Routing for the Pennsylvania Maglev system by a genetic algorithm Y-Y Cao 1 , Z Lin 2 , T C Giras 1 , and D R Disk 3 1 Center of Rail Safety-Critical Excellence, Charlottesville, Virginia, USA 2 Charles L. Brown Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, Virginia, USA 3 Director of Engineering, Maglev Inc., Pittsburgh, Pennsylvania, USA The manuscript was received on 7 April 2005 and was accepted after revision for publication on 4 October 2005. DOI: 10.1243/095440906X77928 Abstract: The scheduling of vehicle movement activities is an important component in high- speed railway transit operations planning process. This paper presents a mathematical pro- gramming approach to vehicle routing for the Pennsylvania Transrapid Maglev Train System. A mathematical model of the routing procedure is first derived. Based on this model, the vehicle routing problem is formulated into a constrained optimization problem, in which the train miles travelled are maximized subject to various operational and safety requirements. This large scale non-linear optimization problem is then solved by a genetic algorithm. Keywords: genetic algorithm, Maglev, vehicle routing 1 INTRODUCTION As transportation evolves in the 21st century, a novel and innovative high-speed ground transportation system, the Transrapid Maglev System, is being deployed as the Pennsylvania Project for use in both passenger and light freight service in Pittsburgh, Pennsylvania region. The system consists of a 47 mile dual guideway with 32 propulsion segments, 15 switches, and four MAGPort TM stations (Fig. 1). Multiple vehicles are to be operated simultaneously on the system. Key to the safe and efficient operation of the Transrapid Maglev System is a vehicle mana- gement algorithm (VMA). An important component of the VMA is a vehicle routing scheduler that generates an optimal vehicle routing schedule that respects all operational and safety requirements [1, 2]. The optimality is usually with respect to the train miles travelled, an indication of the utilization of the system. Such a vehicle routing scheduler should also be computationally feasible for a rapid generation of new optimal routing schedule following the reconfiguration of the guideway system due to, for example, the failure of a guideway segment. This paper proposes a mathematical programming approach to the development of a vehicle routing scheduler in conjunction with the development of a proof-of-concept VMA for the Pennsylvania Trans- rapid Maglev System [3]. Although the development of the vehicle routing scheduler is presented in the context of the Pennsylvania Transrapid Maglev System currently under deployment, it is applicable, with appropriate adaptation, to other transrapid sys- tems to be deployed. The development of the vehicle scheduler consists of the development of a math- ematical model of the vehicle routing procedure, the formulation of the routing problem into a con- strained optimization problem, and the solution algorithm of such an optimization problem. The mathematical model will include various aspects of the operation of the system, including the compu- tation of the miles travelled by a particular train and the guideway segment out-of-service con- straints. The optimization objective function will be the train miles travelled over a given time zone. The optimization constraints include the avoidance of deadlock, guaranteed headways, and minimum MAGPort TM dwell times. Owing to the large number of hard constraints, the resulting optimiz- ation problem is highly non-linear and of large  Corresponding author: Charles L. Brown Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, Virginia, USA. 55 F01305 # IMechE 2006 Proc. IMechE Vol. 220 Part F: J. Rail and Rapid Transit