Document Type : Research Paper


School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran


This paper is an extension of the well-known vehicle routing problem (VRP) consisting of two stages. The first and second stages deal with the vehicle routing and transportation problems, respectively. Waste collection is one of the applications of the considered problem in a real world situation. A new mathematical model for this type of the problem is presented that minimizes the waste collection cost and decreases the risk posed to the environment for hazardous wastes transportation simultaneously. According to the NP-hard nature of the problem, a new multi-objective hybrid cultural and genetic algorithm (MOHCG) is proposed to obtain Pareto solutions. A straightforward representation for coding the given model is proposed to help us in reducing the computational time. To validate the proposed algorithm, a number of test problems are conducted and the obtained results are compared with the results of the well-known multi-objective evolutionary algorithm, namely non-dominated sorting genetic algorithm (NSGA-II), with respect to some comparison metrics. Finally, the conclusion is provided.


Main Subjects

[1]                Golden B.L., Assad A.A., Wasil E.A., (2002). Routing vehicles in the real world: applications in solid waste, beverage food, dairy, and newspaper industries. In: Toth, P.,  Vigo, D.(Eds), The Vehicle Routing Problem. SIAM, Philadelphia, PA, 245-286.
[2]          Sbihi A,. Eglese R.W., (2007). Combinatorial optimization and Green Logistics. 4OR.
[3]            Lin C., Choy K.L., Ho G.T.S., Chung S.H., Lam H.Y., (2014), Survey of Green Vehicle Routing Problem: Past and future trends. Expert Systems with Applications. 31: 1118-1138.
[4]                Dekker R., Fleischmann M., Inderfurth K., Van Wassenhov L.N., (2004). Reverse Logistics: quantitative models for closed loop supply chain. Berlin: Springer.
[5]            Wy J., Kim B., Kim S., (2013). The rollon-rolloff waste collection routing problem with time windows, European Journal of Operational Research. 224: 466-476.
[6]            Bonomo F., Duaran G., Larumbe F., Marenco J., (2012). A method for optimizing waste collection using mathematical programming: A Buenos Aires case study. Waste Management & Research. 30(3): 311-324.
[7]            Sahoo S., Kim S., Kim B.I., Karas B., Popov Jr., (2005) Routing Optimization for waste management interface. 35(1):24-36.
[8]            Kim B.I., Kim S., Sahoo S., (2006). Waste collection vehicle routing problem with time windows. Computers & Operations Research. 33: 3624-3642.
[9]              Alumur S., Kara B.Y., (2007), A new model for the hazardous waste location routing problem. Computers & operations research; 34:1406-1423.
[10]              Erkut E., Verter V., (1995).Hazardous materials logistics. In: Drezner Z, editor. Facility location. New York: Springer
[11]               Gianikos I., (1998), A multi-objective programming model for location treatment sites and routing hazardous wastes. European Journal of Operational Research. 104: 333-342.
[12]                Caballero R., Gonzalez M., Guerrero F.M., Molina J., Paralera C., (2007), Solving a multi-objective location routing problem with a metaheuristic based on tabu search. Application to real case in Andalusia. European Journal of Operational Research. 177: 1751- 1763.
[13]              Martínez-Salazar, I. A., Molina, J., Ángel-Bello, F., Gómez, T., & Caballero, R. (2014). Solving a bi-objective Transportation Location Routing Problem by metaheuristic  algorithms. European Journal of Operational Research, 234(1), 25-36.
[14]             Desrochers M., Laporte G., (1991). Improvements and extensions to the Miller– Tucker– Zemlin subtour elimination constraints, Operations Research Letters 10:27–36.
[15]               Kara I., Laporte G., Bektas T., (2004). A note on the lifted Miller–Tucker–Zemlin sub tour elimination constraints for the capacitated vehicle routing problem, European Journal of Operational Research 15:8793–795.
[16]                Deb K., Agrawal S., Pratab A., Meyunvian T., (2002). A fast elitist non-dominated sorting algorithm for multi-objective optimization NSGA-II. IEEE Transactions on Evolution Computation, 2182-2197.
[17]              Reynolds, R.G., (1994), An introduction to cultural algorithms. In: A.V. Sebald and L.J. Fogel (Eds.), Proceedings of the Third Annual Conference on Evolutionary Programming, pp. 131–139. World Scientific, River Edge, New Jersey, USA.
[18]              Best C., Che X., Reynolds R.G., Liu D., (2010), A multi-objective Cultural Algorithm, Evolutionary Computation (CEC) IEEE Congress on Barcelona, pp 1-9.
[19]                     Kennedy J, Eberhart R. Particle Swarm Optimization. Proceedings of IEEE International Conference on Neural Networks IV 1995; 1942–1948.
[20]             Holland, J. (1975). Adaptation in Natural and Artificial Systems. University of Michigan Press. Second edition, MIT Press, 1992.
[21]                 Konak, A., Coit, Q. W., and Smith, A. (2006). Multi-objective optimization using genetic algorithms: A tutorial. Reliability Engineering & System Safety 91(9), 992-1007.
[22]              Ho W., (2008). A hybrid genetic algorithm for the multi-depot vehicle routing problem,
Engineering Applications of Artificial Intelligence 21:548–557.
[23]                Zitzler E., Thiele L., (1999). Multi-objective evolutionary algorithms: a comparative case study and strength Pareto approaches. IEEE Transactions on Evolutionary Computation, 257-271.