Optimizing on-time arrival probability and percentile travel time for elementary path finding in time-dependent transportation networks: Linear mixed integer programming reformulations

Lixing Yang, Xuesong Zhou

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

Aiming to provide a generic modeling framework for finding reliable paths in dynamic and stochastic transportation networks, this paper addresses a class of two-stage routing models through reformulation of two commonly used travel time reliability measures, namely on-time arrival probability and percentile travel time, which are much more complex to model in comparison to expected utility criteria. A sample-based representation is adopted to allow time-dependent link travel time data to be spatially and temporally correlated. A number of novel reformulation methods are introduced to establish equivalent linear integer programming models that can be easily solved. A Lagrangian decomposition approach is further developed to dualize the non-anticipatory coupling constraints across different samples and then decompose the relaxed model into a series of computationally efficient time-dependent least cost path sub-problems. Numerical experiments are implemented to demonstrate the solution quality and computational performance of the proposed approaches.

Original languageEnglish (US)
Pages (from-to)68-91
Number of pages24
JournalTransportation Research Part B: Methodological
Volume96
DOIs
StatePublished - Feb 1 2017

Fingerprint

Linear networks
Integer programming
Travel time
programming
travel
Decomposition
time
Mixed integer linear programming
Transportation networks
Costs
Experiments
experiment
costs
performance

Keywords

  • Lagrangian relaxation
  • On-time arrival path
  • Percentile path
  • Reliable path finding

ASJC Scopus subject areas

  • Transportation
  • Management Science and Operations Research

Cite this

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title = "Optimizing on-time arrival probability and percentile travel time for elementary path finding in time-dependent transportation networks: Linear mixed integer programming reformulations",
abstract = "Aiming to provide a generic modeling framework for finding reliable paths in dynamic and stochastic transportation networks, this paper addresses a class of two-stage routing models through reformulation of two commonly used travel time reliability measures, namely on-time arrival probability and percentile travel time, which are much more complex to model in comparison to expected utility criteria. A sample-based representation is adopted to allow time-dependent link travel time data to be spatially and temporally correlated. A number of novel reformulation methods are introduced to establish equivalent linear integer programming models that can be easily solved. A Lagrangian decomposition approach is further developed to dualize the non-anticipatory coupling constraints across different samples and then decompose the relaxed model into a series of computationally efficient time-dependent least cost path sub-problems. Numerical experiments are implemented to demonstrate the solution quality and computational performance of the proposed approaches.",
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AB - Aiming to provide a generic modeling framework for finding reliable paths in dynamic and stochastic transportation networks, this paper addresses a class of two-stage routing models through reformulation of two commonly used travel time reliability measures, namely on-time arrival probability and percentile travel time, which are much more complex to model in comparison to expected utility criteria. A sample-based representation is adopted to allow time-dependent link travel time data to be spatially and temporally correlated. A number of novel reformulation methods are introduced to establish equivalent linear integer programming models that can be easily solved. A Lagrangian decomposition approach is further developed to dualize the non-anticipatory coupling constraints across different samples and then decompose the relaxed model into a series of computationally efficient time-dependent least cost path sub-problems. Numerical experiments are implemented to demonstrate the solution quality and computational performance of the proposed approaches.

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