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The new optimization algorithm for the vehicle routing problem with time windows using multi-objective discrete learnable evolution model

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Abstract

This paper presents a new multi-objective discreet learnable evolution model (MODLEM) to address the vehicle routing problem with time windows (VRPTW). Learnable evolution model (LEM) includes a machine learning algorithm, like the decision trees, that can discover the correct directions of the evolution leading to significant improvements in the fitness of the individuals. We incorporate a robust strength Pareto evolutionary algorithm in the LEM presented here to govern the multi-objective property of this approach. A new priority-based encoding scheme for chromosome representation in the LEM as well as corresponding routing scheme is introduced. To improve the quality and the diversity of the initial population, we propose a novel heuristic manner which leads to a good approximation of the Pareto fronts within a reasonable computational time. Moreover, a new heuristic operator is employed in the instantiating process to confront incomplete chromosome formation. Our proposed MODLEM is tested on the problem instances of Solomon’s VRPTW benchmark. The performance of this proposed MODLEM for the VRPTW is assessed against the state-of-the-art approaches in terms of both the quality of solutions and the computational time. Experimental results and comparisons indicate the effectiveness and efficiency of our proposed intelligent routing approach.

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References

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

    MathSciNet  MATH  Google Scholar 

  • Alvarenga GB, Mateus GR, De Tomi G (2007) A genetic and set partitioning two-phase approach for the vehicle routing problem with time windows. Comput Oper Res 34(6):1561–1584. https://doi.org/10.1016/j.cor.2005.07.025

    MATH  Google Scholar 

  • Amini S, Javanshir H, Tavakkoli-Moghaddam R (2010) A PSO approach for solving VRPTW with real case study. Int J Res Rev Appl Sci 4(3):118–126

    Google Scholar 

  • Antes J, Derigs U (1995) A new parallel tour construction algorithm for the vehicle routing problem with time windows

  • Badeau P, Guertin F, Gendreau M, Potvin J-Y, Taillard E (1997) A parallel tabu search heuristic for the vehicle routing problem with time windows. Transp Res C Emerg Technol 5(2):109–122

    MATH  Google Scholar 

  • Baker EK, Schaffer JR (1986) Solution improvement heuristics for the vehicle routing and scheduling problem with time window constraints. Am J Math Manag Sci 6(3–4):261–300

    MATH  Google Scholar 

  • Baldacci R, Bartolini E, Mingozzi A, Roberti R (2010) An exact solution framework for a broad class of vehicle routing problems. CMS 7(3):229–268

    MathSciNet  MATH  Google Scholar 

  • Baldacci R, Mingozzi A, Roberti R (2011) New route relaxation and pricing strategies for the vehicle routing problem. Oper Res 59(5):1269–1283

    MathSciNet  MATH  Google Scholar 

  • Baldacci R, Mingozzi A, Roberti R (2012) Recent exact algorithms for solving the vehicle routing problem under capacity and time window constraints. Eur J Oper Res 218(1):1–6

    MathSciNet  MATH  Google Scholar 

  • BañOs R, Ortega J, Gil C, FernáNdez A, De Toro F (2013a) A simulated annealing-based parallel multi-objective approach to vehicle routing problems with time windows. Expert Syst Appl 40(5):1696–1707

    Google Scholar 

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

    Google Scholar 

  • Barán B, Schaerer M (2003) A multiobjective ant colony system for vehicle routing problem with time windows. In: The 21st IASTED International Multi-Conference on Applied Informatics (AI 2003), February 10–13, 2003, Innsbruck, Austria

  • Barbucha D (2013) An agent-based cooperative population learning algorithm for vehicle routing problem with time windows. In: KES-AMSTA

  • Barbucha D (2014) A cooperative population learning algorithm for vehicle routing problem with time windows. Neurocomputing 146:210–229

    Google Scholar 

  • Bard JF, Kontoravdis G, Yu G (2002) A branch-and-cut procedure for the vehicle routing problem with time windows. Transp Sci 36(2):250–269

    MATH  Google Scholar 

  • Beham A (2007). Parallel tabu search and the multiobjective vehicle routing problem with time windows. In: Parallel and Distributed Processing Symposium. IPDPS 2007. IEEE International, IEEE

  • Bent R, Van Hentenryck P (2004) A two-stage hybrid local search for the vehicle routing problem with time windows. Transp Sci 38(4):515–530

    Google Scholar 

  • Berger J, Barkaoui M (2004) A parallel hybrid genetic algorithm for the vehicle routing problem with time windows. Comput Oper Res 31(12):2037–2053

    MathSciNet  MATH  Google Scholar 

  • Berger J, Barkaoui M, Bräysy O (2003) A route-directed hybrid genetic approach for the vehicle routing problem with time windows. INFOR Inf Syst Oper Res 41(2):179–194

    Google Scholar 

  • Błocho M, Czech ZJ (2011). A parallel algorithm for minimizing the number of routes in the vehicle routing problem with time windows. In: International conference on parallel processing and applied mathematics. Springer

  • Blocho M, Czech ZJ (2012) A parallel EAX-based algorithm for minimizing the number of routes in the vehicle routing problem with time windows. In: 2012 IEEE 14th international conference on high performance computing and communication & 2012 IEEE 9th international conference on embedded software and systems (HPCC-ICESS). IEEE

  • Blocho M, Czech ZJ (2013) A parallel memetic algorithm for the vehicle routing problem with time windows. In: 2013 8th international conference on P2P, parallel, grid, cloud and internet computing (3PGCIC). IEEE

  • Bräysy O (2001) Local search and variable neighborhood search algorithms for the vehicle routing problem with time windows. Universitas Wasaensis, Vaasa

    MATH  Google Scholar 

  • Bräysy O, Dullaert W (2003) A fast evolutionary metaheuristic for the vehicle routing problem with time windows. Int J Artif Intell Tools 12(02):153–172. https://doi.org/10.1142/S0218213003001162

    Article  MATH  Google Scholar 

  • Calvete HI, Galé C, Oliveros M-J, Sánchez-Valverde B (2007) A goal programming approach to vehicle routing problems with soft time windows. Eur J Oper Res 177(3):1720–1733

    MathSciNet  MATH  Google Scholar 

  • Castro J, Landa-Silva D, Pérez J (2009) Exploring feasible and infeasible regions in the vehicle routing problem with time windows using a multi-objective particle swarm optimization approach. In: Nature inspired cooperative strategies for optimization (NICSO 2008), pp 103–114

  • Chabrier A (2006) Vehicle routing problem with elementary shortest path based column generation. Comput Oper Res 33(10):2972–2990

    MathSciNet  MATH  Google Scholar 

  • Chen C-H, Ting C-J (2005) A hybrid ant colony system for vehicle routing problem with time windows. J East Asia Soc Transp Stud 6:2822–2836. https://doi.org/10.11175/easts.6.2822

    Article  Google Scholar 

  • Chiang T-C, Hsu W-H (2014) A knowledge-based evolutionary algorithm for the multiobjective vehicle routing problem with time windows. Comput Oper Res 45:25–37

    MATH  Google Scholar 

  • Chiang W-C, Russell RA (1996) Simulated annealing metaheuristics for the vehicle routing problem with time windows. Ann Oper Res 63(1):3–27

    MATH  Google Scholar 

  • Chiang W-C, Russell RA (1997) A reactive tabu search metaheuristic for the vehicle routing problem with time windows. INFORMS J Comput 9(4):417–430

    MATH  Google Scholar 

  • Cook W, Rich JL (1999) A parallel cutting-plane algorithm for the vehicle routing problem with time windows. Technical Report TR99-04, Computational and Applied Mathematics, Rice University, Housten, USA

  • Cordeau J-F, Maischberger M (2012) A parallel iterated tabu search heuristic for vehicle routing problems. Comput Oper Res 39(9):2033–2050

    Google Scholar 

  • Cordeau J-F, Laporte G, Mercier A (2001) A unified tabu search heuristic for vehicle routing problems with time windows. J Oper Res Soc 52(8):928–936

    MATH  Google Scholar 

  • Czech ZJ, Czarnas P (2002) Parallel simulated annealing for the vehicle routing problem with time windows. In: 10th Euromicro workshop on parallel, distributed and network-based processing. Proceedings. IEEE

  • Dan Z, Cai L, Zheng L (2009) Improved multi-agent system for the vehicle routing problem with time windows. Tsinghua Sci Technol 14(3):407–412

    Google Scholar 

  • Desaulniers G, Desrosiers J, Spoorendonk S (2011) Cutting planes for branch-and-price algorithms. Networks 58(4):301–310

    MathSciNet  MATH  Google Scholar 

  • Desaulniers G, Madsen OB, Ropke S (2014) The vehicle routing problem with time windows. Veh Routing Probl Methods Appl 18:119–159

    Google Scholar 

  • Desrochers M, Desrosiers J, Solomon M (1992) A new optimization algorithm for the vehicle routing problem with time windows. Oper Res 40(2):342–354

    MathSciNet  MATH  Google Scholar 

  • Dhanya K, Kanmani S (2016) Solving vehicle routing problem using hybrid swarm intelligent methods. In: 2016 international conference on communication and signal processing (ICCSP). IEEE

  • Domanski PA, Yashar D, Kaufman KA, Michalski RS (2004) An optimized design of finned-tube evaporators using the learnable evolution model. HVAC&R Res 10(2):201–211

    Google Scholar 

  • Dullaert W, Bräysy O (2003) Routing relatively few customers per route. Top 11(2):325–336

    MathSciNet  MATH  Google Scholar 

  • Farzi S (2012) The design of self-organizing evolved polynomial neural networks based on learnable evolution model 3. Int Arab J Inf Technol 9(2):124–132

    Google Scholar 

  • Feillet D, Dejax P, Gendreau M, Gueguen C (2004) An exact algorithm for the elementary shortest path problem with resource constraints: application to some vehicle routing problems. Networks 44(3):216–229

    MathSciNet  MATH  Google Scholar 

  • Feillet D, Gendreau M, Rousseau L-M (2007) New refinements for the solution of vehicle routing problems with branch and price. INFOR Inf Syst Oper Res 45(4):239–256

    MathSciNet  Google Scholar 

  • Fisher ML, Jörnsten KO, Madsen OB (1997) Vehicle routing with time windows: two optimization algorithms. Oper Res 45(3):488–492

    MathSciNet  MATH  Google Scholar 

  • Gambardella LM, Taillard É, Agazzi G (1999) MACS-VRPTW: a multiple ant colony system for vehicle routing problems with time windows. Technical Report

  • Garcia-Najera A, Bullinaria JA (2009) Bi-objective optimization for the vehicle routing problem with time windows: using route similarity to enhance performance. In: EMO. Springer

  • Garcia-Najera A, Bullinaria JA (2011) An improved multi-objective evolutionary algorithm for the vehicle routing problem with time windows. Comput Oper Res 38(1):287–300

    MathSciNet  MATH  Google Scholar 

  • Gehring H, Homberger J (1999) A parallel hybrid evolutionary metaheuristic for the vehicle routing problem with time windows. In: Paper presented at the Proceedings of EUROGEN99

  • Ghoseiri K, Ghannadpour SF (2010) Multi-objective vehicle routing problem with time windows using goal programming and genetic algorithm. Appl Soft Comput 10(4):1096–1107

    Google Scholar 

  • Gong W, Liu X, Zhang J, Fu Z (2007) Two-generation ant colony system for vehicle routing problem with time windows. In: International conference on wireless communications, networking and mobile computing. WiCom 2007. IEEE

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

    Google Scholar 

  • Hifi M, Wu L (2014) A hybrid metaheuristic for the vehicle routing problem with time windows. In: International conference on control, decision and information technologies (CoDI’14). https://doi.org/10.1109/CoDIT.2014.6996891

  • Homberger J, Gehring H (1999) Two evolutionary metaheuristics for the vehicle routing problem with time windows. INFOR Inf Syst Oper Res 37(3):297–318

    Google Scholar 

  • Hsu W-H, Chiang T-C (2012) A multiobjective evolutionary algorithm with enhanced reproduction operators for the vehicle routing problem with time windows. In: 2012 IEEE congress on evolutionary computation (CEC), IEEE

  • Hu W, Liang H, Peng C, Du B, Hu Q (2013) A hybrid chaos-particle swarm optimization algorithm for the vehicle routing problem with time window. Entropy 15(4):1247–1270. https://doi.org/10.3390/e15041247

    Article  MathSciNet  MATH  Google Scholar 

  • Ioannou G, Kritikos M, Prastacos G (2001) A greedy look-ahead heuristic for the vehicle routing problem with time windows. J Oper Res Soc 52(5):523–537

    MATH  Google Scholar 

  • Irnich S, Villeneuve D (2006) The shortest-path problem with resource constraints and k-cycle elimination for k ≥ 3. INFORMS J Comput 18(3):391–406

    MathSciNet  MATH  Google Scholar 

  • Irnich S, Desaulniers G, Desrosiers J, Hadjar A (2010) Path-reduced costs for eliminating arcs in routing and scheduling. INFORMS J Comput 22(2):297–313

    MathSciNet  MATH  Google Scholar 

  • Jepsen M, Petersen B, Spoorendonk S, Pisinger D (2006) A non-robust branch-and-cut-and-price algorithm for the vehicle routing problem with time windows. Oper Res (forthcoming)

  • Jepsen M, Petersen B, Spoorendonk S, Pisinger D (2008) Subset-row inequalities applied to the vehicle-routing problem with time windows. Oper Res 56(2):497–511

    MATH  Google Scholar 

  • Jiang J, Ng KM, Poh KL, Teo KM (2014) Vehicle routing problem with a heterogeneous fleet and time windows. Expert Syst Appl 41(8):3748–3760

    Google Scholar 

  • Jiang W, Zhang Y, Xie J (2009) A particle swarm optimization algorithm with crossover for vehicle routing problem with time windows. In: IEEE symposium on computational intelligence in scheduling, CI-Sched 2009, pp 103–106. https://doi.org/10.1109/SCIS.2009.4927022

  • Jourdan L, Corne D, Savic D, Walters G (2005) Preliminary investigation of the ‘learnable evolution model’ for faster/better multiobjective water systems design. In: Evolutionary multi-criterion optimization. Springer

  • Jung S, Moon B-R (2002) A hybrid genetic algorithm for the vehicle routing problem with time windows. In: Paper presented at the proceedings of the 4th annual conference on genetic and evolutionary computation

  • Kallehauge B (2008) Formulations and exact algorithms for the vehicle routing problem with time windows. Comput Oper Res 35(7):2307–2330

    MathSciNet  MATH  Google Scholar 

  • Kallehauge B, Larsen J, Madsen OB (2006) Lagrangian duality applied to the vehicle routing problem with time windows. Comput Oper Res 33(5):1464–1487

    MathSciNet  MATH  Google Scholar 

  • Kallehauge B, Boland N, Madsen OB (2007) Path inequalities for the vehicle routing problem with time windows. Networks 49(4):273–293

    MathSciNet  MATH  Google Scholar 

  • Kim M, Hiroyasu T, Miki M, Watanabe S (2004) SPEA2+: improving the performance of the strength Pareto evolutionary algorithm 2. In: International conference on parallel problem solving from nature. Springer

  • Koç Ç, Bektaş T, Jabali O, Laporte G (2015) A hybrid evolutionary algorithm for heterogeneous fleet vehicle routing problems with time windows. Comput Oper Res 64:11–27. https://doi.org/10.1016/j.cor.2015.05.004

    Article  MathSciNet  MATH  Google Scholar 

  • Kohl N, Desrosiers J, Madsen OB, Solomon MM, Soumis F (1999) 2-path cuts for the vehicle routing problem with time windows. Transp Sci 33(1):101–116

    MATH  Google Scholar 

  • Kolen AW, Rinnooy Kan A, Trienekens HW (1987) Vehicle routing with time windows. Oper Res 35(2):266–273

    MathSciNet  MATH  Google Scholar 

  • Kontoravdis G, Bard JF (1995) A GRASP for the vehicle routing problem with time windows. ORSA J Comput 7(1):10–23

    MATH  Google Scholar 

  • Kumar VS, Thansekhar M, Saravanan R, Amali SMJ (2014) Solving multi-objective vehicle routing problem with time windows by FAGA. Procedia Eng 97:2176–2185

    Google Scholar 

  • Labadi N, Prins C, Reghioui M (2008) A memetic algorithm for the vehicle routing problem with time windows. RAIRO Oper Res 42(3):415–431

    MathSciNet  MATH  Google Scholar 

  • Larsen J (2004) Refinements of the column generation process for the vehicle routing problem with time windows. J Syst Sci Syst Eng 13(3):326–341

    Google Scholar 

  • Lau HC, Lim YF, Liu Q (2001) Diversification of search neighborhood via constraint-based local search and its applications to VRPTW. In: Paper presented at the 3rd international workshop on integration of AI and OR techniques (CP-AI-OR), Kent, UK

  • Lau HC, Sim M, Teo KM (2003) Vehicle routing problem with time windows and a limited number of vehicles. Eur J Oper Res 148(3):559–569

    MathSciNet  MATH  Google Scholar 

  • Le Bouthillier A, Crainic TG (2005) A cooperative parallel meta-heuristic for the vehicle routing problem with time windows. Comput Oper Res 32(7):1685–1708

    MATH  Google Scholar 

  • Le Bouthillier A, Crainic TG, Kropf P (2005) A guided cooperative search for the vehicle routing problem with time windows. IEEE Intell Syst 20(4):36–42

    Google Scholar 

  • Lee LH, Tan KC, Ou K, Chew YH (2003) Vehicle capacity planning system: a case study on vehicle routing problem with time windows. IEEE Trans Syst Man Cybern A Syst Hum 33(2):169–178

    Google Scholar 

  • Letchford AN, Salazar-González J-J (2006) Projection results for vehicle routing. Math Program 105(2):251–274

    MathSciNet  MATH  Google Scholar 

  • Li H, Lim A (2003) Local search with annealing-like restarts to solve the VRPTW. Eur J Oper Res 150(1):115–127. https://doi.org/10.1016/S0377-2217(02)00486-1

    Article  MathSciNet  MATH  Google Scholar 

  • Lim A, Zhang X (2007) A two-stage heuristic with ejection pools and generalized ejection chains for the vehicle routing problem with time windows. INFORMS J Comput 19(3):443–457

    MathSciNet  MATH  Google Scholar 

  • Liu F-HF, Shen S-Y (1999) A route-neighborhood-based metaheuristic for vehicle routing problem with time windows. Eur J Oper Res 118(3):485–504

    MATH  Google Scholar 

  • Liu X, Jiang W, Xie J (2009) Vehicle routing problem with time windows: a hybrid particle swarm optimization approach. In: 5th international conference on natural computation, ICNC 2009, pp 502–506. https://doi.org/10.1109/ICNC.2009.353

  • Lozano L, Duque D, Medaglia AL (2015) An exact algorithm for the elementary shortest path problem with resource constraints. Transp Sci 50(1):348–357

    MATH  Google Scholar 

  • Luo J, Li X, Chen M-R, Liu H (2015) A novel hybrid shuffled frog leaping algorithm for vehicle routing problem with time windows. Inf Sci 316:266–292

    Google Scholar 

  • Lysgaard J (2006) Reachability cuts for the vehicle routing problem with time windows. Eur J Oper Res 175(1):210–223

    MathSciNet  MATH  Google Scholar 

  • Melián-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 17:140–152

    Google Scholar 

  • Mester D (2002) An evolutionary strategies algorithm for large scale vehicle routing problem with capacitate and time windows restrictions. In: Paper presented at the proceedings of the conference on mathematical and population genetics, University of Haifa, Israel

  • Mester D, Bräysy O (2005) Active guided evolution strategies for large-scale vehicle routing problems with time windows. Comput Oper Res 32(6):1593–1614. https://doi.org/10.1016/j.cor.2003.11.017

    Article  MATH  Google Scholar 

  • Mester D, Bräysy O, Dullaert W (2007) A multi-parametric evolution strategies algorithm for vehicle routing problems. Expert Syst Appl 32(2):508–517

    Google Scholar 

  • Michalski RS (2000) Learnable evolution model: evolutionary processes guided by machine learning. Mach Learn 38(1–2):9–40

    MATH  Google Scholar 

  • Michalski R (2010) Learning and evolution: an introduction to non-darwinian evolutionary computation. In: Foundations of intelligent systems, pp 21–30

  • Michalski RS, Kaufman KA (2006) Intelligent evolutionary design: a new approach to optimizing complex engineering systems and its application to designing heat exchangers. Int J Intell Syst 21(12):1217–1248

    Google Scholar 

  • Mohemmed AW, Sahoo NC, Geok TK (2008) Solving shortest path problem using particle swarm optimization. Appl Soft Comput 8(4):1643–1653

    Google Scholar 

  • Moradi B (2018a) An intelligent evolutionary computation approach for solving the shortest path problem. J Mult Valued Log Soft Comput 30(4–6):359–377

    MathSciNet  MATH  Google Scholar 

  • Moradi B (2018b) Multi-objective mobile robot path planning problem through learnable evolution model. J Exp Theor Artif Intell 31(2):1–24

    Google Scholar 

  • Moradi B, Mirzaei A (2016) A new automated design method based on machine learning for CMOS analog circuits. Int J Electron 103(11):1868–1881

    Google Scholar 

  • Muñoz-Zavala A, Hernández-Aguirre A, Villa-Diharce E (2009) Particle evolutionary swarm multi-objective optimization for vehicle routing problem with time windows. In: Swarm intelligence for multi-objective problems in data mining, pp 233–257

  • Nagata Y, Bräysy O (2009) A powerful route minimization heuristic for the vehicle routing problem with time windows. Oper Res Lett 37(5):333–338

    MathSciNet  MATH  Google Scholar 

  • Nagata Y, Bräysy O, Dullaert W (2010) A penalty-based edge assembly memetic algorithm for the vehicle routing problem with time windows. Comput Oper Res 37(4):724–737

    MATH  Google Scholar 

  • Nalepa J (2014) Adaptive memetic algorithm for the vehicle routing problem with time windows. In: Proceedings of the companion publication of the 2014 annual conference on genetic and evolutionary computation. ACM

  • Nalepa J, Blocho M (2016) Adaptive memetic algorithm for minimizing distance in the vehicle routing problem with time windows. Soft Comput 20(6):2309–2327

    Google Scholar 

  • Nalepa J, Czech ZJ (2012) A parallel heuristic algorithm to solve the vehicle routing problem with time windows. Stud Inform 33(1):91–106

    Google Scholar 

  • Nalepa J, Czech ZJ (2013). New selection schemes in a memetic algorithm for the vehicle routing problem with time windows. In: International conference on adaptive and natural computing algorithms. Springer

  • Nazif H, Lee LS (2010) Optimized crossover genetic algorithm for vehicle routing problem with time windows. Am J Appl Sci 7(1):95

    Google Scholar 

  • Niu B, Wang H, Tan L, Li L, Wang J-W (2012) Vehicle routing problem with time windows based on adaptive bacterial foraging optimization. In: ICIC, vol 2. Springer

  • Ombuki B, Ross BJ, Hanshar F (2006) Multi-objective genetic algorithms for vehicle routing problem with time windows. Appl Intell 24(1):17–30

    Google Scholar 

  • Pang K-W (2011) An adaptive parallel route construction heuristic for the vehicle routing problem with time windows constraints. Expert Syst Appl 38(9):11939–11946

    Google Scholar 

  • Paraskevopoulos DC, Repoussis PP, Tarantilis CD, Ioannou G, Prastacos GP (2008) A reactive variable neighborhood tabu search for the heterogeneous fleet vehicle routing problem with time windows. J Heuristics 14(5):425–455

    MATH  Google Scholar 

  • Pecin D, Contardo C, Desaulniers G, Uchoa E (2017) New enhancements for the exact solution of the vehicle routing problem with time windows. INFORMS J Comput 29(3):489–502

    MathSciNet  MATH  Google Scholar 

  • Petersen B, Pisinger D, Spoorendonk S (2008) Chvátal-Gomory rank-1 cuts used in a Dantzig-Wolfe decomposition of the vehicle routing problem with time windows. Vehicle Routing Probl Latest Adv New Chall 43:397–419

    MATH  Google Scholar 

  • Pierre DM, Zakaria N (2014) Partially optimized cyclic shift crossover for multi-objective genetic algorithms for the multi-objective vehicle routing problem with time-windows. In: 2014 IEEE symposium on computational intelligence in multi-criteria decision-making (MCDM). IEEE

  • Pierre DM, Zakaria N (2017) Stochastic partially optimized cyclic shift crossover for multi-objective genetic algorithms for the vehicle routing problem with time-windows. Appl Soft Comput 52:863–876

    Google Scholar 

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

    MATH  Google Scholar 

  • Potvin J-Y, Rousseau J-M (1993) A parallel route building algorithm for the vehicle routing and scheduling problem with time windows. Eur J Oper Res 66(3):331–340

    MATH  Google Scholar 

  • Potvin J-Y, Rousseau J-M (1995) An exchange heuristic for routeing problems with time windows. J Oper Res Soc 46(12):1433–1446

    MATH  Google Scholar 

  • Prescott-Gagnon E, Desaulniers G, Rousseau LM (2009) A branch-and-price-based large neighborhood search algorithm for the vehicle routing problem with time windows. Networks 54(4):190–204

    MathSciNet  MATH  Google Scholar 

  • Qi M, Miao L, Zhang L, Xu H (2008) A new tabu search heuristic algorithm for the vehicle routing problem with time windows. In: International conference on management science and engineering. ICMSE 2008. 15th annual conference proceedings. IEEE

  • Qi Y, Hou Z, Li H, Huang J, Li X (2015) A decomposition based memetic algorithm for multi-objective vehicle routing problem with time windows. Comput Oper Res 62:61–77

    MathSciNet  MATH  Google Scholar 

  • Repoussis P, Paraskevopoulos D, Tarantilis C, Ioannou G (2006) A reactive greedy randomized variable neighborhood tabu search for the vehicle routing problem with time windows. In: Hybrid metaheuristics, pp 124–138

  • Repoussis PP, Tarantilis CD, Ioannou G (2009) Arc-guided evolutionary algorithm for the vehicle routing problem with time windows. IEEE Trans Evol Comput 13(3):624–647

    Google Scholar 

  • Righini G, Salani M (2006) Symmetry helps: bounded bi-directional dynamic programming for the elementary shortest path problem with resource constraints. Discrete Optim 3(3):255–273

    MathSciNet  MATH  Google Scholar 

  • Rochat Y, Taillard ÉD (1995) Probabilistic diversification and intensification in local search for vehicle routing. J Heuristics 1(1):147–167

    MATH  Google Scholar 

  • Rousseau L-M, Gendreau M, Pesant G (2002) Using constraint-based operators to solve the vehicle routing problem with time windows. J Heuristics 8(1):43–58

    MATH  Google Scholar 

  • Rousseau L-M, Gendreau M, Feillet D (2007) Interior point stabilization for column generation. Oper Res Lett 35(5):660–668

    MathSciNet  MATH  Google Scholar 

  • Russell RA (1977) An effective heuristic for the m-tour traveling salesman problem with some side conditions. Oper Res 25(3):517–524

    MATH  Google Scholar 

  • Russell RA (1995) Hybrid heuristics for the vehicle routing problem with time windows. Transp Sci 29(2):156–166

    MATH  Google Scholar 

  • Savelsbergh MW (1985) Local search in routing problems with time windows. Ann Oper Res 4(1):285–305

    MathSciNet  Google Scholar 

  • Savelsbergh M (1990) An efficient implementation of local search algorithms for constrained routing problems. Eur J Oper Res 47(1):75–85

    MathSciNet  MATH  Google Scholar 

  • Savelsbergh MW (1992) The vehicle routing problem with time windows: minimizing route duration. ORSA J Comput 4(2):146–154

    MATH  Google Scholar 

  • Sessomboon W, Watanabe K, Irohara T, Yoshimoto K (1998) A study on multi-objective vehicle routing problem considering customer satisfaction with due-time (the creation of Pareto optimal solutions by hybrid genetic algorithm). Trans Jpn Soc Mech Eng. https://doi.org/10.1299/kikaic.64.1108

    Article  Google Scholar 

  • Shaw P (1997) A new local search algorithm providing high quality solutions to vehicle routing problems. Dept of Computer Science, University of Strathclyde, Glasgow, Scotland, UK, APES Group

    Google Scholar 

  • Shehab ME, Badran K, Salama GI (2013a) A generic feature extraction model using learnable evolution models (LEM + ID3). Int J Comput Appl 64(11):27–32

    Google Scholar 

  • Shehab ME, Badran K, Salama GI, Mgeed MZA (2013b) A novel feature extraction model using learnable evolution model. Int J Comput Sci Telecommun 4(4):5–9

    Google Scholar 

  • Sheskin DJ (2011) Handbook of parametric and nonparametric statistical procedures. CRC Press, Boca Raton

    MATH  Google Scholar 

  • Solomon MM (1986) On the worst-case performance of some heuristics for the vehicle routing and scheduling problem with time window constraints. Networks 16(2):161–174

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Solomon MM, Desrosiers J (1988) Survey paper—time window constrained routing and scheduling problems. Transp Sci 22(1):1–13

    MATH  Google Scholar 

  • Taillard É, Badeau P, Gendreau M, Guertin F, Potvin J-Y (1997) A tabu search heuristic for the vehicle routing problem with soft time windows. Transp Sci 31(2):170–186. https://doi.org/10.1287/trsc.31.2.170

    Article  MATH  Google Scholar 

  • Tan K, Lee L, Ou K (2001) Artificial intelligence heuristics in solving vehicle routing problems with time window constraints. Eng Appl Artif Intell 14(6):825–837. https://doi.org/10.1016/S0952-1976(02)00011-8

    Article  Google Scholar 

  • Tan KC, Chew YH, Lee L (2006) A hybrid multiobjective evolutionary algorithm for solving vehicle routing problem with time windows. Comput Optim Appl 34(1):115. https://doi.org/10.1007/s10589-005-3070-3

    Article  MathSciNet  MATH  Google Scholar 

  • Tan L, Lin F, Wang H (2015) Adaptive comprehensive learning bacterial foraging optimization and its application on vehicle routing problem with time windows. Neurocomputing 151:1208–1215

    Google Scholar 

  • Tavakkoli-Moghaddam R, Gazanfari M, Alinaghian M, Salamatbakhsh A, Norouzi N (2011) A new mathematical model for a competitive vehicle routing problem with time windows solved by simulated annealing. J Manuf Syst 30(2):83–92

    Google Scholar 

  • Tavares J, Machado P, Pereira FB, Costa E (2003) On the influence of GVR in vehicle routing. In: Proceedings of the ACM symposium on applied computing, pp 753–758. https://doi.org/10.1145/952532.952679

  • Thangiah SR, Nygard KE, Juell PL (1991) Gideon: a genetic algorithm system for vehicle routing with time windows. In: Seventh IEEE conference on artificial intelligence applications. Proceedings. IEEE

  • Thangiah SR, Osman IH, Sun T (1994) Hybrid genetic algorithm, simulated annealing and tabu search methods for vehicle routing problems with time windows. Computer Science Department, Slippery Rock University, Technical Report SRU CpSc-TR-94-27, 69

  • Ursani Z, Essam D, Cornforth D, Stocker R (2011) Localized genetic algorithm for vehicle routing problem with time windows. Appl Soft Comput 11(8):5375–5390

    Google Scholar 

  • Van Landeghem H (1988) A bi-criteria heuristic for the vehicle routing problem with time windows. Eur J Oper Res 36(2):217–226

    MATH  Google Scholar 

  • Wang C-H, Li C-H (2011) Optimization of an established multi-objective delivering problem by an improved hybrid algorithm. Expert Syst Appl 38(4):4361–4367. https://doi.org/10.1016/j.eswa.2010.09.105

    Article  Google Scholar 

  • Wang W, Wang Z, Qiao F (2008a) An improved genetic algorithm for vehicle routing problem with time-window. In: International symposium on computer science and computational technology. ISCSCT’08. IEEE

  • Wang X, Xu C, Hu X (2008b) Genetic algorithm for vehicle routing problem with time windows and a limited number of vehicles. In: International conference on management science and engineering. ICMSE 2008. 15th annual conference proceedings. IEEE

  • Woch M, Łebkowski P (2009) Sequential simulated annealing for the vehicle routing problem with time windows. Decis Mak Manuf Serv 3(1–2):87–100

    MathSciNet  MATH  Google Scholar 

  • Wojtusiak J (2012) The LEM3 system for multitype evolutionary optimization. Comput Inform 28(2):225–236

    MATH  Google Scholar 

  • Wojtusiak J, Warden T, Herzog O (2012a) The learnable evolution model in agent-based delivery optimization. Memet Comput 4(3):165–181

    MATH  Google Scholar 

  • Wojtusiak J, Warden T, Herzog O (2012b) Machine learning in agent-based stochastic simulation: inferential theory and evaluation in transportation logistics. Comput Math Appl 64(12):3658–3665

    MATH  Google Scholar 

  • Xu H, Fan W, Wei T, Yu L (2008) An Or-opt NSGA-II algorithm for multi-objective vehicle routing problem with time windows. In: IEEE conference on automation science and engineering, CASE 2008, pp 309–314. https://doi.org/10.1109/COASE.2008.4626505

  • Yassen ET, Ayob M, Nazri MZA, Sabar NR (2015) Meta-harmony search algorithm for the vehicle routing problem with time windows. Inf Sci 325:140–158

    Google Scholar 

  • Yu B, Yang Z, Yao B (2011) A hybrid algorithm for vehicle routing problem with time windows. Expert Syst Appl 38(1):435–441. https://doi.org/10.1016/j.eswa.2010.06.082

    Article  Google Scholar 

  • Zhang D, Cai S, Ye F, Si Y-W, Nguyen TT (2017) A hybrid algorithm for a vehicle routing problem with realistic constraints. Inf Sci 394:167–182

    Google Scholar 

  • Zhang J, Yang F, Weng X (2018) An evolutionary scatter search particle swarm optimization algorithm for the vehicle routing problem with time windows. IEEE Access 6:63468–63485

    Google Scholar 

  • Zhao YW, Wu B, Wang W, Ma YL, Wang W, Sun H (2004) Particle swarm optimization for vehicle routing problem with time windows. Mater Sci Forum 471:801–805

    Google Scholar 

  • Zitzler E, Thiele L (1998a) An evolutionary algorithm for multiobjective optimization: the strength pareto approach. Citeseer

  • Zitzler E, Thiele L (1998b) Multiobjective optimization using evolutionary algorithms—a comparative case study. In: International conference on parallel problem solving from nature. Springer

  • Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans Evol Comput 3(4):257–271

    Google Scholar 

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

    Google Scholar 

  • Zitzler E, Laumanns M, Thiele L (2001) SPEA2: improving the strength Pareto evolutionary algorithm. In: Eurogen

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    Behzad Moradi

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Moradi, B. The new optimization algorithm for the vehicle routing problem with time windows using multi-objective discrete learnable evolution model. Soft Comput 24, 6741–6769 (2020). https://doi.org/10.1007/s00500-019-04312-9

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