TY - GEN
A1 - Fujii, Koichi
A1 - Kim, Sunyoung
A1 - Kojima, Masakazu
A1 - Mittelmann, Hans D.
A1 - Shinano, Yuji
T1 - The Largest Unsolved QAP Instance Tai256c Can Be Converted into A 256-dimensional Simple BQOP with A Single Cardinality Constraint
N2 - 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.
T3 - ZIB-Report - 22-18
Y1 - 2022
UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/8808
UR - https://nbn-resolving.org/urn:nbn:de:0297-zib-88086
SN - 1438-0064
ER -