• Journal of the Korean Operations Research and Management Science Society
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• v.28 no.2
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• pp.129-138
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• 2003

The traveling salesman problem (TSP) is an NP-hard problem. As the number of nodes increases, it takes a lot of time to find an optimal solution. Instead of considering all arcs, if we select and consider only some arcs more likely to be included in an optimal solution, we can find efficiently an optimal solution. Arc candidate set is a group of some good arcs. For the Lack of study in the asymmetric TSP. it needs to research arc candidate set for the asymmetric TSP systematically. In this paper, we suggest a regression function determining arc candidate set for the asymmetric TSP. We established the function based on 2100 experiments, and we proved the goodness of fit for the model through various 787problems. The result showed that the optimal solutions obtained from our arc candidate set are equal to the ones of original problems. We expect that this function would be very useful to reduce the complexity of TSP.

• Journal of Korean Institute of Industrial Engineers
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• v.16 no.1
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• pp.17-25
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• 1990

Most of the least cost transportation network design problems are frequently formulated as the minimum spanning arborescence problems in directed networks with bitype are costs. These costs are classified whether the arc is included in the path from the root to a specified node over a given spanning arborescence. We prove that this problem is NP-hard, and develop a polynomial time algorithm for acyclic networks. The probelm in acyclic networks is initially formulated as 0-1 integer programming. Next, we prove that the 0-1 relaxed linear programming has an integral optimum solution by complementary slackness conditions. In this paper, we present an $O(n^2)$ algorithm based on a shortest path algorithm.

• Journal of Korean Institute of Industrial Engineers
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• v.33 no.3
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• pp.303-311
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• 2007

This study deals with a type of vehicle routing problem faced by manager of some department stores during peak sales periods. The problem is to find a set of traveling paths of vehicles that leave a department store and arrive at a destination specified for each vehicle after visiting customers without violating time and capacity constraints. The mathematical model is formulated with the objective of maximizing the sum of the rewards collected by each vehicle. Since the problem is known to be NP-hard, a heuristic algorithm is developed to find the solution. The performance of the algorithm is compared with the optimum solutions obtained from CPLEX for small size problems and a priority-based Genetic Algorithm for large size problems.

• Proceedings of the Korean Information Science Society Conference
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• 2004.10a
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• pp.697-699
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• 2004

Despite many successful spectral clustering algorithm (based on the spectral decomposition of Laplacian(1) or stochastic matrix(2) ) there are several unsolved problems. Most spectral clustering Problems are based on the normalized of algorithm(3) . are close to the classical graph paritioning problem which is NP-hard problem. To get good solution in polynomial time. it needs to establish its convex form by using relaxation. In this paper, we apply a novel optimization technique. semidefinite programming(SDP). to the unsupervised clustering Problem. and present a new multiple Partitioning method. Experimental results confirm that the Proposed method improves the clustering performance. especially in the Problem of being mixed with non-compact clusters compared to the previous multiple spectral clustering methods.

• Journal of information and communication convergence engineering
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• v.17 no.4
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• pp.246-254
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• 2019

This paper proposes a solution to the problem of finding a subgraph for a given instance of many terminals on a Euclidean plane. The subgraph is a tree, whose nodes represent the chosen terminals from the problem instance, and whose edges are line segments that connect two corresponding terminals. The tree is required to have the maximum number of nodes while the length is limited and is not sufficient to interconnect all the given terminals. The problem is shown to be NP-hard, and therefore a genetic algorithm is designed as an efficient practical approach. The method is suitable to various probable applications in layout optimization in areas such as communication network construction, industrial construction, and a variety of machine and electronics design problems. The proposed heuristic can be used as a general-purpose practical solver to reduce industrial costs by determining feasible interconnections among many types of components over different types of physical planes.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.19 no.5
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• pp.73-78
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• 2019

This paper proposes polynomial-time rule for maximum weighted independent set(MWIS) problem that is well known NP-hard. The well known distributed algorithm selects the maximum weighted node as a element of independent set in a local. But the merged independent nodes with less weighted nodes have more weights than maximum weighted node are frequently occur. In this case, existing algorithm fails to get the optimal solution. To deal with these problems, this paper constructs maximum weighted independent set in local area. Application result of proposed algorithm to various networks, this algorithm can be get the optimal solution that fail to existing algorithm.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.22 no.5
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• pp.159-164
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• 2022

The linear assignment problem (LAP) and linear bottleneck assignment problem (LBAP) has been unknown the algorithm to solve the optimal solution within polynomial-time. These problems are classified by NP-hard. Therefore, we can be apply metaheuristic methods or linear programming (LP) software package or Hungarian algorithm (HA) with O(m⁴) computational complexity. This paper suggests polynomial time algorithm with O(mn)=O(m²),m=n time complexity to LAP and LBAP. The select-delete method is simply applied to LAP, and the delete-select method is used to LBAP. For the experimental data without the unique algorithm can be apply to whole data, the proposed algorithm can be obtain the optimal solutions for whole data.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.38 no.5
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• pp.427-436
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• 2010

This paper deals with a task assignment problem of multiple UAVs performing multiple tasks on multiple targets. The task assignment problem of multiple UAVs is a kind of combinatorial optimization problems such as traveling salesman problem or vehicle routing problem, and it has NP-hard computational complexity. Therefore, computation time increases as the size of considered problem increases. To solve the problem efficiently, approximation methods or heuristic methods are widely used. In this study, the problem is formulated as a mixed integer linear program, and is solved by a mixed integer linear programming and a genetic algorithm, respectively. Numerical simulations for the environment of the multiple targets, multiple tasks, and obstacles were performed to analyze the optimality and efficiency of each method.

• The Transactions of the Korea Information Processing Society
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• v.4 no.9
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• pp.2235-2246
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• 1997

This paper presents an effective heuristic task scheduling algorithm for multiprocessor systems. To execute task scheduling effectively which is defined as an allocation of m's tasks onto n's processors(m > n), several problems almost at NP-hard should be cleaned up. The purpose of the task scheduling obtains the minimum execution time by mapping the tasks on a system topology or reduces the total execution time to give a minimum system topology. In order to solve this problem, in this paper, the task scheduling is done by redefining a task graph to a reconstructed task graph (RTG). An RTG is obtained by merging or copying nodes to equal the number of nodes on each level of the task graph to the number of processors of the system topology and then directly scheduled to the system topology. This method obtains a fast scheduling time and a simple scheduling method, and near-optimal execution time without executing steps such as the refinement step and the duplication step after the task scheduling.

• The Transactions of the Korea Information Processing Society
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• v.6 no.4
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• pp.959-968
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• 1999

several papers have reported that parallel heuristics or hybrid approaches combining several heuristics can get better results. However, the parallelization and hybridization of any search methods on the single CPU type computer need enormous computation time. that case, we need more elegant combination method. For this purpose, we propose Fast Model of Parallel Heuristics(FMPH). FMPH is based on the island model of parallel genetic algorithms and takes local search to the elite solution obtained form each island(sub group). In this paper we introduce how can we adapt FMPH to the job-shop scheduling problem notorious as the most difficult NP-hard problem and report the excellent results of several famous benchmark problems.