Constraint reformulation and a Lagrangian relaxation-based solution algorithm for a least expected time path problem

Lixing Yang, Xuesong Zhou

Research output: Contribution to journalArticle

73 Scopus citations

Abstract

Using a sample-based representation scheme to capture spatial and temporal travel time correlations, this article constructs an integer programming model for finding the a priori least expected time paths. We explicitly consider the non-anticipativity constraint associated with the a priori path in a time-dependent and stochastic network, and propose a number of reformulations to establish linear inequalities that can be easily dualized by a Lagrangian relaxation solution approach. The relaxed model is further decomposed into two sub-problems, which can be solved directly by using a modified label-correcting algorithm and a simple single-value linear programming method. Several solution algorithms, including a sub-gradient method, a branch and bound method, and heuristics with additional constraints on Lagrangian multipliers, are proposed to improve solution quality and find approximate optimal solutions. The numerical experiments investigate the quality and computational efficiency of the proposed solution approach.

Original languageEnglish (US)
Pages (from-to)22-44
Number of pages23
JournalTransportation Research Part B: Methodological
Volume59
DOIs
StatePublished - Jan 2014

Keywords

  • A priori least expected time path
  • Branch and bound algorithm
  • Lagrangian relaxation
  • Time-dependent traffic network

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Transportation

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