optimization multiobjective using pso

Hi every one,I need help to identify non-dominated points on a Pareto frontier corresponding to this multi-objective problem using epsilon constraint method;

error(Error using obj_eps1 (line 7)
Not enough input arguments.
Error in main1 (line 11).
[gbest]=PSOalgo(n,maxite,lb,ub,dim,obj_eps1,nonlcon_eps1,EpsVal(i))

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% constraint function

function [C,Ceq,constraintViolation] = nonlcon_eps1(x,EpsVal)
constraintViolation= 0;
Ceq = [];
Tp=140;Tf= 600;
m=3;n=8000;
s=0;q=1;
H=q*(((x+s)/n).^m);
% %%%%% A is a function varying from 0 to 1  
C(1)= EpsVal-(x/(x+Tp+Tf*H));  
if C(1) > 0
    constraintViolation= constraintViolation+ 1;
end
%%%%%%%%%%%%%%%%%%%%%%%%% objective function
function f = obj_eps1(x,~)
Tp=140 ;Tf= 600;
Cp=5000;Cf=35000;
m=3;etta=8000;
s=0;q=1;
% % % % cost function
f=(Cp+Cf*q*(((x+s)/etta)^m))/(x+Tp+Tf*q*(((x+s)/etta)^m));
end
%%%%%%%%%%%%%%%%%%%%%%%%%%% main.m
x0 = 1; % Starting point
ub = 25000; % Upper bound
lb = 1; % Lower bound
maxite = 1000;
dim = 2;
n = 50;         % Number of Pareto points
eps_min = 0.50; 
eps_max = 0.95;
EpsVal = eps_min:(eps_max - eps_min)/(n-1):eps_max; 
for i=1:n
    [gbest]=PSOalgo(n,maxite,lb,ub,dim,obj_eps1,nonlcon_eps1,EpsVal(i));
end
figure(1); 
plot(xopt(:,1), xopt(:,2), 'rs'); 
xlabel('\F')
ylabel('\c')
title('Pareto Front Example - Epsilon Constraint')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [gbest]= PSOalgo(n,maxite,lb,ub,dim,obj_eps1,nonlcon_eps1,EpsVal)
% initialization
% ite= 1000;
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)= obj_eps1(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)] = nonlcon_eps1(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)] = nonlcon_eps1(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

Answer 1

[Walter Roberson]

function f = obj_eps1(x,~)

That says that obj_eps1 expects to be passed two input arguments.

[gbest]=PSOalgo(n,maxite,lb,ub,dim,obj_eps1,nonlcon_eps1,EpsVal(i))

That line says that obj_eps1 should be invoked with no inputs, and whatever it returns should be passed in as the 6th input to

function [gbest]= PSOalgo(n,maxite,lb,ub,dim,obj_eps1,nonlcon_eps1,EpsVal)

and

             [~,constraintViolation(i,1)] = nonlcon_eps1(pbest(i,:), EpsVal);

That says that whatever is passed as the 6th parameter to PSOalgo must be either an array with at least two indices, or else must be a function handle with at least two inputs.

Therefore, when you invoke obj_eps1 in the line

[gbest]=PSOalgo(n,maxite,lb,ub,dim,obj_eps1,nonlcon_eps1,EpsVal(i))

then you need obj_eps1 to return the handle to a function that accepts at least two inputs.

I would suggest to you that what you wanted was

[gbest] = PSOalgo(n, maxite, lb, ub, dim, @obj_eps1, @nonlcon_eps1, EpsVal(i))