A Branch and Bound Algorithm for Bi-level Discrete Network Design Problem

Farvaresh, Hamid; Sepehri, Mohammad Mehdi

doi:10.1007/s11067-012-9173-3

Cited by 66 publications

(38 citation statements)

References 39 publications

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“…The static variant of our problem can be seen as a graph embedding [8] or network design [10] problem. In particular, the problem of computing the optimal static network, that is, the binary search tree that minimizes the communication cost, is related to the classic Minimum Linear Arrangement (MLA) problem which asks for the embedding of an arbitrary "guest graph" on the line: the nodes of the guest graph must be mapped to the line such that the communication cost, i.e., the sum of the lengths of the projected edges, is minimized.…”

Section: Related Workmentioning

confidence: 99%

SplayNet: Towards Locally Self-Adjusting Networks

Schmid

Avin

Scheideler

et al. 2016

IEEE/ACM Trans. Networking

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Abstract-This paper initiates the study of locally selfadjusting networks: networks whose topology adapts dynamically and in a decentralized manner, to the communication pattern σ. Our vision can be seen as a distributed generalization of the selfadjusting datastructures introduced by Sleator and Tarjan [22]: In contrast to their splay trees which dynamically optimize the lookup costs from a single node (namely the tree root), we seek to minimize the routing cost between arbitrary communication pairs in the network.As a first step, we study distributed binary search trees (BSTs), which are attractive for their support of greedy routing. We introduce a simple model which captures the fundamental tradeoff between the benefits and costs of self-adjusting networks. We present the SplayNet algorithm and formally analyze its performance, and prove its optimality in specific case studies. We also introduce lower bound techniques based on interval cuts and edge expansion, to study the limitations of any demand-optimized network. Finally, we extend our study to multi-tree networks, and highlight an intriguing difference between classic and distributed splay trees.

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Section: Related Workmentioning

confidence: 99%

SplayNet: Towards Locally Self-Adjusting Networks

Schmid

Avin

Scheideler

et al. 2016

IEEE/ACM Trans. Networking

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“…However, solving the model is challenging. Potential approaches to solve the model could use existing algorithms to solve the DNDP, for example, the support function method proposed by Gao et al(2005), the active set technique presented by Zhang, et al(2009), the linear approach technique given by Farvaresh and Sepehri (2011), the branch and bound algorithm given by Farvaresh and Sepehri (2013), and the global optimization recently proposed by Wang et al (2013). Beside these existing algorithms it would also be possible to reformulate the model then use software from the sector.…”

Section: Solution Methodsmentioning

confidence: 99%

Joint road toll pricing and capacity development in discrete transport network design problem

Wang

Grant-Muller

et al. 2016

Transportation

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Abstract:The paper demonstrates a method to determine road network improvements that also involve the use of a road toll charge, taking the perspective of the government or authority. A general discrete network design problem with a road toll pricing scheme, to minimize the total travel time under a budget constraint, is proposed. This approach is taken in order to determine the appropriate level of road toll pricing whilst simultaneously addressing the need for capacity. The proposed approach is formulated as a bi-level programming problem. The optimal road capacity improvement and toll level scheme is investigated with respect to the available budget levels and toll revenues.

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“…Zhang et al [35] developed the active-set algorithm, which eliminates complementarity constraints in the DNDP by assigning initial values and solving binary knapsack problems. Farvaresh and Sepehri [36] revised the branch-andbound algorithm proposed by Leblanc [15] for bilevel DNDP.…”

Section: Network Design Problemmentioning

confidence: 99%

Time-Dependent Transportation Network Design considering Construction Impact

Song

Zhang

2018

Journal of Advanced Transportation

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A traditional discrete network design problem (DNDP) always assumes transportation infrastructure projects to be one-time events and ignores travelers' delays caused by construction work. In fact, infrastructure construction usually lasts for a long time, and the impact on traffic can be substantial. In this paper, we introduce time dimension into the traditional DNDP to explicitly consider the impact of road construction and adopt an overtime policy to add flexibility to construction duration. We address the problem of selecting road-widening projects in an urban network, determining the optimal link capacity, and designing the schedule of the selected projects simultaneously. A time-dependent DNDP (T-DNDP) model is developed with the objective of minimizing total weighted net user cost during the entire planning horizon. An active-set algorithm is applied to solve the model. A simple example network is first utilized to demonstrate the necessity of considering the construction process in T-DNDP and to illustrate the tradeoff between the construction impact and the benefit realized through capacity extension. We also solve the T-DNDP model with data from the Sioux Falls network, which contains 24 nodes, 76 links, and 528 origin-destination (O-D) pairs. Computational results for the problem are also presented.

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A Branch and Bound Algorithm for Bi-level Discrete Network Design Problem

Cited by 66 publications

References 39 publications

SplayNet: Towards Locally Self-Adjusting Networks

SplayNet: Towards Locally Self-Adjusting Networks

Joint road toll pricing and capacity development in discrete transport network design problem

Time-Dependent Transportation Network Design considering Construction Impact

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