• Journal of the Korean Operations Research and Management Science Society
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• v.26 no.3
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• pp.79-94
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• 2001

This paper presents a new algorithm for the K shortest paths Problem which develops initial K shortest paths, and repeat to expose hidden shortest paths with dual approach and to replace the longest path in the present K paths. The initial solution comprises K shortest paths among shortest paths to traverse each arc in a Double Shortest Arborescence which is made from bidirectional Dijkstra algorithm. When a crossing node that have two or more inward arcs is found at least three time by turns in this K shortest paths, there may be some hidden paths which are shorter than present k-th path. To expose a hidden shortest path, one inward arc of this crossing node is chose by means of minimum detouring distance calculated with dual variables, and then the hidden shortest path is exposed with joining a detouring subpath from source to this inward arc and a spur of a feasible path from this crossing node to sink. If this exposed path is shorter than the k-th path, the exposed path replaces the k-th path. This algorithm requires worst case time complexity of O(Kn$^2$), and O(n$^2$) in the case k$\leq$3.

• 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.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2006.11a
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• pp.60-66
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• 2006

This paper presents a new algorithm for the K shortest path problem in a directed network. After a shortest path is produced with Dijkstra algorithm, detouring paths through inward arcs to every vertex of the shortest path are generated. A length of a detouring path is the sum of both the length of the inward arc and the difference between the shortest distance from the origin to the head vertex and that to the tail vertex. K-1 shorter paths are selected among the detouring paths and put into the set of K paths. Then detouring paths through inward arcs to every vertex of the second shortest path are generated. If there is a shorter path than the current Kth path in the set, this path is placed in the set and the Kth path is removed from the set, and the paths in the set is rearranged in the ascending order of lengths. This procedure of generating the detouring paths and rearranging the set is repeated for the K-1 st path of the set. This algorithm can be applied to a problem of generating the detouring paths in the navigation system for ITS and also for vehicle routing problems.

• Journal of the military operations research society of Korea
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• v.17 no.2
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• pp.72-89
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• 1991

In transportation network problems, it is often desirable to select multiple number of the shortect paths. On problems of finding these paths, algorithms have been developed to choose single shortest path, k-shortest paths and k-shortest paths via p-specified nodes in a network. These problems consider the time as the main factor. In wartime, we must consider availability as well as time to determine the shortest transportation path, since we must take into account enemy's threat. Therefore, this paper addresses the problem of finding the shortest transportation path considering both time and availability. To accomplish the objective of this study, values of k-shortest paths are computed using the algorithm for finding the k-shortest paths. Then availabilties of those paths are computed through simulation considering factors such as rates of suffering attack, damage and repair rates of the paths. An optimal path is selected using any one of the four decision rules that combine the value and availability of a path.

• Journal of Korea Multimedia Society
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• v.20 no.4
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• pp.649-659
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• 2017

Typically, a smart car is equipped with access to the Internet and a wireless local area network. Moreover, a smart car is equipped with a global positioning system (GPS) based navigation system that presents a map to a user for recommending the shortest path to a desired destination. This paper presents the design and implementation of a real-time shortest path search system for directed and dynamic roads. Herein, we attempt to simulate real-world road environments, while considering changes in the ratio of directed roads and in road conditions, such as traffic accidents and congestions. Further, we analyze the effect of the ratio of directed roads and road conditions on the communication cost between the server and vehicles and the arrival times of vehicles. In this study, we compare and analyze distance-based shortest path algorithms and driving time-based shortest path algorithms while varying the number of vehicles to search for the shortest path, road conditions, and ratio of directed roads.

• Journal of the military operations research society of Korea
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• v.25 no.2
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• pp.73-83
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• 1999

In this paper, we consider the shortest path network problem with fixed charges. A turn penalty algorithm for the shortest path problem with fixed charges or turn penalties is presented, which is using the next node comparison method. The algorithm described here is designed to determine the shortest route in the shortest path network problem including turn penalties. Additionally, the way to simplify the computation for the shortest path problem with turn penalties was pursued.

• Korean Management Science Review
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• v.25 no.2
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• pp.81-88
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• 2008

This paper presents a new algorithm for the K shortest paths problem in a network. After a shortest path is produced with Dijkstra algorithm. detouring paths through inward arcs to every vertex of the shortest path are generated. A length of a detouring path is the sum of both the length of the inward arc and the difference between the shortest distance from the origin to the head vertex and that to the tail vertex. K-1 shorter paths are selected among the detouring paths and put into the set of K paths. Then detouring paths through inward arcs to every vertex of the second shortest path are generated. If there is a shorter path than the current Kth path in the set. this path is placed in the set and the Kth path is removed from the set, and the paths in the set is rearranged in the ascending order of lengths. This procedure of generating the detouring paths and rearranging the set is repeated until the $K^{th}-1$ path of the set is obtained. The computational results for networks with about 1,000,000 nodes and 2,700,000 arcs show that this algorithm can be applied to a problem of generating the detouring paths in the metropolitan traffic networks.

• Korean Management Science Review
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• v.15 no.2
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• pp.229-237
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• 1998

This paper presents a new algorithm for the K Shortest Paths Problem which is developed with a Double Shortest Arborescence and an inward arc breaking method. A Double Shortest Arborescence is made from merging a forward shortest arborescence and a backward one with Dijkstra algorithm. and shows us information about each shorter path to traverse each arc. Then K shorter paths are selected in ascending order of the length of each short path to traverse each arc, and some paths of the K shorter paths need to be replaced with some hidden shorter paths in order to get the optimal paths. And if the cross nodes which have more than 2 inward arcs are found at least three times in K shorter path, the first inward arc of the shorter than the Kth shorter path, the exposed path replaces the Kth shorter path. This procedure is repeated until cross nodes are not found in K shorter paths, and then the K shortest paths problem is solved exactly. This algorithm are computed with complexity o($n^3$) and especially O($n^2$) in the case K=3.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2000.10a
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• pp.113-116
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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. 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-MVA in shortest path problem using an evolutionary algorithm which known as the most efficient algorithm among heuristics. For this, the expression method of individuals compatible with the characteristics of shortest path problem, the parameter values of constitution gene, size of the initial population, crossover rate and mutation rate etc. are specified and then the effective genetic algorithm will be proposed. The method presented in this study is developed using the library of the evolutionary algorithm framework (EAF) and then the performance of algorithm is analyzed through the computer experiment.

• Proceedings of the KSRS Conference
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• 2005.10a
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• pp.759-762
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• 2005

Recently, Intelligent Transportation System(ITS) has been applied to satisfy increasing traffic demand every year and to solve many traffic problems. Especially, Advanced Traveller Information System(ATIS) is a transportation system to optimize the trip of each other vehicle. It is important to provide the driver with quick and comfortable path from source to destination. However, it is difficult to provide a shortest path in a road network with dynamic cost. Because the existing research has a static cost. Therefore, in this paper we propose an operator for searching traffic dependent shortest path. The proposed operator finds the shortest path from source to destination using a current time cost and a difference cost of past time cost. Such a method can be applied to the road status with time. Also, we can expect a predicted arrival time as well as the shortest path from source to destination. It can be applied to efficiently application service as ITS and have the advantages of using the road efficiently, reducing the distribution cost, preparing an emergency quickly, reducing the trip time, and reducing an environmental pollution owing to the saving the fuel.