8808
eng
reportzib
1
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2022-10-27
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The Largest Unsolved QAP Instance Tai256c Can Be Converted into A 256-dimensional Simple BQOP with A Single Cardinality Constraint
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.
1438-0064
urn:nbn:de:0297-zib-88086
10.12752/8808
publish
true
true
Koichi Fujii
Yuji Shinano
Sunyoung Kim
Masakazu Kojima
Hans D. Mittelmann
Yuji Shinano
ZIB-Report
22-18
Mathematics of Computing
OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING
Shinano, Yuji
HPO-NAVI
Applied Algorithmic Intelligence Methods
https://opus4.kobv.de/opus4-zib/files/8808/ZIB-Report_22_18.pdf