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The p-Dispersion Problem with Distance Constraints

Authors Nikolaos Ploskas , Kostas Stergiou , Dimosthenis C. Tsouros

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Nikolaos Ploskas
  • University of Western Macedonia, Kozani, Greece
Kostas Stergiou
  • University of Western Macedonia, Kozani, Greece
Dimosthenis C. Tsouros
  • KU Leuven, Belgium

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Nikolaos Ploskas, Kostas Stergiou, and Dimosthenis C. Tsouros. The p-Dispersion Problem with Distance Constraints. In 29th International Conference on Principles and Practice of Constraint Programming (CP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 280, pp. 30:1-30:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.CP.2023.30

Abstract

In the (maxmin) p-dispersion problem we seek to locate a set of facilities in an area so that the minimum distance between any pair of facilities is maximized. We study a variant of this problem where there exist constraints specifying the minimum allowed distances between the facilities. This type of problem, which we call PDDP, has not received much attention within the literature on location and dispersion problems, despite its relevance to real scenarios. We propose both ILP and CP methods to solve the PDDP. Regarding ILP, we give two formulations derived from a classic and a state-of-the-art model for p-dispersion, respectively. Regarding CP, we first give a generic model that can be implemented within any standard CP solver, and we then propose a specialized heuristic Branch&Bound method. Experiments demonstrate that the ILP formulations are more efficient than the CP model, as the latter is unable to prove optimality in reasonable time, except for small problems, and is usually slower in finding solutions of the same quality than the ILP models. However, although the ILP approach displays good performance on small to medium size problems, it cannot efficiently handle larger ones. The heuristic CP-based method can be very efficient on larger problems and is able to quickly discover solutions to problems that are very hard for an ILP solver.

Subject Classification

ACM Subject Classification
  • Theory of computation → Constraint and logic programming
Keywords
  • Facility location
  • distance constraints
  • optimization

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References

  1. T. Argo and E. Sandstrom. Separation distances in NFPA codes and standards (tech. rep.). Fire Protection Research Foundation. 2014. Google Scholar
  2. O. Berman and R. Huang. The minimum weighted covering location problem with distance constraints. Computers and Operations Research, 35(12):356-372, 2008. Google Scholar
  3. F. Boussemart, F. Heremy, C. Lecoutre, and L. Sais. Boosting systematic search by weighting constraints. In Proceedings of ECAI'04, pages 482-486, 2004. Google Scholar
  4. J. Brimberg and H. Juel. A minisum model with forbidden regions for locating a semi-desirable facility in the plane. Location Science, 6(1):109-120, 1998. Google Scholar
  5. H. Cambazard, D. Mehta, B. O'Sullivan, and L. Quesada. A computational geometry-based local search algorithm for planar location problems. In Proceedings of the 9th International Conference on the Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CPAIOR 2012), pages 97-112, 2012. Google Scholar
  6. S. Chaudhry, T. McCormick, and I. D. Moon. Locating independent facilities with maximum weight: Greedy heuristics. International Journal of Management Science, 14(5):383-389, 1986. Google Scholar
  7. R. L. Church and M. E. Meadows. Results of a new approach to solving the p-median problem with maximum distance constraints. Geographical Analysis, 9(4):364-378, 1977. Google Scholar
  8. V. Chvatal. A greedy heuristic for the set-covering problem. Mathematics of Operations Research, 4(3):233-235, 1979. Google Scholar
  9. W. Comley. The location of ambivalent facilities: Use of a quadratic zero-one programming algorithm. Applied Mathematical Modeling, 19(1):26-29, 1995. Google Scholar
  10. Z. Dai, K. Xu, and M. Ornik. Repulsion-based p-dispersion with distance constraints in non-convex polygons. Annals of Operations Research, 307:75-91, 2021. Google Scholar
  11. Choco development team. An Open-Source java library for constraint programming. https://choco-solver.org/. Google Scholar
  12. OR-Tools development team. OR-Tools, CP-SAT solver. https://developers.google.com/optimization/cp/cp_solver. Google Scholar
  13. T. Drezner, Z. Drezner, and A. Schöbel. The weber obnoxious facility location model: A big arc small arc approach. Computers and Operations Research, 98:240-250, 2018. Google Scholar
  14. Z. Drezner, P. Kalczynski, and S. Salhi. The planar multiple obnoxious facilities location problem: A Voronoi based heuristic. Omega, 87:105-116, 2019. Google Scholar
  15. E. Erkut. The discrete p-dispersion problem. European Journal of Operational Research, 46(1):48-60, 1990. Google Scholar
  16. E. Erkut and S. Neuman. Analytical models for locating undesirable facilities. European Journal of Operational Research, 40(3):275-291, 1989. Google Scholar
  17. M. M. Fazel-Zarandi and J. C. Beck. Solving a location-allocation problem with logic-based benders' decomposition. In Proceedings of the 15th International Conference on Principles and Practice of Constraint Programming (CP 2009), pages 344-351, 2009. Google Scholar
  18. J. B. Ghosh. Computational aspects of the maximum diversity problem. Operations Research Letters, 19(4):175-181, 1996. Google Scholar
  19. C. Gomes and M. Sellmann. Streamlined constraint reasoning. In Proceedings of the International Conference on Principles and Practice of Constraint Programming (CP 2004), pages 274-289, 2004. Google Scholar
  20. T. Guns. Increasing modeling language convenience with a universal n-dimensional array, CPpy as python-embedded example. In Proceedings of the 18th workshop on Constraint Modelling and Reformulation, 2019. Google Scholar
  21. LLC Gurobi Optimization. Gurobi optimizer reference manual. , 2023. URL: https://www.gurobi.com.
  22. N. Isoart and J.-C. Régin. A k-Opt Based Constraint for the TSP. In Proceedings of the 27th International Conference on Principles and Practice of Constraint Programming (CP 2021), 2021. Google Scholar
  23. B. M. Khumawala. An efficient algorithm for the p-median problem with maximum distance constraints. Geographical Analysis, 5(4):309-321, 1973. Google Scholar
  24. R. K. Kincaid. Good solutions to discrete noxious location problems via meta-heuristics. Annals of Operations Research, 40(1):265-281, 1992. Google Scholar
  25. M. J. Kuby. Programming models for facility dispersion: The p-dispersion and maxisum dispersion problems. Mathematical and Computer Modelling, 10(10):792, 1988. Google Scholar
  26. Mikael Zayenz Lagerkvist and Magnus Rattfeldt. Half-checking propagators. In Proceedings of the 19th workshop on Constraint Modelling and Reformulation, 2020. Google Scholar
  27. A. Maier and H.W. Hamacher. Complexity results on planar multifacility location problems with forbidden regions. Mathematical Methods of Operations Research, 89:433-484, 2019. Google Scholar
  28. R. Marti, A. Martinez-Gavara, S. Perez-Pelo, and J. Sanchez-Oro. A review on discrete diversity and dispersion maximization from an OR perspective. European Journal of Operational Research, 299(3):795-813, 2022. Google Scholar
  29. I. D. Moon and S. Chaudhry. An analysis of network location problems with distance constraints. Management Science, 30(3):290-307, 1984. Google Scholar
  30. I. D. Moon and L. Papayanopoulos. Minimax location of two facilities with minimum separation: Interactive graphical solutions. Journal of the Operations Research Society, 42:685-694, 1991. Google Scholar
  31. C.S. Orloff. A theoretical model of net accessibility in public facility location. Geographical Analysis, 9:244-256, 1977. Google Scholar
  32. M. G. Resende, R. Marti, M. Gallego, and A. Duarte. Grasp and path relinking for the max-min diversity problem. Computers and Operations Research, 37(3):498-508, 2010. Google Scholar
  33. B. Saboonchi, P. Hansen, and S. Perron. MaxMinMin p-dispersion problem: A variable neighborhood search approach. Computer & Operations Research, 52:251-259, 2014. Google Scholar
  34. D. Sayah and S. Irnich. A new compact formulation for the discrete p-dispersion problem. European Journal of Operational Research, 256(1):62-67, 2017. Google Scholar
  35. F. Sayyady and Y Fathi. An integer programming approach for solving the p-dispersion problem. European Journal of Operational Research, 253(1):216-225, 2016. Google Scholar
  36. D. R. Shier. A min-max theorem for p-center problems on a tree. Transportation Science, 11(3):243-252, 1977. Google Scholar
  37. S.Y.D. Sorkhabi, D.A. Romero, J.C. Beck, and C. Amon. Constrained multi-objective wind farm layout optimization: Novel constraint handling approach based on constraint programming. Renewable Energy, 126(C):341-353, 2018. Google Scholar
  38. B.C. Tansel, R.L. Francis, T.J. Lowe, and M.L. Chen. Duality and distance constraints for the nonlinear p-center problem and covering problem on a tree network. Operations Research, 30(4):725-744, 1982. Google Scholar
  39. S.B. Welch and S. Salhi. The obnoxious p facility network location problem with facility interaction. European Journal of Operations Research, 102:302-319, 1997. Google Scholar
  40. 49 C.F.R. §175.701. Separation distance requirements for packages containing class 7 (radioactive) materials in passenger-carrying aircraft. Title 49 Code of Federal Regulations, Part 175. 2021. Google Scholar
  41. 29 C.F.R. §1910.157. Portable fire extinguishers. Title 29 Code of Federal Regulations, Part 157. 2021. Google Scholar
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