Pergamon Tmspn. Res.-C, Vol. 3, No. 1, pp. 31-50, 1995 Copyright 0 1995 Elsevier Science Ltd F’rinted in Great Britain. All rights reserved 0968-090x/95 $9.50 + .OO zyxwvutsrqp HYBRID ROUTE GENERATION HEURISTIC ALGORITHM FOR THE DESIGN OF TRANSIT NETWORKS M. HADI BAAJ* Department of Civil Engineering, Arizona State University, Tempe, AZ 85287-5306, zyxwvutsrqponmlkjihgfed U.S.A. HANI S. MAHMASSANI Department of Civil Engineering, The University of Texas at Austin, Austin, TX, 78713, U.S.A.; e-mail:masmah@utxvm.cc.utexas.edu (Received 7 January 1994, in revisedform 27 September 1994) Abstract-In this paper we present a Lisp-implemented route generation algorithm (RCA) for the design of transit networks. Along with an analysis procedure and an improvement algorithm, this algorithm constitutes one of the three major components of an AI-based hybrid solution approach to solving the transit network design problem. Such a hybrid approach incorporates the knowledge and expertise of transit network planners and implements efficient search techniques using AI tools, algo- rithmic procedures developed by others, and modules for tools implemented in conventional languages. RGA is a design algorithm that (a) is heavily guided by the demand matrix, (b) allows the designer’s knowledge to be implemented so as to reduce the search space, and (c) generates different sets of routes corresponding to different trade-offs among conflicting objectives (user and operator costs). We explain in detail the major components of RGA, illustrate it on data generated for the transit network of the city of Austin, TX, and report on the numerical experiments conducted to test the performance of RGA. I. INTRODUCTION The focus of this paper is on a route generation heuristic algorithm (RGA) for the design of transit networks. This algorithm is one of three major components of an AI-based hybrid solution approach to solving the transit network design problem (TNDP); the other two com- ponents are a network analysis procedure and a set of improvement heuristics. The TNDP has been studied by several authors in the past: Ceder and Wilson, (1986); Dubois, Bell, and Llibre, (1979); Hasselstrom, (1981); Lampkin and Saalmans (1967); Mandl, (1979); Newell, (1979); Rea, (1971); Silman, Barzily, and Passy, (1974); and Van Nes, Hamerslag, and Immers (1988) (Table 1 presents a summary of the main features of each procedure). In this problem, one seeks to determine a configuration, consisting of a set of transit routes and associated frequencies, that achieves some desired objective(s), subject to the constraints of the problem. Mathematical formulations of the TNDP have been concerned primarily with the minimization of an overall cost measure, generally a combination of user costs and operator costs. The former is often captured by the total travel time incurred by users in the network, while a proxy for operator costs is the total number of buses required for a particular configuration. Feasibility constraints may include, but are not limited to: (a) minimum operating frequencies on all or selected routes (policy headways, where applicable), (b) a maximum load factor on any bus route, and (c) a maximum allowable bus fleet size. In Baaj and Mahmassani (1991) we discussed the sources of complexity of the TNDP and existing solution approaches to this problem and their limitations, as well as the role and potential of search techniques that have become widely used in artificial intelligence (AI) to produce superior solutions efficiently. We also presented the framework of an AI/OR hybrid solution approach that combines AI search concepts with familiar constructs from OR (Oper- ations Research) vehicle routing heuristics and transit systems analysis methods. The solution framework consists of three major components: 1. Route Generation Design Algorithm (RGA): This algorithm generates different sets of routes corresponding to different trade-offs among the principal objectives. It is the focus of this paper. *Dr. Baaj is currently at the Department of Civil Engineering, American University of Beirut, Beirut, Lebanon. n(c) 3:*-c 31