Multicriteria spatial price equilibrium network design: Theory and computational results

Terry Lee Friesz, Patrick T. Harker

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

In this paper we consider the problem of determining the optimal design of a transportation network using a vector valued criterion function when the flow pattern is assumed to correspond to a spatial price equilibrium. This problem arises in rail and freight network design, where the spatial price equilibrium is a better behavioral description than the Wardropian user equilibrium characteristic of urban transportation applications. We describe two alternative heuristic solution techniques for the multicriteria spatial price equilibrium network design problem. The first is based on iteration between a pure spatial price equilibrium model and a vector optimization model with only nonnegativity constraints. The second solution technique employs the Hooke and Jeeves algorithm for nonlinear programming to solve a vector optimization model with implicit constraints guaranteeing a spatial price equilibrium flow pattern. In these solution procedures, rather than represent the equilibrium problem as a mathematical program, as is normally done for the Wardropian traffic assignment problems used in urban applications, we employ an original nonlinear complementarity formulation of the spatial price equilibrium problem written entirely in terms of nodal and arc variables and solved extremely efficiently through the iterative application of a linear complementarity algorithm. The nonlinear complementarity formulation allows us to address problems with asymmetric transportation cost, commodity demand and commodity supply functions without the specialized diagonalization/relaxation algorithms required by other approaches.

Original languageEnglish (US)
Pages (from-to)411-426
Number of pages16
JournalTransportation Research Part B
Volume17
Issue number5
DOIs
StatePublished - Jan 1 1983

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Flow patterns
Urban transportation
Nonlinear programming
optimization model
Rails
commodity
equilibrium model
Design theory
Multi-criteria
Network design
Equilibrium price
Costs
heuristics
programming
traffic
supply
demand
costs
Complementarity
Optimal design

All Science Journal Classification (ASJC) codes

  • Transportation
  • Management Science and Operations Research

Cite this

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Multicriteria spatial price equilibrium network design : Theory and computational results. / Friesz, Terry Lee; Harker, Patrick T.

In: Transportation Research Part B, Vol. 17, No. 5, 01.01.1983, p. 411-426.

Research output: Contribution to journalArticle

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