A mathematical multi-objective model for routing in the multi-modal public transportation network

The development of a variety of public transportation systems that cover different areas, has made it difficult for passengers and users to choose the type of transportation system and appropriate route between two specified departures. In large cities such as Tehran, a network of public transportation systems, called multi-modal systems, consist of stations as nodes and public transport vehicles intermediate between the two consecutive stations as arcs, is formed. Travelers are looking continuously for a way to find the optimal route in complex multi-modal transportation networks to reach their desired destination with minimal cost and confusion. In this paper, two linear and nonlinear multi-objective programming models with three objective functions have been developed for routing in multi-modal transport systems. The objectives of the proposed model are to minimize the cost, travel time and the number of vehicle types. By examining the validation of models by test issues, two exact and meta-heuristic algorithms (ant colony algorithm) have been developed to solve the proposed model. The results of the evaluation of the performance of the solving methods indicate that problem solving by exact method for networks with more than 15 nodes are non-operating, while the meta-heuristic algorithm provides the same problems with same precision in the exact method but with logical time.