Abstract
Vehicle routing problem with stochastic demands (VRPSD) is a famous and challenging optimization problem which is similar to many real world problems. To resemble the real world scenario, total traveling distance, total driver remuneration, the number of vehicles used and the difference between driver remuneration are considered and formulated in the multi-objective optimization perspective. This paper aims to solve multi-objective VRPSD under the constraints of available time window and vehicle capacity using decomposition-based multi-objective evolutionary algorithm (MOEA/D) with diversity-loss-based selection method incorporates with local search and multi-mode mutation heuristics. We have also compared the optimization performance of the decomposition-based approach with the domination-based approach to study the difference between these two well-known evolutionary multi-objective algorithm frameworks. The simulation results have showed that the decomposition-based approach with diversity-loss-based selection method is able to maintain diverse output solutions.
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Ahmed F, Deb K (2013) Multi-objective optimal path planning using elitist non-dominated sorting genetic algorithms. Soft Comput 17(7):1283–1299
Asafuddoula M, Ray T, Sarker R (2015) A decomposition-based evolutionary algorithm for many objective optimization. Evol Comput IEEE Trans 19(3):445–460
Bertsimas DJ (1992) A vehicle routing problem with stochastic demand. Oper Res 40(3):574–585
Biesinger B, Hu B, Raidl GR (2015) A variable neighborhood search for the generalized vehicle routing problem with stochastic demands. In: Evolutionary computation in combinatorial optimization. Springer, Berlin, pp 48–60
Cheong C, Tan KC, Liu D, Lin C (2010) Multi-objective and prioritized berth allocation in container ports. Ann Oper Res 180(1):63–103
Deb K, Pratap A, Agrawal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6:182–197
Deb K, Mohan M, Mishra S (2005) Evaluating the \(\varepsilon \)-domination based multiobjective evolutionary algorithm for a quick computation of pareto-optimal solutions. Evol Comput J 13(4):501–525
Deb K, Jain H (2014) An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part i: solving problems with box constraints. Evol Comput IEEE Trans 18(4):577–601
Dror M, Trudeau P (1986) Stochastic vehicle routing with modified savings algorithm. Eur J Oper Res 23(2):228–235
Durillo JJ, Nebro AJ (2011) Jmetal: a java framework for multi-objective optimization. Adv Eng Softw 42(10):760–771
Feng L, Ong Y, Lim M, Tsang I (2014) Memetic search with inter-domain learning: a realization between cvrp and carp. Evol Comput IEEE Trans 99:1–1
Gee SB, Qiu X, Tan KC (2013) A novel diversity maintenance scheme for evolutionary multi-objective optimization. In: Intelligent data engineering and automated learning—IDEAL 2013. Springer, Berlin, pp 270–277
Gee SB, Tan KC (2014) Diversity preservation with hybrid recombination for evolutionary multiobjective optimization. In: Evolutionary computation (CEC), 2014 IEEE Congress on. IEEE, pp 1172–1178
Gee SB, Tan KC, Shim VA, Pal NR (2015) Online diversity assessment in evolutionary multiobjective optimization: a geometrical perspective. IEEE Trans Evol Comput 19(4):542–559. doi:10.1109/TEVC.2014.2353672
Goh CK, Tan KC (2009) Handling noise in evolutionary neural network design. In: Evolutionary multi-objective optimization in uncertain environments. Studies in Computational Intelligence, vol 186. Springer, Berlin, Heidelberg, pp 101–21. doi:10.1007/978-3-540-95976-2_4
Gupta A, Ong YS, Zhang A, Tan P (2015) A bi-level evolutionary algorithm for multi-objective vehicle routing problems with time window constraints. In: Handa H, Ishibuchi H, Ong YS, Tan KC (eds) Proceedings of the 18th Asia Pacific symposium on intelligent and evolutionary systems—Volume 2. Proceedings in adaptation, learning and optimization, vol 2. Springer International Publishing, Berlin, pp 27–38
Hastie T, Tibshirani R, Friedman J, Hastie T, Friedman J, Tibshirani R (2009) The elements of statistical learning, vol 2. Springer, Berlin
Heng CK, Zhang AN, Tan PS, Ong YS (2015) Multi-objective heterogeneous capacitated vehicle routing problem with time windows and simultaneous pickup and delivery for urban last mile logistics. In: Proceedings of the 18th Asia Pacific symposium on intelligent and evolutionary systems, vol 1. Springer, Berlin, pp 129–140
Hoff A, Andersson H, Christiansen M, Hasle G, Løkketangen A (2010) Industrial aspects and literature survey: fleet composition and routing. Comput Oper Res 37(12):2041–2061
Jain H, Deb K (2014) An evolutionary many-objective optimization algorithm using reference-point based nondominated sorting approach, part ii: handling constraints and extending to an adaptive approach. Evol Comput IEEE Trans 18(4):602–622
Kallehauge B, Larsen J, Madsen O, Solomon M (2005) Vehicle routing problem with time windows. In: Desaulniers G, Desrosiers J, Solomon M (eds) Column generation. Springer, US, pp 67–98
Liu H, Gu F, Zhang Q (2014) Decomposition of a multiobjective optimization problem into a number of simple multiobjective subproblems. Evol Comput IEEE Trans 18(3):450–455
Li H, Zhang Q (2009) Multiobjective optimization problems with complicated pareto sets, MOEA/D and NSGA-II. IEEE Trans Evol Comput 13:284–301
Marinakis Y, Marinaki M (2014) Combinatorial neighborhood topology bumble bees mating optimization for the vehicle routing problem with stochastic demands. Soft Comput 19(2):353–373
Marinakis Y, Marinaki M, Spanou P (2015) A memetic differential evolution algorithm for the vehicle routing problem with stochastic demands. In: Fister I, Fister Jr I (eds) Adaptation and hybridization in computational intelligence, adaptation, learning, and optimization, vol 18. Springer International Publishing, Berlin, pp 185–204
Mei Y, Li X, Yao X (2014) Cooperative coevolution with route distance grouping for large-scale capacitated arc routing problems. Evol Comput IEEE Trans 18(3):435–449
Nguyen S, Zhang M, Johnston M, Tan KC (2014) Automatic design of scheduling policies for dynamic multi-objective job shop scheduling via cooperative coevolution genetic programming. Evol Comput IEEE Trans 18(2):193–208
Perez D, Togelius J, Samothrakis S, Rohlfshagen P, Lucas SM (2014) Automated map generation for the physical traveling salesman problem. Evol Comput IEEE Trans 18(5):708–720
Russo L, Francisco AP (2014) Quick hypervolume. Evol Comput IEEE Trans 18(4):481–502
Sabar NR, Ayob M, Kendall G, Qu R (2013) Grammatical evolution hyper-heuristic for combinatorial optimization problems. Evol Comput IEEE Trans 17(6):840–861
Sabar N, Ayob M, Kendall G, Qu R (2015) Automatic design of a hyper-heuristic framework with gene expression programming for combinatorial optimization problems. Evol Comput IEEE Trans 19(3):309–325
Tan KC, Lee TH, Chew YH, Lee LH (2003) A multiobjective evolutionary algorithm for solving vehicle routing problem with time windows. In: Systems, man and cybernetics, 2003. IEEE international conference on, vol 1. IEEE, pp 361–366
Tan KC, Tang H, Yi Z (2004) Global exponential stability of discrete-time neural networks for constrained quadratic optimization. Neurocomputing 56:399–406
Tan KC, Tang H, Ge S (2005) On parameter settings of hopfield networks applied to traveling salesman problems. Circuits Syst I Regul Pap IEEE Trans 52(5):994–1002
Tan KC, Chew Y, Lee LH (2006a) A hybrid multi-objective evolutionary algorithm for solving truck and trailer vehicle routing problems. Eur J Oper Res 172(3):855–885
Tan KC, Yu Q, Ang JH (2006b) A coevolutionary algorithm for rules discovery in data mining. Int J Syst Sci 37(12):835–864
Tan KC, Cheong CY, Goh CK (2007) Solving multiobjective vehicle routing problem with stochastic demand via evolutionary computation. Eur J Oper Res 177(2):813–839
Tan KC, Teoh EJ, Yu Q, Goh KC (2009) A hybrid evolutionary algorithm for attribute selection in data mining. Expert Syst Appl 36(4):8616–8630
Tang H, Tan KC, Yi Z (2004) A columnar competitive model for solving combinatorial optimization problems. Neural Netw IEEE Trans 15(6):1568–1574
Tan KC, Li Y (2002) Grey-box model identification via evolutionary computing. Control Eng Pract 10(7):673–684
Van Veldhuizen DA, Lamont GB (1999) Multiobjective evolutionary algorithm test suites. In: Proceedings of the 1999 ACM symposium on applied computing. ACM, pp 351–357
Wang R, Purshouse RC, Fleming PJ (2013) Preference-inspired coevolutionary algorithms for many-objective optimization. Evol Comput IEEE Trans 17(4):474–494
Wang J, Tang K, Lozano J, Yao X (2015) Estimation of distribution algorithm with stochastic local search for uncertain capacitated arc routing problems. Evolutionary Computation, IEEE Transactions on PP(99):1–1
Woodruff M, Herman J (2013) pareto.py: A \(\varepsilon \)-nondomination sorting routine. https://github.com/matthewjwoodruff/pareto.py
Yang S, Li M, Liu X, Zheng J (2013) A grid-based evolutionary algorithm for many-objective optimization. Evol Comput IEEE Trans 17(5):721–736
Zhang Q, Li H (2007) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11:712–731
Zhou A, Jin Y, Zhang Q, Sendhoff B, Tsang E, (2006) Combining model-based and genetics-based offspring generation for multi-objective optimization using a convergence criterion. In: Evolutionary computation (2006) CEC 2006. IEEE Congress on. IEEE, pp 892–899
Zitzler E, Thiele L (1998) Multiobjective optimization using evolutionary algorithms—A comparative case study. In: Parallel problem solving from nature—PPSN V. Springer, Berlin, pp 292–301
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Communicated by S. Deb, T. Hanne and S. Fong.
This work was supported by the Singapore Ministry of Education Academic Research Fund Tier 1 under the project R-263-000-A12-112.
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Gee, S.B., Arokiasami, W.A., Jiang, J. et al. Decomposition-based multi-objective evolutionary algorithm for vehicle routing problem with stochastic demands. Soft Comput 20, 3443–3453 (2016). https://doi.org/10.1007/s00500-015-1830-2
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DOI: https://doi.org/10.1007/s00500-015-1830-2