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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 user
maxV = 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 purposes
pres2plot = 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
