Why Does My Custom SA not Work for Mixed-integer Problem?

I have been trying to customize MATLAB's simulated annealing algorithm to my case, which is a mixed-integer optimization problem. Based on simulannealbnd documentation, I modified my code accordingly. However, it does not work as expected. That is, imagine we have N number of variables. I want to find a solution of which the first N / 2 number of variables are integer-valued and the rest of variables (N / 2 number of them) are float-valued. For demonstration I wrote this minimal reproducible example below:

rng(7, 'twister')

function y = objective(x)
    
    y = abs(sum(x(1) .* (x(2:end - 3) .^ 2 + x(3:end - 2) - 11) .^ 2 - cos(x(2)) .* (x(4:end - 1) + x(5:end) .^ 2 - 7) .^ 2));

end

function newx = sahonorbounds(newx, optimValues, problem)

    if ~problem.bounded
        
        return
    
    end
    
    xin = newx;
    newx = newx(:);
    lb = problem.lb;
    ub = problem.ub;
    lbound = newx < lb;
    ubound = newx > ub;
    alpha = rand;

    if any(lbound) || any(ubound)

        projnewx = newx;
        projnewx(lbound) = lb(lbound);
        projnewx(ubound) = ub(ubound);
        newx = alpha * projnewx + (1 - alpha) * optimValues.x(:);
        newx = globaloptim.internal.validate.reshapeinput(xin, newx);

    else
        
        newx = xin;

    end

    % Round only integer variables

    if isfield(problem, 'IntVars')

        newx(problem.IntVars) = round(newx(problem.IntVars), 0);

    end
    
end

function newx = mynewx(optimValues, problem)
    
    currentx = optimValues.x;
    nvar = numel(currentx);
    newx = currentx;
    newx(:) = currentx(:) + sqrt(optimValues.temperature) .* randn(nvar, 1);
    newx = sahonorbounds(newx, optimValues, problem);

end

F = @(x) objective(x);

options = optimoptions('simulannealbnd', ...
                       'FunctionTolerance', 1e-9, ...
                       'AnnealingFcn', @mynewx, ...
                       'ReannealInterval', 10, ...
                       'InitialTemperature', 10);

N = 6; % NUMBER OF VARIABLES TO CHANGE

problem = struct('solver', 'simulannealbnd', ...
                 'objective', F, ...
                 'IntVars', 1:N / 2, ...
                 'x0', [round(100 .* rand(1, N / 2), 0), 100 .* rand(1, N / 2)], ...
                 'lb', zeros(1, N), ...
                 'ub', 100 .* ones(1, N), ...
                 'options', options);

[x, fval, exitflag, output] = simulannealbnd(problem);
fprintf('\nx* : ');
fprintf('%f ', x);
fprintf(' --- f(x*) : %f\n\n', fval);

When I set N equal to 4, it works, meaning the first two components of solution are integer and the other two are float. If I set it to 6, 8, etc., I get all-float solution. Can anyone explain what goes on here? How can I get what I wanted here, if I can?

Answer 1

[Torsten]

This is the problem structure of "simulannealbnd". I cannot find "IntVars".

problem — Problem structure

structure

Problem structure, specified as a structure with the following fields:

• objective — Objective function
• x0 — Starting point
• lb — Lower bound for x
• ub — Upper bound for x
• solver — 'simulannealbnd'
• options — Options created with optimoptions or an options structure
• rngstate — Optional field to reset the state of the random number generator

Maybe you can tell us where you found that some variables can be defined as integers in the framework of "simulannealbnd".

[Burhan Burak]

Exactly, that is why I wanted to build on top of them with my custom problem definition in which I define 'IntVars' variable. Additionally, I defined my custom function for 'AnnealingFcn' as mynewx function.

[Torsten]

So you have programmed a new version of "simulannealbnd" that can handle the option "IntVars" ? For this to be true, you would have had to rewrite the complete algorithm.

Why don't you use "ga" ? It has the software option to define variables as integers.

[Burhan Burak]

I do not get the point of using 'AnnealingFcn' option at all to define my own annealing function to generate new candidate points. That is, even though I introduced a new variable, namely 'IntVars', in problem structure and added respective condition inside my own sahonorbounds function to catch, it does not work.

I already use Genetic Algorithm, by the way. As part of my study, I just want to compare my results found by two algorithms, one being Genetic Algorithm and the other customized Simulated Annealing Algorithm, for mixed-integer problem in hand. Also I consider writing the algorithm from scratch as you pointed out, but I just wanted to give a shot to existing algorithm if I could readily tweak it to my need.

I better I better work on it more. Thank you for your time to help me though.