• 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.

• The Journal of The Korea Institute of Intelligent Transport Systems
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• v.18 no.5
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• pp.91-99
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• 2019

Existing node-to-node based optimal path searching is built on the assumption that all destination nodes can be arrived at from an origin node. However, the recent appearance of the adaptive path search algorithm has meant that the optimal path solution cannot be derived in node-to-node path search. In order to reflect transportation data at the links in real-time, the necessity of the node-to-link (or link-to-node; NL) problem is being recognized. This research assumes existence of a network with link-label and non-additive path costs as a solution to the node-to-link optimal path problem. At the intersections in which the link-label has a turn penalty, the network retains its shape. Non-additive path cost requires that M-similar paths be enumerated so that the ideal path can be ascertained. In this, the research proposes direction deletion and turn restriction so that regulation of the loop in the link-label entry-link-based network transformation method will ensure that an optimal solution is derived up until the final link. Using this method on a case study shows that the proposed method derives the optimal solution through learning. The research concludes by bringing to light the necessity of verification in large-scale networks.

• Journal of Korea Society of Industrial Information Systems
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• v.11 no.3
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• pp.20-33
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• 2006

Because of rapid expansion of third party logistics, fierce competition in the transportation industry, and the diversification and globalization of transportation channels, an effective transportation planning by means of multimodal transport is badly needed. Accordingly, this study aims to suggest an optimal transport algorithm for the multimodal transport in the international logistics. As a solution for this problem, first of all, we have applied a pruning algorithm to simplify it, suggesting a heuristic algorithm for constrained shortest path problem to find out a feasible area with an effective time range, which has been applied to the Label Setting Algorithm, consequently leading to multiple Pareto optimal solutions. Also, in order to test the efficiency of the algorithm for constrained shortest path problem, this paper has applied it to the actual transportation path from Busan port of Korea to Rotterdam port of Netherlands.

• Journal of Institute of Control, Robotics and Systems
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• v.6 no.6
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• pp.506-513
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• 2000

This paper proposes a path planning algorithm for dispensers to increase the productivity in printed circuit board assembly lines. We analyze the assembly sequence of the dispenser, and formulate it as an integer programming problem. The mathematical formulation can accomodate multiple heads and different types of heads through extended cost matrix. The TSP algorithms are then applied to the formulated problem to find the near-optimal solution. Simulation results are presented to verify the usefulness of the proposed scheme.

• Journal of the Korean Operations Research and Management Science Society
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• v.16 no.2
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• pp.103-117
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• 1991

Two important sensitivity issues over shortest path problems have been discussed. One is the problem of updating shortest paths when nodes are added and when the lengths of some arcs are increased or decreased. The other is the problem of calculating arc tolerances, that is the maximum increase of decrease in the length of a single arc without changing a given optimal tree. In this paper, assuming that there exists a parameter of interest whose perturbation causes the simultaneous changes in arc lengths, we find the invariance condition on these simultaneous changes such that the shortest path between two specified nodes remains unchanged.

• Journal of the Korea Society of Computer and Information
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• v.26 no.3
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• pp.111-117
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• 2021

The delivery problem on a graph is that of minimizing the object delivery time from one vertex to another vertex on a graph with m vertices using n various speed robot agents. In this paper, we propose two optimal solution algorithms for the delivery problem on a graph with time complexity of O(㎥n) and O(㎥). After preprocessing to obtain the shortest path for all pairs of the graph, our algorithm processed by obtaining the shortest delivery path in the order of the vertices with the least delivery time. Assuming that the graph reflects the terrain on which to solve the problem, our O(㎥) algorithm actually has a time complexity of O(㎡n) as only one preprocessing is required for the various deployment of n robot agents.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.717-730
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• 2002

In this paper we use measure theory to solve a wide range of the nonlinear programming problems. First, we transform a nonlinear programming problem to a classical optimal control problem with no restriction on states and controls. The new problem is modified into one consisting of the minimization of a special linear functional over a set of Radon measures; then we obtain an optimal measure corresponding to functional problem which is then approximated by a finite combination of atomic measures and the problem converted approximately to a finite-dimensional linear programming. Then by the solution of the linear programming problem we obtain the approximate optimal control and then, by the solution of the latter problem we obtain an approximate solution for the original problem. Furthermore, we obtain the path from the initial point to the admissible solution.

• 제어로봇시스템학회:학술대회논문집
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• 1989.10a
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• pp.635-642
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• 1989

We formulated the multi-robot trajectory problem into a series of NLP problem, each of which is that of finding the optimal tip positions of the robots for the next time step. The NLP problem is composed of an objective function and three constraints, namely: a) Joint position limits, b) Joint velocity limits, and c) Collision-avoidance constraints. By solving a series of NLP problem, optimally coordinated trajectories can be determined without requiring any prior path information. This is a novel departure from the previous approach in which either all paths or at least one path is assumed to be given. Practical application of the developed method is for optimal synthesis of multiple robot trajectories in off-line. To test the validity and effectiveness of the method, numerical examples are illustrated.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.8
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• pp.122-129
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• 1997

In this paper, we propose a Hopfield model for solving the part-matching in case that is the number of parts and positions are changed. The goal of this paper is to minimize part-connection in pairs and total path of part-connections. Therefore, this kind of problem is referred to as a combinatiorial optimization problem. First of all, we review the theoretical basis for Hopfield model and present two optimal algorithms of part-matching. The first algorithm is Traveling Salesman Problem(TSP) which improved the original and the second algorithm is Wdighted Matching Problem (WMP). Finally, we show demonstration through com- puter simulation and analyze the stability and feasibility of the generated solutions for the proposed con- nection methods. Therefore, we prove that the second algorithm is better than the first algorithm.

• Journal of the military operations research society of Korea
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• v.23 no.2
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• pp.103-119
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• 1997

This paper considers the shortest path problem combined with Min-Min-Sum objective for solving the problem of the military logistics. This paper develops a polynomial-time algorithm for the optimal solution. To analyze the real combat situation, the ability time and distance time of communication line are considered. The complexities of algorithm between previous study and the algorithm developed in this paper is presented. Finally we provide a simple example of application with randomly generated problem.