bbo_tripod.m

%
% Copyright (c) 2015, Yarpiz (www.yarpiz.com)
% All rights reserved. Please read the "license.txt" for license terms.
%
% Project Code: YPEA113
% Project Title: Biogeography-Based Optimization (BBO) in MATLAB
% Publisher: Yarpiz (www.yarpiz.com)
% 
% Developer: S. Mostapha Kalami Heris (Member of Yarpiz Team)
% 
% Contact Info: sm.kalami@gmail.com, info@yarpiz.com
%

clc;
clear;
close all;

%% Problem Definition

CostFunction=@(x,y) Tripod_fn(x,y);        % Cost Function

nVar=2;             % Number of Decision Variables

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

VarMin=-10;         % Decision Variables Lower Bound
VarMax= 10;         % Decision Variables Upper Bound

%% BBO Parameters

MaxIt=1000;          % Maximum Number of Iterations

nPop=50;            % Number of Habitats (Population Size)

KeepRate=0.2;                   % Keep Rate
nKeep=round(KeepRate*nPop);     % Number of Kept Habitats

nNew=nPop-nKeep;                % Number of New Habitats

% Migration Rates
mu=linspace(1,0,nPop);          % Emmigration Rates
lambda=1-mu;                    % Immigration Rates

alpha=0.9;

pMutation=0.1;

sigma=0.02*(VarMax-VarMin);

%% Initialization

% Empty Habitat
habitat.Position=[];
habitat.Cost=[];

% Create Habitats Array
pop=repmat(habitat,nPop,1);

% Initialize Habitats
for i=1:nPop
    pop(i).Position=unifrnd(VarMin,VarMax,VarSize);
    pop(i).Cost=CostFunction(pop(i).Position(1),pop(i).Position(2));
end

% Sort Population
[~, SortOrder]=sort([pop.Cost]);
pop=pop(SortOrder);

% Best Solution Ever Found
BestSol=pop(1);

% Array to Hold Best Costs
BestCost=zeros(MaxIt,1);

%% BBO Main Loop

for it=1:MaxIt
    
    newpop=pop;
    for i=1:nPop
        for k=1:nVar
            % Migration
            if rand<=lambda(i)
                % Emmigration Probabilities
                EP=mu;
                EP(i)=0;
                EP=EP/sum(EP);
                
                % Select Source Habitat
                j=RouletteWheelSelection(EP);
                
                % Migration
                newpop(i).Position(k)=pop(i).Position(k) ...
                    +alpha*(pop(j).Position(k)-pop(i).Position(k));
                
            end
            
            % Mutation
            if rand<=pMutation
                newpop(i).Position(k)=newpop(i).Position(k)+sigma*randn;
            end
        end
        
        % Apply Lower and Upper Bound Limits
        newpop(i).Position = max(newpop(i).Position, VarMin);
        newpop(i).Position = min(newpop(i).Position, VarMax);
        
        % Evaluation
        newpop(i).Cost=CostFunction(newpop(i).Position(1),newpop(i).Position(2));
    end
    
    % Sort New Population
    [~, SortOrder]=sort([newpop.Cost]);
    newpop=newpop(SortOrder);
    
    % Select Next Iteration Population
    pop=[pop(1:nKeep)
         newpop(1:nNew)];
     
    % Sort Population
    [~, SortOrder]=sort([pop.Cost]);
    pop=pop(SortOrder);
    
    % Update Best Solution Ever Found
    BestSol=pop(1);
    
    % Store Best Cost Ever Found
    BestCost(it)=BestSol.Cost;
    
    % Show Iteration Information
    disp(['Iteration ' num2str(it) ': Best Cost = ' num2str(BestCost(it))]);
    
end

%% Results

figure;
%plot(BestCost,'LineWidth',2);
semilogy(BestCost,'LineWidth',2);
xlabel('Iteration');
ylabel('Best Cost');
grid on;