
M_Spacing=Spacing(Obtained_Pareto,True_Pareto);
M_Spread=Spread(Obtained_Pareto,True_Pareto);
M_DeltaP=DeltaP(Obtained_Pareto,True_Pareto);
display(['The IGD Metric obtained by MOSMA is     : ', num2str(M_IGD)]);
display(['The GD Metric obtained by MOSMA is      : ', num2str(M_GD)]);
display(['The HV Metric obtained by MOSMA is      : ', num2str(M_HV)]);
display(['The Spacing Metric obtained by MOSMA is : ', num2str(M_Spacing)]);
display(['The Spread Metric obtained by MOSMA is  : ', num2str(M_Spread)]);
display(['The DeltaP Metric obtained by MOSMA is  : ', num2str(M_DeltaP)]);

ZDT3运行结果：

The IGD Metric obtained by MOSMA is: 0.0026812
The GD Metric obtained by MOSMA is: 0.00043364
The HV Metric obtained by MOSMA is: 0.60026
The Spacing Metric obtained by MOSMA is: 0.0038203
The Spread Metric obtained by MOSMA is: 0.45104
The DeltaP Metric obtained by MOSMA is: 0.004529

3 性能指标

两个性能指标，超容量（HV）和扩展间距（STE）用于测量优化算法的性能。HV用于测量PF的收敛性和扩展性，而STE是PF的间距和范围之间的比率。

其中 $\left | PF \right |$ 表示所获得的PF中的解的数量， $d_{i}$ 是第i个解的目标函数向量与其最近邻居之间的欧几里得距离， $d$ 是所有 $d_{i}$ 的平均值， $M$ 是目标函数的数量， $f_{i}^{max}$ 和 $f_{i}^{min}$ 分别是PF中第 $i$ 个目标函数的最大值和最小值。优越的PF具有较大的HV值和较小的STE值。对于HV度量，值越大，表示PF的收敛性和覆盖性越好。对于STE度量，较小的值表示PF具有更好的一致性和扩展性。