EURO Journal on Computational Optimization

, Volume 5, Issue 3, pp 367–392 | Cite as

Matheuristics for optimizing the network in German wagonload traffic

  • Julia Sender
  • Thomas Siwczyk
  • Petra Mutzel
  • Uwe Clausen
Original Paper


In this paper, we consider a capacitated multiple allocation hub location problem derived from a practical application in network design of German wagonload traffic. Due to the difficulty to solve even small data sets to optimality, we present two matheuristics: a local search matheuristic and an extension of an evolutionary algorithm matheuristic. Computational results are presented to demonstrate and compare the efficiency of both approaches for real-sized instances.


Hub location problems Network design IP Matheuristics Local search Evolutionary algorithms 

Mathematics Subject Classification

90-08 90B06 90B20 90B10 90C11 90C59 90C90 



The paper is based on the parts of the German Ph.D. thesis of Sender (2014) and on the German diploma thesis of Siwczyk (2013). We thank the German Federal Ministry of Education and Research (BMBF) for supporting this research (03MS640B). We also thank our project partner at DB Mobility Logistics AG for supporting us. This work has been partially supported by DFG GRK 1855 (DOTS). Finally, the authors would like to thank the reviewers for their constructive and helpful comments, which helped to improve the presentation of our work.


  1. Aarts E, Lenstra JK (eds) (2003) Local search in combinatorial optimization. Princeton University Press, PrincetonGoogle Scholar
  2. Abdinnour-Helm S (2001) Using simulated annealing to solve the \(p\)-hub median problem. Int J Phys Distrib Logist Manag 31(3):203–220CrossRefGoogle Scholar
  3. Abdinnour-Helm S, Venkataramanan MA (1998) Solution approaches to hub location problems. Ann Oper Res 78:31–50CrossRefGoogle Scholar
  4. Alumur S, Kara BY (2008) Network hub location problems: the state of the art. Eur J Oper Res 190:1–21CrossRefGoogle Scholar
  5. Campbell JF, Ernst AT, Krishnamoorthy M (2002) Hub location problems. In: Drezner Z, Hamacher HW (eds) Facility location. Applications and theory, chapter 12. Springer, Berlin, pp 373–407Google Scholar
  6. Campbell JF, Ernst AT, Krishnamoorthy M (2005a) Hub arc location problems: part I—introduction and results. Manag Sci 51:1540–1555Google Scholar
  7. Campbell JF, Ernst AT, Krishnamoorthy M (2005b) Hub arc location problems: part II—formulations and optimal algorithms. Manag Sci 51:1556–1571Google Scholar
  8. Campbell JF, O’Kelly ME (2012) Twenty-five years of hub location research. Transp Sci 45(2):153–169CrossRefGoogle Scholar
  9. Cánovas L, García S, Marín A (2007) Solving the uncapacitated multiple allocation hub location problem by means of a dual-ascent technique. Eur J Oper Res 179:990–1007CrossRefGoogle Scholar
  10. Carello G, Della Croce F, Ghirardi M, Tadei R (2004) Solving the hub locatin problem in telecommunication network design: a local search approach. Networks 44(2):94–105CrossRefGoogle Scholar
  11. Contreras I, Cordeau JF, Laporte G (2012) Exact solution of large-scale hub-location problems with multiple capacity levels. Transp Sci 46:439–459CrossRefGoogle Scholar
  12. Contreras Aguilar IA (2009) Network hub location: models, algorithms, and related problems. Ph.D. thesis, Universitat Politècnica de CatalunyaGoogle Scholar
  13. Correia I, Nickel S, Saldanha-da Gama F (2010) Single-assignment hub location problems with multiple capacity levels. Transp Res Part B: Methodol 44:1047–1066CrossRefGoogle Scholar
  14. Dijkstra EW (1959) A note on two problems in connexion with graphs. Numer Math 1(1):269–271CrossRefGoogle Scholar
  15. Ernst AT, Krishnamoorthy M (1996) Efficient algorithms for the uncapacitated single allocation \(p\)-hub median problem. Locat Sci 4:139–154CrossRefGoogle Scholar
  16. Ernst AT, Krishnamoorthy M (1998) An exact solution approach based on shortest-paths for \(p\)-hub median problems. INFORMS J Comput 10(2):149–162CrossRefGoogle Scholar
  17. Ernst AT, Krishnamoorthy M (1999) Solution algorithms for the capacitated single allocation hub location problem. Ann Oper Res 86:141–159CrossRefGoogle Scholar
  18. Even S, Itai A, Shamir A (1976) On the complexity of timetable and multi-commodity flow problems. SIAM J Comput 5(4):184–193CrossRefGoogle Scholar
  19. Farahani RZ, Hekmatfar M, Arabani AB, Nikbakhsh E (2013) Hub location problems: a review of models, classification, solution techniques, and applications. Comput Ind Eng 64(4):1096–1109. doi: 10.1016/j.cie.2013.01.012.
  20. Fügenschuh A, Homfeld H, Schülldorf H (2013) Single-car routing in rail freight transport. Transp Sci 49(1):130–148. doi: 10.1287/trsc.2013.0486 CrossRefGoogle Scholar
  21. Gelareh S (2008) Hub location models in public transportation planning. Ph.D. thesis, Technische Universität KaiserslauternGoogle Scholar
  22. Gendreau M, Potvin JY (eds) (2010a) Handbook of metaheuristics, 2nd edn. Springer, New YorkGoogle Scholar
  23. Gendreau M, Potvin JY (2010b) Tabu search. In: Gendreau M, Potvin JY (eds) Handbook of metaheuristics, 2nd edn. Springer, New York, pp 41–59Google Scholar
  24. Ishfaq R, Sox CR (2011) Hub location-allocation in intermodal logistic networks. Eur J Oper Res 210:213–230CrossRefGoogle Scholar
  25. Jailett P, Song G, Yu G (1996) Airline network design and hub location problems. Locat Sci 4:195–212CrossRefGoogle Scholar
  26. Klincewicz JG (1991) Heuristics for the \(p\)-hub location problem. Eur J Oper Res 53:25–37CrossRefGoogle Scholar
  27. Klincewicz JG (1992) Avoiding local optima in the \(p\)-hub location problem using tabu search and grasp. Ann Oper Res 40:282–302CrossRefGoogle Scholar
  28. Klincewicz JG (2002) Enumeration and search procedures for a hub location problem with economies of scale. Ann Oper Res 110:107–122CrossRefGoogle Scholar
  29. Kohani M, Marton P (2009) Methods and techniques for design of effective and competitive single wagon load transportation. Communications 11:63–67Google Scholar
  30. Kratica J, Milanovic M, Stanimirovic Z, Tosic D (2011) An evolutionary-based approach for solving a capacitated hub location problem. Appl Soft Comput 11(2):1858–1866CrossRefGoogle Scholar
  31. Maniezzo V, Stützle T, Voß S (eds) (2009) Matheuristics. Hybridizing metaheuristics and mathematical programming, 1st ed. Springer, New YorkGoogle Scholar
  32. Marianov V, Serra D, ReVelle C (1999) Location of hubs in a competitive enviroment. Eur J Oper Res 114:363–371CrossRefGoogle Scholar
  33. Marín A, Cánovas L, Landete M (2006) New formulations for the uncapacitated multiple allocation hub location problem. Eur J Oper Res 172:274–292CrossRefGoogle Scholar
  34. Marín A, Samerón J (1996) Tactical design of rail freight networks. I: Exact and heuristic methods. Eur J Oper Res 90:26–44CrossRefGoogle Scholar
  35. Mayer G, Wagner B (2002) An exact solution method for the multiple allocation hub location problem. Comput Oper Res 29:715–739CrossRefGoogle Scholar
  36. Meier JF, Clausen U (2013) Strategic planning in ltl logistics—increasing the capacity utilization of trucks. Electron Notes Discrete Math 41:37–44CrossRefGoogle Scholar
  37. Nemani AK, Ahuja RK (2010) OR models in freight railroad industry. In: Wiley encyclopedia of operations research and management science. Wiley, pp 3925–3944Google Scholar
  38. O’Kelly ME, Miller HJ (1994) The hub network design problem: a review and synthesis. J Transp Geogr 2(1):31–40CrossRefGoogle Scholar
  39. Racunica I, Wynter L (2005) Optimal location of intermodal freight hubs. Transp Res Part B 39:453–477CrossRefGoogle Scholar
  40. Reeves CR (2010) Genetic algorithms. In: Gendreau M, Potvin JY (eds) Handbook of metaheuristics, 2nd edn. Springer Publishing Company, Incorporated, New York, pp 109–139CrossRefGoogle Scholar
  41. Rodríguez-Martín I, Salazar-González JJ (2006) An iterated local search heuristic for a capacitated hub location problem. In: Almeida F, Blesa Aguilera MJ, Blum C, Moreno Vega JM, Pérez Pérez M, Roli A, Sampels M (eds) Hybrid metaheuristics, lecture notes in computer science, vol 4030, pp 70–81Google Scholar
  42. Rodríguez-Martín I, Salazar-González JJ (2008) Solving a capacitated hub location problem. Eur J Oper Res 184(2):468–479. doi: 10.1016/j.ejor.2006.11.026.
  43. Sender J (2014) Diskrete Optimierungsmodelle und Algorithmen zur strategischen Standortwahl und Transportnetzplanung im Einzelwagenverkehr. Verlag Dr. HutGoogle Scholar
  44. Sender J, Clausen U (2011a) Hub location problems with choice of different hub capacities and vehicle types. In: Pahl J, Reiners T, Voß S (eds) Network optimization, lecture notes in computer science, vol 6701, pp 535–546Google Scholar
  45. Sender J, Clausen U (2011b) A new hub location model for network design of wagonload traffic. In: Zak J (ed) The state of the art in the European quantitative oriented transportation and logistics research 14th Euro working group on transportation and 26th mini Euro conference and 1st European scientific conference on air transport, Procedia—social and behavioral sciences, vol 20, pp 90–99Google Scholar
  46. Sender J, Clausen U (2013a) Heuristics for solving a capacitated multiple allocation hub location problem with application in german wagonload traffic. Electron Notes Discrete Math 41:13–20Google Scholar
  47. Sender J, Clausen U (2013b) Optimizing the network in german wagonload traffic. In: Proceedings of 5th international seminar on railway operations modelling and analysisGoogle Scholar
  48. Silberholz J, Golden B (2010) Comparision of metaheuristics. In: Gendreau M, Potvin JY (eds) Handbook of metaheuristics, 2nd edn. Springer, Berlin, pp 625–640CrossRefGoogle Scholar
  49. Siwczyk T (2013) Optimierung von Transportnetzen im Schienengüterverkehr mittels evolutionärer Algorithmen. Diploma thesis, Fakultät für Informatik, Technische Universität DortmundGoogle Scholar
  50. Skorin-Kapov D, Skorin-Kapov J (1994) On tabu search for the location of interacting hub facilities. Eur J Oper Res 73(3):502–509CrossRefGoogle Scholar
  51. Yagiura M, Ibaraki T (2002) Local search. In: Pardalos PM, Resende MGC (eds) Handbook of applied optimization. Oxford University Press, New York, pp 104–123Google Scholar

Copyright information

© EURO - The Association of European Operational Research Societies 2016

Authors and Affiliations

  1. 1.Institute of Transport LogisticsTU DortmundDortmundGermany
  2. 2.Chair of Process Dynamics and OperationsTU DortmundDortmundGermany
  3. 3.Chair of Algorithm EngineeringTU DortmundDortmundGermany
  4. 4.Fraunhofer Institute for Material Flow and Logistics, Institute of Transport LogisticsTU DortmundDortmundGermany

Personalised recommendations