A hybrid solution method for fuzzy train formation planning

The train formation plan (TFP) determines the routing and frequency of trains, and assigns the demands to trains. In this paper, in order to consider the real-life condition of railways, a mathematical model with fuzzy costs is proposed for train formation planning in Iranian railway. In this fuzzy model, the costs are considered in three scenarios, namely optimistic, normal and pessimistic. The model is formulated based on the fixed-charge capacitated multicommodity network design problem. Since the TFP problem is NP-hard, an efficient hybrid algorithm combining local branching and relaxation induced neighborhood search methods is presented. A three-step method is applied for parameter tuning using design of experiments approach. To evaluate the efficiency and effectiveness of the proposed algorithm, the results are compared with those of the state-of-the-art optimization software.