Where the Really Hard Quadratic Assignment Problems Are: the QAP-SAT instances

Verel, Sébastien; Thomson, Sarah L; Rifki, Omar

Abstract

The Quadratic Assignment Problem (QAP) is one of the major domains in the field of evolutionary computation, and more widely in combinatorial optimization. This paper studies the phase transition of the QAP, which can be described as a dramatic change in the problem's computational complexity and satisfiability, within a narrow range of the problem parameters. To approach this phenomenon, we introduce a new QAP-SAT design of the initial problem based on submodularity to capture its difficulty with new features. This decomposition is studied experimentally using branch-and-bound and tabu search solvers. A phase transition parameter is then proposed. The critical parameter of phase transition satisfaction and that of the solving effort are shown to be highly correlated for tabu search, thus allowing the prediction of difficult instances.

Citation

Verel, S., Thomson, S. L., & Rifki, O. (2024, April). Where the Really Hard Quadratic Assignment Problems Are: the QAP-SAT instances. Presented at EvoCOP 2024, Aberystwyth, UK

• Presentation Conference Type: Conference Paper (published)
• Conference Name: EvoCOP 2024
• Start Date: Apr 3, 2024
• End Date: Apr 5, 2024
• Acceptance Date: Jan 10, 2024
• Online Publication Date: Apr 18, 2024
• Publication Date: 2024
• Deposit Date: Feb 20, 2024
• Publicly Available Date: Apr 19, 2025
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Pages: 129-145
• Series Title: Lecture Notes in Computer Science
• Series ISSN: 0302-9743
• Book Title: Evolutionary Computation in Combinatorial Optimization 24th European Conference, EvoCOP 2024 Held as Part of EvoStar 2024 Aberystwyth, UK, April 3–5, 2024 Proceedings
• ISBN: 978-3-031-57711-6
• DOI: https://doi.org/10.1007/978-3-031-57712-3_9
• Keywords: Quadratic Assignment Problem, Phase transition