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I have a Linear program (LP) that can solve problem X with two objective functions a and b, I use the weighted sum method. I use Gurobi solver when I optimize the objective alone, the problem takes a lot of time (high complexity) and when I optimize only objective b the problem is solved in a few seconds.

I have implemented metaheuristic PSO using weighted sum and compared it with several metaheuristics. The problem is that the PSO find always the best solution for objective a and finds the worst value in terms of objective b.

So, I try to solve objective a using PSO, then solve objective b using Gurobi(solve my LP while making the first objective as a constraint)

With such a method, can I find the Pareto front? This method can be called hybrid PSO-LP? Have you other suggestions to solve my problem?

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    $\begingroup$ If you would like to depict the Pareto frontier why do not you try using the $\epsilon$-constraint method to do that? It allows you to solve the problem with different algorithms. $\endgroup$
    – A.Omidi
    Commented Dec 10, 2021 at 12:39
  • $\begingroup$ Your suggestion can be good. But I want to know if my method is good? my method is to solve two first objectives using the weighted sum method then make them constraints for my linear program which is solved by Gurobi. $\endgroup$
    – MAJID majid
    Commented Dec 10, 2021 at 14:05
  • $\begingroup$ I don't see how you can be sure your method produces a nondominated solution, since the value of a is determined by a metaheuristic (not guaranteed to find an optimal solution). $\endgroup$
    – prubin ♦
    Commented Dec 29, 2021 at 17:03
  • $\begingroup$ Also, even if your method works, it will only find "supported" Pareto efficient solutions. See this related question: or.stackexchange.com/questions/5000/…. $\endgroup$
    – prubin ♦
    Commented Dec 29, 2021 at 17:09

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