How big is your problem?

In many cases of small to medium size, the uncapacitated facility location problem can be solved straight-of-the-box with branch-and-cut, using a mixed-integer programming solver such as CPLEX or Gurobi. Check the following paper for a formulation and early works on the topic:

Cornuéjols, Gérard, George Nemhauser, and Laurence Wolsey. The Uncapicitated Facility Location Problem. Cornell University Operations Research and Industrial Engineering, 1983.

https://apps.dtic.mil/dtic/tr/fulltext/u2/a140000.pdf

I for one second the sensible suggestion from Dr. Vidal.

I will also say that there must be - somewhere on the web - an explicit mathematical programming model - or even several (using perhaps slightly different variable definitions) that you can code in AMPL, and run on the web, without having any software on your computer..

Dear Koushik Uppangala Ravikrishna If you absolutely need a metaheuristic for such problem, then you may try out differential evolution (DE) it is faster than the GA.

Have you also checked why the GA is slow? What is the population size? number of iterations? crossover rate? mutation rates?

Dear Koushik Uppangala Ravikrishna

If you need an Artificial Intelligence techniques for such problem, then you may try out Particle Swarm Optimization (PSO) it is :

Easy to understand, easy to program, simple to implement, and convergent fast

Here is the answer:

https://en.wikipedia.org/wiki/Facility_location_problem#Uncapacitated_facility_location

You can download exact solvers from it, as well. Start there - as you will learn a lot about the problem. I have never understood why it is sooo attractive to start with a methodology that we know from the start will not provide an optimal solution.

You can learn so much by testing the variants of optimisation models described, and you will find which ones you find faster for the data sets you have. Good luck!

Here is another possible source for ideas:

Solving the deterministic and stochastic uncapacitated facility location problem: from a heuristic to a simheuristic

• Jesica de Armas,
• Angel A. Juan,
• Joan M. Marquès &
• João Pedro Pedroso

Journal of the Operational Research Society volume 68, pages1161–1176 (2017)

I think BSA is a better algorithm to solve uncapacitated facility location problem.

But BSA will not find an optimum, so why bother? It's better to code the model and run it through CPLEX - there are plenty of solvers on the net.

Michael Patriksson $ Thibaut Vidal

Dear all

I want to solve this facility location problem (attached file). I use PulP package which is a linear solver to solve it, but it takes too much runtime for big sizes.

How can I decrease the runtime?

Thank you

Mr. Koushik Uppangala Ravikrishna, I agree with Mr. Abubakar Bala that it will be better to find out why GA works too long. If you provide more details, we might have some useful insights on how to improve the GA. Did you try to check GA's solution quality (e.g., by comparing with the solution of CPLEX) after stopping GA's run within a time limit (e.g., 1 minute)?

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Mr. Esmaeil Amiri, I believe that CPLEX (as suggested by Professor Vidal and Professor Patriksson) is faster than PulP. Please refer to:

https://stackoverflow.com/questions/45017617/pulp-cplex-or-gurobi-for-mixed-integer-programming-mip#:~:text=1%20Answer&text=For%20larger%2C%20more%20difficult%20problems,reliable%20than%20open%20source%20solvers.&text=One%20advantage%20of%20Pulp%20is,without%20changing%20the%20model%20code.

(My colleagues have tested it as well).

There are several methods for reducing the computational times, e.g.:

- Column generation ( https://www.sciencedirect.com/science/article/abs/pii/S0925527315003205 )

- Decomposition ( Article An improved Benders decomposition algorithm for the logistic...

I am sorry to ask, but should not you have any constraint to represent the relationship between x and y variables?

Ivan Kristianto Singgih Thank you very much for your help.

You can try the Jaya algorithm. Simple and effective. Refer to this work Article Solving the Flexible Job Shop Scheduling Problem using an Im...