• Proceedings of the Korean Institute of IIIuminating and Electrical Installation Engineers Conference
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• 2007.05a
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• pp.183-186
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• 2007

Faster, safer and cheaper mailing of the postal matter is essential for surviving in the competitive market of home-delivery service. The Steiner tree connects points minimally in geometrical way and has been used in the distribution system optimization and optimal routing of the transmission lines of the electric power system. This paper proposes a method to select the optimal location of mail distribution center that minimally connect the local mail center of some major cities using the Steiner tree theorem.

• Journal of the Institute of Convergence Signal Processing
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• v.3 no.2
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• pp.89-95
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• 2002

Global routing is to assign each net to routing regions to accomplish the required interconnections. The most popular algorithms for global routing inlcude maze routing algorithm, line-probe algorithm, shortest path based algorithm, and Steiner tree based algorithm. In this paper we propose weighted network heuristic(WNH) as a minimal Steiner tree search method in a routing graph and a genetic algorithm based on WNH for the global routing. We compare the genetic algorithm(GA) with simulated annealing(SA) by analyzing the results of each implementation.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.22 no.9
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• pp.82-87
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• 2008

Faster, safer and cheaper mailing of the postal matter is essential for surviving in the competitive market of home-delivery service. In the past, the domestic delivery business has been nu by only a few number of companies. But more and more number of companies including medium size ones are participating in the business, and the competition is getting severe. This paper proposes a method to select the optimal location of mail distribution centers that minimally connect the local mail centers of some major cities in Korea using the Steiner Tree theory, which is about connecting a finite number of points with a minimal length of paths and has been used in the distribution system optimization and optimal routing of the transmission lines of the electric power system. By using Steiner Tree theory in finding the best location of the postal delivery hub, we may expect the reduction of transportation cost and the increase of profit, resulting in acquiring the superior position in the competitive delivery business. It is expected that we may use the Steiner Tree theory in finding the best location of the electric power substation for the nott higher EHV(extreme high voltage) transmission network.

• Journal of Information Processing Systems
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• v.13 no.1
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• pp.104-113
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• 2017

In this paper, we present an approach to transmit data from the source to the destination through a minimal path (least-cost path) in a computer network of n nodes. The motivation behind our approach is to address the problem of finding a minimal path between the source and destination. From the work we have studied, we found that a Steiner tree with bounded Steiner vertices offers a good solution. A novel algorithm to construct a Steiner tree with vertices and bounded Steiner vertices is proposed in this paper. The algorithm finds a path from each source to each destination at a minimum cost and minimum number of Steiner vertices. We propose both the sequential and parallel versions. We also conducted a comparative study of sequential and parallel versions based on time complexity, which proved that parallel implementation is more efficient than sequential.

• Korean Management Science Review
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• v.23 no.1
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• pp.75-85
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• 2006

The rectilinear Steiner tree problem (RSTP) is to find a minimum-length rectilinear interconnection of a set of terminals in the plane. It is well known that the solution to this problem will be the minimal spanning tree(MST) on some set Steiner points. The RSTP is known to be NP-complete. The RSTP has received a lot of attention in the literature and heuristic and optimal algorithms have been proposed. A key performance measure of the algorithm for the RSTP is the reduction rate that is achieved by the difference between the objective value of the RSTP and that of the MST without Steiner points. A hybrid evolutionary strategy on RSTP based upon nodes set is presented. The computational results show that the hybrid evolutionary strategy is better than the previously proposed other heuristic. The average reduction rate of solutions from the evolutionary strategy is about 11.14%, which is almost similar to that of optimal solutions.

• The Transactions of the Korea Information Processing Society
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• v.5 no.3
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• pp.671-680
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• 1998

Network services, such as teleconferencing, remote diagnostics and education, and CSCW require multicasting. Multicast routing methods can be divided into two categories. One is the shortest path tree method and the other is the minimal Steiner tree method. The latter has an advantage over the former in that only one Steiner tree is needed for a group. However, finding a minimal Steiner tree is an NP-complete problem and it is necessary to find an efficient heuristic algorithm. In this paper, we present an evolutionary optimization method for finding minimal Steiner trees without sacrificing too much computational efforts. In particular, we describe a tree-based genetic encoding scheme which is in sharp constast with binary string representations usually adopted in convetional genetic algorithms. Experiments have been performed to show that the presented method can find optimal Steiner trees for given vetwork configurations. Comparitivie studies have shown that the evolutionary method finds on average a better solution than other conventional heustric algorithms.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2006.11a
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• pp.589-598
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• 2006

The rectilinear Steiner tree problem is to find a minimum-length rectilinear interconnection of a set of terminals in the plane. It is well known that the solution to this problem will be the minimal spanning tree (MST) on some set Steiner points. A hybrid evolutionary algorithm is introduced based upon the Prim algorithm. The Prim algorithm for the fitness evaluation requires heavy calculation time. The fitness value of parents is inherited to their child and the fitness value of child is estimated by the inherited structure of tree. We introduce four alternative evolutionary algorithms, Experiment result shows that the calculation time is reduced to 25% without loosing the solution quality by using the fitness estimation.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2005.10a
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• pp.27-37
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• 2005

The rectilinear Steiner tree problem (RSTP) is to find a minimum-length rectilinear interconnection of a set of terminals in the plane. It is well known that the solution to this problem will be the minimal spanning tree (MST) on some set Steiner points. The RSTP is known to be NP-complete. The RSTP has received a lot of attention in the literature and heuristic and optimal algorithms have been proposed, A key performance measure of the algorithm for the RSTP is the reduction rate that is achieved by the difference between the objective value of the RSTP and that of the MST without Steiner points. A hybrid evolution strategy on RSTP based upon the Prim algorithm was presented. The computational results show that the evolution strategy is better than the previously proposed other heuristic. The average reduction rate of solutions from the evolution strategy is about 11%, which is almost similar to that of optimal solutions.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2003.05a
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• pp.1056-1064
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• 2003

The Euclidean steiner tree problem (ESTP) is to find a minimum-length euclidean interconnection of a set of points in the plane. It is well known that the solution to this problem will be the minimal spanning tree (MST) on some set steiner points, and the ESTP is NP-complete. The ESTP has received a lot of attention in the literature, and heuristic and optimal algorithms have been proposed. In real field, heuristic algorithms for ESTP are popular. A key performance measure of the algorithm for the ESTP is the reduction rate that is achieved by the difference between the objective value of the ESTP and that of the MST without steiner points. In recent survey for ESTP, the best heuristic algorithm showed around $3.14\%$ reduction in the performance measure. We present a evolution programming (EP) for ESTP based upon the Prim algorithm for the MST problem. The computational results show that the EP can generate better results than already known heuristic algorithms.

• Journal of the Korean Operations Research and Management Science Society
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• v.33 no.3
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• pp.17-28
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• 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.