Does MATLAB have a mixed-integer optimization feature that uses metaheuristic algorithms?

I am interested in optimization and know that MATLAB has a built-in metaheuristic algorithm that can be utilized. I have worked with some of these algorithms, such as Genetic Algorithms (GA) and Particle Swarm Optimization (PSO). However, I believe they are typically designed to solve problems with a single type of decision variable.

I am currently working on a problem that involves multiple types of decision variables, including binary, integer, and continuous variables. Can this kind of problem be effectively solved using a heuristic approach?

[Torsten]

I don't know if you would call it efficient, but "ga" can if you have no nonlinear equality constraints that you want to define in "nonlcon".

[Walter Roberson]

ga() and gamultiobj() and intlinprog() are designed for mixed-integer programming.

binary decision variables are integer decision variables over [0 1]

[M.Sattar]

I will check this , thank you @Torsten and @Walter Roberson.

[Mike Croucher]

To add to these, binary problems can be solved with QUBO, part of the quantum computing support package. The algorithm employed is called Tabu Search which is meta heuristic.

[M.Sattar]

Thank you Mike Croucher, can it solve the case in which the descion varaible has multi-type ?

[Walter Roberson]

@M.Sattar

No, QUBO is purely for binary decision variables.

[Sam Chak]

Hi @M.Sattar,

I am curious about the NP-hardness of the problem, as it involves mixed binary, integer, and real variables. Does your problem have a single objective function or multiple objective functions?

[Walter Roberson]

Note that QUBO involves a matrix representation of the objective, not a function-handle representation.

[Sam Chak]

I wonder if the binary variables can be treated as specially constrained integer variables. If so, then the problem is essentially of mixed-integer programming type. The second part of this example shows how to solve a surrogate optimization problem that involves mixed integer and real variables.

[Walter Roberson]

It should certainly be possible to treat binary variables as integer variables constrained to [0 1]

[Torsten]

@M.Sattar

What is a "decision variable of multiple type" ? If you mean that the variable can take more integer values than just 0 and 1, you can define its lower and upper bounds in the arrays lb and ub. It then can take integer values in between lb and ub.

[M.Sattar]

Thanks @Walter Roberson, i took a look at the QUBO and indeed it's for binary optimization,

@Sam Chak Yes, in my problem case, it involves multiple objectives and multiple types of decision variables. During my investigation, I found the Gurobi solver, which involves mathematical optimization and supports mixed-integer decision variables, and it has a variety of features, unfortunatly it's paid, i wonde rif MATLAB optimization toolbox offers the same features and perfermance.

[M.Sattar]

Hi @Torsten

For example i have a vector decision variable X =[x1, x2, x3, x4, x5, x6];

x1 and x2 are binary variables that can be either 1 or 0,

x3 and x4 are discrete integer variables that can be 0,1, 2, 3, 4, 5 ...

x5, x6 are continous varaible 0, 0.5 1.2, 4.54 8.5 .. etc

[Torsten]

As said, you can handle these variables by setting bounds in MATLAB's "ga":

x1 and x2: Set intcon and lb = 0, ub = 1

x3 and x4: Set intcon and lb = 0

x5 and x6: Set intcon and lb = 1, ub = number of values x5 and x6 can take and identify 0 with 1, 0.5 with 2, 1.2 with 3 etc. in the objective function.

Here is a helpful page with the available software for certain problem classes and benchmark tests of commercial and non-commercial solvers:

https://plato.asu.edu/

Answer 1

[M.Sattar]

Hi, I found the way to solve this, Just wanted to say a huge thanks for all the help with my mixed-integer optimization questions. Your advice has been super helpful! Big shoutout to @Torsten, @Walter Roberson , @Sam Chak , and @Mike Croucher for your awesome insights.