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An improved multi-directional local search algorithm for vehicle routing problem with time windows and route balance

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Abstract

The Vehicle Routing Problem with Route Balance (VRPRB) aims to balance distribution costs and workloads and achieve important nonmonetary benefits with a more equitable distribution scheme. Considering time window constraints for the VRPRB will have an impact on the workload balance, which has rarely been studied before. The existence of a time window constraint can significantly affect the allocation of duration, and the analysis method under the traditional model is no longer applicable. This paper combined the time window constraint, established the Vehicle Routing Problem with Time Windows and Route Balance (VRPTWRB) model, and conducted a numerical study on the reasonable selection of workload resources and equity functions. An improved multi-directional local search (IMDLS) algorithm was proposed to solve the model and approximate the Pareto frontier. The IMDLS algorithm limits the archive size and adaptively determines the number of current solutions and the search direction. A large neighbourhood search (LNS) framework was employed as an local search to find effective solutions and update the approximate Pareto frontier in each iteration. The performance of the IMDLS was compared to the MDLS, and the effect of the choice of workload resource and the equity function on fairness were further studied. The computational results showed that the duration was more suitable for evaluating workload resources than distance when considering the time window constraints; and more complex equity functions could effectively find high-quality nondominated solutions with good equity.

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References

  1. Rossit DG, Vigo D, Tohmé F, Frutos M (2019) Visual attractiveness in routing problems: a review. Comput Oper Res 103:13–34

    Article  MathSciNet  MATH  Google Scholar 

  2. Aghighi A, Goli A, Malmir B, Tirkolaee EB (2021) The stochastic location-routing-inventory problem of perishable products with reneging and balking. Journal of Ambient Intelligence and Humanized Computing, pp 1–20

  3. Karsu Z, Morton A (2015) Inequity averse optimization in operational research. Eur J Oper Res 245(2):343–359

    Article  MathSciNet  MATH  Google Scholar 

  4. Dukkanci O, Karsu Ö, Kara Bahar Y (2022) Planning sustainable routes: Economic, environmental and welfare concerns. Eur J Oper Res 301(1):110–123

    Article  MathSciNet  MATH  Google Scholar 

  5. Tirkolaee EB, Goli A, Mardani A (2021) A novel two-echelon hierarchical location-allocation-routing optimization for green energy-efficient logistics systems. Ann Oper Res, pp 1–29

  6. Banos R, Ortega J, Gil C, Marquez AL, De Toro F (2013) A hybrid meta-heuristic for multi-objective vehicle routing problems with time windows. Comput Ind Eng 65(2):286–296

    Article  Google Scholar 

  7. Oyola J, LoKketangen A (2014) Grasp-asp: an algorithm for the cvrp with route balancing. J Heuristics 20(4):361–382

    Article  Google Scholar 

  8. Lacomme P, Prins C, Prodhon C, Ren L (2015) A multi-start split based path relinking (msspr) approach for the vehicle routing problem with route balancing. Eng Appl Artif Intell 38:237–251

    Article  Google Scholar 

  9. Matl P, Hartl RF, Vidal T (2017) Workload equity in vehicle routing problems: a survey and analysis. Transp Sci 52(2):239–260

    Article  Google Scholar 

  10. Lehuede F, Peton O, Tricoire F (2020) A lexicographic minimax approach to the vehicle routing problem with route balancing. Eur J Oper Res 282(1):129–147

    Article  MathSciNet  MATH  Google Scholar 

  11. Galindres-Guancha L, Toro-ocampo E, rendón R (2018) Multi-objective mdvrp solution considering route balance and cost using the ils metaheuristic. Int J Ind Eng Comput 9(1):33–46

    Google Scholar 

  12. Zhang Z, Qin H, Li Y (2019) Multi-objective optimization for the vehicle routing problem with outsourcing and profit balancing. IEEE Trans Intell Transp Syst 21(5):1987–2001

    Article  Google Scholar 

  13. Ibarra-Rojas OJ, Silva-Soto Y (2021) Vehicle routing problem considering equity of demand satisfaction. Optimization Letters, pp 1–23

  14. Jingjing LI, Fang Y, Tang N (2022) A cluster-based optimization framework for vehicle routing problem with workload balance. Computers & Industrial Engineering, pp 108221

  15. Melian-Batista B, De Santiago A, Angelbello F, Alvarez A (2014) A bi-objective vehicle routing problem with time windows: a real case in tenerife. Appl Soft Comput J 17:140–152

    Article  Google Scholar 

  16. Eskandarpour M, Dejax P, Péton O (2021) Multi-directional local search for sustainable supply chain network design. Int J Prod Res 59(2):412–428

    Article  MATH  Google Scholar 

  17. Sivaramkumar V, Thansekhar M, Saravanan R (2018) Demonstrating the importance of using total time balance instead of route balance on a multi-objective vehicle routing problem with time windows. Int J Adv Manuf Technol 98(5):1287–1306

    Article  Google Scholar 

  18. Tricoire F (2012) Multi-directional local search. Comput Oper Res 39(12):3089–3101

    Article  MathSciNet  MATH  Google Scholar 

  19. Molenbruch Y, Braekers K, Caris A, Berghe GV (2017) Multi-directional local search for a bi-objective dial-a-ride problem in patient transportation. Comput Oper Res 77:58–71

    Article  MathSciNet  MATH  Google Scholar 

  20. Defryn C, Sörensen K (2018) Multi-objective optimisation models for the travelling salesman problem with horizontal cooperation. Eur J Oper Res 267(3):891–903

    Article  MathSciNet  MATH  Google Scholar 

  21. Heggen H, Braekers K, Caris A (2018) A multi-objective approach for intermodal train load planning. OR spectrum 40(2):341– 366

    MathSciNet  MATH  Google Scholar 

  22. Zhu S, Xu L, Goodman ED (2021) A new many-objective evolutionary algorithm based on generalized pareto dominance. IEEE Transactions on Cybernetics

  23. Allmendinger R, Jaszkiewicz A, Liefooghe A, Tammer C (2022) What if we increase the number of objectives? theoretical and empirical implications for many-objective combinatorial optimization. Computers & Operations Research, pp 105857

  24. Lian K, Milburn AB, Rardin RL (2016) An improved multi-directional local search algorithm for the multi-objective consistent vehicle routing problem. IIE Trans 48(10):975–992

    Article  Google Scholar 

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

    Article  Google Scholar 

  26. Alinaghian M, Jamshidian M, Tirkolaee EB (2021) The time-dependent multi-depot fleet size and mix green vehicle routing problem: improved adaptive large neighbourhood search. Optimization, pp 1–29

  27. Krzysztof M (2016) Evolutionary algorithm with a directional local search for multiobjective optimization in combinatorial problems. Optim Methods Softw 31(2):392–404

    Article  MathSciNet  MATH  Google Scholar 

  28. Gansterer M, Hartl R, Wieser S (2021) Assignment constraints in shared transportation services. Ann Oper Res 305(1):513–539

    Article  MathSciNet  Google Scholar 

  29. Pisinger David, Ropke Stefan (2007) A general heuristic for vehicle routing problems. Comput Oper Res 34(8):2403–2435

    Article  MathSciNet  MATH  Google Scholar 

  30. Santini A, Ropke S, Hvattum L (2018) A comparison of acceptance criteria for the adaptive large neighbourhood search metaheuristic. J Heuristics 24(5):783–815

    Article  Google Scholar 

  31. Pisinger D, Ropke S (2019) Large neighborhood search Springer

  32. Lwin Khin, Rong Q u, Kendall Graham (2014) A learning-guided multi-objective evolutionary algorithm for constrained portfolio optimization. Appl Soft Comput J 24:757–772

    Article  Google Scholar 

  33. Zitzler E, Thiele L, Laumanns M, Fonseca CM, Da Fonseca VG (2003) Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans Evol Comput 7(2):117– 132

    Article  Google Scholar 

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

    Article  Google Scholar 

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Authors and Affiliations

  1. Engineering Research Center of the Ministry of Education for Intelligent Control System and Intelligent Equipment, Yanshan University, Qinhuangdao, 066004, China

    Bin Feng & Lixin Wei

  2. Key Lab of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao, 066004, China

    Bin Feng & Lixin Wei

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  1. Bin Feng
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  2. Lixin Wei
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Correspondence to Lixin Wei.

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Feng, B., Wei, L. An improved multi-directional local search algorithm for vehicle routing problem with time windows and route balance. Appl Intell 53, 11786–11798 (2023). https://doi.org/10.1007/s10489-022-04061-7

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