Local Search for the Resource Constrained Assignment Problem

Author Markus Reuther



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Markus Reuther

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Markus Reuther. Local Search for the Resource Constrained Assignment Problem. In 14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 42, pp. 62-78, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)
https://doi.org/10.4230/OASIcs.ATMOS.2014.62

Abstract

The resource constrained assignment problem (RCAP) is to find a minimal cost cycle partition in a directed graph such that a resource constraint is fulfilled. The RCAP has its roots in an application that deals with the covering of a railway timetable by rolling stock vehicles. Here, the resource constraint corresponds to maintenance constraints for rail vehicles. Moreover, the RCAP generalizes several variants of vehicle routing problems. We contribute a local search algorithm for this problem that is derived from an exact algorithm which is similar to the Hungarian method for the standard assignment problem. Our algorithm can be summarized as a k-OPT heuristic, exchanging k arcs of an alternating cycle of the incumbent solution in each improvement step. The alternating cycles are found by dual arguments from linear programming. We present computational results for instances from our railway application at Deutsche Bahn Fernverkehr AG as well as for instances of the vehicle routing problem from the literature.
Keywords
  • Assignment Problem
  • Local Search
  • Rolling Stock Rotation Problem
  • Vehicle Routing Problem

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References

  1. M. L. Balinski and R. E. Gomory. A primal method for the assignment and transportation problems. Management Science, 10(3):578-593, 1964. Google Scholar
  2. Timo Berthold. Rens - the optimal rounding. Technical Report 12-17, ZIB, Takustr.7, 14195 Berlin, 2012. Google Scholar
  3. G. Clarke and J. W. Wright. Scheduling of vehicles from a central depot to a number of delivery points. Operations Research, 12(4):568-581, 1964. Google Scholar
  4. Emilie Danna, Edward Rothberg, and Claude Le Pape. Exploring relaxation induced neighborhoods to improve mip solutions. Mathematical Programming, 102(1):71-90, 2005. Google Scholar
  5. I. Dumitrescu. Constrained Path and Cycle Problems. University of Melbourne, Department of Mathematics and Statistics, 2002. Google Scholar
  6. Matteo Fischetti and Andrea Lodi. Local branching. Mathematical Programming, 98(1-3):23-47, 2003. Google Scholar
  7. Chris Groër, Bruce Golden, and Edward Wasil. A library of local search heuristics for the vehicle routing problem. Mathematical Programming Computation, 2(2):79–-101, 2010. Google Scholar
  8. Keld Helsgaun. An effective implementation of k-opt moves for the linkernighan tsp heuristic. Technical report, Roskilde University, 2006. Google Scholar
  9. Keld Helsgaun. General k-opt submoves for the Lin–Kernighan TSP heuristic. Mathematical Programming Computation, 1(2-3):119–-163, 2009. Google Scholar
  10. Paris-C. Kanellakis and Christos H. Papadimitriou. Local search for the asymmetric traveling salesman problem. Operations Research, 28(5):1086-1099, 1980. Google Scholar
  11. H. W. Kuhn. The hungarian method for the assignment problem. Naval Research Logistics Quarterly, 2(1-2):83-97, 1955. Google Scholar
  12. S. Lin and B. W. Kernighan. An effective heuristic algorithm for the traveling-salesman problem. Operations Research, 21(2):498-516, 1973. Google Scholar
  13. C. E. Miller, A. W. Tucker, and R. A. Zemlin. Integer programming formulation of traveling salesman problems. J. ACM, 7(4):326-329, October 1960. Google Scholar
  14. Karl Nachtigall and Jens Opitz. Solving Periodic Timetable Optimisation Problems by Modulo Simplex Calculations. In ATMOS'08, volume 9 of OpenAccess Series in Informatics (OASIcs), Dagstuhl, Germany, 2008. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik. Google Scholar
  15. Luigi Di Puglia Pugliese and Francesca Guerriero. A survey of resource constrained shortest path problems: Exact solution approaches. Networks, 62(3):183-200, 2013. Google Scholar
  16. T. Ralphs. Branch cut and price resource web (http://www.branchandcut.org), June 2014. Google Scholar
  17. G. Reinelt. TSPLIB - A T.S.P. Library. Technical Report 250, Universität Augsburg, Institut für Mathematik, Augsburg, 1990. Google Scholar
  18. Markus Reuther, Ralf Borndörfer, Thomas Schlechte, and Steffen Weider. Integrated optimization of rolling stock rotations for intercity railways. In Proceedings of RailCopenhagen, Copenhagen, Denmark, May 2013. Google Scholar
  19. Edward Rothberg. An evolutionary algorithm for polishing mixed integer programming solutions. INFORMS Journal on Computing, 19(4):534-541, 2007. Google Scholar
  20. Paolo Toth and Daniele Vigo, editors. The Vehicle Routing Problem. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2001. Google Scholar
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