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Integer programming models for the multidimensional assignment problem with star costs

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

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.

Suggested Citation

  • Walteros, Jose L. & Vogiatzis, Chrysafis & Pasiliao, Eduardo L. & Pardalos, Panos M., 2014. "Integer programming models for the multidimensional assignment problem with star costs," European Journal of Operational Research, Elsevier, vol. 235(3), pages 553-568.
    • Handle: RePEc:eee:ejores:v:235:y:2014:i:3:p:553-568
    DOI: 10.1016/j.ejor.2013.10.048
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    References listed on IDEAS

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    Cited by:

    1. Jingqun Li & R. Tharmarasa & Daly Brown & Thia Kirubarajan & Krishna R. Pattipati, 2019. "A novel convex dual approach to three-dimensional assignment problem: theoretical analysis," Computational Optimization and Applications, Springer, vol. 74(2), pages 481-516, November.
    2. Boštjan Gabrovšek & Tina Novak & Janez Povh & Darja Rupnik Poklukar & Janez Žerovnik, 2020. "Multiple Hungarian Method for k -Assignment Problem," Mathematics, MDPI, vol. 8(11), pages 1-18, November.
    3. Jingqun Li & Thia Kirubarajan & R. Tharmarasa & Daly Brown & Krishna R. Pattipati, 2021. "A dual approach to multi-dimensional assignment problems," Journal of Global Optimization, Springer, vol. 81(3), pages 691-716, November.
    4. Cem Evrendilek & Ismail Hakki Toroslu & Seyedsasan Hashemikhabir, 2017. "Task assignment in tree-like hierarchical structures," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 631-655, August.

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