Discrete Optimization

Hi, is it possible to make an optimization with Matlab using discrete variable? Which kind of function can make it?

Thanks

[Walter Roberson]

Duplicate is at http://www.mathworks.com/matlabcentral/answers/13640-genetic-algorithm-optimization

[Alireza Ahani]

Dear Walter,

Thank you, but there is no answer there either.

Answer 1

[Walter Roberson]

ga() and gamultiobj() support discrete variables with general functions.

intlinprog supports discrete variables with matrix instead of function describing the objective.

There is some work with quadratic optimization that I had the impression could handle discrete variables when using Problem Based Optimization, but I did not track down which solver it uses.

[Bruno Luong]

Walter: "There is some work with quadratic optimization that I had the impression could handle discrete variables when using Problem Based Optimization,"

Really?

x=optimvar('x','type','integer');
y=optimvar('y','type','integer');
f=x^2+y^2;
prob = optimproblem("Objective",f);
solve(prob)

returns

>> Solving problem using lsqlin.
Error using optim.problemdef.OptimizationProblem/solve
Quadratic problem with integer variables not supported.

[Walter Roberson]

https://www.mathworks.com/help/optim/ug/miqp-portfolio-problem-based.html

"Mixed-Integer Quadratic Programming Portfolio Optimization: Problem-Based"

[Bruno Luong]

It's interesting, but sorry it's not a solver. It's an example of how to solve a particular MIQP using relaxation. And this page one can read the warning "While this technique works for this example, it might not apply to different problem or constraint types.'

btw this technique can be well implemented with solver-based approach. This page just uses problem-based for illustration, but it is not a requirement.

It's like saying quadprog is a non-linear solver since newton method solves quadratic subproblem at each step, or mtimes is linear system solver since Gauss-Seidel relaxation method requires matrix-vector multiplication at each step.

MATLAB lacks a real MIQP solver.

Answer 2

[PA00]

Can you expose more your problem? You can use "bintprog" when state variables are "1" or "0" like on or off but the method of optimization always depends on the problem itself and on the way you find to create a function to be minimized.

Answer 3

[Mario]

Dear Pedro, thank you for the reply. I exposed my problem here http://www.mathworks.com/matlabcentral/answers/13640-genetic-algorithm-optimization . I was thinking to use a genetic algorithm, but before I start I want to be sure that it's the right choice.