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I know that for some solvers, for example, the constraint programming solver in Google OR-Tools, it is possible to see all the intermediate solutions that the solver finds while it searches for an optimal solution. (An example is in this link.) I need these step-wise partial solutions to visualize the evolution of the optimization process in a physical example where I have a nonlinear 0-1 integer problem that I programmed in AMPL.

My questions are:

  • When solving nonlinear 0-1 integer problems, is it logical to consider such intermediate solutions?

  • Is it possible to obtain the intermediate solutions of solvers using AMPL? Which solvers have such a feature for AMPL?

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Yes it is reasonable. For problems where closing the optimality gap is difficult, you may want to save e.g. the 10 best solutions found before termination. This is called a solution pool and it is a solver specific option that you must pass to the solver from AMPL (check the solvers' manuals for "solution pool").

Most linear solvers support this (including CPLEX and GUROBI) - as for NLP solvers I believe that BARON supports this as well.

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    $\begingroup$ Thank you very much for your helpful answer. I looked at BARON's user manual and found very useful information about ''solution pool". $\endgroup$ – Oguz Toragay Aug 24 '19 at 20:03

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