pso.m

function [x,fval] = psoProjection(fun,np,lb,ub,inertia,correction_factor,iteration)

%   Editor: Yan Ou
%   Date: 2013/10/07


% set the defualt value for the inertia, correction_factor, iteration
if nargin < 7
    iteration = 50;
    if nargin < 6
        correction_factor = 2;
        if nargin < 5
            inertia = 0.1;
        end
    end
end
if isempty(inertia) == 1
    inertia = 0.1;
end
if isempty(correction_factor) == 1
    correction_factor = 2;
end
% neighborhoodNum = round(np/3); % define the neighborhood number as the calculation of the global best solution

xIni = randint(np,length(lb),[round(lb(1)*1000),round(ub(1)*1000)])/1000;
vIni = randint(np,length(lb),[round(-abs(ub(1)-lb(1)))*1000,round(abs(ub(1)-lb(1)))*1000])/1000;
% vIni = (-abs(ub-lb)*ones(1,np)+(abs(ub-lb)+abs(ub-lb))*rand(np,1)')'; % TODO: improve this function by reducing the computational time
swarm = zeros(np,5,size(xIni,2));
% neighborSwarm = zeros(neighborhoodNum,5,size(xIni,2));
swarm(:,1,:) = xIni;
swarm(:,3,:) = xIni;
swarm(:,2,:) = vIni;
swarm(:,4,1) = 1000000000;
[tempValue, tempIndex] = min(swarm(:, 4, 1));
gbest = swarm(tempIndex, 3, :);
gbestValue = []; % the gather of the gbest values
stopValue = 100; % the stop criteria of the iteration

% run particle swarm optimization algorithm to converge the particle swarm
for iter = 1 : iteration
    % pl, pb, pb_val
    for i = 1 : np
        
        % project the particle which is outside the boundary to inside the boundary
        newParticle = swarm(i, 1, :) + swarm(i, 2, :);
        newParticle = min(newParticle,reshape(ub,1,1,length(lb)));
        newParticle = max(newParticle,reshape(lb,1,1,length(lb)));
        % reset the velocity of the particles
        swarm(i, 2, :) = newParticle - swarm(i,1,:);
        % calculate the new particle position
        swarm(i, 1, :) = newParticle;
        
        val = fun(swarm(i,1,:));          % fitness evaluation (you may replace this objective function with any function having a global minima)
        if val < swarm(i, 4, 1)                 % if new position is better
            swarm(i,3,:) = swarm(i,1,:);
            swarm(i, 4, 1) = val;               % and best value
        end
    end

    % pg
%     swarmPosition = reshape(swarm(:,1,:),np,length(lb));
%     particlePosition = reshape(swarm(i,1,:),1,length(lb));
%     swarmDist = bsxfun(@minus, swarmPosition, particlePosition);
%     swarmDist = sqrt(sum(swarmDist.^2,2));
%     sortDist = sort(swarmDist);
%     threshold = sortDist(neighborhoodNum);
%     neighborSwarm = swarm(swarmDist<=threshold,:,:); % find the neighborhood particles
    [tempValue, tempIndex] = min(swarm(:, 4, 1));        % global best position
    if (tempValue < fun(gbest))
        gbest = swarm(tempIndex, 3, :);
    end
    swarm(i,5,:) = gbest;
    gbestValue(end+1) = fun(gbest);
    
    % velocity
    for i = 1:np
        swarm(i, 2, :) = inertia*swarm(i, 2, :) + correction_factor*rand(1,1,size(xIni,2)).*(swarm(i, 3, :) - swarm(i, 1, :)) + correction_factor*rand(1,1,size(xIni,2)).*(gbest - swarm(i, 1, :));   %x velocity component
    end
    
    % stop criteria
    if iter > 11
        stopValue = sum(log(gbestValue(end-10:end)));
        deltaGbestValue = abs(gbestValue(2:end) - gbestValue(1:end-1));
        deltaGbestValueLog = log(deltaGbestValue(deltaGbestValue~=0));
        if length(deltaGbestValueLog) > 10
            sumDelta = sum(deltaGbestValueLog(end-10:end));
        else
            sumDelta = sum(deltaGbestValueLog);
        end
        if sumDelta < stopValue/2
            break;
        end
    end
end

% return the value
[temp, gbest] = min(swarm(:, 4, 1));
x = swarm(gbest, 1, :);
fval = fun(x);
end