nsga2.m

clc;
clear;
close all;

%% Problem Definition

CostFunction=@(x) Objectives(x)        %Objectives;

nVar=3;   %1          % Number of Decision Variables

VarSize=[1 nVar];   % Size of Decision Variables Matrix

VarMin=1.5; %1.5  %az -5        % Lower Bound of Variables
VarMax=2;  %5   % Upper Bound of Variables

% Number of Objective Functions
nObj=numel(CostFunction(unifrnd(VarMin,VarMax,VarSize)));


%% NSGA-II Parameters

MaxIt=100 %50;     %100 % Maximum Number of Iterations

nPop=5  %50      % Population Size

pCrossover=0.4;         %0.7                % Crossover Percentage
nCrossover=2*round(pCrossover*nPop/2);  % Number of Parnets (Offsprings)

pMutation=0.7;             %0.4             % Mutation Percentage
nMutation=round(pMutation*nPop);        % Number of Mutants

mu=0.02;       %0.02             % Mutation Rate

sigma=0.1*(VarMax-VarMin);  % Mutation Step Size


%% Initialization

empty_individual.Position=[];
empty_individual.Cost=[];
empty_individual.Rank=[];
empty_individual.DominationSet=[];
empty_individual.DominatedCount=[];
empty_individual.CrowdingDistance=[];

pop=repmat(empty_individual,nPop,1);

for i=1:nPop
    
    pop(i).Position=unifrnd(VarMin,VarMax,VarSize);
    
    pop(i).Cost=CostFunction(pop(i).Position);
    
end

% Non-Dominated Sorting
[pop F]=NonDominatedSorting(pop);

% Calculate Crowding Distance
pop=CalcCrowdingDistance(pop,F);

% Sort Population
[pop F]=SortPopulation(pop);


%% NSGA-II Main Loop

for it=1:MaxIt
    
    % Crossover
    popc=repmat(empty_individual,nCrossover/2,2);
    for k=1:nCrossover/2
        
        i1=randi([1 nPop]);
        p1=pop(i1);
        
        i2=randi([1 nPop]);
        p2=pop(i2);
        
        [popc(k,1).Position popc(k,2).Position]=Crossover(p1.Position,p2.Position);
        
        popc(k,1).Cost=CostFunction(popc(k,1).Position);
        popc(k,2).Cost=CostFunction(popc(k,2).Position);
        
    end
    popc=popc(:);
    
    % Mutation
    popm=repmat(empty_individual,nMutation,1);
    for k=1:nMutation
        
        i=randi([1 nPop]);
        p=pop(i);
        
        popm(k).Position=Mutate(p.Position,mu,sigma);
        
        popm(k).Cost=CostFunction(popm(k).Position);
        
    end
    
    % Merge
    pop=[pop
         popc
         popm];
     
    % Non-Dominated Sorting
    [pop F]=NonDominatedSorting(pop);

    % Calculate Crowding Distance
    pop=CalcCrowdingDistance(pop,F);

    % Sort Population
    [pop F]=SortPopulation(pop);
    
    % Truncate
    pop=pop(1:nPop);
    
    % Non-Dominated Sorting
    [pop F]=NonDominatedSorting(pop);

    % Calculate Crowding Distance
    pop=CalcCrowdingDistance(pop,F);

    % Sort Population
    [pop F]=SortPopulation(pop);
    
    % Store F1
    F1=pop(F{1});
    
    % Show Iteration Information
    disp(['Iteration ' num2str(it) ': Number of F1 Members = ' num2str(numel(F1))]);
    
    % Plot F1 Costs
    figure(1);
    PlotCosts(F1);
    
end

%% Results