How Can I improve the result of Surrogateopt Optimization?

Hi all, I have a mixed integer nonlinear problem with a lot of constraints and used surrogateopt to find the minimum cost function. It gives a result but It doesn't acceptable one. I changed some default parameters like MaxFunctionEvaluations, MinSampleDistance or MinSurrogatePoints. At the same time, I have added InitialPoints but the result didn't change. I solved the same problem with fmincon without using integer constraints and found a good solution. I modified this result as initialpoints for the surrogate optimization but It still gives the same bad result. It didn't consider the initial points. When I call the function with intialpoints, It gives a better result. For example;

opts = optimoptions('surrogateopt','PlotFcn','surrogateoptplot','InitialPoints',Xint,'MaxFunctionEvaluations',6000);

rng default

[x1,fval,exitflag,output] = surrogateopt(f,LB,UB,intcon,A,b,Aeq,beq,opts);

fval= 1000 $

fval_new=f(Xint) = 800$

So, why can't the surrogate find a good result at least as good as the intial points I gave? How can I improve my result?

Answer 1

[Alan Weiss]

Is your initial point Xint feasible? In other words, does it satisfy

• Xint >= lb
• Xint <= ub
• Aeq*Xint' = beq
• A*Xint' <= b
• f.Ineq(Xint) <= 0

If Xint satisfies all of those constraints then I would be surprised that surrogateopt returns a worse solution thant Xint.

Alan Weiss

MATLAB mathematical toolbox documentation

[Mehmet Türker TAKCI]

Hi Alan, thanks for your reply. Yes, I have checked each variable and all are feasible. I also checked the optimization result x1. The result satisfies all constraints. My Xint also satisfies all constraints when I rechecked according to your suggestion. But when I call the optimization function, f with Xint, the result will be 14508$. But surrogateopt finds it 16618$.

By the way, the A is a 3*7 matrix. I have 3 inequality equations and 7 decision variables which I want to find at end of the optimization. Xint is 7*1 column vector and b is 3*1 column vector. But the objective function requires the x as a row vector that why I convert Xint as a row vector by Xint' . This approach is correct, isn't it?

I have also tried the same problem with GA and it gives a better result like 15600$. But It is still higher than the initial price. I have solved the same problem with GAMS, It gives 14490$. I want to use MATLAB because my initial problem will be more complicated in the second version so Matlab will be more useful than GAMS but I couldn't understand why it doesn't give a good result.

Do you have any suggestions? If you want I can share my all code to try it.

[Alan Weiss]

I would appreciate seeing your code. I cannot understand how surrogateopt would return a worse solution than a feasible initial point.

Alan Weiss

MATLAB mathematical toolbox documentation

[Mehmet Türker TAKCI]

Hi Alan, did you have a chance to examine the code?

Answer 2

[Mehmet Türker TAKCI]

The mathematical equations are :

[Alan Weiss]

I believe that the issue arises because your initial point Xint is not feasible, as you will see if you execute

max(abs(AeqXint - beq))

You get a value of 0.0027, which is large enough for the solver to deem the point infeasible. To examine the issue further, execute

[rr ss] = max(abs(AeqXint - beq)) % ss is the index where it occurs
AeqXint(ss)
beq(ss)

Alan Weiss

MATLAB mathematical toolbox documentation

[Mehmet Türker TAKCI]

Hi Alan, thanks for your help.