Application of Enhanced Particle Swarm Optimization in Euclidean Steiner Tree Problem Solving in RN
Given a fixed set of points in a N-dimensional space (N ≥ 3) with Euclidean metrics, the Euclidean Steiner Tree Problem in RN consists of finding a minimum length tree that spans all these points using, if necessary, extra points (Steiner points). The finding of such solution is a NP-hard problem. This paper presents a modified metaheuristic based on Improved Particle Swarm Optimization to the problem considered. Finally, computational experiments compare the performance of the proposed heuristic, considering solution’s quality and computational time, in regard to previous works in the literature.
The authors acknowledge the reviewers for important and helpful contributions to this work. The development of this research benefited from the UFT Institutional Productivity Research Program (PROPESQ/UFT).
- 1.Alford, C., Brazil, M., Lee, D.H.: Optimisation in Underground Mining, pp. 561–577. Springer, Boston (2007). https://doi.org/10.1007/978-0-387-71815-6_30
- 4.Eberhart, R.C., Shi, Y.: Comparing inertia weights and constriction factors in particle swarm optimization. In: Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512), vol. 1, pp. 84–88 (2000). https://doi.org/10.1109/CEC.2000.870279
- 9.Kuhn, H.W.: “Steiner’s” Problem Revisited, pp. 52–70. Mathematical Association of America, Washington (1974)Google Scholar
- 10.Montenegro, F., Torreão, J.R.A., Maculan, N.: Microcanonical optimization algorithm for the Euclidean Steiner problem in Rn with application to phylogenetic inference. Phys. Rev. E 68 (2003). https://doi.org/10.1103/PhysRevE.68.056702
- 12.Prim, R.C.: Shortest connection networks and some generalizations. Bell Syst. Tech. J. 36(6), 1389–1401 (1957). https://doi.org/10.1002/j.1538-7305.1957.tb01515.x CrossRefGoogle Scholar
- 13.Rocha, M.L.: An hybrid metaheuristic approach to solve the Euclidean Steiner tree problem in Rn. In: Proceedings of XLV Brazilian Symposium on Operational Research, vol. 1, pp. 1881–1892 (2013)Google Scholar