• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.12a
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• pp.314-318
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• 2001

Constructing a shortest path on a graph is a fundamental problem in the area of graph theory. In an application where we cannot exactly determine the weights of edges, fuzzy weights can be used instead of crisp weights, and Type-2 fuzzy weights will be more suitable if this uncertainty varies under some conditions. In this paper, shortest path problem in type-1 fuzzy weighted graphs is extended for type-2 fuzzy weighted graphes. A solution is also given based on possibility theory and extension principle.

• Journal of Korean Institute of Industrial Engineers
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• v.16 no.2
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• pp.71-79
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• 1990

In this paper, the Double Shortest Arborescence & Merging method is presented as an efficient heuristic algorithm for the Public Vehicle Routing Problem which is to find the minimum total cost routes of M or less vehicles to traverse the required arcs(demand streets) at least once and return to their starting depot on a directed network. Double Shortest Arborescence which consists of forward shortest aborescence and backward one informs M or less shortest routes to traverse all required arcs. The number of these routes is reduced to M or less by merging routes. The computational experiment based on randomly generated networks reports that this algorithm is efficient.

• Journal of Korean Institute of Industrial Engineers
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• v.23 no.3
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• pp.487-500
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• 1997

In this paper, we introduce the shortest flow-generating path problem in the generalized network. As the simplest generalized network model, this problem captures many of the most salient core ingredients of the generalized network flows and so it provides both a benchmark and a point of departure for studying more complex generalized network models. We show that the generalized label-correcting algorithm for the shortest flow-generating path problem has O(mn) time complexity if it starts with a good point and also propose an O($n^3m^2$) algorithm for finding a good starting point. Hence, the shortest flow-generating path problem is solved in O($n^3m^2$) time.

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.4
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• pp.379-383
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• 2001

The restricted shortest path problem is known to be weakly NP-hard and solvable in pseudo-polynomial time. Four fully polynomial approximation schemes (FPAS) are available in the literature, and most of these are based on pseudo-polynomial algorithms. In this paper, we propose a new FPAS that can be easily derived from a combination of a set of standard techniques. Although the complexity of the suggested algorithm is not as good as the fastest one available in the literature, it is practical in the sense that it does not rely on the bound tightening phase based on approximate binary search as in Hassin's fastest algorithm. In addition, we provide a review of standard techniques of existing works as a useful reference.

• Journal of the Korean Operations Research and Management Science Society
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• v.23 no.4
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• pp.11-20
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• 1998

This paper deals with a mathematical model and an algorithm for the problem of determining k most vital arcs in the shortest path problem. First, we propose a 0-1 integer programming model for finding k most vital arcs in shortest path problem given the ordered set of paths with cardinality q. Next, we also propose an algorithm for finding k most vital arcs ln the shortest path problem which uses the 0-1 Integer programming model and shortest path algorithm and maximum flow algorithms repeatedly Malik et al. proposed a non-polynomial algorithm to solve the problem, but their algorithm was contradicted by Bar-Noy et al. with a counter example to the algorithm in 1995. But using our algorithm. the exact solution can be found differently from the algorithm of Malik et al.

• Journal of the Korean Operations Research and Management Science Society
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• v.26 no.2
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• pp.47-58
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• 2001

The purpose of this study is to present methods for determining the k most vital arcs (k-MVAs) in shortest path problem (SPP) using evolutionary algorithms. The problem of finding the k-MVAs in SPP is to find a set of k arcs whose simultaneous removal from the network causes the greatest increase in the shortest distance between two specified nodes. Generally, the problem of determining the k-MVAs in SPP has been known as NP-hard. Therefore, to deal with problems of the real world, heuristic algorithms are needed. In this study we present three kinds of evolutionary algorithms for finding the k-MVAs in SPP, and then to evaluate the performance of proposed algorithms.

• Journal of the Korea Institute of Military Science and Technology
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• v.1 no.1
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• pp.166-188
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• 1998

본 논문에서는 쿼터니온 궤환 개념이 기존의 오일러각 궤환 개념에 비해 추력벡터제어(Thrust Vector Control) 방식을 사용하는 전술 유도탄 자세제어에 보다 효과적으로 적용될 수 있음을 보인다. 오일러각 궤환 방식을 택한 기존의 자세제어기에서 오일러각 궤환 부분을 쿼터니온 궤환으로 적절히 바꾸어 주게 되면 자세명령 크기 변화에 따른 시간응답 특성의 변화를 줄일 수 있으며, 쿼터니온 궤환 방식을 택할 경우, 우주비행체 자세제어 분야에서 활발히 연구되고 있는 고유축(Eigen Axis) 회전에 의한 자세변환을 수행할 수 있는 자세제어기 설계가 가능하다. 고유축 회전은 최단경로에 의한 자세변환 개념이므로, 이러한 능력을 갖춘 자세제어기는 신속한 자세변환이 필요한 전술 유도탄의 초기비행에 매우 효과적으로 이용될 수 있다. 더욱이, 제어법칙에 공력모멘트를 보상하는 항을 추가하게 되면 변화가 심한 공력 모멘트가 유도탄의 회전운동에 미치는 영향을 줄일 수 있어 고유축 회전성능을 보다 개선시킬 수 있다. 우선, 오일러각 궤환보다 쿼터니온 궤환이 유리한 점을 논하고, 쿼터니온 궤환에 근거한 자세제어기의 설계 개념과 제안된 제어기에 의해 구성되는 폐루우프에 대한 안정성 문제를 다룬 후, 시뮬레이션을 통해 그 타당성을 검증한다.

• Korean Management Science Review
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• v.19 no.1
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• pp.55-66
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• 2002

Given a directed network, a designated arc, and lowers and upper bounds for the distance of each arc, the preprocessing shortest path problem Is a decision problem that decides whether there is some choice of distance vector such that the distance of each arc honors the given lower and upper bound restriction, and such that the designated arc is on some shortest path from a source node to a destination notre with respect to the chosen distance vector. The preprocessing shortest path problem has many real world applications such as communication and transportation network management and the problem is known to be NP-complete. In this paper, we develop an algorithm that solves the problem using the structural properties of shortest paths.

• Journal of the military operations research society of Korea
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• v.26 no.2
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• pp.120-130
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• 2000

The purpose of this study is to present a method for determining the k most vital arcs in shortest path problem using an evolutionary algorithm. The problem of finding the k most vital arcs in shortest path problem is to find a set of k arcs whose simultaneous removal from the network causes the greatest increase in the total length of shortest path. Generally, the problem determining the k most vital arcs in shortest path problem has known as NP-hard. Therefore, in order to deal with the problem of real world the heuristic algorithm is needed. In this study we propose to the method of finding the k most vital arcs in shortest path problem using an evolutionary algorithm which known as the most efficient algorithm among heuristics. The method presented in this study is developed using the library of the evolutionary algorithm framework and then the performance of algorithm is analyzed through the computer experiment.

• Journal of the military operations research society of Korea
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• v.25 no.1
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• pp.29-36
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• 1999

In this paper, we are concerned with the K-shortest loopless path problem. The MPS algorithm, recently proposed by Martins et al., finds paths efficiently because it solves the shortest path problem only one time unlike other algorithms. But its computational complexity has not been known yet. We propose a few techniques by which the MPS algorithm can be implemented efficiently. First, we use min-heap data structure for the storage of candidate paths in order to reduce searching time for finding minimum distance path. Second, we prevent the eliminated paths from reentering in the list of candidate paths by lower bounding technique. Finally, we choose the source mode as a deviation node, by which selection time for the deviation node is reduced and the performance is improved in spite of the increase of the total number of candidate paths.