Bilevel Optimisation of Transportation Networks

Abstract

The need to reduce traffic congestion is becoming increasingly important. The means of achieving this aim involves optimising parameters such as traffic signal green-times, road prices and public transport fares. This paper will describe a new bilevel method of optimising traffic signals and prices. The method uses the steepest descent direction together with projections in order to define a descent direction which will reduce the objective function subject to the overriding necessity to be in equilibrium.

The paper will provide a description of the bilevel method together with results on two simple problems. Optimisation is performed on two functions simultaneously; the equilibrium function E (which must have value zero for equilibrium) and the objective function Z which is minimised subject to the constraint that E is zero. For most traffic problems equilibrium is not mathematically well behaved and therefore the method approaches equilibrium in stages, at each stage it minimises Z whilst avoiding the difficult equilibrium region.

Citation

Clegg, J. and Smith, M.J. (1998), "Bilevel Optimisation of Transportation Networks", Griffiths, J.D. (Ed.) Mathematics in Transport Planning and Control, Emerald Group Publishing Limited, Leeds, pp. 29-36. https://doi.org/10.1108/9780585474182-003