A Dynamic Multi-objective Rail-car Fleet Sizing Problem Solved by Non-dominated Sorting Genetic Algorithm-II

Document Type : Research Paper


M.Sc. Graduate, Department of Industrial and Systems Engineering, Tarbiat Modarres University, Tehran, Iran


The aim of this paper is to present an efficient method for a rail freight car fleet sizing problem. This problem is modeled mathematically as a multi-period, dynamic and multi-objective, in which the rail freight wagons are assumed to be heterogeneous. Demands for different wagons and all travel times are assumed deterministic. In order to increase the utilization of the available wagons in the network and to reduce the fleet ownership costs, assignment of empty wagons becomes important. Moreover, constraints on line capacity, vehicle capacity and vehicle formation are considered. The model includes determining the optimal number of freight wagons of various types, the optimal amount of unfulfilled demand and the optimal number of full and empty freight wagons. To find the Pareto-optimal front of the problem, a heuristic method based on the Non-dominated Sorting Genetic Algorithm-II is proposed that uses heuristic procedures to generate new solutions. The performance of the proposed algorithm is evaluated in comparison with a simulated annealing algorithm, in which the results demonstrate the good quality of solutions achieved in a reasonable computation time. To do comparisons, the parameters of test problem instances are in accordance with the current state of the Railways of Islamic republic of Iran.


Main Subjects

1-Mafakheri, Z. (1392). "Development model to determine the optimal number of freight cars in iran rail transportation network." MA thesis management and efficiency, Faculty of Engineering, Department of Industrial Engineering, Tarbiat Modarres University.
2- Beaujon, G. J. and Turnquist, M. A. (1991). "A model for fleet sizing and vehicle allocation." Transportation Science, Vol. 25, No. 1, PP. 19-45.
3- Bojovic, N. (2002). "A general system theory approach to rail freight car fleet sizing." European Journal of Operational Research, Vol. 136, No. 1, PP. 136-172.
4- List, G. F., Wood, B., Nozick, L. K., Turnquist, M.A., Jones, D.A., Kjeldgaard, E.A. and Lawton, C. R. (2003). "Robust optimization for fleet planning under uncertainty." Research Transportation, Part E, Vol. 39, No. 3, PP. 209-227.
5- Sayarshad, H. R. and Ghoseiri, K. (2009). "A simulated annealing approach for multi-periodic rail-car fleet sizing problem." Computers and Operations Research, Vol. 36, No. 6, PP. 1789-1799.
6- Sayarshad, H. R. and Tavakkoli-Moghaddam, R. (2010). "Solving a multi periodic stochastic model of the rail–car fleet sizing by two-stage optimization formulation." Applied Mathematical Modeling, Vol. 34, No. 5, PP. 1164-1174.
7- Yaghini, M. and Khandaghabadi, Z. (2013). "A hybrid metaheuristic algorithm for dynamic rail car fleet sizing problem." Applied Mathematical Modelling, Vol. 37, PP. 4127-4138.
8- Mafakheri, Z. and Masihi, E. (1393). " Modeling and solving the rail-car fleet sizing problem with multi-objective and heterogeny in the fleet."  Quarterly Journal of Transportation Engineering, 2550.
9- Deb, K., Agrawal, S., Pratap, A. and Meyarivan, T. (2002). "A fast and elitist multi-objective ge- netic algorithm: NSGA-II." IEEE Transactions on Evolutionary Computation, 6(2), 182–197.
10- Kirkpatrick, S., Gelatt, C. D. and Vecchi, M. P. (1983). "Optimization by simulated annealing." Science, 220, PP. 671–680.
11- Ulungu, E.L., Teghem, J., Fortemps, P.H. and Tuyttens, D. (1999). "MOSA method: a tool for solving multiobjective combinatorial optimization problems." J. Multi-Crit. Decis. Anal., 8: 221–236. doi: 10.1002/(SICI)1099-1360.
12- Husseinzadeh Kashan, A., Karimi, B.  and Jolai, F. (2010). "An effective hybrid multi-objective genetic algorithm for bi-criteria scheduling on a single batch processing machine with non-identical job sizes." Engineering Applications of Artificial Intelligence, Vol. 10.