Implement parameter constraint for surrogateopt

Hello,

I want to run an optimisation using surrogateopt and I have the constraint, that certain parameters can't be smaller than others. So, I guess for other methods my constraint function would look like this (?):

params = [param1, param2, param3, param4]
function [c, ceq] = simple_constraint(params)
c = [params(2)-params(1); 
     params(4)-params(3)];
ceq = [];
end 

As far as I understood in surrogateopt the constraints are set in the objective function.

What is the best way to implement these parameter constraints which are independent of the objective function value?

Just setting and arbitrary high value as value of the objective function? So, something like this:

function f = objFun_surrogateopt(param)

if params(2)> params(1) || params(4) > params(3)
f.Fval = 1000; 
else
    f.Fval = objFun(param);
end

f.Ineq = [params(2)-params(1);         
    params(4)-params(3)]; 

end

Or is there a smarter and more efficient way?

I'm looking forward to any hint on how to improve this!

Answer 1

[Alan Weiss]

The answer depends on your MATLAB version. As the Release Notes show, linear constraints were introduced in R2021a, nonlinear constraints were initroduced in R2020a.

• With R2021a or later, param(2) >= param(1) is equivalent to the linear constraint

A = [1 -1 0 0 0];
b = 0; % This means x(1) - x(2) <= 0, or x(1) <= x(2)

• With R2020a or R2020b, represent the constraint as a nonlinear inequality constraint:

function F = objcon(x)
F.Ineq = x(1) - x(2);
F.Fval = % your objective function here
end

Alan Weiss

MATLAB mathematical toolbox documentation

[Elsa Bunz]

@Alan Weiss Thanks! Does that mean, that for the R2020a/R2020b version the objective function will still be evaluated even if the constraints are not satisfied? So, in order to avoid an unnecessary evaluation (in my case a quite lengthy simulation) I'd need to something as I suggested in my original question (if case, giving an arbitrary high value for the objective function instead of evaluating, if the constraints aren't satisfied)?

Would this issue be solved with the way linear constraints are handled in R2021a?

[Alan Weiss]

Indeed, for R2021a the linear constraints are always satisfied. For R2020a, the constraints can be violated.

Alan Weiss

MATLAB mathematical toolbox documentation

[Elsa Bunz]

Okay, thanks a lot for the clarification!