Journal of Heuristics

, Volume 24, Issue 3, pp 359–394 | Cite as

A constraint-based parallel local search for the edge-disjoint rooted distance-constrained minimum spanning tree problem

  • Alejandro ArbelaezEmail author
  • Deepak Mehta
  • Barry O’Sullivan
  • Luis Quesada


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 the RDCMST has focused on dedicated algorithms and therefore it is difficult to use these algorithms to tackle the ERDCMST. We present a constraint-based parallel local search algorithm for solving the 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 paper 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.


Local search Optical networks Parallelism 



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. The authors would like to thank the anonymous reviewers for their comments and suggestions which helped to improve the paper.


  1. Arbelaez, A., Codognet, P.: Massivelly parallel local search for SAT. In: ICTAI’12, pp. 57–64. IEEE Computer Society, Athens (2012)Google Scholar
  2. Arbelaez, A., Codognet, P.: From sequential to parallel local search for SAT. In: 13th European Conference on Evolutionary Computation in Combinatorial Optimisation (EvoCOP’13), pp. 157–168 (2013a)Google Scholar
  3. Arbelaez, A., Codognet, P.: A survey of parallel local search for sat. In: Theory, Implementation, and Applications of SAT Technology. Workshop at JSAI’13. Toyama (2013b)Google Scholar
  4. Arbelaez, A., Hamadi, Y.: Improving parallel local search for SAT. LION 5, 46–60 (2011)Google Scholar
  5. Arbelaez, A., Mehta, D., O’Sullivan, B., Quesada, L.: Constraint-based local search for the distance-and capacity-bounded network design problem. In: ICTAI’14, pp. 178–185. IEEE (2014)Google Scholar
  6. Arbelaez, A., Mehta, D., O’Sullivan, B., Quesada, L.: A constraint-based parallel local search for disjoint rooted distance-constrained minimum spanning tree problem. In: Workshop on Parallel Methods for Search and Optimization (2014)Google Scholar
  7. Arbelaez, A., Mehta, D., O’Sullivan, B., Quesada, L.: A constraint-based local search for edge disjoint rooted distance-constrained minimum spanning tree problem. In: Michel, L. (ed.) CPAIOR’15, Lecture Notes in Computer Science, vol. 9075, pp. 31–46. Springer (2015). doi: 10.1007/978-3-319-18008-3_3
  8. Baraglia, R., Hidalgo, J.I., Perego, R.: A parallel hybrid heuristic for the TSP. In: EvoWorkshops, pp. 193–202 (2001)Google Scholar
  9. Caniou, Y., Diaz, D., Richoux, F., Codognet, P., Abreu, S.: Performance analysis of parallel constraint-based local search. In: PPOPP, pp. 337–338 (2012)Google Scholar
  10. Crainic, T.G., Gendreau, M.: Cooperative parallel tabu search for capacitated network design. J. Heuristics 8(6), 601–627 (2002)CrossRefGoogle Scholar
  11. Davey, R., Grossman, D., Rasztovits-Wiech, M., Payne, D., Nesset, D., Kelly, A., Rafel, A., Appathurai, S., Yang, S.H.: Long-reach passive optical networks. J. Light. Technol. 27(3), 273–291 (2009)CrossRefGoogle Scholar
  12. Dung, P.Q., Deville, Y., Van Hentenryck, P.: Constraint-based local search for constrained optimum paths problems. In: CPAIOR, pp. 267–281 (2010)Google Scholar
  13. Ho, J.M., Lee, D.T.: Bounded diameter minimum spanning trees and related problems. In: Proceedings of the Fifth Annual Symposium on Computational Geometry, SCG ’89, pp. 276–282. ACM, New York, NY, USA (1989). doi: 10.1145/73833.73864
  14. Hoos, H., Stützle, T.: Stochastic Local Search: Foundations and Applications. Morgan Kaufmann, Burlington (2005)zbMATHGoogle Scholar
  15. Hunter, D.K., Lu, Z., Gilfedder, T.H.: Protection of long-reach PON traffic through router database synchronization. J. Opt. Commun. Netw. 6(5), 535–549 (2007)CrossRefGoogle Scholar
  16. Leitner, M., Ruthmair, M., Raidl, G.R.: Stabilized branch-and-price for the rooted delay-constrained steiner tree problem. In: Pahl, J., Reiners, T., Vo, S. (eds.) INOC, Lecture Notes in Computer Science, vol. 6701, pp. 124–138. Springer, Berlin (2011)Google Scholar
  17. Martins, R., Manquinho, V.M., Lynce, I.: An overview of parallel SAT solving. Constraints 17(3), 304–347 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  18. Michel, L., See, A., Van Hentenryck, P.: Parallel and distributed local search in comet. Comput. Oper. Res. 36, 2357–2375 (2009)CrossRefzbMATHGoogle Scholar
  19. Oh, J., Pyo, I., Pedram, M.: Constructing minimal spanning/steiner trees with bounded path length. Integration 22(1–2), 137–163 (1997)CrossRefzbMATHGoogle Scholar
  20. Payne, D.B.: FTTP deployment options and economic challenges. In: Proceedings of the 36th European Conference and Exhibition on Optical Communication (ECOC 2009) (2009)Google Scholar
  21. Roli, A.: Criticality and parallelism in structured SAT instances. In: Hentenryck, P.V. (ed.) CP’02, LNCS, vol. 2470, pp. 714–719. Springer, Ithaca (2002)Google Scholar
  22. Ruthmair, M., Raidl, G.R.: A kruskal-based heuristic for the rooted delay-constrained minimum spanning tree problem. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds.) EUROCAST, Lecture Notes in Computer Science, vol. 5717, pp. 713–720. Springer, Berlin (2009)Google Scholar
  23. Ruthmair, M., Raidl, G.R.: Variable neighborhood search and ant colony optimization for the rooted delay-constrained minimum spanning tree problem. In: Schaefer, R., Cotta, C., Kolodziej, J., Rudolph, G. (eds.) PPSN (2), Lecture Notes in Computer Science, vol. 6239, pp. 391–400. Springer, Berlin (2010)Google Scholar
  24. Salama, H.F., Reeves, D.S., Viniotis, Y.: The delay-constrained minimum spanning tree problem. In: ISCC, pp. 699–703 (1997)Google Scholar
  25. Shylo, O.V., Middelkoop, T., Pardalos, P.M.: Restart strategies in optimization: parallel and serial cases. Parallel Comput. 37(1), 60–68 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  26. Truchet, C., Arbelaez, A., Richoux, F., Codognet, P.: Estimating parallel runtimes for randomized algorithms in constraint solving. J. Heuristics 22(4), 613–648 (2016)Google Scholar
  27. Van Hentenryck, P., Michel, L.: Constraint-based local search. The MIT Press, Cambridge (2009)zbMATHGoogle Scholar
  28. Verhoeven, M., Aarts, E.: Parallel local search. J. Heuristics 1(1), 43–65 (1995)CrossRefzbMATHGoogle Scholar
  29. Verhoeven, M., Severens, M.: Parallel local search for steiner trees in graphs. Ann. Oper. Res. 90, 185–202 (1999)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Insight Centre for Data AnalyticsUniversity College CorkCorkIreland

Personalised recommendations