A computational status update for exact rational mixed integer programming. (English) Zbl 1482.90125

Singh, Mohit (ed.) et al., Integer programming and combinatorial optimization. 22nd international conference, IPCO 2021, Atlanta, GA, USA, May 19–21, 2021. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 12707, 163-177 (2021).
Summary: The last milestone achievement for the roundoff-error-free solution of general mixed integer programs over the rational numbers was a hybrid-precision branch-and-bound algorithm published by W. Cook et al. [Math. Program. Comput. 5, No. 3, 305–344 (2013; Zbl 1305.90310)]. We describe a substantial revision and extension of this framework that integrates symbolic presolving, features an exact repair step for solutions from primal floating-point heuristics, employs a faster rational LP solver based on LP iterative refinement, and is able to produce independently verifiable certificates of optimality. We study the significantly improved performance and give insights into the computational behavior of the new algorithmic components. On the MIPLIB 2017 benchmark set, we observe an average speedup of 6.6x over the original framework and 2.8 times as many instances solved within a time limit of two hours.
For the entire collection see [Zbl 1476.90004].


90C11 Mixed integer programming


Zbl 1305.90310
Full Text: DOI arXiv


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