Surrogate optimization with different size constraints

I have this problem for optimization (22-dimensional):

Min sum(t1/x1,t2/x2,...,t22/x22)

Subject to:

 x1 + x2 + ... + x22 -140 - tol <= 0
-x1 - x2 - ... - x22 +140 - tol <= 0
-x1  <= -1	
-x2  <= -1
 ...
-x22 <= -1

In surrogate optimization I have to add the constraints into the objective function handle, like this:

function F = transport(x)

% transporte is a 22-D problem

D = 22;

t = [3717,4982,3688,4337,6405,3769,3968,4900,5746,5753,7388,2832,4182,3618,4009,5291,5710,3742,3875,3436,5167,3950];

z = sum(t./x);

tol = 1e-3;
c1 = [sum(x) - 140 - tol;sum(-x) + 140 - tol];

A = ones(1,D)*(-1);
A = diag(A);
b = ones(D,1)*(-1);

c2 = A - b;

c = [c1 c2];

F.Fval = z;
F.Ineq = c;

end

I get this error, because c1 and c2 have different sizes:

Dimensions of arrays being concatenated are not consistent.

How can I create this constraints and pass to surrogate model?

My script:

% Mixed Integer Surrogate Optimization

clear all %#ok
close all
clc

rng default

D = 22;

lb = ones(1,D);
ub = ones(1,D)*10;

IntCon = 1:D;

options = optimoptions('surrogateopt','ConstraintTolerance',1e-6,'ObjectiveLimit',1e-6);

[xmin,fval,exitflag,output] = surrogateopt(@transport,lb,ub,IntCon,options);

Thanks a lot!

Answer 1

[Alan Weiss]

Your problem is this line:

c = [c1 c2];

The variable c1 is a 2-by-1 column. c2 is, I think, a 22-by-22. Maybe a 22-by-1. In any case, they cannot be concatenated like this.

Alan Weiss

MATLAB mathematical toolbox documentation

[David Franco]

You're right, Alan. I found on the page Solve Feasibility Problem the answer:

c(:,1:2) = [sum(x) - 140 - tol, sum(-x) + 140 - tol];
c(:,3:D+2) = (sum(A,2) - b)';

Each column in the structure field Ineq is a constraint.

Write each inequality as a function c(x), meaning the inequalities c(x) ≤ 0.

Thank you!

[David Franco]

Interesting that both GA and Surrogate in Matlab gave me a worse response than GA in Excel. And Surrogate was much slower.