Optimizing a sequence of investments in a congested road network subject to strict Pareto optimality.

John Taplin, Min Qiu

Research output: Chapter in Book/Conference paperConference paper

Abstract

Any improvement in an urban road network will cause some drivers to change routes and so impose increased congestion on others who have not changed. The shifts cause such complex interactions that an optimum sequence of investments can only be achieved by joint optimization, not by ranking projects that have been evaluated singly. Investments in a hypothetical congested network optimized by genetic algorithm (GA) give benefits to almost all drivers but there are disbenefits on some routes. The objective of this study has been to determine whether investments can be made strictly Pareto optimal which, in this context, means that nobody suffers as a result of a series of road projects. This is done with an added goal of eliminating disbenefits to improve equity: no traveller on any route to suffer any deterioration in route travel time in any of the years under consideration. A penalty is applied with a weight sufficient to drive route disbenefits to zero. The GA seeks an optimal ordering of the 40 potential projects (one for each road link). The annual investment budgets are allocated to the projects in the GA order, with incomplete projects spilling into the following year. Each potential solution requires full assignments of traffic in each of eleven successive years. The network traffic assignment model is summarised as follows: • the network has nine centres connected by 326 reasonable routes (over 40 road links); • the number of alternative routes between an origin-destination pair varies from one to 70; • the stochastic user equilibrium (SUE) traffic assignment method is used; • traffic being assigned to routes by a logit function and summed over links; • travel times are calculated using a BPR congestion delay function; • route assignments are equilibrated by the method of successive averages; • with traffic being reassigned in each of fourteen iterations and travel times recalculated. The traffic congestion on links results in the initial logit assignments being substantially modified in the successive iterations, leading to an equilibrium for the particular GA generation. The magnitude of these calculations results in the GA taking considerable computing time to find an approximate optimum. In the optimized schedule, twenty projects are at least partly completed during the ten investment years. The results from this hypothetical model suggest that a timetable of road investments may be one case where strict Pareto optimality can be achieved at no great cost. A 'no losers' outcome may be feasible with only a modest sacrifice of net benefits. However a number of congested links will still take longer to traverse than previously - irritating drivers. Therefore reducing link delays in the otherwise optimized sequence of investments (subject to zero route time delays) has also been tested. Whether road authorities do adjust investment sequences in order to reduce adverse impacts along the lines modelled is an empirical question for the administrative and political world. A similar question arises with respect to congestion effects on links. Even if trip times are not adversely affected by the traffic diversions resulting from road improvements, it has been shown that traffic on some links will be slower. Some authorities prefer plans which minimize such link delays, even at an appreciable cost in benefits. These are real issues because beneficial investments are often endangered by a few potential losers campaigning against the proposal whereas the many potential winners are silent. If there are no losers then the clear benefit is likely to carry the day politically. The point of this study has been to establish that such an outcome may be possible with a moderate sacrifice of general benefits. © MODSIM 2009.All rights reserved.
Original languageEnglish
Title of host publicationInterfacing Modelling and Simulation with Mathematical and Computational Sciences
EditorsR.S. Anderssen, R.D. Braddock, L.T.H. Newham
Place of Publicationhttp://mssanz.org.au/modsim09/
PublisherModelling and Simulation Society of Australia and New Zealand Inc.
Pages1692-1698
Volume18
EditionCairns, Australia
ISBN (Print)9780975840078
Publication statusPublished - 2009
Event18th World IMACS Congress and International Congress on Modelling and Simulation: Interfacing Modelling and Simulation with Mathematical and Computational Sciences, MODSIM 2009 - Cairns, Australia
Duration: 13 Jul 200917 Jul 2009

Conference

Conference18th World IMACS Congress and International Congress on Modelling and Simulation: Interfacing Modelling and Simulation with Mathematical and Computational Sciences, MODSIM 2009
CountryAustralia
CityCairns
Period13/07/0917/07/09

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