Guest editorial Transport bilevel programming problems: recent methodological advances Hai Yang a, * , Michael G.H. Bell b a Department of Civil Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, People's Republic of China b Department of Civil Engineering, The University of Newcastle upon Tyne, NE1 7RU, UK 1. Introduction Most well-founded trac control and management models take the form of a bilevel pro- gramming problem. In the upper-level, the trac planner makes decisions regarding management, control, design, and improvement investments to improve the performance of the system. In the lower level, the network users make choices with regard to route, travel mode, origin and desti- nation of their travel in response to the upper-level decision. This type of bilevel trac modeling and optimization problem has emerged as an important area for progress in handling eective transportation planning. Typical examples include trac signal setting (Allsop, 1974), optimal road capacity improvement (Abdulaal and LeBlanc, 1979), estimation of origin-destination ma- trices from trac counts (Yang et al., 1992), ramp metering in freeway-arterial corridor (Yang and Yagar, 1994), and optimization of road tolls (Yang and Bell, 1997). Due to the intrinsic complexity of model formulation, the problem has been recognized as one of the most dicult, yet challenging problems for global optimality in transportation. In fact, a large number of researchers have developed solution algorithms of one type or another. Abdulaal and LeBlanc (1979) applied the Hook±Jeeves heuristic algorithm for direct search of the solution of the network design problem. Tan et al. (1979) expressed the deterministic user equilibrium problem by a set of nonlinear and non-convex, but dierentiable, constraints in terms of path ¯ow variables. Marcotte (1983) transferred the network design problem into a single level equivalent dierentiable optimization problem, in which the required constraints involve all the extreme points of the closed convex polyhedron for the feasible acyclic multicommodity ¯ow patterns. Fisk (1984) developed an alternative single level optimization model for the optimal signal control problem using a gap function. Suwansirikul et al. (1987) developed an alternative heuristic Transportation Research Part B 35 (2001) 1±4 www.elsevier.com/locate/trb * Corresponding author. Tel.: +852-2358-7178; fax: +852-2358-1534. E-mail addresses: cehyang@ust.hk (H. Yang), m.g.h.bell@newcastle.ac.uk (M.G.H. Bell). 0191-2615/00/$ - see front matter Ó 2000 Elsevier Science Ltd. All rights reserved. PII:S0191-2615(00)00025-4