• Title/Summary/Keyword: Large Scale Problem

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An Integer Programming Model for a Complex University Timetabling Problem: A Case Study

  • Prabodanie, R.A. Ranga
    • Industrial Engineering and Management Systems
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    • v.16 no.1
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    • pp.141-153
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    • 2017
  • A binary integer programming model is proposed for a complex timetabling problem in a university faculty which conducts various degree programs. The decision variables are defined with fewer dimensions to economize the model size of large scale problems and to improve modeling efficiency. Binary matrices are used to incorporate the relationships between the courses and students, and the courses and teachers. The model includes generally applicable constraints such as completeness, uniqueness, and consecutiveness; and case specific constraints. The model was coded and solved using Open Solver which is an open-source optimizer available as an Excel add-in. The results indicate that complicated timetabling problems with large numbers of courses and student groups can be formulated more efficiently with fewer numbers of variables and constraints using the proposed modeling framework. The model could effectively generate timetables with a significantly lower number of work hours per week compared to currently used timetables. The model results indicate that the particular timetabling problem is bounded by the student overlaps, and both human and physical resource constraints are insignificant.

ADMM for least square problems with pairwise-difference penalties for coefficient grouping

  • Park, Soohee;Shin, Seung Jun
    • Communications for Statistical Applications and Methods
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    • v.29 no.4
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    • pp.441-451
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    • 2022
  • In the era of bigdata, scalability is a crucial issue in learning models. Among many others, the Alternating Direction of Multipliers (ADMM, Boyd et al., 2011) algorithm has gained great popularity in solving large-scale problems efficiently. In this article, we propose applying the ADMM algorithm to solve the least square problem penalized by the pairwise-difference penalty, frequently used to identify group structures among coefficients. ADMM algorithm enables us to solve the high-dimensional problem efficiently in a unified fashion and thus allows us to employ several different types of penalty functions such as LASSO, Elastic Net, SCAD, and MCP for the penalized problem. Additionally, the ADMM algorithm naturally extends the algorithm to distributed computation and real-time updates, both desirable when dealing with large amounts of data.

On the near optimal composite regulator problem for the large scale linear time invariant system using matrix sign function (행렬 부호 함수를 이용한 대규모 선형 시불변 계통의 준최적 합성 제어기의 설계에 관한 연구)

  • 천희영;박귀택;이동기
    • 제어로봇시스템학회:학술대회논문집
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    • 1986.10a
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    • pp.566-570
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    • 1986
  • 본 논문의 목적은 대규모 선형 시불변 계통에 대한 합성 제어기의 설계에 관한 새로운 방법을 제시하기 위한 것이다. 주어진 계통을 행렬 부호 함수를 이용하여 그 고유치의 크기에 따라 블럭 대각 분해하고 각부 계통에 대한 최적 제어기 및 전체계통에 대한 준최적 합성 제어기를 설계한다. 이 방법은 주어진 계통의 고유치를 미리 알 필요가 없으며 계통의 블력 분해 과정에서 Riccati 방정식및 Lyapunov 방정식의 해를 구할 필요가 없고 특이섭등 기법이나 Two time scale seperation 방법에서의 제약조건에 관계없이 광범위하게 적용되는 장점이 있다.

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Application of linearization method for large-scale structure optimizations (구조물 최적화를 위한 선형화 기법)

  • 이희각
    • Computational Structural Engineering
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    • v.1 no.1
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    • pp.87-94
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    • 1988
  • The linerization method as one of the recursive quadratic programming method is applied for the optimal design of a large-scale structure supported by Pshenichny's proof of global convergence of the algorithm and convergence rate estimates. The linearization method transforms all constants of the design problem into an equivalent linearized constraint and employs the active-set strategy. This results in substantial computational savings by reducing the number of sate and adjoint to be solved at every design iteration. The illustrative example of plates with beams supported by columns is the typical one of a large-scale structure to give successful optimum solutions with satisfactory convergence criteria. Hopefully, the method may be applicable to all classes of optimization problems.

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Large-Scale Structure of Leading-Edge Separation Bbubble with Local Forcing (국소교란이 가해지는 박리기포의 대형구조)

  • 김유익;성형진
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.19 no.4
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    • pp.1134-1147
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    • 1995
  • POD (proper orthogonal decomposition) is applied to turbulent leading-edge separation bubble to extract coherent structures. A two-dimensional leading-edge separation bubble is simulated by discrete-vortex method, where a time-dependent source forcing is incorporated. Based on the wealth of numerical data, POD is applied in a range of the forcing amplitude ( $A_{o}$ = 0, 0.5, 1.0 and 1.5) and forcing frequency (0 .leq. $f_{F}$H/ $U_{\infty}$.leq. 0.3). It is demonstrated that the structures of POD have noticeable changes with local forcings. In an effort to investigate the mechanism of decreasing reattachment length, dynamic behaviors of the expansion coefficients and contributions of the eigenfunctions of POD are scrutinized. As the forcing amplitude increases, the large-scale vortex structures are formed near the forcing amplitude increases, the large-scale vortex structures are formed near the separation point and the flow structures become more organized and more regular, accompanying with the reduction of reattachment length. By further inverstigation of POD global entropy, it is seen that the reattachment length is closely linked to the degree of organization of the flow structures.es.s.

Observer Design for H- Fault Detection of Large Scale T-S Fuzzy Systems (대규모 T-S 퍼지 시스템의 H- 고장검출을 위한 관측기 설계)

  • Jee, Sung-Chul;Lee, Ho-Jae;Joo, Young-Hoon;Kim, Do-Wan
    • Journal of the Korean Institute of Intelligent Systems
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    • v.20 no.1
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    • pp.15-20
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    • 2010
  • In this paper, we discuss a decentralized observer design problem for the fault detection in the large-scale continuous-time T-S (Takagi-Sugeno) fuzzy system. Since the fault detection residual is desired to be as sensitive as possible, on the fault, we use $\mathfrak{H}_-$ index performance criterion. Sufficient conditions for the existence of such a observer is presented in terms of linear matrix inequalities. Simulation results show the effectiveness of the proposed method.

Parallel Computing of Large Scale FE Model based on Explicit Lagrangian FEM (외연 Lagrangian 유한요소법 기반의 대규모 유한요소 모델 병렬처리)

  • 백승훈;김승조;이민형
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.34 no.8
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    • pp.33-40
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    • 2006
  • A parallel computing strategy for finite element(FE) processing is described and implemented in nonlinear explicit FE code and its parallel performances are evaluated. A self-made linux-cluster supercomputer with 520 CPUs is used as a bench mark test bed. It is observed that speed-up is increased almost idealy even up to 256 CPUs for a large scale model. A communication over head and its effect on the parallel performance is also examined. Parallel performance is compare with the commercial code and developed code shows superior performance as the number of CPUs used are increased.

Interference-free Clustering Protocol for Large-Scale and Dense Wireless Sensor Networks

  • Chen, Zhihong;Lin, Hai;Wang, Lusheng;Zhao, Bo
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.13 no.3
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    • pp.1238-1259
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    • 2019
  • Saving energy is a big challenge for Wireless Sensor Networks (WSNs), which becomes even more critical in large-scale WSNs. Most energy waste is communication related, such as collision, overhearing and idle listening, so the schedule-based access which can avoid these wastes is preferred for WSNs. On the other hand, clustering technique is considered as the most promising solution for topology management in WSNs. Hence, providing interference-free clustering is vital for WSNs, especially for large-scale WSNs. However, schedule management in cluster-based networks is never a trivial work, since it requires inter-cluster cooperation. In this paper, we propose a clustering method, called Interference-Free Clustering Protocol (IFCP), to partition a WSN into interference-free clusters, making timeslot management much easier to achieve. Moreover, we model the clustering problem as a multi-objective optimization issue and use non-dominated sorting genetic algorithm II to solve it. Our proposal is finally compared with two adaptive clustering methods, HEED-CSMA and HEED-BMA, demonstrating that it achieves the good performance in terms of delay, packet delivery ratio, and energy consumption.