【优化算法】多目标粘菌算法（MOSMA）【含Matlab源码 1597期】

一、获取代码方式

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二、部分源代码

%% Multiple Objective Slime Mould Algorithm (MOSMA)%% Objective Function
% The objective function description contains information about the
% objective function. M is the dimension of the objective space, D is the
% dimension of decision variable space, LB and UB are the
% range for the variables in the decision variable space. User has to
% define the objective functions using the decision variables. Make sure to
% edit the function 'evaluate_objective' to suit your needs.
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 == 2plot(Obtained_Pareto(:,1),Obtained_Pareto(:,2),'o','LineWidth',2,...'MarkerEdgeColor','r','MarkerSize',2);hold onplot(True_Pareto(:,1),True_Pareto(:,2),'k'); title('Optimal Solution Pareto Set using MOSMA');legend('MOSMA');xlabel('F_1');ylabel('F_2');
elseif M == 3plot3(Obtained_Pareto(:,1),Obtained_Pareto(:,2),Obtained_Pareto(:,3),'o','LineWidth',2,...'MarkerEdgeColor','r','MarkerSize',2);hold onplot3(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)]);
function [Score,PopObj] = HV(PopObj,PF)
% <metric> <max>
% Hypervolume%% Normalize the population according to the reference point set[N,M]  = size(PopObj);fmin   = min(min(PopObj,[],1),zeros(1,M));fmax   = max(PF,[],1);PopObj = (PopObj-repmat(fmin,N,1))./repmat((fmax-fmin)*1.1,N,1);PopObj(any(PopObj>1,2),:) = [];% The reference point is set to (1,1,...)RefPoint = ones(1,M);if isempty(PopObj)Score = 0;elseif M < 4% Calculate the exact HV valuepl = sortrows(PopObj);S  = {1,pl};for k = 1 : M-1S_ = {};for i = 1 : size(S,1)Stemp = Slice(cell2mat(S(i,2)),k,RefPoint);for j = 1 : size(Stemp,1)temp(1) = {cell2mat(Stemp(j,1))*cell2mat(S(i,1))};temp(2) = Stemp(j,2);S_      = Add(temp,S_);endendS = S_;endScore = 0;for i = 1 : size(S,1)p     = Head(cell2mat(S(i,2)));Score = Score + cell2mat(S(i,1))*abs(p(M)-RefPoint(M));endelse% Estimate the HV value by Monte Carlo estimationSampleNum = 1000000;MaxValue  = RefPoint;MinValue  = min(PopObj,[],1);Samples   = unifrnd(repmat(MinValue,SampleNum,1),repmat(MaxValue,SampleNum,1));if gpuDeviceCount > 0% GPU accelerationSamples = gpuArray(single(Samples));PopObj  = gpuArray(single(PopObj));endfor i = 1 : size(PopObj,1)drawnow();domi = true(size(Samples,1),1);m    = 1;while m <= M && any(domi)domi = domi & PopObj(i,m) <= Samples(:,m);m    = m + 1;endSamples(domi,:) = [];endScore = prod(MaxValue-MinValue)*(1-size(Samples,1)/SampleNum);end
end

三、运行结果

四、matlab版本及参考文献

1 matlab版本
2014a

2 参考文献
[1] 包子阳,余继周,杨杉.智能优化算法及其MATLAB实例（第2版）[M].电子工业出版社，2016.
[2]张岩,吴水根.MATLAB优化算法源代码[M].清华大学出版社，2017.

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