Skip to main content
SpringerLink
Log in

On Efficiently Solving the Vehicle Routing Problem with Time Windows Using the Bat Algorithm with Random Reinsertion Operators

  • Chapter
  • First Online:
Nature-Inspired Algorithms and Applied Optimization

Part of the book series: Studies in Computational Intelligence ((SCI,volume 744))

Abstract

An evolutionary and discrete variant of the Bat Algorithm (EDBA) is proposed for solving the Vehicle Routing Problem with Time Windows, or VRPTW. The EDBA developed not only presents an improved movement strategy, but it also combines with diverse heuristic operators to deal with this type of complex problems. One of the main new concepts is to unify the search process and the minimization of the routes and total distance in the same operators. This hybridization is achieved by using selective node extractions and subsequent reinsertions. In addition, the new approach analyzes all the routes that compose a solution with the intention of enhancing the diversification ability of the search process. In this study, several variants of the EDBA are shown and tested in order to measure the quality of both metaheuristic algorithms and their operators. The benchmark experiments have been carried out by using the 56 instances that compose the 100 customers Solomon’s benchmark. Two statistical tests have also been carried out so as to analyze the results and draw proper conclusions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    https://www.sintef.no/projectweb/top/vrptw/homberger-benchmark/.

References

  1. Laporte, G.: The vehicle routing problem: an overview of exact and approximate algorithms. Eur. J. Operat. Res. 59(3), 345–358 (1992)

    Article  MATH  Google Scholar 

  2. Kirkpatrick, S., Gellat, C., Vecchi, M.: Optimization by simmulated annealing. Science 220(4598), 671–680 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  3. Glover, F.: Tabu search, part I. ORSA J. Comput. 1(3), 190–206 (1989)

    Article  MATH  Google Scholar 

  4. Dorigo, M., Blum, C.: Ant colony optimization theory: a survey. Theor. Comput. Sci. 344(2), 243–278 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Goldberg, D.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley Professional (1989)

    Google Scholar 

  6. De Jong, K.: Analysis of the behavior of a class of genetic adaptive systems. PhD thesis, University of Michigan, Michigan, USA (1975)

    Google Scholar 

  7. Kennedy, J., Eberhart, R., et al.: Particle swarm optimization. In: Proceedings of IEEE International Conference on Neural Networks. Vol. 4., Perth, Australia, pp. 1942–1948 (1995)

    Google Scholar 

  8. Atashpaz-Gargari, E., Lucas, C.: Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. In: Evolutionary Computation, 2007. CEC 2007. IEEE Congress on, IEEE pp. 4661–4667 (2007)

    Google Scholar 

  9. Karaboga, D., Basturk, B.: A powerful and efficient algorithm for numerical function optimization: artificial bee colony (abc) algorithm. J. Glob. Optim. 39(3), 459–471 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  10. Yang, X.S.: A new metaheuristic bat-inspired algorithm. In: Nature Inspired Cooperative Strategies for Optimization. Springer pp. 65–74 (2010)

    Google Scholar 

  11. Yang, X.S., He, X.: Bat algorithm: literature review and applications. Int. J. Bio-Ins. Comput. 5(3), 141–149 (2013)

    Article  Google Scholar 

  12. Parpinelli, R.S., Lopes, H.S.: New inspirations in swarm intelligence: a survey. Int. J. Bio-Ins. Comput. 3(1), 1–16 (2011)

    Article  Google Scholar 

  13. Dhar, S., Alam, S., Santra, M., Saha, P., Thakur, S.: A novel method for edge detection in a gray image based on human psychovisual phenomenon and bat algorithm. In: Computer, Communication and Electrical Technology. CRC Press, pp. 3–7 (2007)

    Google Scholar 

  14. Tharakeshwar, T., Seetharamu, K., Prasad, B.D.: Multi-objective optimization using bat algorithm for shell and tube heat exchangers. Appl. Therm. Eng. 110, 1029–1038 (2017)

    Article  Google Scholar 

  15. Osaba, E., Carballedo, R., Yang, X.S., Diaz, F.: An evolutionary discrete firefly algorithm with novel operators for solving the vehicle routing problem with time windows. In: Nature-Inspired Computation in Engineering. Springer, pp. 21–41 (2016)

    Google Scholar 

  16. Lawler, E.L.: The traveling salesman problem: a guided tour of combinatorial optimization. Wiley-Interscience Series in Discrete Mathematics (1985)

    Google Scholar 

  17. Christofides, N.: The vehicle routing problem. RAIRO Operat. Res. Recherche Opérationnel. 10(V1), 55–70 (1976)

    MathSciNet  MATH  Google Scholar 

  18. Wassan, N., Wassan, N., Nagy, G., Salhi, S.: The multiple trip vehicle routing problem with backhauls: formulation and a two-level variable neighbourhood search. Comput. Operat. Res. 78, 454–467 (2017)

    Article  MathSciNet  Google Scholar 

  19. Veenstra, M., Roodbergen, K.J., Vis, I.F., Coelho, L.C.: The pickup and delivery traveling salesman problem with handling costs. Eur. J. Operat. Res. 257(1), 118–132 (2017)

    Article  MathSciNet  Google Scholar 

  20. Bräysy, O., Gendreau, M.: Vehicle routing problem with time windows, part I: route construction and local search algorithms. Transport. Sci. 39(1), 104–118 (2005)

    Article  Google Scholar 

  21. Potvin, J.Y., Bengio, S.: The vehicle routing problem with time windows part II: genetic search. INFORMS J. Comput. 8(2), 165–172 (1996)

    Article  MATH  Google Scholar 

  22. Laporte, G.: The traveling salesman problem: an overview of exact and approximate algorithms. Eur. J. of Oper. Res. 59(2), 231–247 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  23. Bräysy, O., Gendreau, M.: Vehicle routing problem with time windows, part II: metaheuristics. Transport. Sci. 39(1), 119–139 (2005)

    Article  Google Scholar 

  24. Yang, X.S.: Nature-inspired metaheuristic algorithms. Luniver press (2010)

    Google Scholar 

  25. Taha, A., Hachimi, M., Moudden, A.: Adapted bat algorithm for capacitated vehicle routing problem. Int. Rev. Comput. Soft. (IRECOS) 10(6), 610–619 (2015)

    Article  Google Scholar 

  26. Zhou, Y., Luo, Q., Xie, J., Zheng, H.: A hybrid bat algorithm with path relinking for the capacitated vehicle routing problem. In: Metaheuristics and Optimization in Civil Engineering. Springer, pp. 255–276 (2016)

    Google Scholar 

  27. Yang, X.S.: Nature-Inspired Metaheuristic Algorithms. Luniver Press, UK (2008)

    Google Scholar 

  28. Fister, I., Yang, X.S., Fister, D., Fister Jr, I.: Firefly algorithm: a brief review of the expanding literature. In: Cuckoo Search and Firefly Algorithm. Springer, pp. 347–360 (2014)

    Google Scholar 

  29. Fister, I., Fister Jr., I., Yang, X.S., Brest, J.: A comprehensive review of firefly algorithms. Swarm Evolut. Comput. 13, 34–46 (2013)

    Article  Google Scholar 

  30. Jati, G.K., Suyanto. In: Evolutionary Discrete Firefly Algorithm for Travelling Salesman Problem. Springer, Berlin Heidelberg, pp. 393–403 (2011)

    Google Scholar 

  31. Alinaghian, M., Naderipour, M.: A novel comprehensive macroscopic model for time-dependent vehicle routing problem with multi-alternative graph to reduce fuel consumption: a case study. Comput. Indust. Eng. 99, 210–222 (2016)

    Article  Google Scholar 

  32. Del Ser, J., Torre-Bastida, A.I., Lana, I., Bilbao, M.N., Perfecto, C.: Nature-inspired heuristics for the multiple-vehicle selective pickup and delivery problem under maximum profit and incentive fairness criteria. In: IEEE Congress on Evolutionary Computation (2017)

    Google Scholar 

  33. Yang, X.S., Deb, S.: Cuckoo search via lévy flights. In: World Congress on Nature & Biologically Inspired Computing. IEEE, pp. 210–214 (2009)

    Google Scholar 

  34. Ouaarab, A., Ahiod, B., Yang, X.S.: Discrete cuckoo search algorithm for the travelling salesman problem. Neural Comput. Appl. 24(7–8), 1659–1669 (2014)

    Article  Google Scholar 

  35. Alssager, M., Othman, Z.A.: Taguchi-based parameter setting of cuckoo search algorithm for capacitated vehicle routing problem. In: Advances in Machine Learning and Signal Processing. Springer, pp. 71–79 (2016)

    Google Scholar 

  36. Teymourian, E., Kayvanfar, V., Komaki, G.M., Zandieh, M.: Enhanced intelligent water drops and cuckoo search algorithms for solving the capacitated vehicle routing problem. Informat. Sci. 334, 354–378 (2016)

    Article  Google Scholar 

  37. Chen, X., Wang, J.: A novel hybrid cuckoo search algorithm for optimizing vehicle routing problem in logistics distribution system. J. Comput. Theor. Nanosci. 13(1), 114–119 (2016)

    Article  Google Scholar 

  38. Geem, Z.W., Kim, J.H., Loganathan, G.: A new heuristic optimization algorithm: harmony search. Simulation 76(2), 60–68 (2001)

    Article  Google Scholar 

  39. Manjarres, D., Landa-Torres, I., Gil-Lopez, S., Del Ser, J., Bilbao, M.N., Salcedo-Sanz, S., Geem, Z.W.: A survey on applications of the harmony search algorithm. Eng. Appl. Artific. Intell. 26(8), 1818–1831 (2013)

    Article  Google Scholar 

  40. Assad, A., Deep, K.: Applications of harmony search algorithm in data mining: a survey. In: Proceedings of Fifth International Conference on Soft Computing for Problem Solving. Springer , pp. 863–874 (2016)

    Google Scholar 

  41. Mohd Alia, O., Mandava, R.: The variants of the harmony search algorithm: an overview. Artific. Intell. Rev. 36(1), 49–68 (2011)

    Article  Google Scholar 

  42. Geem, Z.W., Lee, K.S., Park, Y.: Application of harmony search to vehicle routing. Am. J. Appl. Sci. 2(12), 1552–1557 (2005)

    Article  Google Scholar 

  43. Del Ser, J., Bilbao, M.N., Perfecto, C., Salcedo-Sanz, S.: A harmony search approach for the selective pick-up and delivery problem with delayed drop-off. In: Harmony Search Algorithm. Springer, pp. 121–131 (2016)

    Google Scholar 

  44. Rashedi, E., Nezamabadi-Pour, H., Saryazdi, S.: Gsa: a gravitational search algorithm. Informat. Sci. 179(13), 2232–2248 (2009)

    Article  MATH  Google Scholar 

  45. Precup, R.E., David, R.C., Petriu, E.M., Radac, M.B., Preitl, S.: Adaptive gsa-based optimal tuning of pi controlled servo systems with reduced process parametric sensitivity, robust stability and controller robustness. IEEE Trans. Cybernet. 44(11), 1997–2009 (2014)

    Article  Google Scholar 

  46. Precup, R.E., David, R.C., Petriu, E.M., Preitl, S., Rădac, M.B.: Fuzzy logic-based adaptive gravitational search algorithm for optimal tuning of fuzzy-controlled servo systems. IET Control Theor. Appl. 7(1), 99–107 (2013)

    Article  MathSciNet  Google Scholar 

  47. Duman, S., Güvenç, U., Sönmez, Y., Yörükeren, N.: Optimal power flow using gravitational search algorithm. Energy Convers. Manag. 59, 86–95 (2012)

    Article  Google Scholar 

  48. Nodehi, A.N., Fadaei, M., Ebrahimi, P.: Solving the traveling salesman problem using randomized gravitational emulation search algorithm. J. Curr. Res. Sci. 2, 818 (2016)

    Google Scholar 

  49. Hosseinabadi, A.A.R., Kardgar, M., Shojafar, M., Shamshirband, S., Abraham, A.: Gravitational search algorithm to solve open vehicle routing problem. In: Innovations in Bio-Inspired Computing and Applications. Springer, pp. 93–103 (2016)

    Google Scholar 

  50. Hosseinabadi, A.A.R., Rostami, N.S.H., Kardgar, M., Mirkamali, S., Abraham, A.: A new efficient approach for solving the capacitated vehicle routing problem using the gravitational emulation local search algorithm. Appl. Mathemat, Model (2017)

    Google Scholar 

  51. Desaulniers, G., Errico, F., Irnich, S., Schneider, M.: Exact algorithms for electric vehicle-routing problems with time windows. Les Cahiers du GERAD G-2014-110, GERAD, Montréal, Canada (2014)

    Google Scholar 

  52. Belhaiza, S., Hansen, P., Laporte, G.: A hybrid variable neighborhood tabu search heuristic for the vehicle routing problem with multiple time windows. Comput. Operat. Res. 52, 269–281 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  53. Toklu, N.E., Gambardella, L.M., Montemanni, R.: A multiple ant colony system for a vehicle routing problem with time windows and uncertain travel times. J. Traffic Logist. Eng. 2(1) (2014)

    Google Scholar 

  54. Nguyen, P.K., Crainic, T.G., Toulouse, M.: A hybrid generational genetic algorithm for the periodic vehicle routing problem with time windows. J. Heurist. 20(4), 383–416 (2014)

    Article  Google Scholar 

  55. Yassen, E.T., Ayob, M., Nazri, M.Z.A., Sabar, N.R.: Meta-harmony search algorithm for the vehicle routing problem with time windows. Informat. Sci. 325, 140–158 (2015)

    Article  Google Scholar 

  56. Yang, X.S., Deb, S.: Cuckoo search: recent advances and applications. Neural Comput. Appl. 24(1), 169–174 (2014)

    Article  Google Scholar 

  57. Kallehauge, B., Larsen, J., Madsen, O.B., Solomon, M.M.: Vehicle routing problem with time windows. Springer (2005)

    Google Scholar 

  58. Gendreau, M., Tarantilis, C.D.: Solving large-scale vehicle routing problems with time windows: the state-of-the-art. CIRRELT (2010)

    Google Scholar 

  59. Afifi, S., Guibadj, R.N., Moukrim, A.: New lower bounds on the number of vehicles for the vehicle routing problem with time windows. In: Integration of AI and OR Techniques in Constraint Programming. Springer, pp. 422–437 (2014)

    Google Scholar 

  60. Agra, A., Christiansen, M., Figueiredo, R., Hvattum, L.M., Poss, M., Requejo, C.: The robust vehicle routing problem with time windows. Comput. Operat. Res. 40(3), 856–866 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  61. Azi, N., Gendreau, M., Potvin, J.Y.: An exact algorithm for a single-vehicle routing problem with time windows and multiple routes. Eur. J. Operat. Res. 178(3), 755–766 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  62. Bräysy, O., Gendreau, M.: Tabu search heuristics for the vehicle routing problem with time windows. Top 10(2), 211–237 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  63. Cordeau, J.F., Desaulniers, G., Desrosiers, J., Solomon, M.M., Soumis, F.: Vrp with time windows. Vehicle Rout. Prob. 9, 157–193 (2001)

    MathSciNet  MATH  Google Scholar 

  64. Glover, F.: Ejection chains, reference structures and alternating path methods for traveling salesman problems. Discr. Appl. Mathemat. 65(1–3), 223–253 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  65. Osaba, E., Yang, X.S., Diaz, F., Onieva, E., Masegosa, A.D., Perallos, A.: A discrete firefly algorithm to solve a rich vehicle routing problem modelling a newspaper distribution system with recycling policy. Soft Comput. 1–14 (2016)

    Google Scholar 

  66. Irnich, S.: A unified modeling and solution framework for vehicle routing and local search-based metaheuristics. INFORMS J. Comput. 20(2), 270–287 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  67. Campbell, A.M., Savelsbergh, M.: Efficient Insertion heuristics for vehicle routing and scheduling problems. Transport. Sci. 38(3), 369–378 (2004)

    Article  Google Scholar 

  68. Solomon, M.M.: Algorithms for the vehicle routing and scheduling problems with time window constraints. Oper. Res. 35(2), 254–265 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  69. Derrac, J., García, S., Molina, D., Herrera, F.: A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol. Computat. 1(1), 3–18 (2011)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Deusto Institute of Technology (DeustoTech), University of Deusto, Av. Universidades 24, 48007, Bilbao, Spain

    Eneko Osaba, Roberto Carballedo & Pedro Lopez-Garcia

  2. School of Science and Technology, Middlesex University, Hendon Campus, London, NW4 4BT, UK

    Xin-She Yang

  3. Faculty of Electrical Engineering and Computer Science, University of Maribor, Smetanova 17, 2000, Maribor, Slovenia

    Iztok Fister Jr.

  4. TECNALIA, 48160, Derio, Spain

    Javier Del Ser

  5. University of the Basque Country (UPV/EHU), 48013, Bilbao, Spain

    Javier Del Ser

  6. Basque Center for Applied Mathematics (BCAM), 48009, Bilbao, Spain

    Javier Del Ser

Authors
  1. Eneko Osaba
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Roberto Carballedo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xin-She Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Iztok Fister Jr.
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Pedro Lopez-Garcia
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Javier Del Ser
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Eneko Osaba .

Editor information

Editors and Affiliations

  1. School of Science and Technology, Middlesex University, London, United Kingdom

    Xin-She Yang

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Cite this chapter

Osaba, E., Carballedo, R., Yang, XS., Fister Jr., I., Lopez-Garcia, P., Del Ser, J. (2018). On Efficiently Solving the Vehicle Routing Problem with Time Windows Using the Bat Algorithm with Random Reinsertion Operators. In: Yang, XS. (eds) Nature-Inspired Algorithms and Applied Optimization. Studies in Computational Intelligence, vol 744. Springer, Cham. https://doi.org/10.1007/978-3-319-67669-2_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-67669-2_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67668-5

  • Online ISBN: 978-3-319-67669-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation