• Journal of the Korean Operations Research and Management Science Society
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• v.28 no.2
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• pp.129-138
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• 2003

The traveling salesman problem (TSP) is an NP-hard problem. As the number of nodes increases, it takes a lot of time to find an optimal solution. Instead of considering all arcs, if we select and consider only some arcs more likely to be included in an optimal solution, we can find efficiently an optimal solution. Arc candidate set is a group of some good arcs. For the Lack of study in the asymmetric TSP. it needs to research arc candidate set for the asymmetric TSP systematically. In this paper, we suggest a regression function determining arc candidate set for the asymmetric TSP. We established the function based on 2100 experiments, and we proved the goodness of fit for the model through various 787problems. The result showed that the optimal solutions obtained from our arc candidate set are equal to the ones of original problems. We expect that this function would be very useful to reduce the complexity of TSP.

• Journal of the Korean Operations Research and Management Science Society
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• v.33 no.2
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• pp.17-26
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• 2008

The traveling salesman problem is to find tours through all cities at minimum cost ; simply visiting the cities only once that a salesman wants to visit. As such, the traveling salesman problem is a NP-complete problem ; an heuristic algorithm is preferred to an exact algorithm. In this paper, we suggest an effective cost relaxation using a candidate arc set which is obtained from a regression function for the traveling salesman problem. The proposed method sufficiently consider the characteristics of cost of arcs compared to existing methods that randomly choose the arcs for relaxation. For test beds, we used 31 instances over 100 cities existing from TSPLIB and randomly generated 100 instances from well-known instance generators. For almost every instances, the proposed method has found efficiently better solutions than the existing method.

• Journal of the Korean Operations Research and Management Science Society
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• v.25 no.2
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• pp.115-124
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• 2000

The most vital arc in the maximum flow problem is that arc whose removal results in the greatest reduction in the value of the maximal flow between a source node and a sink node. This paper develops an algorithm to determine such a most vital arc in the maximum flow problem. We first define the transformed network corresponding to a given network in order to compute the minimal capacity for each candidate arc. The set of candidate arcs for single most vital arc consists of the arcs whose flow is at least as great as the flow over every arc in a minimal cut. As a result we present a method in which the most vital arc is determined more easily by computing the minimal capacity in the transformed network. the proposed method is demonstrated by numerical example and computational experiment.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.19 no.40
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• pp.263-269
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• 1996

The most vital arc in the maximum flow problem is that arc whose removal results in the greatest reduction in the value of the maximal flow between a source node and a sink node. This paper develops an algorithm to determine such a most vital arc(MVA) in the maximum flow problem. We first define the transformed network corresponding In a given network in order to compute the minimal capacity for each candidate arc. The set of candidate arcs for a MVA consists of the arcs whose flow is at least as greate as the flow over every arc in a minimal cut As a result, we present a method in which the MVA is determined more easily by computing the minimal capacity in the transformed network. The proposed method is demonstrated by numerical example.