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Tai256c is the largest unsolved quadratic assignment problem (QAP) instancein QAPLIB; a 1.48\% gap remains between the best known feasible objective valueand lower bound of the unknown optimal value. This paper shows that theinstance can be converted into a 256 dimensional binary quadratic optimizationproblem (BQOP) with a single cardinality constraint which requires the sum ofthe binary variables to be 92. The converted BQOP is much simpler than theoriginal QAP tai256c and it also inherits some of the symmetry properties.However, it is still very difficult to solve. We present an efficient branchand bound method for improving the lower bound effectively. A new lower boundwith 1.36\% gap is also provided.

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