Particle Swarm Optimization PSO

Question

M 2022-12-1

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1868803-particle-swarm-optimization-pso

评论： Walter Roberson 2022-12-1

The following is the PSO code, the varible that the PSO returns is "x" and its size is 7*1 , Can anyone help me how can I put contrains on x to make the x(7) is always equal 1???

% Project Code: YPEA102
% Project Title: Implementation of Particle Swarm Optimization 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
function [x,err]=pso(CostFunction)
% CostFunction= Cost Function
% nVar= Number of Decision Variables
nVar = 1
VarSize=[7 nVar];   % Size of Decision Variables Matrix
VarMin= 0;         % Lower Bound of Variables
VarMax= 1;         % Upper Bound of Variables
%% PSO Parameters
MaxIt=200;      % Maximum Number of Iterations
nPop=300;        % Population Size (Swarm Size)
% PSO Parameters
w=1;            % Inertia Weight
wdamp=0.99;     % Inertia Weight Damping Ratio
c1=1.5;         % Personal Learning Coefficient
c2=2.0;         % Global Learning Coefficient
% If you would like to use Constriction Coefficients for PSO,
% uncomment the following block and comment the above set of parameters.
% % Constriction Coefficients
% phi1=2.05;
% phi2=2.05;
% phi=phi1+phi2;
% chi=2/(phi-2+sqrt(phi^2-4*phi));
% w=chi;          % Inertia Weight
% wdamp=1;        % Inertia Weight Damping Ratio
% c1=chi*phi1;    % Personal Learning Coefficient
% c2=chi*phi2;    % Global Learning Coefficient
% Velocity Limits
VelMax=0.1*(VarMax-VarMin);
VelMin=-VelMax;
%% Initialization
empty_particle.Position=[];
empty_particle.Cost=[];
empty_particle.Velocity=[];
empty_particle.Best.Position=[];
empty_particle.Best.Cost=[];
particle=repmat(empty_particle,nPop,1);
GlobalBest.Cost=inf;
for i=1:nPop
    
    % Initialize Position
    particle(i).Position=unifrnd(VarMin,VarMax,VarSize);
 
    % Initialize Velocity
    particle(i).Velocity=zeros(VarSize);
    
    % Evaluation
    particle(i).Cost=CostFunction(particle(i).Position);
    
    % Update 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
BestCost=zeros(MaxIt,1);
GB_Previous=zeros(MaxIt,1);
%% PSO Main Loop
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,VelMin);
        particle(i).Velocity = min(particle(i).Velocity,VelMax);
        
        % Update Position
        particle(i).Position = particle(i).Position + particle(i).Velocity;
        
        % Velocity Mirror Effect
        IsOutside=(particle(i).Position<VarMin | particle(i).Position>VarMax);
        particle(i).Velocity(IsOutside)=-particle(i).Velocity(IsOutside);
        
        % Apply Position 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
                GB_Previous=GlobalBest.Cost ;
                GlobalBest=particle(i).Best;
                
            end
            
        end
        
    end
    
    BestCost(it)=GlobalBest.Cost;
    
    disp(['Iteration ' num2str(it) ': Best Cost = ' num2str(BestCost(it))]);
    
    w=w*wdamp;
    
    if abs(GlobalBest.Cost-GB_Previous)<= 1e-15
       break
    end
    
end
BestSol = GlobalBest;
x=BestSol.Position;
err=BestSol.Cost;
%% Results
figure;
plot(BestCost,'LineWidth',2);
semilogy(BestCost,'LineWidth',2);
xlabel('Iteration');
ylabel('Best Cost');
grid on;

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Answer 1

Walter Roberson 2022-12-1

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1868803-particle-swarm-optimization-pso#answer_1117683

在 MATLAB Online 中打开

nVar = 1
VarSize=[7 nVar];   % Size of Decision Variables Matrix

Well that is wrong. You do not have 1 variable, you have 7 variables. You should be using

nVar = 7;
VarSize = [nVar, 1];

Then

VarMin= 0;         % Lower Bound of Variables
VarMax= 1;         % Upper Bound of Variables

When you want x(7) to be forced to be 7 you should use

VarMin = [zeros(nVar-1,1); 1];
VarMax = ones(nVar,1);

and change

        % Apply Velocity Limits
        particle(i).Velocity = max(particle(i).Velocity,VelMin);
        particle(i).Velocity = min(particle(i).Velocity,VelMax);
        

to

        % Apply Velocity Limits
        particle(i).Velocity = max(particle(i).Velocity,VelMin(i));
        particle(i).Velocity = min(particle(i).Velocity,VelMax(i));
        

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M 2022-12-1

@Walter Roberson I got the following error:

Index exceeds the number of array elements (7).

Error in pso (line 99)

particle(i).Velocity = max(particle(i).Velocity,VelMin(i));

Walter Roberson 2022-12-1

You are right, you should not be indexing with (i) there, the original code for that section was fine.

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