Orbital Conflict: Cutting Planes for Symmetric Integer Programs

Linderoth, Jeff; Núñez Ares, José; Ostrowski, James; Rossi, Fabrizio; Smriglio, Stefano

doi:10.1287/ijoo.2019.0044

Orbital Conflict: Cutting Planes for Symmetric Integer Programs

Journal Article · Sun Mar 07 23:00:00 EST 2021 · INFORMS Journal on Optimization

DOI:https://doi.org/10.1287/ijoo.2019.0044· OSTI ID:2339852

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University of Wisconsin–Madison, WI (United States); University of Tennessee
KU Leuven (Belgium)
University of Tennessee, Knoxville, TN (United States)
University of L’Aquila (Italy)

Cutting planes have been an important factor in the impressive progress made by integer programming (IP) solvers in the past two decades. However, cutting planes have had little impact on improving performance for symmetric IPs. Rather, the main breakthroughs for solving symmetric IPs have been achieved by cleverly exploiting symmetry in the enumeration phase of branch and bound. In this work, we introduce a hierarchy of cutting planes that arise from a reinterpretation of symmetry-exploiting branching methods. There are too many inequalities in the hierarchy to be used efficiently in a direct manner. However, the lowest levels of this cutting-plane hierarchy can be implicitly exploited by enhancing the conflict graph of the integer programming instance and by generating inequalities such as clique cuts valid for the stable set relaxation of the instance. We provide computational evidence that the resulting symmetry-powered clique cuts can improve state-of-the-art symmetry-exploiting methods. Furthermore, the inequalities are then employed in a two-phase approach with high-throughput computations to solve heretofore unsolved symmetric integer programs arising from covering designs, establishing for the first time the covering radii of two binary-ternary codes.

View Accepted Manuscript (DOE)

Research Organization:: University of Tennessee, Knoxville, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); Air Force Office of Scientific Research (AFOSR)

Grant/Contract Number:: SC0018175

OSTI ID:: 2339852

Journal Information:: INFORMS Journal on Optimization, Journal Name: INFORMS Journal on Optimization Journal Issue: 2 Vol. 3; ISSN 2575-1484

Publisher:: Institute for Operations Research and the Management Sciences (INFORMS)Copyright Statement

Country of Publication:: United States

Language:: English

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