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I would start using MIP solver for the research on the tiling.

I know (heard of) the open source solver jump:

https://github.com/JuliaOpt/JuMP.jl

and also the gold standard solver from IBM cplex.

I need to do a series of MIP calculations and probably construct programs to automatically call the computations in cplex or jump and then use another mathematical software like polymake to analyze the data in terms of polytope.

I have no prior knowledge in jump, cplex, or polymake and I just know some super basic knowledge in C. Which solver do you think it would suit my purpose or do you have some suggestion on how shall I (computationally) approach this problem?

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    $\begingroup$ An excellent open source MIP is scip. I also often use gurobi. It has a free academic licence (with full functionality), and the performance is about the same as that of cplex. $\endgroup$
    – Peter Mueller
    Commented Jun 4, 2014 at 6:22
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    $\begingroup$ Probably you want to try out scicomp.stackexchange? I suspect that the question is a better fit over there... $\endgroup$
    – Dirk
    Commented Jun 4, 2014 at 16:18

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