پیدا کردن کمینه تابع Egg Holder با الگوریتم بهینه‌ سازی اجتماع ذرات

x1 = xx(1);
x2 = xx(2);
Temp1 = -(x2+47) * sin(sqrt(abs(x2+x1/2+47)));
Temp2 = -x1 * sin(sqrt(abs(x1-(x2+47))));
y = Temp1 + Temp2;

function [y] = egg(xx)

x1 = xx(1);
x2 = xx(2);
Temp1 = -(x2+47) * sin(sqrt(abs(x2+x1/2+47)));
Temp2 = -x1 * sin(sqrt(abs(x1-(x2+47))));
y = Temp1 + Temp2;

end

clc;
clear;
close all;

%% Problem Definiton

problem.CostFunction = @(x) egg(x);  % Cost Function
problem.nVar = 2;       % Number of Unknown (Decision) Variables
problem.VarMin =  -512;  % Lower Bound of Decision Variables
problem.VarMax =  512;   % Upper Bound of Decision Variables

%% Parameters of PSO

params.MaxIt = 1000;                          % Maximum Number of Iterations
params.nPop = 25;                            % Population Size (Swarm Size)                                

% Intertia Coefficient                         
% Damping Ratio of Inertia Coefficient
params.c1 = 2;                               % Personal Acceleration Coefficient
params.c2 = 3;                               % Social Acceleration Coefficient
params.w = 1.4;
params.MaxVelocity=0.1*(problem.VarMax-problem.VarMin);      % maxVelocity of particles
params.MinVelocity=-0.1*(problem.VarMax-problem.VarMin);     % minVelocity of particles
params.ShowIterInfo = true;                  % Flag for Showing Iteration Informatin
params.wdamp = 0.99;
%% Calling PSO

out = PSO(problem, params);

BestSol = out.BestSol;
BestCosts = out.BestCosts;

%% Results

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

function out = PSO(problem, params)
    %% Problem Definiton

    CostFunction = problem.CostFunction;  % Cost Function

    nVar = problem.nVar;        % Number of Unknown (Decision) Variables

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

    VarMin = problem.VarMin;	% Lower Bound of Decision Variables
    VarMax = problem.VarMax;    % Upper Bound of Decision Variables
    %% Parameters of PSO
    MaxIt = params.MaxIt;   % Maximum Number of Iterations
    nPop = params.nPop;     % Population Size (Swarm Size)
    w = params.w;           % Intertia Coefficient
    wdamp = params.wdamp;   % Damping Ratio of Inertia Coefficient
    c1 = params.c1;         % Personal Acceleration Coefficient
    c2 = params.c2;         % Social Acceleration Coefficient
    % The Flag for Showing Iteration Information
    ShowIterInfo = params.ShowIterInfo;    
    MaxVelocity =params.MaxVelocity; 
    MinVelocity =params.MinVelocity; 
   %% Initialization
    % The Particle Template
    empty_particle.Position = [];
    empty_particle.Velocity = [];
    empty_particle.Cost = [];
    empty_particle.Best.Position = [];
    empty_particle.Best.Cost = [];
    % Create Population Array
    particle = repmat(empty_particle, nPop, 1);
    % Initialize Global Best
    GlobalBest.Cost = inf;
    % Initialize Population Members
    for i=1:nPop

        % Generate Random Solution
        particle(i).Position = unifrnd(VarMin, VarMax, VarSize);

        % Initialize Velocity
        particle(i).Velocity = zeros(VarSize);

        % Evaluation
        particle(i).Cost = CostFunction(particle(i).Position);

        % Update the Personal Best
        particle(i).Best.Position = particle(i).Position;
        particle(i).Best.Cost = particle(i).Cost;

        % Update Global Best
        if particle(i).Best.Cost < GlobalBest.Cost
            GlobalBest = particle(i).Best;
        end

    end

    % Array to Hold Best Cost Value on Each Iteration
    BestCosts = zeros(MaxIt, 1);


    %% Main Loop of PSO

    for it=1:MaxIt

        for i=1:nPop

            % Update Velocity
            particle(i).Velocity = w*particle(i).Velocity ...
                + c1*rand(VarSize).*(particle(i).Best.Position - particle(i).Position) ...
                + c2*rand(VarSize).*(GlobalBest.Position - particle(i).Position);

            % Apply Velocity Limits
            particle(i).Velocity = max(particle(i).Velocity, MinVelocity);
            particle(i).Velocity = min(particle(i).Velocity, MaxVelocity);
            
            % Update Position
            particle(i).Position = particle(i).Position + particle(i).Velocity;
            
            % Apply Lower and Upper Bound Limits
            particle(i).Position = max(particle(i).Position, VarMin);
            particle(i).Position = min(particle(i).Position, VarMax);

            % Evaluation
            particle(i).Cost = CostFunction(particle(i).Position);

            % Update Personal Best
            if particle(i).Cost < particle(i).Best.Cost

                particle(i).Best.Position = particle(i).Position;
                particle(i).Best.Cost = particle(i).Cost;

                % Update Global Best
                if particle(i).Best.Cost < GlobalBest.Cost
                    GlobalBest = particle(i).Best;
                end            

            end

        end
        % Store the Best Cost Value
        BestCosts(it) = GlobalBest.Cost;
        
        %% 
        % Display Iteration Information
        if ShowIterInfo
            disp(['Iteration ' num2str(it) ': Best Cost = ' num2str(BestCosts(it))]);
        end

        % Damping Inertia Coefficient
        w = w * wdamp;

    end
    
    out.pop = particle;
    out.BestSol = GlobalBest;
    out.BestCosts = BestCosts;
    
end

clc
clear all
close all
%% [-۶۵٫۵۳۶, ۶۵٫۵۳۶
x1=-512:1:512; 
x2=-512:1:512;
for i=1:length(x1)
    
    for j=1:length(x2)
y(i,j)=egg([x1(i) x2(j)]);
    end
end
meshc(x1,x2,y) % Plot 3-D function
colorbar
xlabel('x1')
ylabel('x2')
zlabel('y')