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 language | English (US) |
|---|---|
| Pages (from-to) | 22-44 |
| Number of pages | 23 |
| Journal | Transportation Research Part B: Methodological |
| Volume | 59 |
| DOIs | |
| State | Published - Jan 2014 |
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Keywords
- A priori least expected time path
- Branch and bound algorithm
- Lagrangian relaxation
- Time-dependent traffic network
ASJC Scopus subject areas
- Management Science and Operations Research
- Transportation
Cite this
Constraint reformulation and a Lagrangian relaxation-based solution algorithm for a least expected time path problem. / Yang, Lixing; Zhou, Xuesong.
In: Transportation Research Part B: Methodological, Vol. 59, 01.2014, p. 22-44.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Constraint reformulation and a Lagrangian relaxation-based solution algorithm for a least expected time path problem
AU - Yang, Lixing
AU - Zhou, Xuesong
PY - 2014/1
Y1 - 2014/1
N2 - 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.
AB - 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.
KW - A priori least expected time path
KW - Branch and bound algorithm
KW - Lagrangian relaxation
KW - Time-dependent traffic network
UR - http://www.scopus.com/inward/record.url?scp=84888423622&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84888423622&partnerID=8YFLogxK
U2 - 10.1016/j.trb.2013.10.012
DO - 10.1016/j.trb.2013.10.012
M3 - Article
AN - SCOPUS:84888423622
VL - 59
SP - 22
EP - 44
JO - Transportation Research, Series B: Methodological
JF - Transportation Research, Series B: Methodological
SN - 0191-2615
ER -