Abstract
In the last few years, a number of books and survey papers devoted to the vehicle routing problem (VRP) or to its variants or to the methods used for the solution of one or more variants of the VRP have been published. Also, in these years, the field of swarm intelligence algorithms has had a significant growth. One of the most important swarm intelligence algorithms is the particle swarm optimization (PSO). Although the particle swarm optimization was first published in 1995, it took around 10 years in order researchers to publish papers using a PSO algorithm for the solution of variants of the VRP. However, in the last 10 years, many journal papers, conference papers, and book chapters have been published where a variant of VRP is solved using a PSO algorithm. Thus, it is significant to present a survey paper where a review and brief analysis of the most important of these papers will be given. This is the main focus of this chapter.
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References
Adulyasak Y, Cordeau JF, Jans R (2014) Optimization-based adaptive large neighborhood search for the production routing problem. Transport Sci 48(1):20–45
Ai TJ, Kachitvichyanukul V (2009) A particle swarm optimisation for vehicle routing problem with time windows. Int J Oper Res 6(4):519–537
Ai TJ, Kachitvichyanukul V (2009) A particle swarm optimization for the vehicle routing problem with simultaneous pickup and delivery. Comput Oper Res 36:1693–1702
Ai TJ, Kachitvichyanukul V (2009) Particle swarm optimization and two solution representations for solving the capacitated vehicle routing problem. Comput. Ind. Eng. 56:380–387
Angelelli E, Speranza MG (2002) The periodic vehicle routing problem with intermediate facilities. Eur J Oper Res 137(2):233–247
Archetti C, Speranza MG, Hertz A (2006) A tabu search algorithm for the split delivery vehicle routing problem. Transp Sci 40(1):64–73
Archetti C, Speranza MG (2008) The split delivery vehicle routing problem: a survey. In: Golden B, Raghavan S, Wasil E (eds) The vehicle routing problem: latest advances and new challenges. Springer, Boston, pp 103–122
Archetti C, Speranza MG, Vigo D (2014) Vehicle routing problems with profits. In: Toth P, Vigo D (eds) Vehicle routing: problems, methods, and applications. MOS-SIAM series on optimization. SIAM, Philadelphia, pp 273–298
Assad AA, Golden BL (1995) Arc routing methods and applications. In: Ball MO, Magnanti TL, Momma CL, Nemhauser GL (eds) Network routing, handbooks in operations research and management science, vol 8. Elsevier Science B V, Amsterdam, pp 375–483
Ball MO, Magnanti TL, Momma CL, Nemhauser GL (eds) Network routing, handbooks in operations research and management science, vol 8. Elsevier Science B V, Amsterdam
Banks A, Vincent J, Anyakoha C (2007) A review of particle swarm optimization. Part I: background and development. Nat Comput 6(4):467–484
Banks A, Vincent J, Anyakoha C (2008) A review of particle swarm optimization. Part II: hybridisation, combinatorial, multicriteria and constrained optimization, and indicative applications. Nat Comput 7:109–124
Bard, JF, Nananukul N (2009) The integrated production inventory distribution routing problem. J Sched 12(3):257–280
Bashiri M, Fallahzade E (2012) A Particle swarm optimization algorithm for multi-depot capacitated location-routing problem with inventory decisions in supply chain network design. In: CIE42 proceedings, Cape Town, 16–18 July 2012. CIE and SAIIE, pp 25-1–25-9
Bektas T, Laporte G (2011) The pollution-routing problem. Transp Res B Methodol 45(8):1232–1250
Belmecheri F, Prins C, Yalaoui F, Amodeo L (2013) Particle swarm optimization algorithm for a vehicle routing problem with heterogeneous fleet, mixed backhauls, and time windows. J Intell Manuf 24(4):775–789
Berbeglia G, Cordeau JF, Gribkovskaia I, Laporte G (2007) Static pickup and delivery problems: a classification scheme and survey. TOP 15(1):1–31
Bianchi L, Birattari M, Manfrin M, Mastrolilli M, Paquete L, Rossi-Doria O, Schiavinotto T (2006) Hybrid metaheuristics for the vehicle routing problem with stochastic demands. J Math Model Algorithm 5(1):91–110
Bodin L, Golden B (1981) Classification in vehicle routing and scheduling. Networks 11: 97–108
Bodin L, Golden B, Assad A, Ball M (1983) The state of the art in the routing and scheduling of vehicles and crews. Comput Oper Res 10:63–212
Bortfeldt A (2012) A hybrid algorithm for the capacitated vehicle routing problem with three-dimensional loading constraints. Comput Oper Res 39(9):2248–2257
Bozorgi-Amiri A, Jabalameli MS, Alinaghian M, Heydari M (2012) A modified particle swarm optimization for disaster relief logistics under uncertain environment. Int J Adv Manuf Technol 60(1–4):357–371
Braysy O, Gendreau M (2005) Vehicle routing problem with time windows, Part I: route construction and local search algorithms. Transp Sci 39(1): 104–118
Braysy O, Gendreau M (2005) Vehicle routing problem with time windows, Part II: metaheuristics. Transp Sci 39(1): 119–139
Brito J, Exposito A, Moreno-P\(\acute {e}\)rez JA (2015) Bi-objective discrete PSO for service-oriented VRPTW (Chapter 29). In: Greiner D et al (eds) Advances in evolutionary and deterministic methods for design, optimization and control in engineering and sciences. Computational methods in applied sciences, vol 36. Springer International Publishing, Cham, pp 445–460. https://doi.org/10.1007/978-3-319-11541-2_29
Campbell A, Clarke L, Kleywegt A, Sawelsberg M (1998) The inventory routing problem. In: Crainic TG, Laporte G (eds) Fleet management and logistics. Kluwer Academic Publishers, Boston, pp 95–113
Campbell A, Clarke L, Sawelsberg M (2002) Inventory routing in practice. In: Toth P, Vigo D (eds) The vehicle routing problem. Monographs on discrete mathematics and applications. Siam, Philadelphia, pp 309–330
Caceres-Cruz J, Arias P, Guimarans D, Riera D, Juan AA (2015). Rich vehicle routing problem: survey. ACM Comput Surv (CSUR) 47(2):32
Caretto C, Baker B (2002) A GRASP interactive approach to the vehicle routing problem with backhauls. In: Ribeiro CC, Hansen P (eds) Essays and surveys on metaheuristics. Kluwer Academic Publishers, Norwell, pp 185–199
Casco DO, Golden BL, Wasil EA (1988) Vehicle routing with backhauls: models, algorithms, and case studies. In: Golden BL, Assad AA (eds) Vehicle routing: methods and studies. North Holland, Amsterdam, pp 127–147
Castro JP, Landa-Silva D, Moreno Perez JA (2009) Exploring feasible and infeasible regions in the vehicle routing problem with time windows using a multi-objective particle swarm optimization approach (Chapter 9). In: Krasnogor N et al (eds) Nature inspired cooperative strategies for optimization. SCI, vol 236. Springer, Berlin/Heidelberg, pp 103–114
Chao IM, Golden BL, Wasil E (1993) A new heuristic for the multi-depot vehicle routing problem that improves upon best-known solutions. Am J Math Manag Sci 13(3–4):371–406
Chen A-L, Yang G-K, Wu Z-M (2006) Hybrid discrete particle swarm optimization algorithm for capacitated vehicle routing problem. J Zhejiang Univ Sci A 7(4):607–614
Chen J-Q, Li W-L, Murata T (2013) Particle swarm optimization for vehicle routing problem with uncertain demand. In: Proceedings of 2013 4th IEEE international conference on software engineering and service science (ICSESS), Beijing, 23–25 May 2013, pp 857–860
Chen S-K, Wu G-H, Ti Y-W, Wang R-Z, Fang W-P, Lu C-J (2014) Hierarchical particle swarm optimization algorithm of IPSVR problem. In: Pan J-S et al (eds) Genetic and evolutionary computing. Advances in intelligent systems and computing, vol 238. Springer International Publishing, Cham, pp 231–238. https://doi.org/10.1007/978-3-319-01796-9_24
Chen MC, Hsiao YH, Reddy RH, Tiwari MK (2016) The self-learning particle swarm optimization approach for routing pickup and delivery of multiple products with material handling in multiple cross-docks. Transp Res E 91:208–226
Christiansen M, Fagerholt K, Ronen D (2004) Ship routing and scheduling: status and perspectives. Transp Sci 38(1):1–18
Christiansen M, Fagerholt K, Nygreen B, Ronen D (2013) Ship routing and scheduling in the new millennium. Eur J Oper Res 228:467–483
Christofides N (1985) Vehicle routing. In: Lawer EL, Lenstra JK, Rinnoy Kan AHG, Shmoys DB (eds) The traveling salesman problem: a guided tour of combinatorial optimization. Wiley, Chichester, pp 431–448
Christofides N, Mignozzi A, Toth P (1979) The vehicle routing problem. In: Christofides N (ed) Combinatorial optimization. Wiley, Chichester, pp 315–338
Clerc M (2006) Particle swarm optimization. ISTE, London
Clerc M, Kennedy J (2002) The particle swarm: explosion, stability and convergence in a multi-dimensional complex space. IEEE Trans Evol Comput 6:58–73
Cordeau JF, Deasulniers G, Desrosiers J, Solomon MM, Soumis F (2002) VRP with time windows. In: Toth P, Vigo D (eds) The vehicle routing problem. Monographs on discrete mathematics and applications. SIAM, Philadelphia, pp 157–193
Dallard H, Lam SS, Kulturel-Konak S (2007) Solving the orienteering problem using attractive and repulsive particle swarm optimization. In: Proceedings of IEEE international conference on Information Reuse and Integration (IRI 2007), Las Vegas, 13–15 Aug 2007, pp 2–17
Dang D-C, Guibadj RN, Moukrim A (2011) A PSO-based memetic algorithm for the team orienteering problem. In: Di Chio C et al (eds) EvoApplications 2011, Part II. LNCS, vol 6625. Springer, Berlin/Heidelberg, pp 471–480
Dantzig GB, Ramser JH (1959) The truck dispatching problem. Manag Sci 6(1):80–91
Daskin M (1995) Network and discrete location. Models, algorithms and applications. Wiley, New York
De A, Mamanduru VKR, Gunasekaran A, Subramanian N, Tiwari MK (2016) Composite particle algorithm for sustainable integrated dynamic ship routing and scheduling optimization. Comput Ind Eng 96:201–215
Desrochers M, Lenstra JK, Savelsberg MWP, Soumis F (1988) Vehicle routing with time windows: optimization and approximation. In: Golden BL, Assad AA (eds) Vehicle routing: methods and studies. North Holland, Amsterdam, pp 65–84
Desrosiers J, Dumas Y, Solomon MM, Soumis F (1995) Time constraint routing and scheduling. In: Ball MO, Magnanti TL, Momma CL, Nemhauser GL (eds) Network routing, handbooks in operations research and management science, vol 8. Elsevier Science B V, Amsterdam, pp 35–140
Di-Ming A, Zhe Z, Rui Z, Feng P (2011) Research of pareto-based multi-objective optimization for multi-vehicle assignment problem based on MOPSO. In: Tan Y et al (eds) ICSI 2011, Part II. LNCS, vol 6729. Springer, Berlin/Heidelberg, pp 10–16
Eksioglu B, Vural AV, Reisman, A (2009) The vehicle routing problem: a taxonomic review. Comput Ind Eng 57(4):1472–1483
Engelbrecht AP (2007) Computational intelligence: an introduction, 2nd edn. Wiley, Chichester
Fedegruen A, Simchi-Levi D (1995) Analysis of vehicle routing and inventory routing problems. In: Ball MO, Magnanti TL, Momma CL, Nemhauser GL (eds) Network routing. Handbooks in operations research and management science, vol 8. Elsevier Science B V, Amsterdam, pp 297–373
Fisher ML (1995) Vehicle routing. In: Ball MO, Magnanti TL, Momma CL, Nemhauser GL (eds) Network routing. Handbooks in operations research and management science, vol 8. North Holland, Amsterdam, pp 1–33
Francis PM, Smilowitz KR, Tzur M (2008) The period vehicle routing problem and its extensions. In: Golden B et al (eds) The vehicle routing problem: latest advances and new challenges. Springer LLC, Boston, pp 73–102
Gan X, Wang Y, Yu Y, Niu B (2013) An emergency vehicle scheduling problem with time utility based on particle swarm optimization. In: Huang D-S et al (eds) ICIC 2013. LNAI, vol 7996. Springer, Berlin/Heidelberg, pp 614–623
Gan X, Kuang J, Niu B (2014) Particle swarm optimizations for multi-type vehicle routing problem with time windows. In: Huang D-S et al (eds) ICIC 2014. LNAI, vol 8589. Springer International Publishing, Cham, pp 808–815
Gan X, Liu LJ, Chen JS, Niu B (2016) Comprehensive learning PSO for solving environment heterogeneous fixed fleet VRP with time windows. In: Tan Y et al (eds) ICSI 2016, Part II. LNCS, vol 9713. Springer, Cham, pp 424–432
Gavalas D, Konstantopoulos C, Mastakas K, Pantziou G (2014) A survey on algorithmic approaches for solving tourist trip design problems. J Heuristics 20(3):291–328
Gendreau M, Potvin JY (1998) Dynamic vehicle routing and dispatching. In: Crainic TG, Laporte G (eds) Fleet management and logistics. Kluwer Academic Publishers, Boston, pp 115–125
Gendreau M, Laport G, Seguin R (1996) Stochastic vehicle routing. Eur J Oper Res 88:3–12
Gendreau M, Laporte G, Potvin J-Y (1997) Vehicle routing: modern heuristics. In: Aarts EHL, Lenstra JK (eds) Local search in combinatorial optimization. Wiley, Chichester, pp 311–336
Gendreau M, Laporte G, Musaraganyi C, Taillard ED (1999) A tabu search heuristic for the heterogeneous fleet vehicle routing problem. Comput Oper Res 26:1153–1173
Gendreau M, Laporte G, Potvin J-Y (2002) Metaheuristics for the capacitated VRP. In: Toth P, Vigo D (eds) The vehicle routing problem. Monographs on discrete mathematics and applications. SIAM, Philadelphia, pp 129–154
Gendreau M, Iori M, Laporte G, Martello S (2008) A Tabu search heuristic for the vehicle routing problem with two-dimensional loading constraints. Networks 51(1):4–18
Glover F, Laguna M, Marti R (2003) Scatter search and path relinking: advances and applications. In: Glover F, Kochenberger GA (eds) Handbook of metaheuristics. Kluwer Academic Publishers, Boston, pp 1–36
Goksal FP, Altiparmak F, Karaoglan I (2010) A hybrid particle swarm optimization for vehicle routing problem with simultaneous pickup and delivery. In: Proceedings of 2010 40th international conference on Computers and Industrial Engineering (CIE), Awaji, 25–28 July 2010, pp 1–6
Goksal FP, Karaoglan I, Altiparmak F (2013) A hybrid discrete particle swarm optimization for vehicle routing problem with simultaneous pickup and delivery. Comput Ind Eng 65: 39–53
Golden BL, Assad AA (1988) Vehicle routing: methods and studies. North Holland, Amsterdam
Golden BL, Wasil EA, Kelly JP, Chao IM (1998) The impact of metaheuristics on solving the vehicle routing problem: algorithms, problem sets, and computational results. In: Crainic TG, Laporte G (eds) Fleet management and logistics. Kluwer Academic Publishers, Boston, pp 33–56
Golden BL, Raghavan S, Wasil EA (eds) (2008) The vehicle routing problem: latest advances and new challenges. Operations research/computer science interfaces series, vol 43. Springer LLC, Boston
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
Hansen P, Mladenovic N (2001) Variable neighborhood search: principles and applications. Eur J Oper Res 130:449–467
Hu F, Wu F (2010) Diploid hybrid particle swarm optimization with differential evolution for open vehicle routing problem. In: Proceedings of the 8th world congress on intelligent control and automation, Jinan, 6–9 July 2010
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 15:1247–1270. https://doi.org/10.3390/e15041247
Jaillet P, Odoni AR (1988) The probabilistic vehicle routing problem. In: Golden BL, Assad AA (eds) Vehicle routing: methods and studies. North Holland, Amsterdam, pp 293–318
Javid AA, Azad N (2010) Incorporating location, routing and inventory decisions in supply chain network design. Transport Res E Log Transp Rev 46(5):582–597
Jian L (2009) Solving capacitated vehicle routing problems via genetic particle swarm optimization. In: Proceedings of 2009 third international symposium on intelligent information technology application, Nanchang, 21–22 Nov 2009, pp 528–531
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 ’09), Nashville, 30 Mar 2009–2 Apr 2009, pp 103–106
Jozefowiez N, Semet F, Talbi EG (2008) Multi-objective vehicle routing problems. Eur J Oper Res 189(2):293–309
Kachitvichyanukul V, Sombuntham P, Kunnapapdeelert S (2015) Two solution representations for solving multi-depot vehicle routing problem with multiple pickup and delivery requests via PSO. Comput Ind Eng 89:125–136
Kanthavel K, Prasad P (2011) Optimization of capacitated vehicle routing problem by nested particle swarm optimization. Am J Appl Sci 8(2):107–112
Kechagiopoulos PN, Beligiannis GN (2014) Solving the urban transit routing problem using a particle swarm optimization based algorithm. Appl Soft Comput 21:654–676
Kennedy J (1997) The particle swarm: social adaptation of knowledge. In: Proceedings of the IEEE international conference on evolutionary computation, Indianapolis, 13–16 Apr 1997, pp 303–308
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of 1995 IEEE international conference on neural networks, vol 4, pp 1942–1948
Kennedy J, Eberhart R (1997) A discrete binary version of the particle swarm algorithm. In: Proceedings of 1997 IEEE international conference on systems, man, and cybernetics, vol 5, pp 4104–4108
Kirkpatrick S (1984) Optimization by simulated annealing – quantitative studies. J Stat Phys 34:975–986
Khouadjia MR, Alba E, Jourdan L, Talbi E-G (2010) Multi-swarm optimization for dynamic combinatorial problems: a case study on dynamic vehicle routing problem. In: Dorigo M et al (eds) ANTS 2010. LNCS, vol 6234. Springer, Berlin/Heidelberg, pp 227–238
Khouadjia MR, Jourdan L, Talbi E-G (2010) Adaptive particle swarm for solving the dynamic vehicle routing problem. In: Proceedings of 2010 IEEE/ACS international conference on computer systems and applications (AICCSA), Hammamet, 16–19 May 2010, pp 1–8
Khouadjia MR, Sarasola B, Alba E, Jourdan L, Talbi E-G (2012) A comparative study between dynamic adapted PSO and VNS for the vehicle routing problem with dynamic requests. Appl Soft Comput 12:1426–1439
Kim B-I, Son S-J (2012) A probability matrix based particle swarm optimization for the capacitated vehicle routing problem. J Intell Manuf 23(4):1119–1126
Kou M, Ye C, Chen Z (2011) A bee evolutionary particle swarm optimization algorithm for vehicle routing problem. In: Proceedings of 2011 6th IEEE joint international information technology and artificial intelligence conference (ITAIC), Chongqing, vol 2, 20–22 Aug 2011, pp 398–401
Kumar RS, Kondapaneni K, Dixit V, Goswami A, Thakur LS, Tiwari MK (2016) 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
Kuo RJ, Zulvia FE, Suryadi K (2012) Hybrid particle swarm optimization with genetic algorithm for solving capacitated vehicle routing problem with fuzzy demand – a case study on garbage collection system. Appl Math Comput 219:2574–2588
Lahyani R, Khemakhem M, Semet F (2015) Rich vehicle routing problems: from a taxonomy to a definition. Eur J Oper Res 241:1–14
Laporte G (1988) Location routing problems. In: Golden BL, Assad AA (eds) Vehicle routing: methods and studies. North Holland, Amsterdam, pp 163–198
Laporte G, Semet F (2002) Classical heuristics for the capacitated VRP. In: Toth P, Vigo D (eds) The vehicle routing problem. Monographs on discrete mathematics and applications. SIAM, Philadelphia, pp 109–128
Laporte G, Nobert Y, Taillefer S (1988) Solving a family of multi-depot vehicle routing and location routing problems. Transp Sci 22:161–172
Laporte G, Gendreau M, Potvin, J-Y, Semet F (2000) Classical and modern heuristics for the vehicle routing problem. Int Trans Oper Res 7:285–300
Li Y, Li D, Wang D ( 2012) Quantum-behaved particle swarm optimization algorithm based on border mutation and chaos for vehicle routing problem. In: Tan Y, Shi Y, Ji Z (eds) ICSI 2012, Part I. LNCS, vol 7331, Springer, Berlin/Heidelberg, pp 63–73
Lichtblau D (2002) Discrete optimization using mathematica. In: Callaos N, Ebisuzaki T, Starr B, Abe JM, Lichtblau D (eds) World multi-conference on systemics, cybernetics and informatics (SCI 2002), vol 16. International Institute of Informatics and Systemics, pp 169–174
Lin C, Choy KL, Ho GTS, Chung SH, Lam HY (2014) Survey of green vehicle routing problem: past and future trends. Expert Syst Appl 41:1118–1138
Liu J, Kachitvichyanukul V (2013) A new solution representation for solving location routing problem via particle swarm optimization. In: Lin Y-K et al (eds) Proceedings of the institute of industrial engineers asian conference. Springer Science+Business Media, Singapore. https://doi.org/10.1007/978-981-4451-98-7_12
Liu X, Jiang W, Xie J (2009) Vehicle routing problem with time windows: a hybrid particle swarm optimization approach. In: Proceedings of 2009 fifth international conference on natural computation, Tianjin, 14–16 Aug 2009, pp 502–506
Liu SC, Lu MC, Chung CH (2016) A hybrid heuristic method for the periodic inventory routing problem. Int J Adv Manuf Technol 85:2345–2352
Marinakis Y (2015) An improved particle swarm optimization algorithm for the capacitated location routing problem and for the location routing problem with stochastic demands. Appl Soft Comput 37:680–701
Marinakis Y, Marinaki M (2008) A particle swarm optimization algorithm with path relinking for the location routing problem. J Math Model Algorithms 7(1):59–78
Marinakis Y, Marinaki M (2010) A hybrid genetic – particle swarm optimization algorithm for the vehicle routing problem. Expert Syst Appl 37:1446–1455
Marinakis Y, Marinaki M (2012) A hybrid particle swarm optimization algorithm for the open vehicle routing problem. In: Dorigo M et al (eds) ANTS 2012. LNCS, vol 7461. Springer, Berlin/Heidelberg, pp 180–187
Marinakis Y, Marinaki M (2013) Combinatorial neighborhood topology particle swarm optimization algorithm for the vehicle routing problem. In: Middendorf M, Blum C (eds) EvoCOP 2013. LNCS, vol 7832, pp 133–144
Marinakis Y, Marinaki M (2013) Combinatorial expanding neighborhood topology particle swarm optimization for the vehicle routing problem with stochastic demands. In: Proceedings of GECCO 2013, genetic and evolutionary computation conference, Amsterdam, 6–10 July 2013, pp 49–56
Marinakis Y, Migdalas Á (2002) Heuristic solutions of vehicle routing problems in supply chain management. In: Pardalos PM, Migdalas A, Burkard R (eds) Combinatorial and global optimization. World Scientific Publishing Co, Singapore, pp 205–236
Marinakis Y, Migdalas A, Pardalos PM (2005) Expanding neighborhood GRASP for the traveling salesman problem. Comput Optim Appl 32:231–257
Marinakis Y, Migdalas A, Pardalos PM (2009) Multiple phase neighborhood search GRASP based on lagrangean relaxation and random backtracking Lin-Kernighan for the traveling salesman problem. J Comb Optim 17:134–156
Marinakis Y, Marinaki M, Dounias G (2010) A hybrid particle swarm optimization algorithm for the vehicle routing problem. Eng Appl Artif Intel 23:463–472
Marinakis Y, Iordanidou G, Marinaki M (2013) Particle swarm optimization for the vehicle routing problem with stochastic demands. Appl Soft Comput 13(4):1693–1704
Marinakis Y, Marinaki M, Migdalas A (2014) An adaptive particle swarm optimization algorithm for the vehicle routing problem with time windows. In: Proceedings of LOT 2014, logistics, optimization and transportation conference, Molde, 1–2 Nov 2014
Min H, Jayaraman V, Srivastava R (1998) Combined location-routing problems: a synthesis and future research directions. Eur J Oper Res 108:1–15
MirHassani SA, Abolghasemi N (2011) A particle swarm optimization algorithm for open vehicle routing problem. Expert Syst Appl 38:11547–11551
Moghaddam BF, Ruiz R, Sadjadi SJ (2012)Vehicle routing problem with uncertain demands: an advanced particle swarm algorithm. Comput Ind Eng 62:306–317
Montoya-Torres JR, Franco JL, Isaza SN, Jimenez HF, Herazo-Padilla N (2015) A literature review on the vehicle routing problem with multiple depots. Comput Ind Eng 79: 115–129
Mosheiov G (1998) Vehicle routing with pickup and delivery: tour – partitioning heuristics. Comput Ind Eng 34:669–684
Mu\(\tilde {n}\)oz-Zavala A, Hern\(\acute {a}\)ndez-Aguirre A, Villa-Diharce E (2009) Particle evolutionary swarm multi-objective optimization for vehicle routing problem with time windows. In: Coello Coello CA et al (eds) Swarm intelligence for multi-objective problems in data mining. SCI, vol 242. Springer, Berlin/Heidelberg, pp 233–257
Muthuswamy S, Lam SS (2011) Discrete particle swarm optimization for the team orienteering problem. Memetic Comput 3:287–303
Nagy G, Salhi S (2007) Location-routing: issues, models and methods. Eur J Oper Res 177:649–672
Ngueveu SU, Prins C, Calvo RW (2010) An effective memetic algorithm for the cumulative capacitated vehicle routing problem. Comput Oper Res 37(11):1877–1885
Norouzi N, Tavakkoli-Moghaddam R, Ghazanfari M, Alinaghian M, Salamatbakhsh A (2012) A new multi-objective competitive open vehicle routing problem solved by particle swarm optimization. Netw Spat Econ 12(4):609–633
Norouzi N, Sadegh-Amalnick M, Mehdi A (2015) Evaluating of the particle swarm optimization in a periodic vehicle routing problem. Measurement 62:162–169
Norouzi N, Sadegh-Amalnick M, Tavakkoli-Moghaddam R (2016) Modified particle swarm optimization in a time-dependent vehicle routing problem: minimizing fuel consumption. Opt Lett. https://doi.org/10.1007/s11590-015-0996-y
Okulewicz M, Ma\(\acute {n}\)dziuk J (2013) Application of particle swarm optimization algorithm to dynamic vehicle routing problem. In: Rutkowski L et al (eds) ICAISC 2013, Part II. LNAI, vol 7895. Springer, Berlin/Heidelberg, pp 547–558
Okulewicz M, Ma\(\acute {n}\)dziuk J (2017) The impact of particular components of the PSO-based algorithm solving the dynamic vehicle routing problem. Appl Soft Comput 58:586–604
Olivera AC, Garc\(\acute {i}\) a-Nieto JM, Alba E (2014) Reducing vehicle emissions and fuel consumption in the city by using particle swarm optimization. Applied intelligence. Springer Science+Business Media, New York. https://doi.org/10.1007/s10489-014-0604-3
Peng Y (2009) Hybrid particle swarm optimization for vehicle routing problem with reverse logistics. In: Proceedings of 2009 international conference on intelligent human-machine systems and cybernetics, Hangzhou, 26–27 Aug 2009, pp 462–465
Peng Y, Chen Z-X (2009) Two-phase particle swarm optimization for multi-depot location-routing problem. In: Proceedings of 2009 international conference on new trends in information and service science, Beijing, 30 June 2009–2 July 2009, pp 240–245
Peng Y, Chen J (2010) Vehicle routing problem with fuzzy demands and the particle swarm optimization solution. In: Proceedings of 2010 international conference on management and service science (MASS), Wuhan, 24–26 Aug 2010, pp 1–4
Peng Y, Zhu H-Y (2008) Research on vehicle routing problem with stochastic demand and PSO-DP algorithm with inver-over operator. Syst Eng Theory Pract (SETP) 28(10):76–81
Pereira FB, Tavares J (2008) Bio-inspired algorithms for the vehicle routing problem. Studies in computational intelligence, vol 161. Springer, Berlin/Heideberg
Perwira Redi AAN, Maghfiroh MFN, Yu VF (2013) Discrete particle swarm optimization with path-relinking for solving the open vehicle routing problem with time windows. In: Lin Y-K et al (eds) Proceedings of the institute of industrial engineers Asian conference 2013. Springer Science+Business Media, Singapore, pp 853–859. https://doi.org/10.1007/978-981-4451-98-7_102
Pillac V, Gendreau M, Gueret C, Medaglia AL (2013) A review of dynamic vehicle routing problems. Eur J Oper Res 225:1–11
Poli R, Kennedy J, Blackwell T (2007) Particle swarm optimization. An overview. Swarm Intell 1:33–57
Powell WB, Jaillet P, Odoni A (1995) Stochastic and dynamic networks and routing. In: Ball MO, Magnanti TL, Momma CL, Nemhauser GL (eds) Network routing. Handbooks in operations research and management science, vol 8. Elsevier Science B V, Amsterdam, pp 141–295
Prins C (2004) A simple and effective evolutionary algorithm for the vehicle routing problem. Comput Oper Res 31:1985–2002
Prodhon C, Prins C (2014) A survey of recent research on location-routing problems. Eur J Oper Res 238:1–17
Psaraftis HN (1988) Dynamic vehicle routing problems. In: Golden BL, Assad AA (eds) Vehicle routing: methods and studies. North Holland, Amsterdam, pp 223–248
Psaraftis HN (1995) Dynamic vehicle routing: status and prospects. Ann Oper Res 61: 143–164
Qi C (2011) Application of improved discrete particle swarm optimization in logistics distribution routing problem. Proc Eng Adv Control Eng Inf Sci 15:3673–3677
Rabbani M, Manavizadeh N, Shamekhi A (2013) A particle swarm optimization method for periodic vehicle routing problem with pickup and delivery in transportation. Adv Railw Eng Int J 1(1):51–60
Renaud J, Laporte G, Boctor FF (1996) A Tabu search heuristic for the multidepot vehicle routing problem. Comput Oper Res 23(3):229–235
Ronen D (1983) Cargo ships routing and scheduling: survey of models and problems. Eur J Oper Res 12:119–126
Ronen D (1993) Ships scheduling: the last decade. Eur J Oper Res 71(3):325–333
Sariklis D, Powell S (2000) A heuristic method for the open vehicle routing problem. J Oper Res Soc 51(5):564–573
Sevkli Z, Sevilgen FE (2010) Discrete particle swarm optimization for the orienteering problem. In: Proceedings of 2010 IEEE Congress on Evolutionary Computation (CEC), Barcelona, 18–23 July 2010, pp 1–8
Sevkli AZ, Sevilgen FE (2012) Discrete particle swarm optimization for the team orienteering problem. Turk J Electr Eng Comput Sci 20(2):231–239
Shao Z-J, Gao S-P, Wang S-S (2009) A hybrid particle swarm optimization algorithm for vehicle routing problem with stochastic travel time. In: Cao B-Y, Zhang C-Y, Li T-F (eds) Fuzzy information and engineering. ASC, vol 54. Springer, Berlin/Heidelberg, pp 566–574
Shen H, Zhu Y, Liu T, Jin L (2009) Particle swarm optimization in solving vehicle routing problem. In: Proceedings 2009 second international conference on intelligent computation technology and automation, Changsha, 10–11 Oct 2009, pp 287–291
Shi Y, Eberhart R (1998) A modified particle swarm optimizer. In: Proceedings of 1998 IEEE world congress on computational intelligence, pp 69–73
Solomon MM (1987) Algorithms for the vehicle routing and scheduling problems with time window constraints. Oper Res 35(2):254–265
Solomon MM, Desrosiers J (1988) Time window constrained routing and scheduling problems. Transp Sci 22(1):1–13
Solomon MM, Baker EK, Schaffer JR (1988) Vehicle routing and scheduling problems with time windows constraints. In: Golden BL, Assad AA (eds) Vehicle routing: methods and studies. North Holland, Amsterdam, pp 85–105
Sombuntham P, Kachitvichayanukul V (2010) A particle swarm optimization algorithm for multi-depot vehicle routing problem with pickup and delivery Requests. In: Proceedings of the international multiconference of engineers and computer scientists (IMECS 2010), vol III, Hong Kong, 17–19 Mar 2010. ISBN:978-988-18210-5-8
Stewart WR, Golden BL (1983) Stochastic vehicle routing: a comprehensive approach. Eur J Oper Res 14:371–385
Tang H (2011) Vehicle route optimization in logistics distribution based on extension-coded particle swarm algorithm. In: Proceedings of 2011 international conference on computer science and network technology, Harbin, 24–26 Dec 2011, pp 2350–2354
Tang C, Wang T (2011) An improved particle swarm optimization for the vehicle routing problem with simultaneous deliveries and pick-ups. In: Shen G, Huang X (eds) CSIE 2011, Part II. CCIS, vol 153. Springer, Berlin/Heidelberg, pp 294–300
Tarantilis CD (2005) Solving the vehicle routing problem with adaptive memory programming methodology. Comput Oper Res 32(9):2309–2327
Tavakkoli Moghaddam R, Mohmmad Zohrevand A, Rafiee K (2012) Solving a new mathematical model for a periodic vehicle routing problem by particle swarm optimization. Transp Res J 1:77–87
Tavakoli MM, Sami A (2013) Particle swarm optimization in solving capacitated vehicle routing problem. Buletin Teknik Elektro dan Informatika (Bull Electr Eng Inf) 2(4):252–257
Ting C-J, Wu K-C, Chou H (2014) Particle swarm optimization algorithm for the berth allocation problem. Expert Syst Appl 41:1543–1550
Tlili T, Faiz S, Krichen S (2014) A hybrid metaheuristic for the distance-constrained capacitated vehicle routing problem. Procedia – social and behavioral sciences, 2nd world conference on business, economics and management-WCBEM 2013, vol 109, pp 779–783
Toth P, Vigo D (2002) The vehicle routing problem. Monographs on discrete mathematics and applications. SIAM, Philadelphia
Toth P, Vigo D (2002) VRP with backhauls. In: Toth P, Vigo D (eds) The vehicle routing problem. Monographs on discrete mathematics and applications. SIAM, Philadelphia, pp 195–224
Toth P, Vigo D (2014) Vehicle routing: problems, methods and applications, 2nd edn. MOS-SIAM series on optimization. SIAM, Philadelphia
Vahdani B, Tavakkoli-Moghaddam R, Zandieh M, Razmi J (2012) Vehicle routing scheduling using an enhanced hybrid optimization approach. J Intel Manuf 23(3):759–774
Vansteenwegen P, Souffriau W, Berghe GV, Oudheusden DV (2009) A guided local search metaheuristic for the team orienteering problem. Eur J Oper Res 196:118–127
Varthanan PA, Murugan N, Kumar GM (2012) A simulation based heuristic discrete particle swarm algorithm for generating integrated production-distribution plan. Appl Soft Comput 12:3034–3050
Venkatesan SR, Logendran D, Chandramohan D (2011) Optimization of capacitated vehicle routing problem using PSO. Int J Eng Sci Technol (IJEST) 3(10):7469–7469
Vidal T, Crainic TG, Gendreau M, Prins C (2013) Heuristics for multi-attribute vehicle routing problems: a survey and synthesis. Eur J Oper Res 231(1):1–21
Vigo D (1996) A heuristic algorithm for the asymmetric capacitated vehicle routing problem. Eur J Oper Res 89(1):108–126
Wang T-J, Wu K-J (2012) Adaptive particle swarm optimization based on population entropy for MDVRPTW. In: Proceedings of 2012 2nd international conference on computer science and network technology, Changchun, 29–31 Dec 2012, pp 753–756
Wang W, Wu B, Zhao Y, Feng D (2006) Particle swarm optimization for open vehicle routing problem. In: Huang D-S, Li K, Irwin GW (eds) ICIC 2006. LNAI, vol 4114. Springer, Berlin/Heidelberg, pp 999–1007
Wang S, Wang L, Yuan H, Ge M, Niu B, Pang W, Liu Y (2009) Study on multi-depots vehicle scheduling problem and its two-phase particle swarm optimization. In: Huang D-S et al (eds) ICIC 2009. LNAI, vol 5755. Springer, Berlin/Heidelberg, pp 748–756
Wang Z, Li J, Fan J, Fan C (2010) Research on improved hybrid particle swarm optimization for vehicle routing problem with time windows. In: Proceedings of 2010 international conference on artificial intelligence and computational intelligence, Sanya, 23–24 Oct 2010, pp 179–183
Wang B, Wang K, Bao F, Zhang L, Shen L (2012) Mixed climbing particle swarm algorithm in the VRP. In: Proceedings of 2012 second international conference on business computing and global informatization, pp 554–557
Wei R, Zhang T, Tang H (2010) An improved particle swarm optimization algorithm for vehicle routing problem with simultaneous pickup and delivery. In: Zhu R et al (eds) ICICA 2010, Part I. CCIS, vol 105. Springer, Berlin/Heidelberg, pp 430–436
Xu J, Yan F, Li S (2011) Vehicle routing optimization with soft time windows in a fuzzy random environment. Transp Res E 47:1075–1091
Yan F, Xu M, Yu H (2015) The vehicle routing optimization with uncertain demands and traveling time. In: Xu J et al (eds) Proceedings of the ninth international conference on management science and engineering Management. Advances in intelligent systems and computing, vol 362, pp 267–274
Yang SY, Wang M, Jiao LC (2004) A quantum particle swarm optimization. In: Proceedings of the 2004 IEEE congress on evolutionary computation, vol 1, pp 320–324
Yao B, Yu B, Hu P, Gao J (2016) An improved particle swarm optimization for carton heterogeneous vehicle routing problem with a collection depot. Ann Oper Res 242: 303–320
Yusoff M, Ariffin J, Mohamed A (2011) A multi-valued discrete particle swarm optimization for the evacuation vehicle routing problem. In: Tan Y et al (eds) ICSI 2011, Part I. LNCS, vol 6728. Springer, Berlin/Heidelberg, pp 182–193
Yusoff M, Ariffin J, Mohamed A (2012) DPSO based on random particle priority value and decomposition procedure as a searching strategy for the evacuation vehicle routing problem. In: Huang T et al (eds) ICONIP 2012, Part III. LNCS, vol 7665. Springer, Berlin/Heidelberg, pp 678–685
Yusoff M, Ariffin J, Mohamed A (2015) DPSO based on a min-max approach and clamping strategy for the evacuation vehicle assignment problem. Neurocomputing 148:30–38
Zeimpekis VS, Tarantilis CD, Giaglis GM, Minis I (eds) (2007) Dynamic fleet management – concepts, systems, algorithms and case studies. Book series: operations research/computer science interfaces series, vol 38. Springer
Zhan Z-H, Zhang J (2009) Discrete particle swarm optimization for multiple destination routing problems. In: Giacobini M et al (eds) EvoWorkshops 2009. LNCS, vol 5484. Springer, Berlin/Heidelberg, pp 117–122
Zhang W, Ye J (2010) An improved particle swarm optimization for the multi-depot vehicle routing problem. In: Proceedings of 2010 international conference on E-business and E-government, Guangzhou, 7–9 May 2010, pp 3188–3191
Zhang N-Z, Sun G-H, Wu Y-H, Geng, F-H (2009) A modified particle swarm optimization for the vehicle routing problem with simultaneous pickup and delivery. In: Proceedings of the 7th Asian control conference, Hong Kong, 27–29 Aug 2009, pp 1679–1684
Zhang T, Chaovalitwongse WA, Zhang Y (2012) Scatter search for the stochastic travel-time vehicle routing problem with simultaneous pick-ups and deliveries. Comput Oper Res 39:2277–2290
Zhang L, Li Y, Fei T, Chen X, Ting G (2014) Research of emergency logistics routing optimization based on particle swarm optimization. In: Patnaik S, Li X (eds) Proceedings of international conference on computer science and information technology. Advances in intelligent systems and computing, vol 255, Springer, pp 415–421. https://doi.org/10.1007/978-81-322-1759-6_48
Zhao Y, Li C, Zhang J-L, Ren X, Ren W (2011) Research on vehicle routing problem with stochastic demand based on multi-objective method. In: Huang D-S et al (eds) ICIC 2011. LNCS, vol 6838. Springer, Berlin/Heidelberg, pp 153–161
Zhen T, Zhu Y, Zhang Q (2009) A particle swarm optimization algorithm for the open vehicle routing problem. In: Proceedings of 2009 international conference on environmental science and information application technology, Wuhan, 4–5 July 2009, pp 560–563
Zhu Q, Qian L, Li Y, Zhu S (2006) An improved particle swarm optimization algorithm for vehicle routing problem with time windows. In: Proceedings of 2006 IEEE congress on evolutionary computation, Vancouver, 16–21 July 2006, pp 1386–1390
Zong X, Xiong S, Fang Z (2014) A conflict-congestion model for Pedestrian-vehicle mixed evacuation based on discrete particle swarm optimization algorithm. Comput Oper Res 44: 1–12
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Marinakis, Y., Marinaki, M., Migdalas, A. (2018). Particle Swarm Optimization for the Vehicle Routing Problem: A Survey and a Comparative Analysis. In: Martí, R., Pardalos, P., Resende, M. (eds) Handbook of Heuristics. Springer, Cham. https://doi.org/10.1007/978-3-319-07124-4_42
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