Abstract
Today, companies need to collect and to deliver goods from and to their depots and their customers. This problem is described as a Vehicle Routing Problem with Mixed Linehaul and Backhaul customers (VRPMB). The goods delivered from the depot to the customers can be alternated with the goods picked up. Other variants of VRP added to VRPMB are Heterogeneous fleet and Time Windows. This paper studies a complex VRP called HVRPMBTW which concerns a logistic/transport society, a problem rarely studied in literature. In this paper, we propose a Particle Swarm Optimization (PSO) with a local search. This approach has shown its effectiveness on several combinatorial problems. The adaptation of this approach to the problem studied is explained and tested on the benchmarks. The results are compared with our previous methods and they show that in several cases PSO improves the results.
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References
Ai T. J., Kachitvichyanukul V. (2007) A particle swarm optimization for the capacitated vehicle routing problem. Logistics and Supply Chain Management Systems, 2(1): 50–55
Ai T. J., Kachitvichyanukul V. (2009a) Particle swarm optimization and two solution representations for solving the capacitated vehicle routing problem. Computers and Industrial Engineering 56(1): 380–387
Ai T. J., Kachitvichyanukul V. (2009b) A particle swarm optimization for the vehicle routing problem with simultaneous pickup and delivery. Computers and Operations Research 5(4): 1693–1702
Belmecheri, F., Prins, C., Yalaoui, F., & Amodeo, L. (2009a). An ant colony optimization algorithm for a vehicle routing problem with heterogeneous fleet, mixed backhauls, and time windows. In 13th IFAC Symposium on INformation COntrol problems in Manufacturing (Vol. 13, pp. 1533–1538), Moscow, Russia.
Belmecheri, F., Prins, C., Yalaoui, F., & Amodeo, L. (2010a). A new particle swarm optimization on vehicle routing problem with heterogeneous fleet, mixed backhauls, and time windows. In 5th International Symposium on Hydrocarbons and Chemistry-Session: Optimizations and Logistics (Layout, Transportation, Scheduling), Algiers, Algeria.
Belmecheri, F., Prins, C., Yalaoui, F., & Amodeo, L. (2010b). Particle swarm optimization to solve the vehicle routing problem with heterogeneous fleet, mixed backhauls, and time windows. In 24th IEEE International Parallel and Distributed Processing Symposium, Atlanta, GA, USA.
Belmecheri, F., Yalaoui, F., Prins C., & Amodeo, L. (2009b). A metaheuristic approach for solving the vehicle routing problem with heterogeneous fleet, mixed backhauls, time windows. In 40th Annual Conference of the Italian Operational Research Society, Siena, Italy.
Casco, D. O., Golden, B. L., & Wasil, E. A. (1988). Vehicle routing with backhauls: Models, algorithms and case studies (pp. 127–147), North-Holland, Amsterdam
Chen A. L., Yang G. K., Wu Z. M. (2006) Hybrid discrete particle swarm optimization algorithm for capacitated vehicle routing problem. Journal of Zhejiang University-Science A 7(4): 607–614
Clerc, M. (2000). Discrete particle swarm optimization for traveling salesman problem. http://clerc.maurice.free.fr/pso/pso_tsp/Discrete_PSO_TSP.htm.
Clerc M. (2005) L’optimisation par essaim prticulaire. Lavoisier, France
Dethloff J. (2001) Vehicle routing and reverse logistics: The vehicle routing problem with simultaneous delivery and pick-up. Operations Research Spectrum 23: 79–96
Dong, G., Tang, J., Lai, K. K., & Kong, Y. (2009). An exact algorithm for vehicle routing and scheduling problem of free pickup and delivery service in flight ticket sales companies based on set-partitioning model. Journal of Intelligent Manufacturing. doi:10.1007/s10845-009-0311-9.
Ellabib I., Calamai P., Basir O. (2007) Exchange strategy for multiple ant colony system. Information Sciences 177(5): 1248–1264
Gendreau M., Laporte G., Musaraganyi C., Taillard E. D. (1999) A tabu search heuristic for the heterogeneous fleet vehicle routing problem. Computers and Operations Research 26: 1153– 1173
Goldberg D. E., David E. (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley Longman Publishing, Boston, MA
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 (pp. 103–106), Nashville, TN.
Kennedy J., Eberhart R. C. (1995) Particle swarm optimization. Perth-Australie, Perth, pp 1942–1948
Kennedy, J., & Eberhart, R. C. (1997). A discrete binary version of the particle swarm algorithm. In IEEE International Conference on Computational Cybernetics and Simulation (Vol. 5, pp. 4104–4108), Orlando, FL, USA.
Kim, B. T., & Son S. J. (2010). A probability matrix based particle swarm optimization for the capacitated vehicle routing problem. Journal of Intelligent Manufacturing, (Online). doi:10.1007/s10845-010-0455-7.
Landrieu A., Mati Y., Binder Z. (2001) A tabu search heuristic for the single vehicle pickup and delivery problem with time windows. Journal of Intelligent Manufacturing 12(5–6): 497– 508
Lin, C. T. (2008). Using predicting particle swarm optimization to solve the vehicle routing problem with time windows. In: Industrial Engineering and Engineering Management, (pp. 810–814)
Liu S. C., Chung C. H. (2009) A heuristic method for the vehicle routing problem with backhauls and inventory. Journal of Intelligent Manufacturing 20(1): 29–42
Machado T. R., Lopes H. S. (2005) A hybrid particle swarm optimization model for the traveling salesman problem. Springer, Vienna, pp 255–258
Parragh S. N., Doerner K. F., Hartl R. F. (2008) A survey on pick up and delivery problems: Part I: Transportation between customers and depot. Journal fur Betriebswirtschaft 58(1): 21–51
Prins C. (2009) Two memetic algorithms for heterogeneous fleet vehicle routing problems. Engineering Applications of Artificial Intelligence 22(6): 916–928
Reimann M., Ulrich H. (2006) Comparing backhauling strategies in vehicle routing using ant colony optimization. Central European Journal of Operations Research 14(2): 105–123
Rieck J., Zimmermann J. (2009) A hybrid algorithm for vehicle routing of less-than-truckload carriers. Springer, Berlin Heidelberg, pp 155–171
Rieck J., Zimmermann J., Glagow M. (2007) Tourenplanung mittelständischer speditionsunternehmen in stückgutkooperationen: Modellierung und heuristische lösungsverfahren. Zeitschrift Planung and Unternehmenssteuerung 17: 365–388
Salhi S., Nagy G. (1999) A cluster insertion heuristic for single and multiple depot vehicle routing problems with backhauling. Journal of the Operational Research Society 50(10): 1034–1042
Shi X. H., Liang Y. C., Lee H. P., Lu C., Wang Q. X. (2007) Particle swarm optimization-based algorithms for tsp and generalized TSP. Information Processing Letters 103: 169–176
Solomon, M. M. http://w.cba.neu.edu/~msolomon/problems.htm.
Solomon M. M. (1987) Algorithms for the vehicle routing and scheduling problem with time windows constraints. Operation Research 35: 254–265
Süral H., Bookbinder J. H. (2003) The single-vehicle routing problem with unrestricted backhauls. Networks 41(3): 127–136
Talbi E. G. (2009) Metaheuristics: From design to implementation. Wiley, New York
Tang Montané F. A., Galvao R. D. (2006) A tabu search algorithm for the vehicle routing problem with simultaneous pick-up and delivery service. Computers and Operations Research 33(3): 595–619
Vahdani, B., Tavakkoli-Moghaddam, R., Zandieh, M., & Razmi, J. (2010). Vehicle routing scheduling using an enhanced hybrid optimization approach. Journal of Intelligent Manufacturing. doi:10.1007/s10845-010-0427-y.
Voudouris C., Tsang E. P. K. (1999) Guided local search and its application to the traveling salesman problem. European Journal of Operational Research 113: 469–499
Wang, K. P., Huang, L., Zhou, C. G., & Pang, W. (2003). Particle swarm optimization for traveling salesman problem. In International Conference on Machine Learning and Cybernetics (Vol. 3, pp. 1583–1585).
Wassan N. A., Osman I. H. (2002) Tabu search variants for the mix fleet vehicle routing problem. Operational Research Society 53(7): 768–782
Xu, Y., Wang, Q., & Hu, J. (2008). An improved discrete particle swarm optimization based on cooperative swarms. In IEEE/WIC/ACM International Conference on Intelligent Agent Technology (pp. 79–82).
Yalaoui, N., Mahdi, H., Amodeo, L., & Yalaoui, F. (2009). A new approach for workshop design. doi:10.1007/s10845-009-0368-5.
Yazgi Tütüncü G. (2010) An interactive GRAMPS algorithm for the heterogeneous fixed fleet vehicle routing problem with and without backhauls. European Journal of Operational Research 201(2): 593–600
Yazgi Tütüncü G., Carreto C. A. C., Baker B. M. (2009) A visual interactive approach to classical and mixed vehicle routing problems with backhauls. Omega 37(1): 138–154
Zhu, Q., Qian, L., Li, Y., & Zhu, S. (2006). An improved particle swarm optimization algorithm for vehicle routing problem with time windows. In IEE Congress on Evolutionary Computation (pp. 1386–1390).
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Belmecheri, F., Prins, C., Yalaoui, F. et al. Particle swarm optimization algorithm for a vehicle routing problem with heterogeneous fleet, mixed backhauls, and time windows. J Intell Manuf 24, 775–789 (2013). https://doi.org/10.1007/s10845-012-0627-8
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DOI: https://doi.org/10.1007/s10845-012-0627-8