Very Large-Scale Neighborhood Search for the Multidimensional Assignment Problem

Alla R. Kammerdiner () and Charles F. Vaughan ()
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Alla R. Kammerdiner: New Mexico State University
Charles F. Vaughan: Joint Navigation Warfare Center

A chapter in Optimization Methods and Applications, 2017, pp 251-262 from Springer

Abstract: Abstract The multidimensional assignment problem is an extension of the linear assignment problem to higher dimensions. This NP-hard problem in combinatorial optimization has applications in scheduling, multiple target tracking, and healthcare. In combinatorial optimization, algorithms utilizing very large-scale neighborhood search are proven to be particularly effective for some computationally difficult problems. In this chapter, we present two such algorithms, which are some of the first proposed for this problem in the literature. The two algorithms are distinct. One uses theory of cyclic transfers to construct and exploit the improvement graph. Another relies on polynomial schemes for finding optimal permutation. Because both methods depend on multiple restarts for effective exploration of search space, we propose and discuss some new multi-start strategies motivated by the design of experiments.

Keywords: Multidimensional Assignment Problem (MAP); Very Large-scale Neighborhood (VLSN); Multi-start Strategy; Graphic Improvement; Linear Assignment Problem (LAP) (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/978-3-319-68640-0_12

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