New Heuristics to Solve the ”CSOP” Railway Timetabling Problem L. Ingolotti 1 , A. Lova 2 , F. Barber 1 , P. Tormos 2 , M. A. Salido 1 , and M. Abril 1 1 DSIC, Polytechnic University of Valencia, Spain {lingolotti, fbarber, msalido, mabril}@dsic.upv.es 2 DEIOAC, Polytechnic University of Valencia, Spain {allova, ptormos}@eio.upv.es Abstract. The efficient use of infrastructures is a hard requirement for railway companies. Thus, the scheduling of trains should aim toward op- timality, which is an NP-hard problem. The paper presents a friendly and flexible computer-based decision support system for railway timetabling. It implements an efficient method, based on meta-heuristic techniques, which provides railway timetables that satisfy a realistic set of constraints and, that optimize a multi-criteria objective function. Key Words : Constraint Satisfaction, Decision Support, Planning and Scheduling 1 Introduction The main motivations for this work are the need of obtaining an automatic timetabling process for railway companies, the hard requirement of using effi- ciently railway infrastructures and the challenge that this process implies for the application and research of techniques in the Artificial Intelligence field. The literature of the 1960s, 1970s, and 1980s relating to rail optimization was relatively limited. Compared to the airline and bus industries, optimization was generally overlooked in favor of simulation or heuristic-based methods. However, Cordeau et al. [1] point out greater competition, privatization, deregulation, and increasing computer speed as reasons for the more prevalent use of optimization techniques in the railway industry. Our review of the methods and models that have been published indicates that the majority of authors use models that are based on the Periodic Event Scheduling Problem (PESP) introduced by Serafini and Ukovich [7]. The PESP considers the problem of scheduling as a set of pe- riodically recurring events under periodic time-window constraints. The model generates disjunctive constraints that may cause the exponential growth of the computational complexity of the problem depending on its size. Schrijver and Steenbeek [5] have developed CADANS, a constraint programming- based algorithm to find a feasible timetable for a set of PESP constraints. The scenario considered by this tool is different from the scenario that we used; therefore, the results are not easily comparable. Nachtigall and Voget [4] also use PESP constraints to model the cyclic behavior of timetables and to consider