# Accelerating the Performance of Parallel Depth-First-Search Branch-and-Bound Algorithm in Transportation Network Design Problem

### Amirali Zarrinmehr, Yousef Shafahi

#### Abstract

Transportation Network Design Problem (TNDP) aims at selection of a subset of proposed urban projects in budget constraint to minimize the network usersâ€™ total travel time. This is a well-known resource-intensive problem in transportation planning literature. Application of parallel computing, as a result, can be useful to address the exact solution of TNDP. This paper is going to investigate how the performance of a parallel Branch-and-Bound (B&B) algorithm with Depth-First-Search (DFS) strategy can be accelerated. The paper suggests assigning greedy solutions to idle processors at the start of the algorithm. A greedy solution, considered in this paper, is a budget-wise feasible selection of projects to which no further project can be added while holding the budget constraint. The paper evaluates the performance of parallel algorithms through the theoretical speedup and efficiency which are based on the number of parallel B&B iterations. It is observed, in four cases of TNDP in Sioux-Falls transportation network, that achieving high-quality solutions by idle processors can notably improve the performance of parallel DFS B&B algorithm. In all four cases, super-linear speedups are reported.

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#### Paper Citation

#### in Harvard Style

Zarrinmehr A. and Shafahi Y. (2015). **Accelerating the Performance of Parallel Depth-First-Search Branch-and-Bound Algorithm in Transportation Network Design Problem** . In *Proceedings of the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-758-075-8, pages 359-366. DOI: 10.5220/0005220103590366

#### in Bibtex Style

@conference{icores15,

author={Amirali Zarrinmehr and Yousef Shafahi},

title={Accelerating the Performance of Parallel Depth-First-Search Branch-and-Bound Algorithm in Transportation Network Design Problem},

booktitle={Proceedings of the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

year={2015},

pages={359-366},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005220103590366},

isbn={978-989-758-075-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

TI - Accelerating the Performance of Parallel Depth-First-Search Branch-and-Bound Algorithm in Transportation Network Design Problem

SN - 978-989-758-075-8

AU - Zarrinmehr A.

AU - Shafahi Y.

PY - 2015

SP - 359

EP - 366

DO - 10.5220/0005220103590366