Parallel Constraint-Based Local Search: An Application to Designing Resilient Long-Reach Passive Optical Networks

  • Alejandro Arbelaez
  • Deepak Mehta
  • Barry O’Sullivan
  • Luis Quesad


Many network design problems arising in areas as diverse as VLSI circuit design, QoS routing, traffic engineering, and computational sustainability require clients to be connected to a facility under path-length constraints and budget limits. These problems can be seen as instances of the Rooted Distance-Constrained Minimum Spanning-Tree problem (RDCMST), which is NP-hard. An inherent feature of these networks is that they are vulnerable to a failure. Therefore, it is often important to ensure that all clients are connected to two or more facilities via edge-disjoint paths.We call this problem the Edge-disjoint RDCMST (ERDCMST). Previous work on RDCMST has focused on dedicated algorithms and, therefore, it is difficult to use these algorithms to tackle ERDCMST. We present a constraint-based parallel local search algorithm for solving ERDCMST. Traditional ways of extending a sequential algorithm to run in parallel perform either portfolio-based search in parallel or parallel neighbourhood search. Instead, we exploit the semantics of the constraints of the problem to perform multiple moves in parallel by ensuring that they are mutually independent. The ideas presented in this chapter are general and can be adapted to other problems as well. The effectiveness of our approach is demonstrated by experimenting with a set of problem instances taken from real-world passive optical network deployments in Ireland, Italy, and the UK. Our results show that performing moves in parallel can significantly reduce the elapsed time and improve the quality of the solutions of our local search approach.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



This work was supported by DISCUS (FP7 Grant Agreement 318137), and Science Foundation Ireland (SF) Grant No. 10/CE/I1853. The Insight Centre for Data Analytics is also supported by SFI under Grant Number SFI/12/RC/2289.


  1. [1]
    A. Arbelaez and P. Codognet. Massivelly parallel local search for SAT. In 24th IEEE International Conference on Tools with Artificial Intelligence, ICTAI’12, pages 57–64, Athens, Greece, November 2012. IEEE Computer Society.Google Scholar
  2. [2]
    A. Arbelaez and P. Codognet. From sequential to parallel local search for SAT. In 13th European Conference on Evolutionary Computation in Combinatorial Optimisation, EvoCOP’13, volume 7832 of Lecture Notes in Computer Science, pages 157–168. Springer, 2013.Google Scholar
  3. [3]
    A. Arbelaez and P. Codognet. A survey of parallel local search for SAT. In Theory, Implementation, and Applications of SAT Technology. Workshop at JSAI’13, Toyama, Japan, June 2013.Google Scholar
  4. [4]
    A. Arbelaez and Y. Hamadi. Improving parallel local search for SAT. In 5th International Conference on Learning and Intelligent Optimization LION 5, volume 6683 of Lecture Notes in Computer Science, pages 46–60. Springer, 2011.Google Scholar
  5. [5]
    A. Arbelaez, D. Mehta, B. O’Sullivan, and L. Quesada. Constraint-based local search for the distance-and capacity-bounded network design problem. In 26th IEEE International Conference on Tools with Artificial Intelligence, ICTAI’14, pages 178–185. IEEE, 2014.Google Scholar
  6. [6]
    A. Arbelaez, D. Mehta, B. O’Sullivan, and L. Quesada. A constraint-based local search for edge disjoint rooted distance-constrained minimum spanning tree problem. In 12th International Conference on Integration of AI and OR Techniques in Constraint Programming, CPAIOR’15, volume 9075 of Lecture Notes in Computer Science, pages 31–46. Springer, 2015.Google Scholar
  7. [7]
    R. Baraglia, J. I. Hidalgo, and R. Perego. A parallel hybrid heuristic for the TSP. In Applications of Evolutionary Computing, EvoWorkshops 2001: EvoCOP, EvoFlight, EvoIASP, EvoLearn, and EvoSTIM, volume 2037 of Lecture Notes in Computer Science, pages 193–202. Springer, 2001.Google Scholar
  8. [8]
    Y. Caniou, D. Diaz, F. Richoux, P. Codognet, and S. Abreu. Performance analysis of parallel constraint-based local search. In 17th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming, PPOPP’12, pages 337–338. ACM, 2012.Google Scholar
  9. [9]
    T. G. Crainic and M. Gendreau. Cooperative parallel tabu search for capacitated network design. J. Heuristics, 8(6):601–627, 2002.Google Scholar
  10. [10]
    P. Q. Dung, Y. Deville, and P. Van Hentenryck. Constraint-based local search for constrained optimum paths problems. In 9th International Conference on Integration of AI and OR Techniques in Contraint Programming for Combinatorial Optimzation Problems, CPAIOR’19, volume 7298 of Lecture Notes in Computer Science, pages 267–281. Springer, 2010.Google Scholar
  11. [11]
    E. Eaton, C. P. Gomes, and B. C. Williams. Computational sustainability. AI Magazine, 35(2):3–7, 2014.Google Scholar
  12. [12]
    C. Gao, Y. Shi, Y. T. Hou, H. D. Sherali, and H. Zhou. Multicast communications in multi-hop cognitive radio networks. IEEE Journal on Selected Areas in Communications, 29(4):784–793, 2011.Google Scholar
  13. [13]
    J. M. Ho and D. T. Lee. Bounded diameter minimum spanning trees and related problems. In Proceedings of the Fifth Annual Symposium on Computational Geometry, SCG ’89, pages 276–282, New York, USA, 1989. ACM.Google Scholar
  14. [14]
    H. Hoos and T. Stützle. Stochastic Local Search: Foundations and Applications. Morgan Kaufmann, 2005.Google Scholar
  15. [15]
    D. K. Hunter, Z. Lu, and T. H. Gilfedder. Protection of long-reach PON traffic through router database synchronization. Journal of Optical Communications and Networking, 6(5):535–549, 2007.Google Scholar
  16. [16]
    M. Leitner, M. Ruthmair, and G. R. Raidl. Stabilized branch-and-price for the rooted delay-constrained Steiner tree problem. In J. Pahl, T. Reiners, and S. Voß, editors, INOC, volume 6701 of Lecture Notes in Computer Science, pages 124–138. Springer, 2011. ISBN 978-3-642-21526-1.Google Scholar
  17. [17]
    R. Martins, V. M. Manquinho, and I. Lynce. An overview of parallel SAT solving. Constraints, 17(3):304–347, 2012.Google Scholar
  18. [18]
    L. Michel, A. See, and P. Van Hentenryck. Parallel and distributed local search in comet. Computers and Operations Research, 36:2357–2375, 2009.Google Scholar
  19. [19]
    J. Oh, I. Pyo, and M. Pedram. Constructing minimal spanning/Steiner trees with bounded path length. Integration, 22(1-2):137–163, 1997.Google Scholar
  20. [20]
    S. Pant. Design and Analysis of Power Distribution Networks in VLSI Circuits. PhD thesis, The School of Electrical Engineering in The University of Michigan, 2008.Google Scholar
  21. [21]
    D. B. Payne. FTTP deployment options and economic challenges. In Proceedings of the 36th European Conference and Exhibition on Optical Communication (ECOC 2009), 2009.Google Scholar
  22. [22]
    A. Roli. Criticality and parallelism in structured SAT instances. In 8th International Conference on Principles and Practice of Constraint Programming, CP’02, volume 2470 of Lecture Notes in Computer Science, pages 714–719, Ithaca, NY, USA, 2002. Springer.Google Scholar
  23. [23]
    M. Ruffini, L. Wosinska, M. Achouche, J. Chen, N. J. Doran, F. Farjady, J. Montalvo-Garcia, P. Ossieur, B. O’Sullivan, N. Parsons, T. Pfeiffer, X. Qiu, C. Raack, H. Rohde, M. Schiano, P. D. Townsend, R. Wessäly, X. Yin, and D. B. Payne. DISCUS: an end-to-end solution for ubiquitous broadband optical access. IEEE Communications Magazine, 52(2):24–56, 2014.Google Scholar
  24. [24]
    M. Ruthmair and G. R. Raidl. A Kruskal-based heuristic for the rooted delayconstrained minimum spanning tree problem. In R. Moreno-Díaz, F. Pichler, and A. Quesada-Arencibia, editors, EUROCAST, volume 5717 of Lecture Notes in Computer Science, pages 713–720. Springer, 2009. ISBN 978-3-642-04771-8.Google Scholar
  25. [25]
    M. Ruthmair and G. R. Raidl. Variable neighborhood search and ant colony optimization for the rooted delay-constrained minimum spanning tree problem. In R. Schaefer, C. Cotta, J. Kolodziej, and G. Rudolph, editors, PPSN (2), volume 6239 of Lecture Notes in Computer Science, pages 391–400. Springer, 2010. ISBN 978-3-642-15870-4.Google Scholar
  26. [26]
    O. V. Shylo, T. Middelkoop, and P. M. Pardalos. Restart Strategies in Optimization: Parallel and Serial Cases. Parallel Computing, 37(1):60–68, 2011.Google Scholar
  27. [27]
    R. Sigua. Fundamentals of Traffic Engineering. University of the Philippines Press, 2008.Google Scholar
  28. [28]
    C. Truchet, A. Arbelaez, F. Richoux, and P. Codognet. Estimating parallel runtimes for randomized algorithms in constraint solving. J. of Heuristics, 22 (4):613–648, 2016.Google Scholar
  29. [29]
    P. Van Hentenryck and L. Michel. Constraint-based local search. The MIT Press, 2009.Google Scholar
  30. [30]
    M. Verhoeven and E. Aarts. Parallel local search. Journal of Heuristics, 1(1): 43–65, 1995.Google Scholar
  31. [31]
    M. Verhoeven and M. Severens. Parallel local search for Steiner trees in graphs. Annals of Operations Research, 90:185–202, 1999.Google Scholar
  32. [32]
    X. Yuan and A. Saifee. Path selection methods for localized quality of service routing. In 10th International Conference on Computer Communications and Networks, ICCCN’01, pages 102–107. IEEE, 2001.Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Alejandro Arbelaez
    • 1
  • Deepak Mehta
    • 1
  • Barry O’Sullivan
    • 1
  • Luis Quesad
    • 1
  1. 1.Insight Centre for Data AnalyticsUniversity College CorkCorkIreland

Personalised recommendations