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 users’ 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.

References

  1. Anstreicher, K., Brixius, N., Goux, J.-P., and Linderoth, J., 2002. Solving large quadratic assignment problems on computational grids. Mathematical Programming, 91(3), 563-588.
  2. Bar-Gera, H., 2011. Transportation network test problems. http://www.bgu.ac.il/bargera/tntp.
  3. Barney, B., 2010. Introduction to parallel computing. Lawrence Livermore Natl. Libr.
  4. Farahani, R. Z., Miandoabchi, E., Szeto, W. Y., and Rashidi, H., 2013. A Review of Urban Transportation Network Design Problems, European Journal of Operational Research, 229(2), 281-302.
  5. Gendron, B., Crainic, T. G., 1994. Parallel Branch-andBranch Algorithms: Survey and synthesis. Operations Research, 42(6), 1042-1066.
  6. Henrich, D., 1993. Initialization of Parallel Branch-andBound Algorithms. Proceedings of the Second International Workshop on Parallel Processing and Artificial Intelligence, Chamberry, France.
  7. Lai, T. H., Sahni, S., 1984. Anomalies in parallel branchand-bound algorithms. Communications of the ACM, 27(6), 594-602.
  8. LeBlanc, L. J., 1975. An algorithm for the discrete network design problem. Transportation Science., 9(3), 183-199.
  9. Li, G. J., Wah, B. W., 1986. Coping with anomalies in parallel branch-and-bound algorithms. IEEE Transactions on Computers, 100(6), 568-573.
  10. Li, G. J., Wah, B. W., 1990. Computational efficiency of parallel combinatorial or-tree searches. IEEE Transactions on Software Engineering, 16(1), 13-31.
  11. Poorzahedy, H., 1980. Efficient algorithms for solving the network design problem. Ph.D. Diss., Department of Civil Engineering, Northwest University, Evanston, Ill.
  12. Poorzahedy, H., Abulghasemi, F., 2005. Application of ant system to network design problem. Transportation, 32(3), 251-273.
  13. Pruul, E., Nemhauser, G., Rushmeier, R., 1988. Branchand-bound and parallel computation: A historical note. Operations Research Letters, 7(2), 65-69.
  14. Roucairol, C., 1996. Parallel processing for difficult combinatorial optimization problems. European Journal of Operations Research, 92(3), 573-590.
  15. Sheffi, Y., 1985. Urban transportation networks: equilibrium analysis with mathematical programming methods. Prentice Hall.
  16. Vitins, B. J., Axhausen, K. W., 2010. Patterns and Grammars for Transport Network Generation. Proceedings of 14th Swiss Transport Research Conference.
  17. Zarrinmehr, A., 2011. Discrete network design using parallel branch-and-bound algorithms. M.Sc. Thesis, Department of Civil and Environmental Engineering, Sharif University of Technology.
  18. Zarrinmehr, A., Shafahi, Y., 2014. Enumeration of Dominant Solutions: An Application in Transport Network Design. M.Sc. International Journal of Transportation Engineering, 1(4), 335-348.
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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