1 简介
MVO算法源于多元宇宙理论，该理论认为：多元宇宙源于宇宙大爆炸，每一个宇宙都存在一个膨胀率使其膨胀，宇宙间存在黑洞和白洞，黑洞引力很大能够通过虫洞链接到另一个时空，黑洞会吸入所有物质甚至光，白洞就是由黑洞吸收过多物质后而开始吐出的物质。MVO算法依据多元宇宙理论的3个主要概念：白洞、黑洞和虫洞来建立数学模型，定义候选解为宇宙，候选解的适应度为宇宙的膨胀率。迭代过程中，每一个候选解为黑洞，适应度好的宇宙依轮盘赌原理成为白洞，黑洞和白洞交换物质(维度更换)，部分黑洞可以通过虫洞链接穿越到最优宇宙附近(群体最优附近搜索)。本文绘出多元宇宙优化内部循环结构的逻辑流程，如图1所示。
2 部分代码
%______________________________________________________________________________________
% Multi-Objective Multi-Verse Optimization (MOMVO) algorithm source codes version 1.0
%
%______________________________________________________________________________________
clear all;
close all;
clc;
format long g
% Initial parameters of the MODA algorithm
max_iter=100;
N=100;
ArchiveMaxSize=100;
obj_no=2;
Archive_F1=load('weldedbeam.txt');
%-------------------------- MOMVO -----------------------------------------
for i=1:5 % Numbver of independent runs
[Best_universe_score,Best_universe_pos,Archive_F]=MOMVO(max_iter,N,ArchiveMaxSize);
%% using the matlab codes for calculating metric values
hv = hypeIndicatorExact8(Archive_F, ones(1, obj_no), obj_no);
gd = GD_matlab(Archive_F, Archive_F1);
epsilonNew = epsilon_matlab(Archive_F, Archive_F1);
spread = Spread_matlab(Archive_F, Archive_F1);
generalizedspread = GeneralizedSpread_matlab(Archive_F, Archive_F1);
igd = IGD_matlab(Archive_F, Archive_F1);
disp(['hv = ' num2str(hv) ' GD = ' num2str(gd) ' epsilon = ' num2str(epsilonNew) ' Spread = ' num2str(spread) ' GSpread = ' num2str(generalizedspread) ' IGD = ' num2str(igd) ]);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
GD=Generational_distance(Archive_F,Archive_F1);
S=metric_of_spacing(Archive_F);
DELTA= Diversity_metric_delta(Archive_F,Archive_F1);
MS=metric_of_maximum_spread(Archive_F,Archive_F1);
disp(['GD = ' num2str(GD) ' S = ' num2str(S) ' DELTA = ' num2str(DELTA) ' MS = ' num2str(MS) ]);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
plot(Archive_F1(:,1),Archive_F1(:,2),'Color','b','LineWidth',4);
hold on
plot(Archive_F(:,1),Archive_F(:,2),'ro','LineWidth',2,...
'MarkerEdgeColor','r',...
'MarkerFaceColor','r',...
'MarkerSize',6);
legend('True PF','Obtained PF');
title('MOMVO FOR Welded beam design PROBLEM');
xlabel('obj_1');
ylabel('obj_2');
hold off
fprintf('%d %20.15f %20.15f %20.15f %20.15f\n',i,GD,S,DELTA,MS);
fprintf('%d %20.15f %20.15f %20.15f %20.15f %20.15f %20.15f\n',i,hv,gd,epsilonNew,spread,generalizedspread,igd);
GGD(i)=GD;
SS(i)=S;
DELTAA(i)=DELTA;
MSS(i)=MS;
hvd(i)=hv;
gdd(i)=gd;
epsilonNewd(i)=epsilonNew;
spreadd(i)=spread;
generalizedspreadd(i)=generalizedspread;
igdd(i)=igd;
end
Min_Generational_distance=min(GGD)
Average_Generational_distance=mean(GGD)
Max_Generational_distance=max(GGD)
SD_Generational_distance=std(GGD)
Min_metric_of_spacing=min(SS)
Average_metric_of_spacing=mean(SS)
Max_metric_of_spacing=max(SS)
SD_metric_of_spacing=std(SS)
Min_Diversity_metric_delta=min(DELTAA)
Average_Diversity_metric_delta=mean(DELTAA)
Max_Diversity_metric_delta=max(DELTAA)
SD_Diversity_metric_delta=std(DELTAA)
Min_metric_of_maximum_spread=min(MSS)
Average_metric_of_maximum_spread=mean(MSS)
Max_metric_of_maximum_spread=max(MSS)
SD_metric_of_maximum_spread=std(MSS)
Min_hypeIndicatorExact8=min(hvd)
Average_hypeIndicatorExact8=mean(hvd)
Max_hypeIndicatorExact8=max(hvd)
SD_hypeIndicatorExact8=std(hvd)
Min_Generational_distance1=min(gdd)
Average_Generational_distance1=mean(gdd)
Max_Generational_distance1=max(gdd)
SD_Generational_distance1=std(gdd)
Min_epsilon=min(epsilonNewd)
Average_epsilon=mean(epsilonNewd)
Max_epsilon=max(epsilonNewd)
SD_epsilon=std(epsilonNewd)
Min_spread=min(spreadd)
Average_spread=mean(spreadd)
Max_spread=max(spreadd)
SD_spread=std(spreadd)
Min_generalizedspread=min(generalizedspreadd)
Average_generalizedspread=mean(generalizedspreadd)
Max_generalizedspread=max(generalizedspreadd)
SD_generalizedspread=std(generalizedspreadd)
Min_IGD=min(igdd)
Average_IGD=mean(igdd)
Max_IGD=max(igdd)
SD_IGD=std(igdd)
Best_universe_score
Best_universe_pos
3 仿真结果
4 参考文献
[1]刘京昕. 多元宇宙优化算法的改进及应用. Diss. 广西民族大学, 2019.
部分理论引用网络文献，若有侵权联系博主删除。
5 MATLAB代码与数据下载地址
见博客主页
