粒子群优化算法—Matlab

PSO算法

clc;
clear ;
close ;
%%  Problem Definition

CostFunction = @(x) sphere(x);  % Cost Function

nVar = 5;                       % Dimension of Decision Variables

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

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

%%  Parameters of PSO

MaxIt = 1000;            % Maximum Number of Iterations

nPop = 50;               % Population Size 

w  = 1;                  % Inertia Coefficient
wdamp = 0.81;            % Damping Ratio of Inertia Coefficient
c1 = 2;                  % Personal Acceleration Coefficient
c2 = 2;                  % Social Acceleration Coefficient

%%  Initialization

% The Patticle Template
empty_partical.Position = [];
empty_partical.Velocity = [];
empty_partical.Cost = [];
empty_partical.Best.Position = [];
empty_partical.Best.Cost = [];

% Create Population Array
particle = repmat(empty_partical,nPop,1);

% Initialize Global Best
GlobalBest.Cost = inf;

% Iniitialize 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
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);
        % Update Position
        particle(i).Position = particle(i).Position + particle(i).Velocity;

        % 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
    disp(['Iteration ' num2str(it) ': Best Cost = ' num2str(BestCosts(it))]);

    % Damping Inertia Coefficient
    w = w * wdamp;

end

%%  Results

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

测试函数

function z = sphere(x)
%%  目标函数
    z = sum(x.^2);
end