BPSO-Discrete optimization(1)

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问题描述：

目标函数o=sum(x.^2)，X的值取0/1，选取BPSO优化

文件目录：

BPSO.m

ObjectiveFunction.m

BPSO.m
clear all
close all
clc

% Define the details of the binary optimization problem
nVar = 20 ; 
ub =ones(1,nVar);
lb = zeros(1,nVar);
fobj = @ObjectiveFunction; 

% Define the PSO's paramters 
noP = 30;
maxIter = 500;
wMax = 0.9;
wMin = 0.2;
c1 = 2;
c2 = 2;
vMax = (ub - lb) .* 0.2; 
vMin  = -vMax;

% Initialize the particles 
for k = 1 : noP
    Swarm.Particles(k).X = round ( (ub-lb) .* rand(1,nVar) + lb ); 
    Swarm.Particles(k).V = zeros(1, nVar); 
    Swarm.Particles(k).PBEST.X = zeros(1,nVar); 
    Swarm.Particles(k).PBEST.O = inf; 
    Swarm.GBEST.X = zeros(1,nVar);
    Swarm.GBEST.O = inf;
end

% Main loop
for t = 1 : maxIter 
    % Calcualte the objective value
    for k = 1 : noP
        currentX = Swarm.Particles(k).X;
        Swarm.Particles(k).O = fobj(currentX);          
        if Swarm.Particles(k).O < Swarm.Particles(k).PBEST.O     %update the PBEST
            Swarm.Particles(k).PBEST.X = currentX;
            Swarm.Particles(k).PBEST.O = Swarm.Particles(k).O;
        end
        if Swarm.Particles(k).O < Swarm.GBEST.O                  %update the GBEST
            Swarm.GBEST.X = currentX;
            Swarm.GBEST.O = Swarm.Particles(k).O;
        end
    end
    
    % Update the X and V vectors 
    w = wMax - t .* ((wMax - wMin) / maxIter);
    for k = 1 : noP
        Swarm.Particles(k).V = w .* Swarm.Particles(k).V + c1 .* rand(1,nVar) .* (Swarm.Particles(k).PBEST.X - Swarm.Particles(k).X) ...
                                                         + c2 .* rand(1,nVar) .* (Swarm.GBEST.X - Swarm.Particles(k).X);
        index1 = find(Swarm.Particles(k).V > vMax);             % Check velocities 
        index2 = find(Swarm.Particles(k).V < vMin);
        Swarm.Particles(k).V(index1) = vMax(index1);
        Swarm.Particles(k).V(index2) = vMin(index2);
       % Sigmoid transfer function 
       s = 1 ./ (1 + exp(Swarm.Particles(k).V)); 
       for d = 1 : nVar                                         % Update position 
            r = rand(); 
            if r < s(d)
                Swarm.Particles(k).X(d) = 0;
            else
                Swarm.Particles(k).X(d) = 1;
            end
       end
    end
    outmsg = ['Iteration# ', num2str(t) , ' Swarm.GBEST.O = ' , num2str(Swarm.GBEST.O)];
    disp(outmsg);
    cgCurve(t) = Swarm.GBEST.O;
end
 
semilogy(cgCurve);
xlabel('Iteration#')
ylabel('Weight')

ObjectiveFunction.m
function [ o ] = ObjectiveFunction ( x )
o = sum (x .^ 2);  % Sphere test function 
end

结果：

Iteration# 164 Swarm.GBEST.O = 1
Iteration# 165 Swarm.GBEST.O = 1
Iteration# 166 Swarm.GBEST.O = 1
Iteration# 167 Swarm.GBEST.O = 0
Iteration# 168 Swarm.GBEST.O = 0
Iteration# 169 Swarm.GBEST.O = 0
Iteration# 170 Swarm.GBEST.O = 0
Iteration# 171 Swarm.GBEST.O = 0
Iteration# 172 Swarm.GBEST.O = 0
Iteration# 173 Swarm.GBEST.O = 0

心得：

      1. varible的值只有0和1，ub, lb, Swarm.Particles(k).X均要做出调整;

      2. 在PSO.m中，原迭代式X和V的关系要通过sigmoid函数建立s(V)并将s的值映射到X