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
N1 - Funding Information:
The research of the first author was supported by the National Natural Science Foundation of China (No. 71271020 ), Program for New Century Excellent Talents in University under Grant No. NCET-10-0218 , and National Basic Research Program of China (No. 2012CB725400 ). We are grateful to the referees for their helpful suggestions. The work presented in this paper remains the sole responsibility of the authors.
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
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U2 - 10.1016/j.trb.2013.10.012
DO - 10.1016/j.trb.2013.10.012
M3 - Article
AN - SCOPUS:84888423622
SN - 0191-2615
VL - 59
SP - 22
EP - 44
JO - Transportation Research Part B: Methodological
JF - Transportation Research Part B: Methodological
ER -