PSO-constrained optimization

问题描述：

用PSO优化多目标约束问题

文件目录：

PSO.m

ObjectiveFunction.m

DrawLandscape.m

PSO.m
clear all
close all
clc

%define the details of this problem
nVar = 2;
ub = [10 10];
lb = [-10 -10];
fobj = @ObjectiveFunction;

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

%initialise the particles
for k = 1 : noP
    Swarm.Particles(k).X = (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
    %calculate 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);
        Swarm.Particles(k).X = Swarm.Particles(k).X + Swarm.Particles(k).V;
        index1 = find(Swarm.Particles(k).X > ub);     %check positions
        index2 = find(Swarm.Particles(k).V < lb);
        Swarm.Particles(k).X(index1) = ub(index1);
        Swarm.Particles(k).X(index2) = lb(index2);
    end

    outmsg = ['Iteration#' , num2str(t) , 'Swarm.GBEST.O = ' , num2str(Swarm.GBEST.O)];
    disp(outmsg);
    cgCurve(t) = Swarm.GBEST.O;
end

semilogy(cgCurve);

ObjectiveFunction.m
function[o] = ObjectiveFunction(x)

%List of your constraints
const1 = x(2) <= 3.2 || x(2) >= 6.4;
const2 = (x(1)^2 + x(2)^2) >= 1;
const3 = x(1) ~= x(2);

if const1 == 1 && const2 == 1 && const3 == 1
    o = sum(x.^2);
else
    o = sum(x.^2) + 200;
end

end

DrawLandscape.m
%Visualise the landscape
fobj = @ObjectiveFunction
x = -10 : 0.05 : 10;
y = -10 : 0.05 : 10;
[x_new , y_new] = meshgrid(x,y);     %生成绘制3D图形所需的网格数据
for i = 1 : size(x_new , 1)       
    for j =1 : size(x_new , 2)
        currentX = [ x_new(i,j), y_new(i,j) ];
        o(i,j) = fobj(currentX);
    end
end

surfc(x_new , y_new , o)
shading interp
camlight

xlabel('x_1')
ylabel('x_2')

结果：

Iteration#491Swarm.GBEST.O = 1
Iteration#492Swarm.GBEST.O = 1
Iteration#493Swarm.GBEST.O = 1
Iteration#494Swarm.GBEST.O = 1
Iteration#495Swarm.GBEST.O = 1
Iteration#496Swarm.GBEST.O = 1
Iteration#497Swarm.GBEST.O = 1
Iteration#498Swarm.GBEST.O = 1
Iteration#499Swarm.GBEST.O = 1
Iteration#500Swarm.GBEST.O = 1
>> Swarm.GBEST.X

ans =

    0.8900   -0.4559

对结果分析：

有 landscape 及 const2 = (x1^2+x2^2) >=1 , Swarm.GBEST.O = 1 且 Swarm.GBEST.X 的 x1^2+x2^2 接近 1，故此优化结果可靠准确

心得：

1. 对目标约束问题的求解，PSO.m部分与TableDesignProblem的PSO.m部分几乎一致;

2. 多目标优化的代码部分体现在ObjectiveFunction的设计中，引入惩罚函数;

3. meshgrid();%生成绘制3D图形所需的网格数据，并对网格点采样，在三维图形中画出目标函数的landscape

PSO-constrained optimization

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