TY - JOUR

T1 - A Dantzig-Wolfe Decomposition Based Heuristic Scheme for Bi-level Dynamic Network Design Problem

AU - Lin, Dung Ying

AU - Karoonsoontawong, Ampol

AU - Waller, S. Travis

PY - 2011/3

Y1 - 2011/3

N2 - We present a heuristic to solve the NP-hard bi-level network design problem (NDP). The heuristic is developed based on the Dantzig-Wolfe decomposition principle such that it iteratively solves a master problem and a pricing problem. The master problem is the budget allocation linear program solved by CPLEX to determine the budget allocation and construct a modified cell transmission network for the pricing problem. The pricing problem is the user-optimal dynamic traffic assignment (UODTA) solved by an existing combinatorial algorithm. To facilitate the decomposition principle, we propose a backward connectivity algorithm and complementary slackness procedures to efficiently approximate the required dual variables from the UODTA solution. The dual variables are then employed to augment a new column in the master program in each iteration. The iterative process repeats until a stopping criterion is met. Numerical experiments are conducted on two test networks. Encouraging results demonstrate the applicability of the heuristic scheme on solving large-scale NDP. Though a single destination problem is considered in this paper, the proposed scheme can be extended to solve multi-destination problems as well.

AB - We present a heuristic to solve the NP-hard bi-level network design problem (NDP). The heuristic is developed based on the Dantzig-Wolfe decomposition principle such that it iteratively solves a master problem and a pricing problem. The master problem is the budget allocation linear program solved by CPLEX to determine the budget allocation and construct a modified cell transmission network for the pricing problem. The pricing problem is the user-optimal dynamic traffic assignment (UODTA) solved by an existing combinatorial algorithm. To facilitate the decomposition principle, we propose a backward connectivity algorithm and complementary slackness procedures to efficiently approximate the required dual variables from the UODTA solution. The dual variables are then employed to augment a new column in the master program in each iteration. The iterative process repeats until a stopping criterion is met. Numerical experiments are conducted on two test networks. Encouraging results demonstrate the applicability of the heuristic scheme on solving large-scale NDP. Though a single destination problem is considered in this paper, the proposed scheme can be extended to solve multi-destination problems as well.

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U2 - 10.1007/s11067-008-9093-4

DO - 10.1007/s11067-008-9093-4

M3 - Article

AN - SCOPUS:79953063896

VL - 11

SP - 101

EP - 126

JO - Networks and Spatial Economics

JF - Networks and Spatial Economics

SN - 1566-113X

IS - 1

ER -