Hi everyone,

I have been using CPLEX to solve some pure binary linear programming problems in the LP format that arise from tiling finite regions of the plane with polyominoes. Basically I'm just solving very large undetermined linear systems for their binary solutions. All coefficients are either 0 or 1 except for a few values on the right hand side of the system that may be positive integers. I use a constant objective function of 0. Well I recently downloaded CPLEX v12.10 and it seems to be slower than v12.8 at finding either an optimal solution, or finding all solutions of a tiling problem. For example, with an LP problem with 67,396 variables and 1,213 constraints, CPLEX v12.8 finds an optimal solution in about 9 minutes, but CPLEX v12.10 still has not found a solution in over 3 hours of computation. I do not use any special setting for the problem solution, just

CPLEX> read test.lp
CPLEX> optimize

Please when answering this question bear in mind that my knowledge of CPLEX is very limited and that my background is not in optimization, although I am a mathematician. Thank you for your help.

Marcus.

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Marcus Garvie
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#DecisionOptimization

It's possible that 12.10 is slower than 12.8 on this particular instance of you problem, or even on your problems in general. New releases are generally faster than their predecessors on the bulks of IBM's test suite, but given the perverse nature of integer programs, it's asking a bit much for a new version to be faster across the board.

It is possible that by adjusting some parameters off their default settings you might do better with 12.10. CPLEX has a tuning tool which can automatically try various parameter combinations and make suggestions. If you decide to try it, I would suggest running it on a fairly small (but not trivial) problem instance. If you want to post one of the instances to the forum, possibly someone would have time to play with it and see if the reason for the slowness can be identified. (If you do post it, I would recommend a .sav file rather than a .lp file, as the .sav file is a bit more accurate numerically.)

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Paul Rubin
Professor Emeritus
Michigan State University
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Hi everyone,
as recommended I am attaching the LP file that is causing me so much trouble! I would be really grateful if someone could have a look at what is causing this problem to run so slowly in CPLEX v12.10 (and fast in v12.8). If anyone is interested the background to this problem is described in a recent paper (see Example 4.11) of Contributions to Discrete Mathematics linked at https://cdm.ucalgary.ca/article/view/62866/54224 .
Thank you!
Marcus.

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Marcus Garvie
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