New recombination operator in genetic algorithm for solving the bounded diameter minimum spanning tree problem Nghia N.D., Binh H.T.T. Faculty of Information Technology, Ha Noi University of Technology, Ha Noi, Viet Nam Abstract: Given a connected, weighted, undirected graph G=(V, E) and a bound D, Bounded Diameter Minimum Spanning Tree problem (BDMST) seeks spanning tree on G with smallest weight in which no path between two vertices contains more than D edges. This problem is NP-hard for 4 ≤ D ≤ |V| - 1. In present paper a new randomized greedy heuristic algorithm and a new recombination method in genetic algorithm for solving BDMST are developed Results of computational experiments are reported to show the efficiency of these algorithms. © 2007 IEEE. Author Keywords: Bounded diameter minimum spanning tree; Genetic algorithm; Greedy heuristic Index Keywords: Computational efficiency; Genetic algorithms; Heuristic algorithms; Optimization; Problem solving; Greedy heuristic method; Minimum spanning tree problem; Spanning trees; Trees (mathematics) Year: 2007 Source title: 2007 IEEE International Conference on Research, Innovation and Vision for the Future, RIVF 2007 Art. No.: 4223060 Page : 108-113 Link: Scorpus Link Correspondence Address: Nghia, N.D.; Faculty of Information Technology, Ha Noi University of Technology, Ha Noi, Viet Nam; email:
[email protected] Conference name: 2007 IEEE International Conference on Research, Innovation and Vision for the Future, RIVF 2007 Conference date: 5 March 2007 through 9 March 2007 Conference location: Hanoi Conference code: 69816 ISBN: 1424406943; 9781424406944 DOI: 10.1109/RIVF.2007.369143 Language of Original Document: English Abbreviated Source Title: 2007 IEEE International Conference on Research, Innovation and Vision for the Future, RIVF 2007 Document Type: Conference Paper Source: Scopus Authors with affiliations: 1. Nghia, N.D., Faculty of Information Technology, Ha Noi University of Technology, Ha Noi, Viet Nam
2. Binh, H.T.T., Faculty of Information Technology, Ha Noi University of Technology, Ha Noi, Viet Nam
References: 1.
Garey, M.R., Johnson, D.S., (1979) Computers and Intraobility: A Guide to the Theory of NP-Completeness
2.
Raymond, K., A tree-based algorithm for distributed mutual exclusion (1989) ACM Transactions on Computer Systems, 7 (1), pp. 61-77
3.
Bala, K., Petropoulos, K., Stern, T.E., Multicasting in a linear lightwave network (1993) IEEE INFOCOM'93, pp. 1350-1358
4.
Palmer, C.C., Kershenbaum, A., Representing trees in genetic algorithms (1994) Proceedings of the Forst IEEE Conference on Evolutionary Computation
5.
N.R.Achuthan, L.Caccetta, P.Caccetta and Geelen, Computational methods for the diameter restricted minimum weight spanning tree problem, 1994Bookstein, A., Klein, S.T., (1996) Compression of correlated bit-vectors, , Information Systems
6.
Kortsarz, G., Peleg, D., Approximating shallow-light trees (1997) Proceedings of the 8th Symposium on Discrete Algorithms
7.
Abdalla, A., Deo, N., Gupta, P., (2000) Random-tree diameter and the diameter constrained MST, Congressus Numerantium
8.
Gottlieb, J., Julstrom, B.A., Rothlauf, F., Raidl, G.R., Prufer numbers: A poor representation of spanning trees for evolutionary search (2000) Proceedings of the 2001 Genetic and Evolutionary Computation Conference
9.
Abdalla, (2001) Computing a diameter-constrained minimum spanning tree, , PhD dissertation in the School of Electrical Engineering and Computer Science, University of Centre Florida
10. Raidl, G.R., Julstrom, B.A., Edge-sets: An effective evolutionary coding of spanning trees (2003) IEEE Transactions on Evolutionary Computation 11. Raidl, G.R., Julstrom, B.A., (2003) Greedy Heuristics and an Evolutionary Algorithm for the Bounded-Diameter Minimum Spanning Tree Problem, , ACM Press 12. Julstrom, B.A., Raild, G.R., A permutation coded evolutionary for the bounded diameter minimum spanning tree problem (2003) Genetic and Evolutionary Computation Conference's Workshop Proceedings 13. Julstrom, B.A., Encoding bounded diameter minimum spanning trees with permutations and with random keys (2004) Genetic and Evolutionary Computationa Conference 14. Gouveia, L., Magnanti, T.L., Requejo, C., (2004) A 2 path approach for odd diameter constrained minimum spanning and Steiner, , trees 15. Gruber, M., Raild, G.R., A new 0-1 ILP approach for the bounded diameter minimum spanning tree problem (2005) Proceedings of the 2nd International Network Optimization Conference, , 16 16. Gruber, M., Raild, G.R., Variable neighbourhood search for the bounded diameter minimum spanning tree problem (2005) Proceedings of the 18th Mini Euro Conference on Variable Neighborhood Search, , Spain 17. Gruber, M., Jano van Hemert, G.R., (2006) Neighbourhood Searches for the Bounded Diameter Minimum Spanning tree problem embedded in a VNS, EA and ACO, GECCO 18. Rothlauf, F., (2006) Representations for Genetic and Evolutionary Algorithms, , Springer-Verlag Berlin Heidelberg
