Bilevel programming applied to optimising urban transportation

Janet Clegg, Mike Smith, Yanling Xiang and Robert Yarrow

Transportation Research Part B: Methodological, 2001, vol. 35, issue 1, 41-70

Abstract: This paper outlines a multi-modal, elastic, equilibrium transportation model in which signal green-times and prices charged to traverse a route (public transport fares, parking charges or road-use charges) are explicitly included. An algorithm is specified which, for a fairly general objective function, continually moves current traffic flows, green-times and prices within the model toward locally optimal values while taking account of users' responses. The directions of movement of current traffic flows, green-times and prices are determined by solving linear approximations to the actual problem. The results of applying a simplified form of the algorithm to a small network model with five routes and two signal-controlled junctions are given. It is proved that under realistic conditions the sequence of (traffic flows, green-times, prices) triples generated by the algorithm does indeed approach those triples which possess a reasonable local optimality property. However the optimal control problem discussed here is non-convex and just a Karush-Kuhn-Tucker point is the "answer" sought.

Date: 2001
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