Multiobjective Genetic Algorithm to Solve the Train Crew Scheduling Problem MING-SHEN JIAN * , and TA-YUAN CHOU + * Dept. of Computer Science and Information Engineering, National Formosa University, Yunlin County, Taiwan + Dept. of Computer Science and Engineering, National Sun Yat-sen University, Kaohsiung, Taiwan * jianms@nfu.edu.tw, + tayuan@gmail.com Abstract: -This paper presents a multiobjective genetic algorithm (MOGA)to solve the train crew pairing problem in railway companies. The proposed MOGA has several features, such as 1) A permutation-based model is proposed rather than the 0-1 set partition model. 2) Instead of pre-assigning a fixed group number of crewmembers, the proposed method can determine it by performing the evolutionary process. 3) The crossover and mutation operators are enhanced so that the duty time and the duty period can be integrated and considered during the evolutionary process. Experiments show that the proposed MOGA can find out optimal solution with exact group number of crewmembers instead of pre-assigning it so that the effective and efficient crew pairing can be yielded. Keywords-component; train crew pairing, genetic algorithm, multiobjective 1 Introduction crew pairing is one of the important operations since it contributes to the second large cost, personnel cost in airline companies. After completing the processes of duty scheduling, fleet assignment, and aircraft routing, the crew scheduling process, including the crew pairing and crew rostering are performed to combine the duties into several pairings and assign these pairings to crewmembers, respectively. A pairing is a sequence of duties that can be assigned to a group of crew members that starts and ends in crew bases. Crew bases, or home bases, are designated stations where crews are based. Crew pairing is an important and complicated process. Comparing with crew rostering, crew pairing is more important since its results can affect the operations and results of crew rostering. Also, when performing the crew pairing processes, there are lots of objectives and constraints to be considered, such as minimizing total cost and satisfying the safety constraints declared by the laws and regulations of Civil Aeronautics Administration (CAA). When considering the processes of crew pairing, several topics related to safety and cost should be considered. Two of the safety considerations are flying time and duty period. On the other aspect, topics of cost considerations are deadhead and layover. In general, the crew pairing problem are categorized as pairing generation and optimization [1]-[5]. In this paper, we would like to propose a dynamic size-based multiobjective genetic algorithm to solve the crew pairing problem, which can yield the exact group size of crewmembers. In general, crew pairing consists of two phases, such as pairing generation and pairing optimization. In pairing generation phase, planners generate a group of possible pairings for a given set of duties to satisfy the constraints declared in the laws and regulations. On the other aspect, in pairing optimization phase, the generated pairings are optimized to minimize the total cost. Gopalakrishnan and Johnsin [6] demonstrated a detailed survey of crew pairing about both problem models and solution methodologies. Crew scheduling was the first to receive significant attention within the OR community. Currently, operations research based methods are used to solve the crew pairing problem. In pairing generation, most use three broad approaches, such as row approach, column approach, and network approach to generate legal crew pairings. Various researches of aircrew pairing are given as follows. Chu et al. [7] applied a graph based branching heuristic to a restricted set partitioning problem representing a collection of best pairings. They can exploit the integer properties of crew pairing problem. Desauliniers et al. [8] modeled the aircrew pairing problem as an integer, nonlinear multi-commodity flow network model. Pairing generation is performed by the approach of resource constrained shortest path subproblem. Stojković et al. [9] also modeled the aircrew pairing problem as a set partitioning problem and used a column generation method embedded in a branch-and-bound search tree to solve it. Barnhart et al. [10] developed a heuristic methodology by using dual solutions determined in solving the linear programming relaxation of the crew pairing problem. Also, the deadhead selection procedure is tested and shown the significant improvement of crew costs by reducing deadhead hours and total duration of rest periods. Barnhart and Shenoi [11] proposed an approximation model of the problem and then used its solution approach NEW ASPECTS of SYSTEMS THEORY and SCIENTIFIC COMPUTATION ISSN: 1792-4626 100 ISBN: 978-960-474-218-9