A dynamic-programming bound for the quadratic assignment problem

Authors:
Ambros Marzetta;Adrian Brüngger
Affiliations:
International Computer Science Institute, Berkeley;Novartis Pharma AG, Basel, Switzerland
Venue:
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Year:
1999

Citing 4
Cited 2

Solving large-scale QAP problems in parallel with the search library ZRAM

Journal of Parallel and Distributed Computing - Special issue on irregular problems in supercomputing applications
On the Applicability of Lower Bounds for Solving RectilinearQuadratic Assignment Problems in Parallel

Computational Optimization and Applications
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
QAPLIB – A Quadratic Assignment ProblemLibrary

Journal of Global Optimization

Selected topics on assignment problems

Discrete Applied Mathematics
Multistart tabu search and diversification strategies for the quadratic assignment problem

IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans

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Abstract

The quadratic assignment problem (QAP) is the NP-complete optimization problem of assigning n facilities to n locations while minimizing certain costs. In practice, proving the optimality of a solution is hard even for moderate problem sizes with n ≅ 20. We present a new algorithm for solving the QAP. Based on the dynamic-programming paradigm, the algorithm constructs a table of subproblem solutions and uses the solutions of the smaller subproblems for bounding the larger ones. The algorithm can be parallelized, performs well in practice, and has solved the previously unsolved instance NUG25. A comparison between the new dynamic-programming bound (DPB) and the traditionally used Gilmore-Lawler bound (GLB) shows that the DPB is stronger and leads to much smaller search trees than the GLB.