Skip to main content

Parallel Multi-Start Non-dominated Sorting Particle Swarm Optimization Algorithms for the Minimization of the Route-Based Fuel Consumption of Multiobjective Vehicle Routing Problems

  • Chapter
  • First Online:
Optimization Methods and Applications

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 130))

Abstract

In this paper, a Multiobjective Route-based Fuel Consumption Vehicle Routing problem (MRFCVRPs) is solved using a new variant of a Multiobjective Particle Swarm Optimization algorithm, the Parallel Multi-Start Non-dominated Sorting Particle Swarm Optimization algorithm (PMS-NSPSO). Three different versions of this algorithm are used and their results are compared with a Parallel Multi-Start NSGA II algorithm and a Parallel Multi-Start NSDE algorithm. All these algorithms use more than one initial populations of solutions. The Variable Neighborhood Search algorithm is used in all algorithm for the improvement of each solution separately. The Multiobjective Symmetric and Asymmetric Delivery Route-based Fuel Consumption Vehicle Routing Problem and the Multiobjective Symmetric and Asymmetric Pick-up Route-based Fuel Consumption Vehicle Routing Problem are the problems that are solved. The objective functions correspond to the optimization of the time needed for the vehicle to travel between two customers or between the customer and the depot and to the Route based Fuel Consumption of the vehicle considering the traveled distance, the load of the vehicle, the slope of the road, the speed and the direction of the wind, and the driver’sbehavior when the decision maker plans delivery or pick-up routes. A number of modified Vehicle Routing Problem instances are used in order to measure the quality of the proposed algorithms.

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

Access this chapter

Institutional subscriptions

References

  1. Ai, T.J., Kachitvichyanukul, V.: A particle swarm optimization for vehicle routing problem with time windows. Int. J. Oper. Res. 6(4), 519–537 (2009)

    Google Scholar 

  2. Ai, T.J., Kachitvichyanukul, V.: A particle swarm optimization for the vehicle routing problem with simultaneous pickup and delivery. Comput. Oper. Res. 36, 1693–1702 (2009)

    Google Scholar 

  3. Ai, T.J., Kachitvichyanukul, V.: Particle swarm optimization and two solution representations for solving the capacitated vehicle routing problem. Comput. Ind. Eng. 56, 380–387 (2009)

    Google Scholar 

  4. Bandeira, J.M., Fontes, T., Pereira, S.R., Fernandes, P., Khattak, A., Coelho, M.C.: Assessing the importance of vehicle type for the implementation of eco-routing systems. Transp. Res. Procedia 3, 800–809 (2014)

    Google Scholar 

  5. Banks, A., Vincent, J., Anyakoha, C.: A review of particle swarm optimization. Part I: background and development. Nat. Comput. 6(4), 467–484 (2007)

    Google Scholar 

  6. Banks, A., Vincent, J., Anyakoha, C.: A review of particle swarm optimization. Part II: hybridisation, combinatorial, multicriteria and constrained optimization, and indicative applications. Nat. Comput. 7, 109–124 (2008)

    Google Scholar 

  7. Bartz-Beielstein, T., Limbourg, P., Parsopoulos, K.E., Vrahatis, M.N., Mehnen, J., Schmitt, K.: Particle swarm optimizers for pareto optimization with enhanced archiving techniques. In: IEEE Congress on Evolutionary Computation (CEC2003), vol. 3, pp. 1780–1787 (2003)

    Google Scholar 

  8. Bektas, T., Laporte, G.: The pollution-routing problem. Transp. Res. B 45, 1232–1250 (2011)

    Google Scholar 

  9. Brits, R., Engelbrecht, A.P., Van Den Bergh, F.: Locating multiple optima using particle swarm optimization. Appl. Math. Comput. 189, 1859–1883 (2007)

    Google Scholar 

  10. Charoenroop, N., Satayopas, B., Eungwanichayapant, A.: City bus routing model for minimal energy consumption. Asian J. Energy Environ. 11(01), 19–31 (2010)

    Google Scholar 

  11. Chen, A.-L., Yang, G.-K., Wu, Z.-M.: Hybrid discrete particle swarm optimization algorithm for capacitated vehicle routing problem. J. Zheijang Univ. Sci. A 7(4), 607–614 (2006)

    Google Scholar 

  12. Chow, C., Tsui, H.: Autonomous agent response learning by a multi-species particle swarm optimization. In: IEEE Congress on Evolutionary Computation (CEC2004), vol. 1, pp. 778–785 (2004)

    Google Scholar 

  13. Cicero-Fernandez, P., Long, J.R., Winer, A.M.: Effects of grades and other loads on on-road emissions of hydrocarbons and carbon monoxide. J. Air Waste Manage. Assoc. 47, 898–904 (1997)

    Google Scholar 

  14. Clerc, M.: Particle Swarm Optimization. ISTE, London (2006)

    Google Scholar 

  15. Clerc, M., Kennedy, J.: The particle swarm: explosion, stability and convergence in a multi-dimensional complex space. IEEE Trans. Evol. Comput. 6, 58–73 (2002)

    Google Scholar 

  16. Coello Coello, C.A., Van Veldhuizen, D.A., Lamont, G.B.: Evolutionary Algorithms for Solving Multi-Objective Problems. Springer, Berlin (2007)

    Google Scholar 

  17. Deb, K., Pratap, A., Agarwal, S., Meyarivan T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)

    Google Scholar 

  18. Dehuri, S., Jagadev, A.K., Panda, M.: Multi-Objective Swarm Intelligence: Theoretical Advances and Applications. Springer, Berlin (2002)

    Google Scholar 

  19. Dekker, R., Fleischmann, M., Inderfurth, K., Van Wassenhove, L.N.: Reverse Logistics: Quantitative Models for Closed-Loop Supply Chains. Springer, Berlin (2004)

    Google Scholar 

  20. Demir, E., Bektas, T., Laporte, G.: The bi-objective pollution-routing problem. Eur. J. Oper. Res. 232, 464–478 (2014)

    Google Scholar 

  21. Dethloff, J.: Vehicle routing and reverse logistics: the vehicle routing problem with simultaneous delivery and pick-up. OR Spektrum 23, 79–96 (2001)

    Google Scholar 

  22. Erdogan, S., Miller-Hooks, E.: A green vehicle routing problem. Transp. Res. E 48, 100–114 (2012)

    Google Scholar 

  23. Fan, J., Zhao, L., Du, L., Zheng, Y.: Crowding-distance-based multi-objective particle swarm optimization. Comput. Intell. Intell. Syst. Commun. Comput. Inf. Sci. 107, 218–225 (2010)

    Google Scholar 

  24. Feo, T.A., Resende, M.G.C.: Greedy randomized adaptive search procedure. J. Glob. Optim. 6, 109–133 (1995)

    Google Scholar 

  25. Fieldsend, J.E., Singh, S.: A multiobjective algorithm based upon particle swarm optimisation, an efficient data structure and turbulence. In: Proceedings of the 2002 U.K. Workshop on Computational Intelligence, pp. 37–44 (2002)

    Google Scholar 

  26. Figliozzi, M.: Vehicle routing problem for emissions minimization. Transp. Res. Rec. J. Transp. Res. Board 2, 1–7 (2011)

    Google Scholar 

  27. Fleischmann, M., Bloemhof-Ruwaard, J.M., Dekker, R., Van Der Laan, E., Van Nunen, J.A.E.E., Van Wassenhove, L.N.: Quantitative models for reverse logistics: a review. Eur. J. Oper. Res. 103, 1–17 (1997)

    Google Scholar 

  28. Goksal, F.P., Karaoglan, I., Altiparmak, F.: A hybrid discrete particle swarm optimization for vehicle routing problem with simultaneous pickup and delivery. Comput. Ind. Eng. 65, 39–53 (2013)

    Google Scholar 

  29. Gong, Y.-J., Zhang, J., Liu, O., Huang, R.-Z., Chung, H.S.-H., Shi, Y.-H.: Optimizing the vehicle routing problem with time windows: a discrete particle swarm optimization approach. IEEE Trans. Syst. Man Cybern. Part C Appl. Rev. 42(2), 254–267 (2012)

    Google Scholar 

  30. Hansen, P., Mladenovic, N.: Variable neighborhood search: principles and applications. Eur. J. Oper. Res. 130, 449–467 (2001)

    Google Scholar 

  31. Ho, S.L., Shiyou, Y., Guangzheng, N., Lo, E.W.C., Wong, H.C.: A particle swarm optimization-based method for multiobjective design optimizations. IEEE Trans. Magn. 41, 1756–1759 (2005)

    Google Scholar 

  32. Hu, X., Eberhart, R.C.: Multiobjective optimization using dynamic neighborhood particle swarm optimization. In: IEEE Congress on Evolutionary Computation (CEC2002), vol. 2, pp. 1677–1681 (2002)

    Google Scholar 

  33. Hu, X., Eberhart, R.C., Shi, Y.: Particle swarm with extended memory for multiobjective optimization. In: Proceedings of the 2003 IEEE Swarm Intelligence Symposium, pp. 193–197 (2003)

    Google Scholar 

  34. Janson S., Merkle D.: A new multiobjective particle swarm optimization algorithm using clustering applied to automated docking. In: Hybrid Metaheuristics, 2nd International Workshop, HM 2005, pp. 128–142 (2005)

    Google Scholar 

  35. Jemai, J., Zekri, M., Mellouli, K.: An NSGA-II algorithm for the green vehicle routing problem. In: Evolutionary Computation in Combinatorial Optimization. Lecture Notes in Computer Science, vol. 7245, pp. 37–48. Springer, Berlin/Heidelberg (2012)

    Google Scholar 

  36. Johnson, D.S., Papadimitriou, C.H.: Computational complexity. In: Lawer, E.L., Lenstra, J.K., Rinnoy Kan, A.H.D., Shmoys, D.B. (eds.) The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization, pp. 37–85. Wiley and Sons, Hoboken (1985)

    Google Scholar 

  37. Jozefowiez, N., Semet, F., Talbi, E.G.: Multi-objective vehicle routing problems. Eur. J. Oper. Res. 189, 293–309 (2008)

    Google Scholar 

  38. Kara, I., Kara, B.Y., Yetis, M.K.: Energy minimizing vehicle routing problem. In: COCOA 2007, pp. 62–71 (2007)

    Google Scholar 

  39. Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of 1995 IEEE International Conference on Neural Networks, vol. 4, pp. 1942–1948 (1995)

    Google Scholar 

  40. Khouadjia, M.R., Sarasola, B., Alba, E., Jourdan, L., Talbi, E.-G.: A comparative study between dynamic adapted PSO and VNS for the vehicle routing problem with dynamic requests. Appl. Soft Comput. 12, 1426–1439 (2012)

    Google Scholar 

  41. Kim, H., Yang, J., Lee, K.D.: Vehicle routing in reverse logistics for recycling end-of-life consumer electronic goods in South Korea. Transp. Res. D 14(5), 291–299 (2009)

    Google Scholar 

  42. Kim, H., Yang, J., Lee, K.D.: Reverse logistics using a multi-depot VRP approach for recycling end-of-life consumer electronic products in South Korea. Int. J. Sustain. Transp. 5(5), 289–318 (2011)

    Google Scholar 

  43. Koc, C., Bektas, T., Jabali, O., Laporte, G.: The fleet size and mix pollution-routing problem. Transp. Res. B 70, 239–254 (2014)

    Google Scholar 

  44. Kontovas, C.A.: The green ship routing and scheduling problem (GSRSP): a conceptual approach. Transp. Res. D 31, 61–69 (2014)

    Google Scholar 

  45. Kumar, R.S., Kondapaneni, K., Dixit, V., Goswami, A., Thakur, L.S., Tiwari, M.K.: Multi-objective modeling of production and pollution routing problem with time window: a self-learning particle swarm optimization approach. Comput. Ind. Eng. 99, 29–40 (2015). PII: S0360-8352(15)00287-9

    Google Scholar 

  46. Kuo, Y.: Using simulated annealing to minimize fuel consumption for the time-dependent vehicle routing problem. Comput. Ind. Eng. 59(1), 157–165 (2010)

    Google Scholar 

  47. Labadie, N., Prodhon, C.: A survey on multi-criteria analysis in logistics: Focus on vehicle routing problems. In: Applications of Multi-Criteria and Game Theory Approaches. Springer Series in Advanced Manufacturing, pp. 3–29. Springer, London (2014)

    Google Scholar 

  48. Lahyani, R., Khemakhem, M., Semet, F.: Rich vehicle routing problems: from a taxonomy to a definition. Eur. J. Oper. Res. 241, 1–14 (2015)

    Google Scholar 

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

    Google Scholar 

  50. Lawer, E.L., Lenstra, J.K., Rinnoy Kan, A.H.G.R., Shmoys, D.B.: The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization. Wiley and Sons, Hoboken (1985)

    Google Scholar 

  51. Leonardi, J., Baumgartner, M.: CO 2 efficiency in road freight transportation: status quo, measures and potential. Transp. Res. D 9, 451–464 (2004)

    Google Scholar 

  52. Li, X.: A non-dominated sorting particle swarm optimizer for multiobjective optimization. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO2003), pp. 37–48 (2003)

    Google Scholar 

  53. Li, J.: Vehicle routing problem with time windows for reducing fuel consumption. J. Comput. 7(12), 3020–3027 (2012)

    Google Scholar 

  54. Li, H., Lv, T., Li, Y.: The tractor and semitrailer routing problem with many-to-many demand considering carbon dioxide emissions. Transp. Res. D 34, 68–82 (2015)

    Google Scholar 

  55. Lichtblau, D.: Discrete optimization using mathematica, In: Callaos, N., Ebisuzaki, T., Starr, B., Abe, J.M., Lichtblau, D. (eds.) World Multi-conference on Systemics, Cybernetics and Informatics (SCI 2002), vol. 16, pp. 169–174. International Institute of Informatics and Systemics, Winter Garden (2002)

    Google Scholar 

  56. Lin, S.: Computer solutions of the traveling salesman problem. Bell Syst. Tech. J. 44, 2245–2269 (1965)

    Google Scholar 

  57. Lin, C., Choy, K.L., Ho, G.T.S., Ng, T.W.: A genetic algorithm-based optimization model for supporting green transportation operations. Expert Syst. Appl. 41, 3284–3296 (2014)

    Google Scholar 

  58. Lin, C., Choy, K.L., Ho, G.T.S., Chung, S.H., Lam, H.Y.: Survey of green vehicle routing problem: past and future trends. Expert Syst. Appl. 41(4), 1118–1138 (2014)

    Google Scholar 

  59. Marinakis, Y., Marinaki, M.: A particle swarm optimization algorithm with path relinking for the location routing problem. J. Math Model. Algor. 7(1), 59–78 (2008)

    Google Scholar 

  60. Marinakis, Y., Marinaki, M.: A hybrid genetic - particle swarm optimization algorithm for the vehicle routing problem. Expert Syst. Appl. 37, 1446–1455 (2010)

    Google Scholar 

  61. Marinakis, Y., Marinaki, M.: A hybrid multi-swarm particle swarm optimization algorithm for the probabilistic traveling salesman problem. Comput. Oper. Res. 37, 432–442 (2010)

    Google Scholar 

  62. Marinakis, Y., Marinaki, M.: A hybrid particle swarm optimization algorithm for the open vehicle routing problem. In: Dorigo, M., et al. (eds.) ANTS 2012. Lecture Notes in Computer Science, vol. 7461, pp. 180–187. Springer, Berlin/Heidelberg (2012)

    Google Scholar 

  63. Marinakis, Y., Marinaki, M.: Combinatorial neighborhood topology particle swarm optimization algorithm for the vehicle routing problem. In: Middendorf, M., Blum, C. (eds.) EvoCOP 2013. Lecture Notes in Computer Science, vol. 7832, pp. 133–144. Springer, Berlin/Heidelberg (2013)

    Google Scholar 

  64. Marinakis, Y., Marinaki, M.: Combinatorial expanding neighborhood topology particle swarm optimization for the vehicle routing problem with stochastic demands. In: GECCO: 2013, Genetic and Evolutionary Computation Conference, Amsterdam, 6–10 July 2013, pp. 49–56

    Google Scholar 

  65. Marinakis, Y., Marinaki, M., Dounias, G.: A hybrid particle swarm optimization algorithm for the vehicle routing problem. Eng. Appl. Artif. Intell. 23, 463–472 (2010)

    Google Scholar 

  66. Marinakis, Y., Iordanidou, G., Marinaki, M.: Particle swarm optimization for the vehicle routing problem with stochastic demands. Appl. Soft Comput. 13(4), 1693–1704 (2013)

    Google Scholar 

  67. Marinakis, Y., Marinaki, M., Migdalas, A.: An adaptive particle swarm optimization algorithm for the vehicle routing problem with time windows. In: LOT 2014, Logistics, Optimization and Transportation Conference, 1–2 November 2014, Molde, Norway (2014)

    Google Scholar 

  68. McKinnon, A.: A logistical perspective on the fuel efficiency of road freight transport. In: OECD, ECMT and IEA: Workshop Proceedings, Paris (1999)

    Google Scholar 

  69. McKinnon, A.: Green logistics: the carbon agenda. Electron. Sci. J. Logist. 6(3), 1–9 (2010)

    MathSciNet  Google Scholar 

  70. Molina, J.C., Eguia, I., Racero, J, Guerrero, F.: Multi-objective vehicle routing problem with cost and emission functions. Procedia Soc. Behav. Sci. 160, 254–263 (2014)

    Article  Google Scholar 

  71. Moore, J.: Application of particle swarm to multiobjective optimization. Department of Computer Science and Software Engineering, Auburn University (1999)

    Google Scholar 

  72. Mostaghim, S., Teich, J.: Covering pareto-optimal fronts by subswarms in multi-objective particle swarm optimization. In: IEEE Congress on Evolutionary Computation (CEC2004), vol. 2, pp. 1404–1411 (2004)

    Google Scholar 

  73. Niu, B., Zhu, Y., He, X., Wu, H.: MCPSO: a multi-swarm cooperative particle swarm optimizer. Appl. Math. Comput. 185, 1050–1062 (2007)

    MATH  Google Scholar 

  74. Niu, B., Zhu, Y., He, X., Shen, H.: A multi-swarm optimizer based fuzzy modeling approach for dynamic systems processing. Neurocomputing 71, 1436–1448 (2008)

    Article  Google Scholar 

  75. Okabe, T., Jin, Y., Sendhoff, B.: A critical survey of performance indices for multi-objective optimization. Evol. Comput. 2, 878–885 (2003)

    Google Scholar 

  76. Parsopoulos, K.E., Tasoulis, D.K., Vrahatis, M.N.: Multiobjective optimization using parallel vector evaluated particle swarm optimization. In: Proceedings of the IASTED International Conference on Artificial Intelligence and Applications (AIA 2004), vol. 2, pp. 823–828 (2004)

    Google Scholar 

  77. Poli, R., Kennedy, J., Blackwell, T.: Particle swarm optimization. An overview. Swarm Intell. 1, 33–57 (2007)

    Article  Google Scholar 

  78. Psychas, I.D., Marinaki, M., Marinakis, Y.: A parallel multi-start NSGA II algorithm for multiobjective energy reduction vehicle routing problem. In: Gaspar-Cunha, A., et al. (eds.) 8th International Conference on Evolutionary Multicriterion Optimization, EMO 2015, Part I. Lecture Notes in Computer Science, vol. 9018, pp. 336–350. Springer International Publishing, Cham (2015)

    Google Scholar 

  79. Psychas, I.D., Marinaki, M., Marinakis, Y. Migdalas, A.: Non-dominated sorting differential evolution algorithm for the minimization of route based fuel consumption multiobjective vehicle routing problems. Energy Syst. 1–30 (2016). https://doi.org/10.1007/s12667-016-0209-5

  80. Psychas, I.D., Marinaki, M., Marinakis, Y. Migdalas, A.: Minimizing the fuel consumption of a multiobjective vehicle routing problem using the parallel multi-start NSGA II algorithm. In: Kalyagin, V.A., et al. (eds.) Models, Algorithms and Technologies for Network Analysis, pp. 69–88. Springer, Cham (2016)

    Chapter  Google Scholar 

  81. Pulido, G.T., Coello Coello, C.A.: Using clustering techniques to improve the performance of a particle swarm optimizer. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO2004), pp. 225–237 (2004)

    Google Scholar 

  82. Raquel, C.R., Prospero, J., Naval, C.: An effective use of crowding distance in multiobjective particle swarm optimization. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2005), pp. 257–264 (2005)

    Google Scholar 

  83. Reyes-Sierra, M., Coello Coello, C.A.: Multi-objective particle swarm optimizers: a survey of the state of the art. Int. J. Comput. Intell. Res. 2(3), 287–308 (2006)

    MathSciNet  Google Scholar 

  84. Sarker, R., Coello Coello, C.A.: Assessment methodologies for multiobjective evolutionary algorithms. In: Evolutionary Optimization. International Series in Operations Research and Management Science, vol. 48, pp. 177–195. Springer, Boston (2002)

    Google Scholar 

  85. Sbihi, A., Eglese, R.W.: Combinatorial optimization and green logistics. 4OR, 5(2), 99–116 (2007)

    Google Scholar 

  86. Shi, Y., Eberhart, R.: A modified particle swarm optimizer. In: Proceedings of 1998 IEEE World Congress on Computational Intelligence, pp. 69–73 (1998)

    Google Scholar 

  87. Srinivasan, D., Seow, T.H.: Particle swarm inspired evolutionary algorithm (PS-EA) for multiobjective optimization problem. In: IEEE Congress on Evolutionary Computation (CEC2003), vol. 3, pp. 2292–2297 (2003)

    Google Scholar 

  88. Suzuki, Y.: A new truck-routing approach for reducing fuel consumption and pollutants emission. Transp. Res. D 16, 73–77 (2011)

    Article  Google Scholar 

  89. Tajik, N., Tavakkoli-Moghaddam, R., Vahdani, B., Meysam Mousavi, S.: A robust optimization approach for pollution routing problem with pickup and delivery under uncertainty. J. Manuf. Syst. 33, 277–286 (2014)

    Article  Google Scholar 

  90. Tillett, T., Rao, T.M., Sahin, F., Rao R.: Darwinian particle swarm optimization. In: Proceedings of the 2nd Indian International Conference on Artificial Intelligence, Pune, pp. 1474–1487 (2005)

    Google Scholar 

  91. Tiwari, A., Chang, P.C.: A block recombination approach to solve green vehicle routing problem. Int. J. Prod. Econ. 64, 1–9 (2002)

    Google Scholar 

  92. Toth, P., Vigo, D.: The Vehicle Routing Problem, Monographs on Discrete Mathematics and Applications. SIAM, Philadelphia (2002)

    Book  MATH  Google Scholar 

  93. Toth, P., Vigo, D.: Vehicle Routing: Problems, Methods and Applications, 2nd edn. MOS-Siam Series on Optimization, SIAM, Philadelphia (2014)

    Book  MATH  Google Scholar 

  94. Weizhen, R., Chun, J.: A model of vehicle routing problem minimizing energy consumption in urban environment. In: Asian Conference of Management Science & Applications, September 2012, Chengdu-Jiuzhaigou, pp. 21–29 (2012)

    Google Scholar 

  95. Xiao, Y., Zhao, Q., Kaku, I., Xu, Y.: Development of a fuel consumption optimization model for the capacitated vehicle routing problem. Comput. Oper. Res. 39(7), 1419–1431 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  96. Zhang, S., Lee, C.K.M., Choy, K.L., Ho, W., Ip, W.H.: Design and development of a hybrid artificial bee colony algorithm for the environmental vehicle routing problem. Transp. Res. D 31, 85–99 (2014)

    Article  Google Scholar 

  97. Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: empirical results. Evol. Comput. 8(2), 173–195 (2000)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yannis Marinakis .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Psychas, ID., Marinaki, M., Marinakis, Y., Migdalas, A. (2017). Parallel Multi-Start Non-dominated Sorting Particle Swarm Optimization Algorithms for the Minimization of the Route-Based Fuel Consumption of Multiobjective Vehicle Routing Problems. In: Butenko, S., Pardalos, P., Shylo, V. (eds) Optimization Methods and Applications . Springer Optimization and Its Applications, vol 130. Springer, Cham. https://doi.org/10.1007/978-3-319-68640-0_20

Download citation

Publish with us

Policies and ethics