【多目标优化求解】基于matlab自适应风驱动算法求解多目标优化问题【含Matlab源码 1414期】

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二、部分源代码

function MO_AWDO_v01()
%-------------------------------------------------------------------------tic; clear; close all; clc;
format long g;
%--------------------------------------------------------------ArchiveParetoFronts = [];% User defined parameters:
param.popsize = 100;   % population size.
param.npar = 10;         % Dimension of the problem.
param.maxit = 100;     % Maximum number of iterations.
maximumV = 0.5;             % maximum allowed speed.
%--------------------------------------------------------------% AWDO will select the coefficient values; alpha, RT, g, c, and Vmax:
rec.arx = rand(5,param.popsize);   %consistent with the CMAES indexing
%---------------------------------------------------------------% Initialize WDO population, position and velocity:
% Randomize population position in the range of [-1, 1]:
pos = 2*(rand(param.popsize,param.npar)-0.5);
% Randomize velocity in the range of [-Vmax, Vmax]:
vel = maximumV * 2 * (rand(param.popsize,param.npar)-0.5);
%---------------------------------------------------------------% Evaluate initial population via multi-objective function:
for K=1:param.popsize,
%     [f1,f2] = kursawe(pos(K,:));
%     [f1,f2] = kita(pos(K,:));
%     [f1,f2] = schaffer(pos(K,:));
%     [f1,f2] = ZDT1(pos(K,:));[f1,f2] = ZDT4(pos(K,:));pres(K,:) = [f1,f2];
end
%----------------------------------------------------------------
%
% Call non-dominated sorting to identify the Pareto-front that each particle belongs:
posF=[pos, pres];
f = non_domination_sort_mod(posF, 2,param.npar);  % f = [pos, f1, f2, rank]% extract the rank index, i.e. which Pareto-front the particle belongs:
rank_ind = f(:,param.npar+3);% Select the Pareto-front == 1 particles as Global Best Position:
globalposPOP = f( (f(:,param.npar+3) ==1) , 1:param.npar);
% Archieve the rank 1 particles:
ArchiveParetoFronts = [ArchiveParetoFronts; f( (f(:,param.npar+3) ==1) , 1:(param.npar+2) )];%-----------------------------------------------------------------
% Start iterations :
iter = 1;   % iteration counter
for ij = 2:param.maxit,ij% Update the velocity:for i=1:param.popsize% choose random dimensions:a = randperm(param.npar);                 % choose velocity based on random dimension:velot(i,:) = vel(i,a);% randomly select a globalpos from the 1st Pareto-front members[aa, bb] = size(globalposPOP);globalpos = globalposPOP(round(((aa-1) * rand(1,1)) + 1),:);vel(i,:) = (1-rec.arx(1,i))*vel(i,:)-(rec.arx(2,i)*pos(i,:))+ ...abs(1-1/rank_ind(i))*((globalpos-pos(i,:)).*rec.arx(3,i))+ ...(rec.arx(4,i)*velot(i,:)/rank_ind(i));   end% maxV is optimized by CMAES. Limit it maximumV defined by usermaxV = rec.arx(5,:);maxV = min(maxV, repmat(maximumV, size(rec.arx(5,:),1),  size(rec.arx(5,:),2)) );maxV = max(maxV, repmat(-maximumV, size(rec.arx(5,:),1),  size(rec.arx(5,:),2)) );% Check velocity limits:vel = min(vel, repmat(maxV',1,param.npar));vel = max(vel, -repmat(maxV',1,param.npar));% Update air parcel positions:pos = pos + vel;pos = min(pos, 1.0);pos = max(pos, -1.0); % Evaluate population: (Pressure)for K=1:param.popsize,
%             [f1,f2] = kursawe(pos(K,:));
%             [f1,f2] = kita(pos(K,:));
%             [f1,f2] = schaffer(pos(K,:));
%             [f1,f2] = ZDT1(pos(K,:));[f1,f2] = ZDT4(pos(K,:));pres(K,:) = [f1,f2];end% Call non-dominated sorting to identify the Pareto-front that each particle belongs:posF=[pos, pres];f = non_domination_sort_mod(posF, 2,param.npar);  % f = [pos, f1, f2, rank]% extract the rank index, i.e. which Pareto-front the particle belongs:rank_ind = f(:,param.npar+3);% Select the Pareto-front == 1 particles and add them to the archieve along previous Pareto-fronts:ArchiveParetoFronts = [ArchiveParetoFronts; f( (f(:,param.npar+3) ==1) , 1:(param.npar+2) )];% Run the non-dominated sort among the Archieve members:f = non_domination_sort_mod(ArchiveParetoFronts, 2,param.npar);        % Replace the archieve with only the rank=1 members:ArchiveParetoFronts = f( (f(:,param.npar+3) ==1) , 1:(param.npar+2) );% Use rank=1 members as global position:globalposPOP = f( (f(:,param.npar+3) ==1) , 1:param.npar);  %--------------------------------% call CMAES [rec] = purecmaes_wdo(ij,rec,param.popsize,pres(:, mod(ij,2)+1));%%% PRES has two values, pass one of the pres values at each iter%%% alternating between two.%----------------------------------------------------end%%% PLOT RESULTS:% Call non-dominant sorting:f = non_domination_sort_mod(ArchiveParetoFronts, 2,param.npar);% Plot the MO-results -- debugging purposespres2plot = f( (f(:,param.npar+3) ==1) , param.npar+1 : param.npar+2);plot(pres2plot(:,1), pres2plot(:,2),'ko')xlabel('F1'); ylabel('F2')grid on
%         save('Results.mat','pres2plot')hold on% load the known-Pareto-front data for plotting:z = load('paretoZDT4.dat');[a,b]=sort(z(:,2));z = z(b,:);plot(z(:,1),z(:,2),'-k')end
% end-of-WDO.%----------------------------------------------------------------------
%----------------------------------------------------------------------
%----------------------------------------------------------------------

三、运行结果

四、matlab版本及参考文献

1 matlab版本
2014a

2 参考文献
《智能优化算法及其MATLAB实例（第2版）》包子阳余继周杨杉著电子工业出版社

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