• 한국국방경영분석학회지
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• 제26권2호
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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.

• 한국경영과학회지
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• 제26권3호
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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.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 2000년도 추계학술대회 및 정기총회
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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.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 2006년도 추계학술대회
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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.

• 한국국방경영분석학회지
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• 제25권2호
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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.

• 경영과학
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• 제15권2호
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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.

• 한국경영과학회지
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• 제23권4호
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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.

• 경영과학
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• 제25권2호
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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.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.1-23
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• 2005

The shortest-paths problem is a fundamental problem in graph theory and finds diverse applications in various fields. This is why shortest path algorithms have been designed more thoroughly than any other algorithm in graph theory. A large number of optimization problems are mathematically equivalent to the problem of finding shortest paths in a graph. The shortest-path between a pair of vertices is defined as the path with shortest length between the pair of vertices. The shortest path from one vertex to another often gives the best way to route a message between the vertices. This paper presents an $O(n^2)$ time sequential algorithm and an $O(n^2/p+logn)$ time parallel algorithm on EREW PRAM model for solving all pairs shortest paths problem on circular-arc graphs, where p and n represent respectively the number of processors and the number of vertices of the circular-arc graph.

• 정보처리학회논문지A
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• 제8A권2호
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• pp.179-188
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• 2001

We analyze the property of candidate node set in the network graph, and propose an algorithm to decrease shortest path-finding computation time by using multiple dynamic-range queue(MDRQ) structure. This MDRQ structure is newly created for effective management of the candidate node set. The MDRQ algorithm is the shortest path-finding algorithm that varies range and size of queue to be used in managing candidate node set, in considering the properties that distribution of candidate node set is constant and size of candidate node set rapidly change. This algorithm belongs to label-correcting algorithm class. Nevertheless, because re-entering of candidate node can be decreased, the shortest path-finding computation time is noticeably decreased. Through the experiment, the MDRQ algorithm is same or superior to the other label-correcting algorithms in the graph which re-entering of candidate node didn’t frequently happened. Moreover the MDRQ algorithm is superior to the other label-correcting algorithms and is about 20 percent superior to the other label-setting algorithms in the graph which re-entering of candidate node frequently happened.