• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.765-778
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• 2017

Finding an initial feasible solution on the central path is the main difficulty of feasible interior-point methods. Although, some algorithms have been suggested to remedy this difficulty, many practical implementations often do not use perfectly centered starting points. Therefore, it is worth to analyze the case that the starting point is not exactly on the central path. In this paper, we propose a weighted-path following interior-point algorithm for solving the Cartesian $P_{\ast}({\kappa})$-linear complementarity problems (LCPs) over symmetric cones. The convergence analysis of the algorithm is shown and it is proved that the algorithm terminates after at most $O\((1+4{\kappa}){\sqrt{r}}{\log}{\frac{x^0{\diamond}s^0}{\varepsilon}}\)$ iterations.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2007.10a
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• pp.565-569
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• 2007

To find optimal path is killer application in the telematics system. The shortest path of conventional system, however, isn't always optimal path. That is, the path with minimum travelling time could be defined as optimal path in the road networks. There are techniques and algorithms for finding optimal path. Hierarchical path algorithm categorizes road networks into major layer and minor layer so that the performance of operational time increases. The path searched is accurate as much as optimal path. At above 2 system, a method to allocate minor roads to major road region influences the performance extremely. This paper proposes methods to determine search space for selecting major roads in the hierarchical path algorithm. In addition, methods which apply the proposed methods to hierarchical route algorithm is presented.

• Management Science and Financial Engineering
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• v.12 no.2
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• pp.87-110
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• 2006

In a hierarchical road network, all roads can be classified according to their attributes such as speed limit, number of lanes, etc. By splitting the whole road network into the subnetworks of the highlevel and low-level roads, we can reduce the size of the network to be calculated at once, and find a path in the way that drivers usually adopt when searching out a travel route. To exploit the hierarchical property of road networks, we define a convenient path and propose an algorithm for finding convenient paths. We introduce a parameter indicating the driver's tolerance to the difference between the length of a convenient path and that of a shortest convenient path. From this parameter, we can determine how far we have to search for the entering and exiting gateway. We also propose some techniques for reducing the number of pairs of entries and exits to be searched in a road network. A result of the computational experiment on a real road network is given to show the efficiency of the proposed algorithm.

• Proceedings of the KIEE Conference
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• 2000.07d
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• pp.2732-2734
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• 2000

This paper proposes a path planning algorithm for mobile robots. To generate a minimum-distance path for mobile robots, we use the Genetic Algorithm(GA) and Visibility Graph. After finding a minimum-distance path between a start and a goal point, the path is revised to find the smooth subminimum-distance path by a path-smoothing algorithm. Simulation results show that the proposed algorithms are effective.

• Journal of Korea Game Society
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• v.13 no.1
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• pp.31-40
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• 2013

A* algorithm is a well known pathfinding algorithm. However, there may be a limit to use A* algorithm in real-time in a map where many interactions occur between objects or many obstacles exist. Therefore, it may be necessary to find a naturally looking path quickly instead of finding a shortest path in games. In this paper, we propose a new heuristic function to exploit path information in a map. We also show that the pathfinding algorithm based on the proposed heuristic function can find a good path much faster than A* algorithm on several grid maps.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2008.08a
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• pp.87-90
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• 2008

Dynamic Heuristic(DH) is not fixed data and is dynamically modified using transferred real time road data from server In this paper, we propose path-finding algorithm with Maximum Speed Dynamic Heuristic (DH-MAX) and do an experiment. The DH-MAX is to be used the highest speed as DH, in real map divided by same sire. And proposed algorithm searches path using the priority searching only of the fixed data, but also the highest speed with real time information. In the performance test, the quality of path is enhanced but the cost of searching is increased than $A^*$ algorithm.

• Management Science and Financial Engineering
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• v.10 no.1
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• pp.53-75
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• 2004

Most existing studies on time-dependent networks have been focused on finding a minimum delay path given a departure time at the origin. There, however, frequently happens a situation where users can select any departure time in a certain time interval and want to spend as little time as possible on traveling the networks. In that case. the delay spent on traveling networks depends on not only paths but also the actual departure time at the origin. In this paper, we propose a new problem in time-dependent networks whose objective is to find an optimal departure time given possible departure time interval at the origin. From the optimal departure time, we can obtain a path with minimum delay among all paths for possible departure times at the origin. In addition, we present an algorithm for finding an optimal departure time by enumerating trees which remain shortest path tree for a certain time interval.

• The Journal of Korea Robotics Society
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• v.13 no.2
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• pp.142-149
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• 2018

$RRT^*$ (Rapidly exploring Random $Tree^*$) based algorithms are widely used for path planning. Informed $RRT^*$ uses $RRT^*$ for generating an initial path and optimizes the path by limiting sampling regions to the area around the initial path. $RRT^*$ algorithms have several limitations such as slow convergence speed, large memory requirements, and difficulties in finding paths when narrow aisles or doors exist. In this paper, we propose an algorithm to deal with these problems. The proposed algorithm applies the image skeletonization to the gridmap image for generating an initial path. Because this initial path is close to the optimal cost path even in the complex environments, the cost can converge to the optimum more quickly in the proposed algorithm than in the conventional Informed $RRT^*$. Also, we can reduce the number of nodes and memory requirement. The performance of the proposed algorithm is verified by comparison with the conventional Informed $RRT^*$ and Informed $RRT^*$ using initial path generated by $A^*$.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2008.10a
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• pp.147-150
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• 2008

The real road network is regarded as a grid, and the grid is divided by fixed-sized cells. The path-finding is composed of two step searching. First searching travels on the abstract graph which is composed of a set of psuedo vertexes and a set of psuedo edges that are created by real road network and fixed-sized cells. The result of the first searching is a psuedo path which is composed of a set of selected psuedo edges. The cells intersected with the psuedo path are called as valid cells. The second searching travels with $A^*$ algorithm on valid cells. As pruning search space by removing the invalid cells, it would be possible to reduce the cost of exploring on real road network. In this paper, we present the method of creating the abstract graph and propose a path-finding algorithm on the abstract graph for extracting search space before traveling on real road network.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.34 no.3
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• pp.90-96
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• 2011

Finding the critical path (or the longest path) on acyclic directed graphs, which is well-known as PERT/CPM, the ambiguity of each acr's length can be modeled as a range or an interval, in which the actual length of arc may realize. In this case, the min-max regret criterion, which is widely used in the decision making under uncertainty, can be applied to find the critical path minimizing the maximum regret in the worst case. Since the min-max regret critical path problem with the interval arc's lengths is known as NP-hard, this paper proposes a heuristic algorithm to diminish the maximum regret. Then the computational experiments shows the proposed algorithm contributes to the improvement of solution compared with the existing heuristic algorithms.