Sequential constraint augmentation with variable neighbourhood search for the multidimensional assignment problem

Authors:
Eduardo L. Pasiliao;Panos M. Pardalos
Affiliations:
Air Force Research Laboratory, 101 West Eglin Boulevard, Eglin AFB FL 32542-5427, USA.;Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, Gainesville FL 32611-6595, USA
Venue:
International Journal of Computational Science and Engineering
Year:
2007

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Abstract

This work proposes the Sequential Constraint Augmentation (SCA)procedure for the Multidimensional Assignment Problem (MAP).Although the two-dimensional assignment problem has been shown tobe solvable in polynomial time, the problem becomes NP-hard when itis extended to three dimensions. We investigate the benefits ofimplementing an intra-permutation 2 exchange and variableneighbourhood search for the SCA. The variable neighbourhoodapproach utilises the intra-permutation 2 and n-exchanges and theinter permutation 2-exchange. All three κ-exchangeneighbourhoods are motivated by the permutation formulation of theMAP. Computational results show that the SCA procedure provides atight upper bound with little computational effort. Exploring ourvariable neighbourhood significantly improves the SCA solutionwithin a relatively short amount of computation time.