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Mathematics > Optimization and Control

arXiv:2210.15963 (math)
[Submitted on 28 Oct 2022]

Title:The Largest Unsolved QAP Instance Tai256c Can Be Converted into A 256-dimensional Simple BQOP with A Single Cardinality Constraint

Authors:Koichi Fujii, Sunyoung Kim, Masakazu Kojima, Hans D. Mittelmann, Yuji Shinano
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Abstract:Tai256c is the largest unsolved quadratic assignment problem (QAP) instance in QAPLIB; a 1.48\% gap remains between the best known feasible objective value and lower bound of the unknown optimal value. This paper shows that the instance can be converted into a 256 dimensional binary quadratic optimization problem (BQOP) with a single cardinality constraint which requires the sum of the binary variables to be 92. The converted BQOP is much simpler than the original QAP tai256c and it also inherits some of the symmetry properties. However, it is still very difficult to solve. We present an efficient branch and bound method for improving the lower bound effectively. A new lower bound with 1.36\% gap is also provided.
Comments: 13 pages, 6 figures
Subjects: Optimization and Control (math.OC)
MSC classes: 90C20, 90C22, 90C25, 90C26
Cite as: arXiv:2210.15963 [math.OC]
  (or arXiv:2210.15963v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2210.15963

Submission history

From: Sunyoung Kim [view email]
[v1] Fri, 28 Oct 2022 07:51:40 UTC (253 KB)
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