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Refined Integer Programs and Polyhedral Results for the Target Visitation Problem

Author Sven Mallach

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OASIcs.ATMOS.2025.8.pdf
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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial optimization
  • Applied computing → Transportation
  • Mathematics of computing → Linear programming
  • Mathematics of computing → Integer programming
Keywords
  • Route planning
  • Transportation
  • Logistics
  • Traveling salesman problem
  • Linear ordering problem
  • Polyhedral Combinatorics
  • Branch-and-cut
  • Integer Programming
  • Linear programming

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Abstract

The Target Visitation Problem (TVP) combines the Traveling Salesman Problem and the Linear Ordering Problem, and thus serves as a natural model for route planning applications where both the travel costs and the order of the sites to visit matter. More precisely, in addition to the costs that apply for the selected links connecting two subsequently visited sites, the relative urgency of visiting one site before another is quantified and taken into account. In this article, we present refined integer linear programming formulations for the TVP, along with clarifications and extensions regarding the description of the polytopes associated with their feasible solution sets by a minimal set of linear equations and facet-defining inequalities. The practical effectiveness of exploiting the proposed improvements by means of a branch-and-cut algorithm is demonstrated in a computational study. In addition, we report the optimal values for some previously unsolved instances.

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Sven Mallach. Refined Integer Programs and Polyhedral Results for the Target Visitation Problem. In 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025). Open Access Series in Informatics (OASIcs), Volume 137, pp. 8:1-8:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/OASIcs.ATMOS.2025.8

Author Details

Sven Mallach
  • Chair of Management Science, University of Siegen, Germany
  • University of Bonn, Germany

References

  1. Ashwin Arulselvan, Clayton W. Commander, and Panos M. Pardalos. A random keys based genetic algorithm for the target visitation problem. In Panos M. Pardalos, Robert Murphey, Don Grundel, and Michael J. Hirsch, editors, Advances in Cooperative Control and Optimization, pages 389-397, Berlin, Heidelberg, 2007. Springer Berlin Heidelberg. Google Scholar
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  5. Achim Hildenbrandt. The Target Visitation Problem. PhD thesis, Universität Heidelberg, Germany, 2015. URL: https://doi.org/10.11588/heidok.00017993.
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  7. Philipp Hungerländer. A semidefinite optimization approach to the target visitation problem. Optimization Letters, 9(8):1703-1727, December 2015. URL: https://doi.org/10.1007/s11590-014-0824-9.
  8. Sven Mallach. Binary programs for asymmetric betweenness problems and relations to the quadratic linear ordering problem. EURO Journal on Computational Optimization, 11:1-21, 2023. URL: https://doi.org/10.1016/j.ejco.2023.100071.
  9. George L. Nemhauser and Laurence A. Wolsey. Integer and Combinatorial Optimization. John Wiley & Sons, Inc., New York, NY, USA, 1988. Google Scholar
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