Global optimization method for network design problem with stochastic user equilibrium

•Continuous network design problem with stochastic user equilibrium is explored.•The problem is reformulated as a nonlinear nonconvex programming.•A tight mixed-integer linear programming relaxation is derived.•A global optimization method based on range reduction technique is proposed. In this pape...

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Veröffentlicht in:Transportation research. Part B: methodological Jg. 72; S. 20 - 39
Hauptverfasser: Liu, Haoxiang, Wang, David Z.W.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 01.02.2015
Schlagworte:
Global optimization
Linear programming
Mathematical models
Mixed-integer linear programming
Network design problem
Networks
Nonlinearity
Optimization
Range reduction technique
Roads
Stochastic user equilibrium
Stochasticity
Transportation
Global optimization
Stochastic user equilibrium
Mixed-integer linear programming
Range reduction technique
Network design problem
ISSN:0191-2615, 1879-2367
Online-Zugang:Volltext
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Zusammenfassung:•Continuous network design problem with stochastic user equilibrium is explored.•The problem is reformulated as a nonlinear nonconvex programming.•A tight mixed-integer linear programming relaxation is derived.•A global optimization method based on range reduction technique is proposed. In this paper, we consider the continuous road network design problem with stochastic user equilibrium constraint that aims to optimize the network performance via road capacity expansion. The network flow pattern is subject to stochastic user equilibrium, specifically, the logit route choice model. The resulting formulation, a nonlinear nonconvex programming problem, is firstly transformed into a nonlinear program with only logarithmic functions as nonlinear terms, for which a tight linear programming relaxation is derived by using an outer-approximation technique. The linear programming relaxation is then embedded within a global optimization solution algorithm based on range reduction technique, and the proposed approach is proved to converge to a global optimum.
Bibliographie:ObjectType-Article-1
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ISSN:0191-2615
1879-2367
DOI:10.1016/j.trb.2014.10.009