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An Ant Colony Optimization Algorithm to Solve Steiner Tree Problem  

Seo, Min-Seok (펜실바니아 주립대학교 산업공학과)
Kim, Dae-Cheol (한양대학교 경영학부)
Publication Information
Journal of the Korean Operations Research and Management Science Society / v.33, no.3, 2008 , pp. 17-28 More about this Journal
Abstract
The Steiner arborescence problem is known to be NP-hard. The objective of this problem is to find a minimal Steiner tree which starts from a designated node and spans all given terminal nodes. This paper proposes a method based on a two-step procedure to solve this problem efficiently. In the first step, graph reduction rules eliminate useless nodes and arcs which do not contribute to make an optimal solution. In the second step. ant colony algorithm with use of Prim's algorithm is used to solve the Steiner arborescence problem in the reduced graph. The proposed method based on a two-step procedure is tested in the five test problems. The results show that this method finds the optimal solutions to the tested problems within 50 seconds. The algorithm can be applied to undirected Steiner tree problems with minor changes. 18 problems taken from Beasley are used to compare the performances of the proposed algorithm and Singh et al.'s algorithm. The results show that the proposed algorithm generates better solutions than the algorithm compared.
Keywords
Steiner Arborescence Problem; Ant Colony Optimization; Directed Graph;
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