Beating the SDP bound for the floor layout problem: A simple combinatorial idea
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Author(s)
Dey, Santanu S.
Huchette, Joey
Vielma Centeno, Juan Pablo
Date Issued
August 2017
Journal
INFOR Information Systems and Operational Research
Publisher
University of Toronto Press Inc
Citation
Huchette, Joey et al. “Beating the SDP Bound for the Floor Layout Problem: A Simple Combinatorial Idea.” INFOR Information Systems and Operational Research 56, 4 (August 2017): 457–481. doi:10.1080/03155986.2017.1363592. © 2017 The Author(s)
Version
Original manuscript
Abstract
For many mixed-integer programming (MIP) problems, high-quality dual bounds can be obtained either through advanced formulation techniques coupled with a state-of-the-art MIP solver, or through semi-definite programming (SDP) relaxation hierarchies. In this paper, we introduce an alternative bounding approach that exploits the ‘combinatorial implosion’ effect by solving portions of the original problem and aggregating this information to obtain a global dual bound. We apply this technique to the one-dimensional and two-dimensional floor layout problems and compare it with the bounds generated by both state-of-the-art MIP solvers and by SDP relaxations. Specifically, we prove that the bounds obtained through the proposed technique are at least as good as those obtained through SDP relaxations, and present computational results that these bounds can be significantly stronger and easier to compute than these alternative strategies, particularly for very difficult problem instances.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Sloan School of Management
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1080/03155986.2017.1363592
