Solving a multi-objective train makeup model with locomotive limitation by using a firefly algorithm: A case study

Abstract

A train makeup problem specifies the frequency of freight trains and allocates the shipment to trains based on the desired shipment-to-train allocation scheme. In this study, a multi-objective model is presented for train makeup, taking into account the locomotive limitations on a railway network. The objective functions include maximization of the total profit and the customers' satisfaction level as well as minimization of the total number of shunting operations in yards, the unused capacity of trains, the total lost demand, the transfer time of trains and the total fuel consumed. The main constraints of the model are the establishment of flow balance for each yard and each demand, the upper and lower limits of the train length, and the upper limit of the following: train makeup in each yard, shunting operations in each yard, capacity of each train and locomotive utilization in each period. Goal programming and Lp metric methods are used for the multi-objective problem considered. For solving this problem, a hybrid firefly algorithm is also proposed. A number of test problems based on the simulation are generated and solved by using the proposed algorithm. Furthermore, a real-time case study based on the Iranian Railway Network is used. The results show the potential of the presented model and the efficiency of the hybrid algorithm, which can be used for real-time railway problems.