How to include an nonlinear equality constraint when using surrogateopt

I am creating a program that optimizes a mixed integer non linear objective function. I am not sure how to implement a nonlinear equality constraint using surrogateopt. I have gone through the live editor tool and through the documentation and am still not sure how to do this :(. Any help is much appreciated. Right now I have a inequality constraint as shown below but I want it to be an equality constraint.

clear;
clc;

nvar = 3;
deadline = 25;
upperBounds = [10,10,deadline];
lowerBounds = [1,1,1];
intcon = 1:nvar;

% Solve
[solution,objectiveValue] = surrogateopt(@objConstrFcn,lowerBounds,...
    upperBounds,intcon);

disp(solution);
disp(objectiveValue);

function f = objConstrFcn(optimInput)
% variables
fill = optimInput(1);
cap = optimInput(2);
days = optimInput(3);

% objective function
f.Fval = days*(fill+cap);

% constraint 
f.Ineq = days - optimwelders(fill,cap); % how do I make this an equality constraint?? so that days = optimwelders(fill,cap)
end

The function optimwelders:

function time = optimwelders(fill,cap)
    time = ((fill+cap)/(cap*3))+4;
end

[Matt J]

The problem you've shown isn't really a fitting application of surrogateopt. There are only 2500 feasible solutions. You could easily loop through them all to find the minimum.

Answer 1

[Matt J]

Your nonlinear equality constraint is,

days= ((fill+cap)/(cap*3))+4;

In order for this to be satisfied, all terms on the right hand side must be integers, which means that fill must be an integer multiple of cap,

fill=k*cap

You can now rewrite the problem in terms of the variables k,cap, and days. Your objective becomes,

f.Fval=days*(k+1)*cap

and your nonlinear equality constraint reduces to a linear constraint, which surrogateopt can accept,

days=(k+1)/3+4

Your bounds on cap and days remain the same, but the bounds on fill become,

1<=k*cap<=10

but these are nonlinear inequalities, which surrogateopt can also accept.

Answer 2

[Matt J]

Another solution might be to re-arrange your nonlinear equality constraint in the form,

3*cap*(days-4) - (fill+cap)=0

Although surrogateopt cannot handle this directly, the left hand side is always going to be integer-valued, so you can equivalently write it as two inequalities:

3*cap*(days-4) - (fill+cap) <= 0.5
3*cap*(days-4) - (fill+cap) >= -0.5

This leads to the following revision of your code:

function f = objConstrFcn(optimInput)
% variables
fill = optimInput(1);
cap = optimInput(2);
days = optimInput(3);
% objective function
f.Fval = days*(fill+cap);


% constraint 
f.Ineq(1) =   ( 3*cap*(days-4) - (fill+cap) - 0.5);   %3*cap*(days-4) - (fill+cap) <= 0.5
f.Ineq(2) =  -( 3*cap*(days-4) - (fill+cap) + 0.5);   %3*cap*(days-4) - (fill+cap) >= -0.5
end