a dynamic multi-objective rail-car fleet sizing problem solved by non-dominated sorting genetic algorithm-ii

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.