Two-row and two-column mixed-integer presolve using hashing-based pairing methods

Patrick Gemander (), Wei-Kun Chen (), Dieter Weninger (), Leona Gottwald (), Ambros Gleixner () and Alexander Martin ()
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Patrick Gemander: Friedrich-Alexander-Universität Erlangen-Nürnberg
Wei-Kun Chen: Beijing Institute of Technology
Dieter Weninger: Friedrich-Alexander-Universität Erlangen-Nürnberg
Leona Gottwald: Zuse Institute Berlin
Ambros Gleixner: Zuse Institute Berlin
Alexander Martin: Friedrich-Alexander-Universität Erlangen-Nürnberg

EURO Journal on Computational Optimization, 2020, vol. 8, issue 3, No 2, 205-240

Abstract: Abstract In state-of-the-art mixed-integer programming solvers, a large array of reduction techniques are applied to simplify the problem and strengthen the model formulation before starting the actual branch-and-cut phase. Despite their mathematical simplicity, these methods can have significant impact on the solvability of a given problem. However, a crucial property for employing presolve techniques successfully is their speed. Hence, most methods inspect constraints or variables individually in order to guarantee linear complexity. In this paper, we present new hashing-based pairing mechanisms that help to overcome known performance limitations of more powerful presolve techniques that consider pairs of rows or columns. Additionally, we develop an enhancement to one of these presolve techniques by exploiting the presence of set-packing structures on binary variables in order to strengthen the resulting reductions without increasing runtime. We analyze the impact of these methods on the MIPLIB 2017 benchmark set based on an implementation in the MIP solver SCIP.

Keywords: Linear programming; Mixed-integer linear programming; Optimization solver; Presolve; 90C05; 90C10; 90C11; 65Y05 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s13675-020-00129-6

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