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Where the Really Hard Quadratic Assignment Problems Are: the QAP-SAT 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.
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