• Title/Summary/Keyword: NP-Hard Problem

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A Study on the Optimization of Stowage Planning for Container Terminal Considered by Hatch (Hatch를 고려한 컨테이너 터미널 적재순서 최적화 연구)

  • Lee, Sang-Heon;Kim, Moon-Gyu;Ahn, Tae-Ho
    • IE interfaces
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    • v.19 no.4
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    • pp.270-280
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    • 2006
  • The shipping plan for an efficient augmentation of terminal is NP-hard problem which is subordinate to a shipping quantity. The load location problem and stowage planning problem are two important tactical problems for the efficient operations of container terminals. This paper is concerned with reduction of feasible region in constraints for stowage planning. After designing model which minimizes the number of shifting and the travel distance of the transfer crane, the simulated annealing algorithm is employed to search optimal solution quickly and accurately. In order to apply more realistic approach, the partial restriction through adding hatch is complemented to stowage planning decision problem applied in cluster. A variety of numerical experiments demonstrated that solutions by simulated annealing algorithm are useful and applicable in practice.

An Algorithm for the Edge Coloring Problem (호의 색칠문제의 해법)

  • Park, Sung-Soo
    • Journal of Korean Institute of Industrial Engineers
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    • v.18 no.2
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    • pp.43-49
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    • 1992
  • Edge coloring problem is to find a minimum cardinality coloring of the edges of a graph so that any pair of edges incident to a common node do not have the same colors. Edge coloring problem is NP-hard, hence it is unlikely that there exists a polynomial time algorithm. We formulate the problem as a covering of the edges by matchings and find valid inequalities for the convex hull of feasible solutions. We show that adding the valid inequalities to the linear programming relaxation is enough to determine the minimum coloring number(chromatic index). We also propose a method to use the valid inequalities as cutting planes and do the branch and bound search implicitly. An example is given to show how the method works.

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Approximation Algorithms for Scheduling Parallel Jobs with More Machines

  • Kim, Jae-Hoon
    • Journal of information and communication convergence engineering
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    • v.9 no.4
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    • pp.471-474
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    • 2011
  • In parallel job scheduling, each job can be executed simultaneously on multiple machines at a time. Thus in the input instance, a job $J_i$ requires the number $m_i$ of machines on which it shall be processed. The algorithm should determine not only the execution order of jobs but also the machines on which the jobs are executed. In this paper, when the jobs have deadlines, the problem is to maximize the total work of jobs which is completed by their deadlines. The problem is known to be strongly NP-hard [5] and we investigate the approximation algorithms for the problem. We consider a model in which the algorithm can have more machines than the adversary. With this advantage, the problem is how good solution the algorithm can produce against the optimal algorithm.

K-Way Graph Partitioning: A Semidefinite Programming Approach (Semidefinite Programming을 통한 그래프의 동시 분할법)

  • Jaehwan, Kim;Seungjin, Choi;Sung-Yang, Bang
    • 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.

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A Genetic Algorithm Approach to the Frequency Assignment Problem on VHF Network of SPIDER System

  • Kwon, O-Jeong
    • Journal of the military operations research society of Korea
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    • v.26 no.1
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    • pp.56-69
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    • 2000
  • A frequency assignment problem on time division duplex system is considered. Republic of Korea Army (ROKA) has been establishing an infrastructure of tactical communication (SPIDER) system for next generation and it will be a core network structure of system. VHF system is the backbone network of SPIDER, that performs transmission of data such as voice, text and images. So, it is a significant problem finding the frequency assignment with no interference under very restricted resource environment. With a given arbitrary configuration of communications network, we find a feasible solution that guarantees communication without interference between sites and relay stations. We formulate a frequency assignment problem as an Integer Programming model, which has NP-hard complexity. To find the assignment results within a reasonable time, we take a genetic algorithm approach which represents the solution structure with available frequency order, and develop a genetic operation strategies. Computational result shows that the network configuration of SPIDER can be solved efficiently within a very short time.

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A Study of Solving the Generalized Vehicle Routing Problem Using Reinforcement Learning (강화학습 기반의 차량 경로 문제 일반화 방안 연구)

  • Jung, Chul-Hwan;Kim, Kwang-Su;Kim, Han-Sol
    • Proceedings of the Korean Society of Computer Information Conference
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    • 2022.07a
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    • pp.705-707
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    • 2022
  • 본 연구에서는 기존 차량 경로 문제(Vehicle Routing Problem)의 범위를 확장시켜 일반화된 차량 경로문제(Generalized Vehicle Routing Problem)를 제시하고, 이 문제를 해결하기 위한 강화학습 모델을 제안한다. 기존의 차량 경로 문제는 depot에서 각 node(또는 각 node에서 depot)의 단방향만 존재해 제한된 문제만을 해결할 수 있었다. 이 한계점을 극복하기 위해 depot을 제외한 모든 node가 서로 연결된 형태의 일반화된 차량 경로 문제를 정의하고 이를 해결하고자 한다. 차량 경로 문제는 NP-hard 문제로 최근에는 강화학습을 이용해 이를 해결하고자 하는 모델이 연구되고 있다. 본 연구에서는 새로 정의한 일반화된 차량 경로 문제를 해결하기 위한 강화학습 모델을 제안한다.

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Distributed Algorithm for Maximal Weighted Independent Set Problem in Wireless Network (무선통신망의 최대 가중치 독립집합 문제에 관한 분산형 알고리즘)

  • Lee, Sang-Un
    • 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.

Code Size Reduction Through Efficient use of Multiple Load/store Instructions (복수의 메모리 접근 명령어의 효율적인 이용을 통한 코드 크기의 감소)

  • Ahn Minwook;Cho Doosan;Paek Yunheung;Cho Jeonghun
    • Journal of KIISE:Software and Applications
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    • v.32 no.8
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    • pp.819-833
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    • 2005
  • Code size reduction is ever becoming more important for compilers targeting embedded processors because these processors are often severely limited by storage constraints and thus the reduced code size can have a positively significant Impact on their performance. Various code size reduction techniques have different motivations and a variety of application contexts utilizing special hardware features of their target processors. In this work, we propose a novel technique that fully utilizes a set of hardware instructions, called the multiple load/store (MLS), that are specially featured for reducing code size by minimizing the number of memory operations in the code. To take advantage of this feature, many microprocessors support the MLS instructions, whereas no existing compilers fully exploit the potential benefit of these instructions but only use them for some limited cases. This is mainly because optimizing memory accesses with MLS instructions for general cases is an NP-hard problem that necessitates complex assignments of registers and memory off-sets for variables in a stack frame. Our technique uses a couple of heuristics to efficiently handle this problem in a polynomial time bound.

Solving the test resource allocation using variable group genetic algorithm (가변 그룹 유전자알고리즘 기반의 시험자원할당 문제 해결)

  • Mun, Chang-min
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.20 no.8
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    • pp.1415-1421
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    • 2016
  • There are considerable concern on the methods for the efficient utilization of the test-resources as increasing of the number of the tests for functionality and performance verification of weapon systems. Furthermore, with an increase in the complexity of the resource assignment the decision support is required. Test resource allocation is basically the same problems as conventional NP-hard FJSP(Flexible Job Shop Problem), therefore empirical test resource allocation method that has been used in many decades is limited in the time performance. Although research has been conducted applying the genetic algorithm to the FJSP, it is limited in the test resource allocation domain in which more than one machine is necessary for a single operation. In this paper, a variable group genetic algorithm is proposed. The algorithm is expected to improve the test plan efficiency by automating and optimizing the existing manual based allocation. The simulation result shows that the algorithm could be applicable to the test plan.

An Efficient Task Assignment Algorithm for Heterogeneous Multi-Computers (이종의 다중컴퓨터에서 태스크 할당을 위한 효율적인 알고리즘)

  • Seo, Kyung-Ryong;Yeo, Jeong-Mo
    • The Transactions of the Korea Information Processing Society
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    • v.5 no.5
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    • pp.1151-1161
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    • 1998
  • In this paper, we are considering a heterogeneous processor system in which each processor may have different performance and reliability characteristics. In other to fully utilize this diversity of processing power it is advantageous to assign the program modules of a distributed program to the processors in such a way that the execution time of the entire program is minimized. This assignment of tasks to processors to maximize performance is commonly called load balancing, since the overloaded processors can perform their own processing with the performance degradation. For the task assignment problem, we propose a new objective function which formulates this imbalancing cost. Thus the task assignment problem is to be carried out so that each module is assigned to a processor whose capabilities are most appropriate for the module, and the total cost is minimized that sum of inter-processor communication cost and execution cost and imbalance cost of the assignment. To find optimal assignment is known to be NP-hard, and thus we proposed an efficient heuristic algorithm with time complexity $O(n^2m)$ in case of m task modules and n processors.

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