How to implement theses constraints in the cost function ?

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Anwar 2022-11-16

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评论： Anwar 2022-11-17

I am working on a constrained PSO program (S decision variable) where the constraints are arrays that there elements should be lower or egual to 0.4 :

1) dx = [S(1) - 0.3, diff(S)];

2) ds = [0.3 - S(1),S(1:end-1)-S(2:end)];

abs(dx)<=0.4

abs(ds)<=0.4

in a simpler way,dx and ds should be arrays with elements that are less or egual to 0.4

i tried this : le(abs(dx),0.4)

le(abs(ds),0.4)

but when runing the main pso i dont see constrained results

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Matt J 2022-11-16

i tried this

Where? How? pso() doesn't have an input for such constraints. Maybe use ga() or patternsearch(). Also, the constraints are linear, so you should put them in the form A*S<=b.

Matt J 2022-11-16

Also, from your expressions we can see that dx=-ds. Therefore, the constraints, abs(dx)<=0.4 and abs(ds)<=0.4 are the same thing.

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回答（1 个）

Matt J 2022-11-16

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编辑：Matt J 2022-11-16

在 MATLAB Online 中打开

pso() doesn't have an input for such constraints. Maybe use ga() or patternsearch().

Here's how it would look when solved with ga():

lb=-inf(nvars,1); 
ub=-lb;
e=0.4*ones(nvars-1,1);
D=diff(eye(nvars));
%constraint matrices
lb(1)=-0.1;  
ub(1)=0.7;
A=[D;-D];
b=[e;e];
%run optimization
S = ga(fun,nvars,A,b,[],[],lb,ub)

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Anwar 2022-11-16

For sure ,Here's the Pso's Script

CostFunction =@costfunction; % Cost Function

nVar = 10; % Number of Decision Variables

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

VarMin = 0.30; % Lower Bound of Variables

VarMax = 0.80; % Upper Bound of Variables

%% PSO Parameters

MaxIt = 1000; % Maximum Number of Iterations

nPop = 100; % 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

% 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

BestCost = 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

GlobalBest = particle(i).Best;

end

BestCost(it) = GlobalBest.Cost;

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

w = w*wdamp;

end

BestSol = GlobalBest;

Matt J 2022-11-17

The objective function came out of your brain. If it's returning the wrong value, I have no way of knowing what it should be returning instead.

Anwar 2022-11-17

Here is the original syntax of my function :

I don't know if there's a way out to this last step but this was really helpful,i mean getting steps forward with thoses constraints seting.Thanks a lot Matt J ,I appreciate .

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