EUROCAST 2011: Computer Aided Systems Theory – EUROCAST 2011 pp 256-263 | Cite as
A Multilevel Heuristic for the Rooted Delay-Constrained Minimum Spanning Tree Problem
Abstract
The rooted delay-constrained minimum spanning tree problem is an NP-hard combinatorial optimization problem. The problem appears in practice for example when designing a distribution network with a guarantee of timely delivery. Another example is be a centralized broadcasting network where the delaybound represents a quality of service constraint. We introduce a multilevel-based construction heuristic which uses a new measurement for the suitability of edges to create a solution for the problem. In comparison to existing heuristics the main intention is not to create a minimum cost spanning tree, but a solution with a high potential for further improvement. Experimental results indicate that in most cases our approach produces solutions that after local improvement are of higher quality than those of other existing construction techniques.
Keywords
Span Tree Variable Neighborhood Search Ranking Score Scatter Search Minimum Span Tree ProblemPreview
Unable to display preview. Download preview PDF.
References
- 1.Dahl, G., Gouveia, L., Requejo, C.: On formulations and methods for the hop-constrained minimum spanning tree problem. In: Handbook of Optimization in Telecommunications. ch. 19, pp. 493–515. Springer Science + Business Media, Heidelberg (2006)CrossRefGoogle Scholar
- 2.Ghaboosi, N., Haghighat, A.T.: A Path Relinking Approach for Delay-Constrained Least-Cost Multicast Routing Problem. In: Proceedings of the 19th IEEE International Conference on Tools with Artificial Intelligence, pp. 383–390 (2007)Google Scholar
- 3.Gouveia, L., Paias, A., Sharma, D.: Modeling and Solving the Rooted Distance-Constrained Minimum Spanning Tree Problem. Computers and Operations Research 35(2), 600–613 (2008)MathSciNetCrossRefMATHGoogle Scholar
- 4.Leggieri, V., Haouari, M., Triki, C.: An Exact Algorithm for the Steiner Tree Problem with Delays. Electronic Notes in Discrete Mathematics 36, 223–230 (2010)CrossRefMATHGoogle Scholar
- 5.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 2009. LNCS, vol. 5717, pp. 713–720. Springer, Heidelberg (2009)CrossRefGoogle Scholar
- 6.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., Kołodziej, J., Rudolph, G. (eds.) PPSN XI, Part II. LNCS, vol. 6239, pp. 391–400. Springer, Heidelberg (2010)Google Scholar
- 7.Ruthmair, M., Raidl, G.R.: A Layered Graph Model and an Adaptive Layers Framework to Solve Delay-Constrained Minimum Tree Problems. In: Günlük, O., Woeginger, G.J. (eds.) IPCO 2011, Part XV. LNCS, vol. 6655, pp. 376–388. Springer, Heidelberg (2011)CrossRefGoogle Scholar
- 8.Salama, H.F., Reeves, D.S., Viniotis, Y.: An Efficient Delay-Constrained Minimum Spanning Tree Heuristic. In: Proceedings of the 5th International Conference on Computer Communications and Networks (1996)Google Scholar
- 9.Walshaw, C.: Multilevel refinement for combinatorial optimisation problems. Annals of Operations Research 131(1), 325–372 (2004)MathSciNetCrossRefMATHGoogle Scholar
- 10.Xu, Y., Qu, R.: A GRASP approach for the Delay-constrained Multicast routing problem. In: Proceedings of the 4th Multidisplinary International Scheduling Conference (MISTA4), Dublin, Ireland, pp. 93–104 (2009)Google Scholar
- 11.Xu, Y., Qu, R.: A hybrid scatter search meta-heuristic for delay-constrained multicast routing problems. Applied Intelligence 1–13 (2010)Google Scholar