• Title/Summary/Keyword: polynomial optimization

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Source Localization Techniques for Magnetoencephalography (MEG)

  • Kwang-Ok An;Chang-Hwan Im;Hyun-Kyo Jung;Yong-Ho Lee;Hyuk-Chan Kwon
    • KIEE International Transaction on Systems and Control
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    • v.2D no.2
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    • pp.53-58
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    • 2002
  • In this paper, various aspects in magnetoencephalography (MEG) source localization are studied. To minimize the errors in experimental data, an approximation technique using a polynomial function is proposed. The simulation shows that the proposed technique yields more accurate results. To improve the convergence characteristics in the optimization algorithm, a hybrid algorithm of evolution strategy and sensitivity analysis is applied to the neuromagnetic inverse problem. The effectiveness of the hybrid algorithm is verified by comparison with conventional algorithms. In addition, an artificial neural network (ANN) is applied to find an initial source location quickly and accurately. The simulation indicates that the proposed technique yields more accurate results effectively.

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Augmenting Path Algorithm for Routing Telephone Calls Problem

  • Lee, Sang-Un
    • Journal of the Korea Society of Computer and Information
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    • v.21 no.6
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    • pp.77-81
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    • 2016
  • This paper deals with the optimization problem that decides the routing of connection between multi-source and multi-sink. For this problem, there is only in used the mathematical approach as linear programming (LP) software package and has been unknown the polynomial time algorithm. In this paper we suggest the heuristic algorithm with $O(mn)^2$ time complexity to solve the optimal solution for this problem. This paper suggests the simple method that assigns the possible call flow quantity to augmenting path of ($s_i,t_i$) city pair satisfied with demand of ($s_i,t_i$). The proposed algorithm can be get the same optimal solution as LP for experimental data.

Variable Structure Controller with Time-Varying Switching Surface under the Bound of Input using Evolution Strategy (진화전략과 입력제약조건에 의한 시변스위칭면의 가변구조제어기 설계)

  • Lee, Min-Jeong;Kim, Hyeon-Sik;Choe, Yeong-Gyu;Jeon, Seong-Jeup
    • The Transactions of the Korean Institute of Electrical Engineers A
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    • v.48 no.4
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    • pp.402-409
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    • 1999
  • Variable structure control law is well known to be a robust control algorithm and evolution strategy is used as an effective search algorithm in optimization problems. In this paper, we propose a variable structure controller with time-varying switching surface. We calculate the maximum value of seitching surface gradient that is of the 3rd order polynomial form. Evolution strategy is used to optimize the parameters of the switching surface gradient. Finally, the proposed method is applied to position tracking control for BLDC motor. Experimental results show that the proposed method is more useful than the conventional variable structure controller.

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Implementation of Simulated Annealing for Distribution System Loss Minimum Reconfiguration (배전 계토의 손실 최소 재구성을 위한 시뮬레이티드 어닐링의 구현)

  • Jeon, Young-Jae;Choi, Seung-Kyo;Kim, Jae-Chul
    • The Transactions of the Korean Institute of Electrical Engineers A
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    • v.48 no.4
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    • pp.371-378
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    • 1999
  • This paper presents an efficient algorithm for loss reduction of distribution system by automatic sectionalizing switch operation in large scale distribution systems of radial type. Simulated Annealing algorithm among optimization techniques can avoid escape from local minima by accepting improvements in cost, but the use of this algorithm is also responsible for an excessive computation time requirement. To overcome this major limitation of Simulated Annealing algorithm, we may use advanced Simulated Annealing algorithm. All constaints are divided into two constraint group by using perturbation mechanism and penalty factor, so all trail solutions are feasible. The polynomial-time cooling schedule is used which is based on the statistics calculation during the search. This approaches results in saving CPU time. Numerical examples demonstrate the validity and effectiveness of the proposed methodology.

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Tailoring the second mode of Euler-Bernoulli beams: an analytical approach

  • Sarkar, Korak;Ganguli, Ranjan
    • Structural Engineering and Mechanics
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    • v.51 no.5
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    • pp.773-792
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    • 2014
  • In this paper, we study the inverse mode shape problem for an Euler-Bernoulli beam, using an analytical approach. The mass and stiffness variations are determined for a beam, having various boundary conditions, which has a prescribed polynomial second mode shape with an internal node. It is found that physically feasible rectangular cross-section beams which satisfy the inverse problem exist for a variety of boundary conditions. The effect of the location of the internal node on the mass and stiffness variations and on the deflection of the beam is studied. The derived functions are used to verify the p-version finite element code, for the cantilever boundary condition. The paper also presents the bounds on the location of the internal node, for a valid mass and stiffness variation, for any given boundary condition. The derived property variations, corresponding to a given mode shape and boundary condition, also provides a simple closed-form solution for a class of non-uniform Euler-Bernoulli beams. These closed-form solutions can also be used to check optimization algorithms proposed for modal tailoring.

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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Estimation Method of the Best-Approximated Form Factor Using the Profile Measurement of the Aspherical Ophthalmic Lens (단면 형상 측정을 이용한 비구면 안경 렌즈의 최적 근사화된 설계 계수의 추정 방법)

  • Lee Hocheol
    • Journal of the Korean Society for Precision Engineering
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    • v.22 no.5 s.170
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    • pp.55-62
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    • 2005
  • This paper presents mainly a procedure to get the mathematical form of the manufactured aspherical lens. Generally Schulz formula describes the aspherical lens profile. Therefore, the base curvature, conic constant. and high-order polynomial coefficient should be set to get the approximated design equation. To find the best-approximated aspherical form, lens profile is measured by a commercial stylus profiler, which has a sub-micrometer measurement resolution. The optimization tool is based on the minimization of the root mean square of error sum to get the estimated aspherical surface equation from the scanned aspherical profile. Error minimization step uses the Nelder-Mead simplex (direct search) method. The result of the lens refractive power measurement shows the experimental consistency with the curvature distribution of the best-approximated aspherical surface equation

Optimization of the Spring Design Parameters of a Circuit Breaker for Satisfying Specified Dynamic Characteristics (규정된 동적특성을 위한 회로차단기의 스프링 설계변수의 최적화)

  • 안길영;정광영
    • Journal of the Korean Society for Precision Engineering
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    • v.21 no.3
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    • pp.132-138
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    • 2004
  • In a vacuum circuit breaker mechanism, a spring-actuated linkage system is used to satisfy the desired opening and closing characteristics of electric contacts. If the type and structure of the linkage system required to the circuit breaker is predetermined, the stiffness, free length and attachment points of a spring become the important design parameters. In this paper, based on the energy conservation that the total system energy is constant throughout the operating range of the mechanism, a systematic procedure for optimizing the spring design parameters is developed and applied to the simplified mechanism of a circuit breaker. Then, in order to consider the complex dynamics of the circuit breaker mechanism rather well, the developed procedure is converted to the environment of a multi-body dynamics program ADAMS.

ON CLIQUES AND LAGRANGIANS OF HYPERGRAPHS

  • Tang, Qingsong;Zhang, Xiangde;Zhao, Cheng
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.3
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    • pp.569-583
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    • 2019
  • Given a graph G, the Motzkin and Straus formulation of the maximum clique problem is the quadratic program (QP) formed from the adjacent matrix of the graph G over the standard simplex. It is well-known that the global optimum value of this QP (called Lagrangian) corresponds to the clique number of a graph. It is useful in practice if similar results hold for hypergraphs. In this paper, we attempt to explore the relationship between the Lagrangian of a hypergraph and the order of its maximum cliques when the number of edges is in a certain range. Specifically, we obtain upper bounds for the Lagrangian of a hypergraph when the number of edges is in a certain range. These results further support a conjecture introduced by Y. Peng and C. Zhao (2012) and extend a result of J. Talbot (2002). We also establish an upper bound of the clique number in terms of Lagrangians for hypergraphs.

Axial load prediction in double-skinned profiled steel composite walls using machine learning

  • G., Muthumari G;P. Vincent
    • Computers and Concrete
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    • v.33 no.6
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    • pp.739-754
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    • 2024
  • This study presents an innovative AI-driven approach to assess the ultimate axial load in Double-Skinned Profiled Steel sheet Composite Walls (DPSCWs). Utilizing a dataset of 80 entries, seven input parameters were employed, and various AI techniques, including Linear Regression, Polynomial Regression, Support Vector Regression, Decision Tree Regression, Decision Tree with AdaBoost Regression, Random Forest Regression, Gradient Boost Regression Tree, Elastic Net Regression, Ridge Regression, and LASSO Regression, were evaluated. Decision Tree Regression and Random Forest Regression emerged as the most accurate models. The top three performing models were integrated into a hybrid approach, excelling in accurately estimating DPSCWs' ultimate axial load. This adaptable hybrid model outperforms traditional methods, reducing errors in complex scenarios. The validated Artificial Neural Network (ANN) model showcases less than 1% error, enhancing reliability. Correlation analysis highlights robust predictions, emphasizing the importance of steel sheet thickness. The study contributes insights for predicting DPSCW strength in civil engineering, suggesting optimization and database expansion. The research advances precise load capacity estimation, empowering engineers to enhance construction safety and explore further machine learning applications in structural engineering.