# Replace the fmincon function with another optimization algorithm

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Maroco Sc on 1 Oct 2019
Commented: Walter Roberson on 20 Oct 2019
In this source code, how can I replace the fmincon function with PSO or GA optimization algorithm (I do not want to use a build-in function).
x0 = [1 1]; % Starting point
UB = [1 1]; % Upper bound
LB = [0 0]; % Lower bound
options = optimset('LargeScale', 'off', 'MaxFunEvals', 1000, ...
'TolFun', 1e-6, 'TolCon', 1e-6, 'disp', 'off');
% Create constraint bound vector:
n = 50; % Number of Pareto points
eps_min = -1;
eps_max = 0;
eps = eps_min:(eps_max - eps_min)/(n-1):eps_max;
% Solve scalarized problem for each epsilon value:
xopt = zeros(n,length(x0));
for i=1:n
xopt(i,:)=fmincon('obj_eps', x0, [], [], [], [], LB, UB,...
'nonlcon_eps', options, eps(i));
end
function [C,constraintViolation] = nonlcon_eps(x, eps)
constraintViolation= 0;
Ceq = [];
C(1) =x(2)+(x(1)-1)^3;
if C(1) > 0
constraintViolation= constraintViolation+ 1;
end
C(2) = -x(1) - eps;
if C(2) > 0
constraintViolation= constraintViolation+ 1;
end
function f = obj_eps(x, ~)
f = 2*x(1)-x(2);
This part:
for i=1:n
xopt(i,:)=fmincon('obj_eps', x0, [], [], [], [], LB, UB,'nonlcon_eps', options, eps(i));
end
Becomes:
maxIteration = 1000;
dim = 2;
n = 50; % Number of Pareto points
eps_min = -1;
eps_max = 0;
EpsVal = eps_min:(eps_max - eps_min)/(n-1):eps_max;
for i=1:n
[gbest]= PSOalgo(N,T,lb,ub,dim,fobj,fcon,EpsVal(i));
end
function [gbest]= PSOalgo(N,maxite,lb,ub,dim,fobj,fcon,EpsVal)
% initialization
wmax=0.9; % inertia weight
wmin=0.4; % inertia weight
c1=2; % acceleration factor
c2=2; % acceleration factor
% pso initialization
X=initialization(N,dim,ub,lb);
v = 0.1*X; % initial velocity
for i=1:N
fitnessX(i,1)= fobj(X(i,:));
end
[fmin0,index0]= min(fitnessX);
pbest= X; % initial pbest
pbestfitness = fitnessX;
gbest= X(index0,:); % initial gbest
gbestfitness = fmin0;
ite=0; % Loop counter
while ite<maxite
w=wmax-(wmax-wmin)*ite/maxite; % update inertial weight
% pso velocity updates
for i=1:N
for j=1:dim
v(i,j)=w*v(i,j)+c1*rand()*(pbest(i,j)- X(i,j)) + c2*rand()*(gbest(1,j)- X(i,j));
end
end
% pso position update
for i=1:N
for j=1:dim
X(i,j)= X(i,j)+v(i,j);
end
% Check boundries
FU=X(i,:)>ub;
FL=X(i,:)<lb;
X(i,:)=(X(i,:).*(~(FU+FL)))+ub.*FU+lb.*FL;
% evaluating fitness
fitnessX(i,1) = fobj(X(i,:));
[~,consentViolation(i,1)] = fcon(X(i,:), EpsVal);
end
% updating pbest and fitness
for i=1:N
if fitnessX(i,1) < pbestfitness(i,1) && constraintViolation(i,1) == 0
pbest(i,:)= X(i,:);
pbestfitness(i,1)= fitnessX(i,1);
end
[~,constraintViolation(i,1)] = fcon(pbest(i,:), EpsVal);
end
% updating gbest and best fitness
for i=1:N
if pbestfitness(i,1)<gbestfitness && constraintViolation(i,1) == 0
gbest=pbest(i,:);
gbestfitness= pbestfitness(i,1);
end
end
ite = ite+1;
end
end
The obtained result by using PSO algorithm is not correct.
fmincon () result:
PSO algorithm result:
##### 7 CommentsShow 5 older commentsHide 5 older comments
Maroco Sc on 19 Oct 2019
The code in the link is what I want to replace it with PSO. he used fmincon with epsilon-constraint method.
Walter Roberson on 20 Oct 2019

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