Where the Really Hard Quadratic Assignment Problems Are: the QAP-SAT instances
This work addresses the identification of hard instances in combinatorial optimization for researchers and practitioners, but it is incremental as it builds on existing QAP studies with a new design.
The paper tackles the phase transition in Quadratic Assignment Problem (QAP) computational complexity by introducing QAP-SAT instances based on submodularity, and shows that critical parameters for satisfaction and solving effort are highly correlated for tabu search, enabling prediction of difficult instances.
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.