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A simheuristic algorithm for solving the arc-routing problem with stochastic demands

  • S Gonzalez-Martin
  • A A Juan
  • D Riera
  • M G Elizondo
  • J J Ramos
Original Article

Abstract

This paper proposes a simheuristic algorithm for solving the Arc-Routing Problem with Stochastic Demands. Our approach combines Monte Carlo Simulation (MCS) with the RandSHARP metaheuristic, which was originally designed for solving the Capacitated Arc-Routing Problem with deterministic demands (CARP). The RandSHARP metaheuristic is a biased-randomized version of a savings-based heuristic for the CARP, which allows it to obtain competitive results for this problem in low computational times. The RandSHARP is then combined with MCS to cope with the stochastic variant of the problem in a natural and efficient way. Our work is based on the use of a safety stock during the route-design stage. This safety stock can then be used during the delivery stage to satisfy unexpected demands. A reliability index is also defined to evaluate the robustness of each solution with respect to possible route failures caused by random demands. Some numerical experiments contribute to validate our approach and to illustrate its potential benefits.

Keywords

arc-routing problem with stochastic demands simheuristics reliability indices simulation-optimization 

Notes

Acknowledgements

This work has been partially supported by the Spanish Ministry of Economy and Competitiveness (TRA2013-48180-C3-P and TRA2015-71883-REDT), FEDER, and the Department of Universities, Research & Information Society of the Catalan Government (2014-CTP-00001).

References

  1. Ahr D (2004). Contributions to multiple postmen problems. Ph D Thesis, University of Heidelberg, Heidelberg, Germany.Google Scholar
  2. Amberg A, Domschke W and Voß S (2000). Multiple center capacitated arc routing problems: A tabu search algorithm using capacitated trees. European Journal of Operational Research 124 (2): 360–376.Google Scholar
  3. Amberg A and Voß S (2002). A hierarchical relaxation lower bound for the capacitated arc routing problem. In: Proceedings of the 35th Annual Hawaii International Conference on System Sciences, IEEE Computer Society: Los Alamitos, CA.Google Scholar
  4. Assad A and Golden B (1995). Arc routing methods and applications. In: Ball MG, Magnanti TL, Monma CL and Nemhauser GL (eds). Network Routing. Handbooks of Operations Research and Management Science, Vol. 8. Elsevier: Amsterdam, pp 375–483.Google Scholar
  5. Baldacci R and Maniezzo V (2006). Exact methods based on node routing formulations for undirected arc-routing problems. Networks 47 (1): 52–60.Google Scholar
  6. Belenguer J and Benavent E (1998). The capacitated arc routing problem: Valid inequalities and facets. Computational Optimization and Applications 10 (2): 165–187.Google Scholar
  7. Belenguer J and Benavent E (2003). A cutting plane algorithm for the capacitated arc routing problem. Computers & Operations Research 30 (5): 705–728.Google Scholar
  8. Beltrami E and Bodin L (1974). Networks and vehicle routing for municipal waste collection. Networks 4 (1): 65–94.Google Scholar
  9. Benavent R, Campos V, Corberán A and Mota E (1992). The capacitated arc routing problem: Lower bounds. Networks 22 (7): 669–690.Google Scholar
  10. Bertsimas D and Howell L (1993). Further results on the probabilistic traveling salesman problem. European Journal of Operational Research 65 (1): 68–95.Google Scholar
  11. Beullens P, Muyldermans L, Cattrysse D and Oudheusden D (2003). A guided local search heuristic for the capacitated arc routing problem. European Journal of Operational Research 147 (3): 629–643.Google Scholar
  12. Bodin L and Kursh S (1979). A detailed description of a computer system for the routing and scheduling of street sweepers. Computers & Operations Research 6 (4): 181–198.Google Scholar
  13. Brandâo J and Eglese R (2008). A deterministic tabu search algorithm for the capacitated arc routing problem. Computers & Operations Research 35 (4): 1112–1126.Google Scholar
  14. Chapleau L, Ferland J, Lapalme G and Rousseau J (1984). A parallel insert method for the capacitated arc routing problem. Operations Research Letters 3 (2): 95–99.Google Scholar
  15. Chen S, Golden B, Wong R and Zhong H (2009). Arc-routing models for small-package local routing. Transportation Science 43 (1): 43–55.Google Scholar
  16. Christiansen C and Lysgaard J (2007). A branch-and-price algorithm for the capacitated vehicle routing problem with stochastic demands. Operations Research Letters 35 (6): 773–781.Google Scholar
  17. Christiansen C, Lysgaard J and Wøhlk S (2009). A branch-and-price algorithm for the capacitated arc routing problem with stochastic demands. Operations Research Letters 37 (6): 392–398.Google Scholar
  18. Doerner K, Hartl R, Maniezzo V and Reimann M (2003). An ant system metaheuristic for the capacitated arc routing problem. In: Preprints of 5th Meta-heuristics International Conference, Kyoto.Google Scholar
  19. Dror M (2000). Arc Routing: Theory, Solutions and Applications. Kluwer Academic Publishers: Boston.Google Scholar
  20. Eglese R (1994). Routeing winter gritting vehicles. Discrete Applied Mathematics 48 (3): 231–244.Google Scholar
  21. Eglese R and Letchford A (2000). Polyhedral theory for arc routing problems. In: Dror M (ed). Arc Routing: Theory, Solutions and Applications. Kluwer Academic Publishers: Dordrecht, pp 199–230.Google Scholar
  22. Eglese R and Li L (1992). Efficient routing for winter gritting. Journal of the Operational Research Society 43 (11): 1031–1034.Google Scholar
  23. Eiselt H, Gendreau M and Laporte G (1995). Arc routing problems, part II: The rural postman problem. Operations Research 43 (3): 399–414.Google Scholar
  24. Fleury G, Lacomme P and Prins C (2004). Evolutionary algorithms for stochastic arc routing problems. In: Raidl GR et al (eds). Applications of Evolutionary Computing. Springer-Verlag: Berlin and Heidelberg, pp 501–512.Google Scholar
  25. Fleury G, Lacomme P, Prins C and Ramdane-Chérif W (2002). Robustness evaluation of solutions for the capacitated arc routing problem. In: Proceedings of the Conference on AI Simulation and Planning in High Autonomy Systems, The Society for Modeling & Simulation International: Vista, CA, pp 290–295.Google Scholar
  26. Fleury G, Lacomme P, Prins C and Ramdane-Chérif W (2005). Improving robustness of solutions to arc routing problems. Journal of the Operational Research Society 56 (5): 526–538.Google Scholar
  27. Golden B, Dearmon J and Baker E (1983). Computational experiments with algorithms for a class of routing problems. Computers & Operations Research 10 (1): 47–59.Google Scholar
  28. Golden B and Wong R (1981). Capacitated arc routing problems. Networks 11 (3): 305–315.Google Scholar
  29. Gonzalez-Martin S, Juan A, Riera D, Castella Q, Muñoz R and Perez A (2012). Development and assessment of the SHARP and RandSHARP algorithms for the arc routing problem. AI Communications 25 (2): 173–189.Google Scholar
  30. Grasas A, Juan A and Ramalhinho H (2016). SimILS: A simulation-based extension of the iterated local search metaheuristic for stochastic combinatorial optimization. Journal of Simulation 10 (1): 69–77.Google Scholar
  31. Greistorfer P (2003). A tabu scatter search metaheuristic for the arc routing problem. Computers & industrial Engineering 44 (2): 249–266.Google Scholar
  32. Hertz A, Laporte G and Mittaz M (2000). A tabu search heuristic for the capacitated arc routing problem. Operations Research 48 (1): 129–135.Google Scholar
  33. Hertz A and Mittazl M (2001). A variable neighborhood descendent algorithm for the undirected capacitated arc routing problem. Transportation Science 35 (4): 425–434.Google Scholar
  34. Hirabayashi R, Nishida N and Saruwatari Y (1992a). Node duplication lower bounds for the capacitated arc routing problems. Journal of the Operations Research Society of Japan 35 (2): 119–133.Google Scholar
  35. Hirabayashi R, Nishida N and Saruwatari Y (1992b). Tour construction algorithm for the capacitated arc routing problem. Asia-Pacific Journal of Operational Research 9 (2): 155–175.Google Scholar
  36. Ismail Z and Ramli M (2011). Implementation weather-type models of capacitated arc routing problem via heuristics. American Journal of Applied Sciences 8 (4): 382–392.Google Scholar
  37. Jaillet P (1988). A priori solution of a traveling salesman problem in which a random subset of the customers are visited. Operations Research 36 (9): 929–936.Google Scholar
  38. Juan A, Faulin J, Grasman SE, Rabe M and Figueira G (2015). A review of simheuristics: Extending metaheuristics to deal with stochastic combinatorial optimization problems. Operations Research Perspectives 2 (December): 62–72.Google Scholar
  39. Juan A, Faulin J, Grasman S, Riera D, Marull J and Mendez C (2011). Using safety stocks and simulation to solve the vehicle routing problem with stochastic demands. Transportation Research Part C 19 (5): 751–765.Google Scholar
  40. Juan A, Faulin J, Ruiz R, Barrios B and Caballe S (2010). The SR-GCWS hybrid algorithm for solving the capacitated vehicle routing problem. Applied Soft Computing 10 (1): 215–224.Google Scholar
  41. Juan A, Goentzel J and Bektas T (2014). Routing fleets with multiple driving ranges: Is it possible to use greener fleet configurations? Applied Soft Computing 21 (August): 84–94.Google Scholar
  42. Kiuchi M, Shinano Y, Hirabayashi R and Saruwatari Y (1995). An exact algorithm for the capacitated arc routing problem using parallel branch and bound method. In: Proceedings of the 1995 Spring National Conference of the Oper. Res. Soc. of Japan, pp 28–29.Google Scholar
  43. Lacomme P, Prins C and Ramdane-Chérif W (2001). Competitive genetic algorithms for the capacitated arc routing problem and its extensions. Lecture Notes in Computer Science 2037: 473–483.Google Scholar
  44. Lacomme P, Prins C and Ramdane-Chérif W (2004). Competitive memetic algorithms for arc routing problems. Annals of Operations Research 131 (1): 159–185.Google Scholar
  45. Lacomme P, Prins C and Tanguy A (2004). First competitive ant colony scheme for the CARP. Lecture Notes in Computer Science 3172: 426–427.Google Scholar
  46. Laporte G, Louveaux F and Mercure H (1994). A priori optimization of the probabilistic traveling salesman problem. Operations Research 42 (3): 543–549.Google Scholar
  47. Laporte G, Musmanno R and Vocaturo F (2010). An adaptive large neighbourhood search heuristic for the capacitated arc-routing problem with stochastic demands. Transportation Science 44 (1): 125–135.Google Scholar
  48. Letchford A and Oukil A (2009). Exploiting sparsity in pricing routines for the capacitated arc routing problem. Computers & Operations Research 36 (7): 2734–2742.Google Scholar
  49. Li L (1992). Vehicle routeing for winter gritting. PhD Thesis, Department of Management Science, Lancaster University.Google Scholar
  50. Longo H, Aragão M and Uchoa E (2006). Solving capacitated arc routing problems using a transformation to the CVRP. Computers & Operations Research 33 (6): 1823–1837.Google Scholar
  51. Pearn W (1988). New lower bounds for the capacitated arc routing problem. Networks 18 (3): 181–191.Google Scholar
  52. Pearn W (1989). Approximate solutions for the capacitated arc routing problem. Computers & Operations Research 16 (6): 589–600.Google Scholar
  53. Pearn W (1991). Argument-insert algorithms for the capacitated arc routing problem. Computers & Operations Research 18 (2): 189–198.Google Scholar
  54. Pearn W, Assad A and Golden B (1987). Transforming arc routing into node routing problems. Computers & Operations Research 14 (4): 285–288.Google Scholar
  55. Salazar-Aguilar M, Langevin A and Laporte G (2012). Synchronized arc routing for snow plowing operations. Computers & Operations Research 39 (7): 1432–1440.Google Scholar
  56. Sipahioglu A, Kirlik G, Parlaktuna O and Yazici A (2010). Energy constrained multi-robot sensor-based coverage path planning using capacitated arc routing approach. Robotics and Autonomous Systems 58 (7): 529–538.Google Scholar
  57. Stern H and Dror M (1979). Routing electric meter readers. Computers & Operations Research 6 (4): 209–223.Google Scholar
  58. Ulusoy B (1985). The fleet size and mix problem for capacitated arc routing. European Journal of Operational Research 22 (3): 329–337.Google Scholar
  59. Vansteenwegen P, Souffriau W and Sörensen K (2010). Solving the mobile mapping van problem: A hybrid metaheuristic for capacitated arc routing with soft time windows. Computers & Operations Research 37 (11): 1870–1876.Google Scholar
  60. Welz S (1994). Optimal solutions for the capacitated arc routing problem using integer programming. PhD Thesis, Department of QT and OM, University of Cincinnati.Google Scholar
  61. Win Z (1988). Contributions to routing problems. PhD Thesis, University of Augsburg, Germany.Google Scholar
  62. Wøhlk S (2005). Contributions to arc routing. PhD Thesis, Faculty of Social Sciences, University of Southern Denmark.Google Scholar
  63. Wøhlk S (2006). New lower bound for the capacitated arc routing problem. Computers & Operations Research 33 (12): 3458–3472.Google Scholar
  64. Wøhlk S (2008). A decade of capacitated arc routing. In: Golden B, Raghavan S and Wasil E (eds). The Vehicle Routing Problem: Latest Advances and New Challenges. Operations Research/Computer Science Interfaces Series Springer: Boston, pp 29–48.Google Scholar

Copyright information

© Operational Research Society 2016

Authors and Affiliations

  • S Gonzalez-Martin
    • 1
  • A A Juan
    • 1
  • D Riera
    • 1
  • M G Elizondo
    • 2
  • J J Ramos
    • 3
  1. 1.Open University of CataloniaBarcelonaSpain
  2. 2.Centro de Investigación y Desarrollo Tecnológico Universidad Autónoma de Nueva León, San Nicolás de los GarzaMéxico
  3. 3.Universitat Autònoma de BarcelonaBarcelonaSpain

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