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I am not a math student so I am sometimes a bit confused when it comes to math lingo. For me non-convex would mean its concave which means functions have local minima in case of a minimization problem... In the paper I am working with genetic algorithms and tabu-search. I would figure the reason for the usage are the concave terms.

Am I on the right track of understanding?

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This here is the non-convex contrain where z are the number of containers being unloaded and loaded.

enter image description here

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Non-convex means not convex, which could mean concave but also neither convex nor concave, such as a bilinear term $xy$.

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  • $\begingroup$ this means we can't use exact methods anymore? So it is solved with Genetic algorithm and tabu search? $\endgroup$
    – Eddiee
    Dec 17 '21 at 18:06
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    $\begingroup$ Exact methods can be used, it's just that it is no longer a mixed integer linear program (MILP), but a mixed integer nonlinear program (MINLP), which typically is significantly harder with less developed solvers. In my opinion, genetic algorithms etc are used when you just give up, but that's my personal view. $\endgroup$ Dec 17 '21 at 18:10
  • $\begingroup$ Well, in fairness, (a) in practice you don't always need a provably optimal solution (and perhaps cannot afford to wait for an exact solver to terminate) and (b) sometimes you simply cannot get an exact solution (problem too big, problem too hard, ...). A "good" solution obtained reasonably quickly via a metaheuristic may be just fine. $\endgroup$
    – prubin
    Dec 17 '21 at 20:42
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    $\begingroup$ True, agree so give up means giving up certificates of optimality. I guess I am just a bit tired of all the swarming pregnant fruit fly algorithms thrown in before carefully looking at the problem... $\endgroup$ Dec 17 '21 at 21:10
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    $\begingroup$ @EduardKrutitsky: If they're using genetic-algorithms, then, yeah, it's not a matter of getting a guaranteed optima anymore. If you do want to go for a global-optima, then the counter-part method would be branch-and-bound (where the distinction would be that you'd have to prove that particular genetic-lines are optimal). $\endgroup$
    – Nat
    Dec 18 '21 at 15:13

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