Integer programming models for the multidimensional assignment problem with star costs

Jose L. Walteros, Chrysafis Vogiatzis, Eduardo L. Pasiliao and Panos M. Pardalos

European Journal of Operational Research, 2014, vol. 235, issue 3, 553-568

Abstract: We consider a variant of the multidimensional assignment problem (MAP) with decomposable costs in which the resulting optimal assignment is described as a set of disjoint stars. This problem arises in the context of multi-sensor multi-target tracking problems, where a set of measurements, obtained from a collection of sensors, must be associated to a set of different targets. To solve this problem we study two different formulations. First, we introduce a continuous nonlinear program and its linearization, along with additional valid inequalities that improve the lower bounds. Second, we state the standard MAP formulation as a set partitioning problem, and solve it via branch and price. These approaches were put to test by solving instances ranging from tripartite to 20-partite graphs of 4 to 30 nodes per partition. Computational results show that our approaches are a viable option to solve this problem. A comparative study is presented.

Keywords: Combinatorial optimization; Multidimensional assignment problem; Star covering; Multi-sensor multi-target tracking problem; Graph partitioning; Branch and price (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:235:y:2014:i:3:p:553-568

DOI: 10.1016/j.ejor.2013.10.048

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