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‎Main.m‎

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clear all
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close all
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clc
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%% Author
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% Author : Federico Giai Pron
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% Mail : federico.giaipron@gmail.com
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% Avilability : support, projects / thesis development, script /
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% codes / controls writing, etc.
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% Experience : automotive, controls, modelling, finite element method,
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% optimization, etc.
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%% Input
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% Strategy
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% 1: 1D minimization test case
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% 2: 2D minimization test case
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% 3: 1D maximization test case
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% 4: 2D maximization test case
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Data.Function = 4;
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% Problem size
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switch Data.Function
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case 1
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Sett.Type = 'min';
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Sett.LengthX = 1;
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case 2
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Sett.Type = 'min';
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Sett.LengthX = 2;
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case 3
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Sett.Type = 'max';
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Sett.LengthX = 1;
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case 4
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Sett.Type = 'max';
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Sett.LengthX = 2;
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end
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% Optimization variables limits
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XLim(1,:) = -1000*ones(1,Sett.LengthX);
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XLim(2,:) = +1000*ones(1,Sett.LengthX);
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% Settings
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Sett.NumPop = 5;
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Sett.NumChr = 5;
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Sett.NumIter = 2000;
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Sett.FlagPlots = true;
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%% Run GA
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[Results.Xpbest,Results.ObjFunpbest,Data] = Optimization_GA_v01(XLim, Sett, Data);
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%% Plot
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run('MainPlot.m');

‎MainPlot.m‎

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%% Author
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% Author : Federico Giai Pron (federico.giaipron@gmail.com)
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% Mail : federico.giaipron@gmail.com
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%% Plot
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% 1D
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if(Data.Function == 1 || Data.Function == 3)
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NPlot = 250;
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XPlot = linspace(XLim(1,1),XLim(2,1),NPlot);
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ObjFunPlot = zeros(1,NPlot);
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for IndexPlot = 1:1:NPlot
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ObjFunPlot(IndexPlot) = ObjFun_fun(XPlot(IndexPlot),Data);
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end
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figure;
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plot(XPlot,ObjFunPlot,'Linewidth',1.5);
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hold on;
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plot(Results.Xpbest,Results.ObjFunpbest,'ro','Linewidth',5,'MarkerFaceColor','r');
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title('Optimum point');
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xlabel('X');
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ylabel('ObjFun');
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grid on;
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end
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% 2D
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if(Data.Function == 2 || Data.Function == 4)
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NPlot = 50;
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XPlot1 = linspace(XLim(1,1),XLim(2,1),NPlot);
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XPlot2 = linspace(XLim(1,2),XLim(2,2),NPlot);
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ObjFunPlot = zeros(NPlot,NPlot);
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for IndexPlot1 = 1:1:NPlot
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for IndexPlot2 = 1:1:NPlot
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ObjFunPlot(IndexPlot1,IndexPlot2) = ObjFun_fun([XPlot1(IndexPlot1),XPlot2(IndexPlot2)],Data);
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end
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end
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figure;
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surf(XPlot1,XPlot2,ObjFunPlot);
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hold on;
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scatter3(Results.Xpbest(1),Results.Xpbest(2),Results.ObjFunpbest,150,'filled','r');
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title('Optimum point');
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xlabel('X_{1}');
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ylabel('X_{2}');
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zlabel('ObjFun');
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colorbar;
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grid on;
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view([3,3,6]);
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end

‎ObjFun_fun.m‎

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%% Author
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% Author : Federico Giai Pron (federico.giaipron@gmail.com)
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% Mail : federico.giaipron@gmail.com
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%% Objective function
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function [ObjFun] = ObjFun_fun(X, Data)
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switch Data.Function
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case 1
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ObjFun = +(X-27)^2+25;
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case 2
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ObjFun = +(X(1)-50)^2+(X(2)-25)^2+100;
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case 3
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ObjFun = -(X-27)^2-25;
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case 4
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ObjFun = -(X(1)-50)^2-(X(2)-25)^2-100;
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end
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end

‎Optimization_GA_v01.m‎

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%% Author
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% Author : Federico Giai Pron (federico.giaipron@gmail.com)
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% Mail : federico.giaipron@gmail.com
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%% Genetic algorithm (GA)
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function [Xpbest, ObjFunpbest, Data] = Optimization_GA_v01(XLim, Sett, Data)
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% Initialization
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X = zeros(Sett.NumChr,Sett.LengthX);
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Xcbest = zeros(1,Sett.LengthX);
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Xpbest = zeros(1,Sett.LengthX);
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ObjFun = zeros(Sett.NumChr,1);
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ObjFuncbestPlot = zeros(Sett.NumPop,Sett.NumIter);
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switch Sett.Type
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case 'min'
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ObjFunpbest = +inf;
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ObjFunpbestPlot = +inf*ones(1,Sett.NumIter);
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case 'max'
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ObjFunpbest = -inf;
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ObjFunpbestPlot = -inf*ones(1,Sett.NumIter);
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end
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% Calculation
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for IndexPop = 1:1:Sett.NumPop
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fprintf('- IndexPop: %3i out of %3i\n',IndexPop,Sett.NumPop);
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% X initialization
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for IndexChr = 1:1:Sett.NumChr
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for IndexX = 1:1:Sett.LengthX
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X(IndexChr,IndexX) = XLim(1,IndexX) + (XLim(2,IndexX) - XLim(1,IndexX))*rand(1);
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end
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end
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% Iteration
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for IndexIter = 1:1:Sett.NumIter
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fprintf('-- IndexIter: %3i out of %3i\n',IndexIter,Sett.NumIter);
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% ObjFun calculation
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for IndexChr = 1:1:Sett.NumChr
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fprintf('--- IndexChr: %3i out of %3i\n',IndexChr,Sett.NumChr);
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ObjFun(IndexChr) = ObjFun_fun(X(IndexChr,:),Data);
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end
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% Natural selection
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switch Sett.Type
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case 'min'
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[~,Indexc] = sort(ObjFun,'ascend');
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case 'max'
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[~,Indexc] = sort(ObjFun,'descend');
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end
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ObjFuncbest = ObjFun(Indexc(1));
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Xcbest = X(Indexc(1),:);
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% Xcbest and ObjFuncbest output
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fprintf('-- ObjFuncbest: %-+1.10e,',ObjFuncbest);
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for IndexX = 1:1:Sett.LengthX
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if(IndexX < Sett.LengthX)
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fprintf(' Xcbest(%i) = %-+1.10d,',IndexX,Xcbest(IndexX));
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else
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fprintf(' Xcbest(%i) = %-+1.10d\n',IndexX,Xcbest(IndexX));
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end
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end
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% Uniform crossover
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for IndexChr = 1:1:Sett.NumChr
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for IndexX = 1:1:Sett.LengthX
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Coin = round(rand(1));
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IndexParent = randi(2);
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if(IndexChr ~= Indexc(1) && IndexChr ~= Indexc(2) && Coin == true)
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X(IndexChr,IndexX) = X(Indexc(IndexParent),IndexX);
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end
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end
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end
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% Mutation
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for IndexX = 1:1:Sett.LengthX
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Coin = round(rand(1));
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if(Coin == true)
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X(Indexc(end),IndexX) = XLim(1,IndexX) + (XLim(2,IndexX) - XLim(1,IndexX))*rand(1);
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end
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end
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% Plot
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ObjFuncbestPlot(IndexPop,IndexIter) = ObjFuncbest;
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switch Sett.Type
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case 'min'
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if(ObjFuncbest < ObjFunpbestPlot(IndexIter))
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ObjFunpbestPlot(IndexIter) = ObjFuncbest;
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end
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case 'max'
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if(ObjFuncbest > ObjFunpbestPlot(IndexIter))
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ObjFunpbestPlot(IndexIter) = ObjFuncbest;
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end
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end
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end
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% Xpbest and ObjFunpbest determination
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switch Sett.Type
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case 'min'
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if(ObjFuncbest < ObjFunpbest)
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Xpbest = Xcbest;
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ObjFunpbest = ObjFuncbest;
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end
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case 'max'
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if(ObjFuncbest > ObjFunpbest)
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Xpbest = Xcbest;
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ObjFunpbest = ObjFuncbest;
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end
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end
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% Xpbest and ObjFunpbest output
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fprintf('- ObjFunpbest: %-+1.10e,',ObjFunpbest);
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for IndexX = 1:1:Sett.LengthX
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if(IndexX < Sett.LengthX)
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fprintf(' Xpbest(%i) = %-+1.10d,',IndexX,Xpbest(IndexX));
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else
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fprintf(' Xpbest(%i) = %-+1.10d\n',IndexX,Xpbest(IndexX));
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end
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end
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end
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%% Plot
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if(Sett.FlagPlots == true)
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figure;
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semilogy(ObjFunpbestPlot,'LineWidth',10);
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for IndexPop = 1:1:Sett.NumPop
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hold on;
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semilogy(ObjFuncbestPlot(IndexPop,:),'LineWidth',1.5);
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title('Objective function optimization');
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xlabel('NumIter');
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ylabel('ObjFun_{c,best}(Pop)');
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grid on;
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end
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end
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end

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