• 한국경영과학회지
• /
• 제33권3호
• /
• pp.17-28
• /
• 2008

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.

• 대한산업공학회지
• /
• 제25권4호
• /
• pp.500-509
• /
• 1999

In this paper, we consider an optimal routing problem when point-to-point and point-to-multipoint connection traffics are offered in an ATM network. We propose a mathematical model for cost-minimizing configuration of a logical network for a given ATM-based BISDN. Our model is essentially identical to the previous one proposed by Kim(Kim, 1996) which finds a virtual-path configuration where the relevant gains obtainable from the ATM technology such as the statistical multiplexing gain and the switching/control cost-saving gain are optimally traded-off. Unlike the Kim's model, however, ours explicitly considers the VP's QoS(Quality of Service) for more efficient utilization of bandwidth. The problem is a large-scale, nonlinear, and mixed-integer problem. The proposed algorithm is based on the local linearization of equivalent-capacity functions and the relaxation of link capacity constraints. As a result, the problem can be decomposed into moderate-sized shortest path problems, Steiner arborescence problems, and LPs. This fact renders our algorithm a lot faster than the previous nonlinear programming algorithm while the solution quality is maintained, hence application to large-scale network problems.