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Binary Quadratic Programming Relaxation

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Mohammad Al ja'idi
Mohammad Al ja'idi on 12 Jul 2020
what is the best solver to solve Binary Quadratic Programming Problem in Matlab, and is it neccessary to relax the {0,1} to solve it.
Knowng that my problem has linear equality and linear inequality constraints (the constraints are linear).

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Answers (1)

John D'Errico
John D'Errico on 12 Jul 2020
While you could just use a tool like quadprog with continuous varibles in the interval [0,1], then round the result at the end, but there is no assurance the result is then optimal. And if you do round the solution at the end, it will probably no longer even satisfy the eqaulity constraints. So you would just be wasting your time.
Therefore GA is probably your main choice, with binary variables and a quadratic objective.

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Mohammad Al ja'idi
Mohammad Al ja'idi on 12 Jul 2020
you mean no need to relax the variables {0,1} using for example positive semidefinite programming (PSD) technique. you recommend just using GA to solve the problem.
Mohammad Al ja'idi
Mohammad Al ja'idi on 12 Jul 2020
Sorry for bothering, but do you see if I use quadprog to solve the problem with binary values {0,1} will get better result than making relaxaion of the variabls 0,1

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