• Title/Summary/Keyword: 수학적 최적화

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Exploring the power of physics-informed neural networks for accurate and efficient solutions to 1D shallow water equations (물리 정보 신경망을 이용한 1차원 천수방정식의 해석)

  • Nguyen, Van Giang;Nguyen, Van Linh;Jung, Sungho;An, Hyunuk;Lee, Giha
    • Journal of Korea Water Resources Association
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    • v.56 no.12
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    • pp.939-953
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    • 2023
  • Shallow water equations (SWE) serve as fundamental equations governing the movement of the water. Traditional numerical approaches for solving these equations generally face various challenges, such as sensitivity to mesh generation, and numerical oscillation, or become more computationally unstable around shock and discontinuities regions. In this study, we present a novel approach that leverages the power of physics-informed neural networks (PINNs) to approximate the solution of the SWE. PINNs integrate physical law directly into the neural network architecture, enabling the accurate approximation of solutions to the SWE. We provide a comprehensive methodology for formulating the SWE within the PINNs framework, encompassing network architecture, training strategy, and data generation techniques. Through the results obtained from experiments, we found that PINNs could be an accurate output solution of SWE when its results were compared with the analytical method. In addition, PINNs also present better performance over the Artificial Neural Network. This study highlights the transformative potential of PINNs in revolutionizing water resources research, offering a new paradigm for accurate and efficient solutions to the SVE.

Sensitivity analysis for freight rate change in liner shipping industry - Comparison between slot chartering model and non-collaborating model - (정기선 해운사의 해상운송 요율 변화에 대한 민감도 분석 - 단독 운송과 제휴 운송 비교 -)

  • Chung, Ki-Ho
    • Management & Information Systems Review
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    • v.34 no.4
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    • pp.1-13
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    • 2015
  • This paper presents a mathematical formulation for container slot chartering model through strategic alliance between liner shipping companies. This paper develops a solution procedure to apply the model to real world problems and its applicability is demonstrated by a numerical example. The model presented in this paper has some important features which have never been considered in the previous researches. The model is linear model and pursuits profit maximization. And also it considers slot chartering capacity selection. This paper attempts to perform sensitivity analysis and compares slot chartering model with basic non-collaborating model in which there is no alliance and collaboration. As a result of sensitivity analysis, some interesting findings are obtained; Even though freight rate is more and more decreasing, the profit by slot chartering model is always higher than the basic model but the profit gaps become smaller. But The ratio of the profit gap to the profit of basic model is more increasing.

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Prediction of Shore Tide level using Artificial Neural Network (인공신경망을 이용한 해안 조위예측)

  • Rhee Kyoung Hoon;Moon Byoung Seok;Kim Tae Kyoung;Oh jong yang
    • Proceedings of the Korea Water Resources Association Conference
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    • 2005.05b
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    • pp.1068-1072
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    • 2005
  • 조석이란, 해면의 완만한 주기적 승강을 말하며, 보통 그 승강은 1일 약 2회이나, 곳에 따라서는 1일 1회의 곳도 있다. 조석에 있어서는 이 밖에 수일의 주기를 갖는 약간 불규칙한 승강, 반년, 또는 1년을 주기로 하는 다소 규칙적인 승강까지 포함하여 취급한다. 그러나, 각 항만마다 갖는 특정적인 주기인 수분내지 수십분의 주기의 승강은 조석으로 취급하지 않는다. 조석은 해양의 제현상 중에서 예측가능성이 가장 큰 현장으로 이는 조석이 천체의 운행과 연관되기 때문이다. 조석이란 지구로부터 일정한 거리에서 각 고유의 속도를 가지는 적도상을 운행하는 무수의 가상천체에 기인하는 규칙적인 개개의 조석을 합성한 것이며 이 개개의 조석을 분조(Constituent)라 한다. 여기에서 사용되는 신경망 모형은 입력과 출력으로 구성되는 블랙박스 모형으로서 하나의 시스템을 병렬적으로 비선형적으로 구축할 수 있다는 장점 때문에 과거 하천유역의 강우-유출과정에서의 경우 유출현상을 해석하고 유출과정을 모형화 하기 위해 사용하였다. 본 연구에서는 기존의 조위 예측방법인 조화분석법이 아닌 인공신경망을 이용하여 조위예측을 실시하였다. 학습이라는 최적화 과정을 통해 구조와 기능이 복잡한 자연현상을 그대로 받아들여 축적시킴으로써 이를 지식으로 현상에 대한 재현능력이 뛰어나고, 또한 신경회로망의 연상기억능력에 적용하여 수학적으로 표현이 불가능한 불확실한 조위곡선에 적용하기에 유리한 장점을 가지고 있다. 본 연구의 목적은 과거 조위이론을 통해 이루었던 조위예측을 우리가 알기 쉬운 여러 기후인자(해면기압, 풍향, 풍속, 음력 등)에 따른 조위곡선을 예측하기 위해 신경망 모형을 이용하여 여수지역의 조위에 적용하여 비교 분석하고자 한다. May가 제안한 공식을 더 확장하여 적용할 수 있는 실험 공식으로 개선하였으며 다양한 조건에 대한 실험을 수행하여 보다 정밀한 공식으로 개선할 수 있었다.$10,924m^3/s$ 및 $10,075m^3/s$로서 실험 I의 $2,757m^3/s$에 비해 통수능이 많이 개선되었음을 알 수 있다.함을 알 수 있다. 상수관로 설계 기준에서는 관로내 수압을 $1.5\~4.0kg/cm^2$으로 나타내고 있는데 $6kg/cm^2$보다 과수압을 나타내는 경우가 $100\%$로 밸브를 개방하였을 때보다 $60\%,\;80\%$ 개방하였을 때가 더 빈번히 발생하고 있으므로 대상지역의 밸브 개폐는 $100\%$ 개방하는 것이 선계기준에 적합한 것으로 나타났다. 밸브 개폐에 따른 수압 변화를 모의한 결과 밸브 개폐도를 적절히 유지하여 필요수량의 확보 및 누수방지대책에 활용할 수 있을 것으로 판단된다.8R(mm)(r^2=0.84)$로 지수적으로 증가하는 경향을 나타내었다. 유거수량은 토성별로 양토를 1.0으로 기준할 때 사양토가 0.86으로 가장 작았고, 식양토 1.09, 식토 1.15로 평가되어 침투수에 비해 토성별 차이가 크게 나타났다. 이는 토성이 세립질일 수록 유거수의 저항이 작기 때문으로 생각된다. 경사에 따라서는 경사도가 증가할수록 증가하였으며 $10\% 경사일 때를 기준으로 $Ro(mm)=Ro_{10}{\times}0.797{\times}e^{-0.021s(\%)}$로 나타났다.천성 승모판 폐쇄 부전등을 초래하는 심각한 선

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Analysis of the Effectiveness of Big Data-Based Six Sigma Methodology: Focus on DX SS (빅데이터 기반 6시그마 방법론의 유효성 분석: DX SS를 중심으로)

  • Kim Jung Hyuk;Kim Yoon Ki
    • KIPS Transactions on Software and Data Engineering
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    • v.13 no.1
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    • pp.1-16
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    • 2024
  • Over recent years, 6 Sigma has become a key methodology in manufacturing for quality improvement and cost reduction. However, challenges have arisen due to the difficulty in analyzing large-scale data generated by smart factories and its traditional, formal application. To address these limitations, a big data-based 6 Sigma approach has been developed, integrating the strengths of 6 Sigma and big data analysis, including statistical verification, mathematical optimization, interpretability, and machine learning. Despite its potential, the practical impact of this big data-based 6 Sigma on manufacturing processes and management performance has not been adequately verified, leading to its limited reliability and underutilization in practice. This study investigates the efficiency impact of DX SS, a big data-based 6 Sigma, on manufacturing processes, and identifies key success policies for its effective introduction and implementation in enterprises. The study highlights the importance of involving all executives and employees and researching key success policies, as demonstrated by cases where methodology implementation failed due to incorrect policies. This research aims to assist manufacturing companies in achieving successful outcomes by actively adopting and utilizing the methodologies presented.

A Non-Uniform Convergence Tolerance Scheme for Enhancing the Branch-and-Bound Method (비균일 수렴허용오차 방법을 이용한 분지한계법 개선에 관한 연구)

  • Jung, Sang-Jin;Chen, Xi;Choi, Gyung-Hyun;Choi, Dong-Hoon
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.36 no.4
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    • pp.361-371
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    • 2012
  • In order to improve the efficiency of the branch-and-bound method for mixed-discrete nonlinear programming, a nonuniform convergence tolerance scheme is proposed for the continuous subproblem optimizations. The suggested scheme assigns the convergence tolerances for each continuous subproblem optimization according to the maximum constraint violation obtained from the first iteration of each subproblem optimization in order to reduce the total number of function evaluations needed to reach the discrete optimal solution. The proposed tolerance scheme is integrated with five branching order options. The comparative performance test results using the ten combinations of the five branching orders and two convergence tolerance schemes show that the suggested non-uniform convergence tolerance scheme is obviously superior to the uniform one. The results also show that the branching order option using the minimum clearance difference method performed best among the five branching order options. Therefore, we recommend using the "minimum clearance difference method" for branching and the "non-uniform convergence tolerance scheme" for solving discrete optimization problems.

A DEVS-based Modeling & Simulation Methodology of Enabling Node Mobility for Ad Hoc Network (노드 이동성을 고려한 애드 혹 네트워크의 이산 사건 시스템 기반 모델링 및 시뮬레이션 방법론)

  • Song, Sang-Bok;Lee, Kyou-Ho
    • Journal of the Korea Society for Simulation
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    • v.18 no.4
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    • pp.127-136
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    • 2009
  • Modeling and Simulation, especially in mobile ad hoc network(MANET), are the most effective way to analyze performance or optimize system parameters without establishing real network environment. Focusing mainly on overall network behaviors in MANET concerns dynamics of network transport operations, which can efficiently be characterized with event based system states rather than execution details of protocols. We thus consider the network as a discrete event system to analyze dynamics of network transport performance. Zeigler's set-theoretic DEVS(Discrete Event Systems Specification) formalism can support specification of a discrete event system in hierarchical, modular manner. The DEVSim++ simulation environment can not only provide a rigorous modeling methodology based on the DEVS formalism but also support modelers to develop discrete event models using the hierarchical composition methodology in object-orientation. This environment however hardly supports to specify connection paths of network nodes, which are continuously altered due to mobility of nodes. This paper proposes a DEVS-based modeling and simulation methodology of enabling node mobility, and develops DEVS models for the mobile ad hoc network. We also simulate developed models with the DEVSim++ engine to verify the proposal.

The Performance Analysis of GPU-based Cloth simulation according to the Change of Work Group Configuration (워크 그룹 구성 변화에 따른 GPU 기반 천 시뮬레이션의 성능 분석)

  • Choi, Young-Hwan;Hong, Min;Lee, Seung-Hyun;Choi, Yoo-Joo
    • Journal of Internet Computing and Services
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    • v.18 no.3
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    • pp.29-36
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    • 2017
  • In these days, 3D dynamic simulation is closely related to many industries. In the past, physically-based 3D simulation was used mainly in the car crash or construction related fields, but it also plays an important role in movies or games today. Many mathematical computations are needed to represent the 3D object realistically, but it is difficult to process a large amount of calculations for simulation of application based on CPU in real-time. Recently, with the advanced graphic hardware and improved architecture, GPU can be utilized for the general purposes of computation function as well as graphic computation. Many approaches using GPU have been applied for various research fields. In this paper, we analyze the performance variation of two cloth simulation algorithms based on GPU according to the change of execution properties of GPU shaders in oder to optimize the performance of GPU-based cloth simulation. Cloth simulation is implemented by the spring centric algorithm and node centric algorithm with GPU parallel computing using compute shader of GLSL 4.3. We compare the performance of between these algorithms according to the change of the size and dimension of work group. The experiment is repeated to 10 times during 5,000 frames for each test and experimental results are provided by averaging of FPS. The experimental result shows that the node centric algorithm is executed in higher speed than the spring centric algorithm.

An integrated framework of security tool selection using fuzzy regression and physical programming (퍼지회귀분석과 physical programming을 활용한 정보보호 도구 선정 통합 프레임워크)

  • Nguyen, Hoai-Vu;Kongsuwan, Pauline;Shin, Sang-Mun;Choi, Yong-Sun;Kim, Sang-Kyun
    • Journal of the Korea Society of Computer and Information
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    • v.15 no.11
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    • pp.143-156
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    • 2010
  • Faced with an increase of malicious threats from the Internet as well as local area networks, many companies are considering deploying a security system. To help a decision maker select a suitable security tool, this paper proposed a three-step integrated framework using linear fuzzy regression (LFR) and physical programming (PP). First, based on the experts' estimations on security criteria, analytic hierarchy process (AHP) and quality function deployment (QFD) are employed to specify an intermediate score for each criterion and the relationship among these criteria. Next, evaluation value of each criterion is computed by using LFR. Finally, a goal programming (GP) method is customized to obtain the most appropriate security tool for an organization, considering a tradeoff among the multi-objectives associated with quality, credibility and costs, utilizing the relative weights calculated by the physical programming weights (PPW) algorithm. A numerical example provided illustrates the advantages and contributions of this approach. Proposed approach is anticipated to help a decision maker select a suitable security tool by taking advantage of experts' experience, with noises eliminated, as well as the accuracy of mathematical optimization methods.

Optimization and Development of Prediction Model on the Removal Condition of Livestock Wastewater using a Response Surface Method in the Photo-Fenton Oxidation Process (Photo-Fenton 산화공정에서 반응표면분석법을 이용한 축산폐수의 COD 처리조건 최적화 및 예측식 수립)

  • Cho, Il-Hyoung;Chang, Soon-Woong;Lee, Si-Jin
    • Journal of Korean Society of Environmental Engineers
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    • v.30 no.6
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    • pp.642-652
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    • 2008
  • The aim of our research was to apply experimental design methodology in the optimization condition of Photo-Fenton oxidation of the residual livestock wastewater after the coagulation process. The reactions of Photo-Fenton oxidation were mathematically described as a function of parameters amount of Fe(II)($x_1$), $H_2O_2(x_2)$ and pH($x_3$) being modeled by the use of the Box-Behnken method, which was used for fitting 2nd order response surface models and was alternative to central composite designs. The application of RSM using the Box-Behnken method yielded the following regression equation, which is an empirical relationship between the removal(%) of livestock wastewater and test variables in coded unit: Y = 79.3 + 15.61x$_1$ - 7.31x$_2$ - 4.26x$_3$ - 18x$_1{^2}$ - 10x$_2{^2}$ - 11.9x$_3{^2}$ + 2.49x$_1$x$_2$ - 4.4x$_2$x$_3$ - 1.65x$_1$x$_3$. The model predicted also agreed with the experimentally observed result(R$^2$ = 0.96) The results show that the response of treatment removal(%) in Photo-Fenton oxidation of livestock wastewater were significantly affected by the synergistic effect of linear terms(Fe(II)($x_1$), $H_2O_2(x_2)$, pH(x$_3$)), whereas Fe(II) $\times$ Fe(II)(x$_1{^2}$), $H_2O_2$ $\times$ $H_2O_2$(x$_2{^2}$) and pH $\times$ pH(x$_3{^2}$) on the quadratic terms were significantly affected by the antagonistic effect. $H_2O_2$ $\times$ pH(x$_2$x$_3$) had also a antagonistic effect in the cross-product term. The estimated ridge of the expected maximum response and optimal conditions for Y using canonical analysis were 84 $\pm$ 0.95% and (Fe(II)(X$_1$) = 0.0146 mM, $H_2O_2$(X$_2$) = 0.0867 mM and pH(X$_3$) = 4.704, respectively. The optimal ratio of Fe/H$_2O_2$ was also 0.17 at the pH 4.7.

Development of the Meta-heuristic Optimization Algorithm: Exponential Bandwidth Harmony Search with Centralized Global Search (새로운 메타 휴리스틱 최적화 알고리즘의 개발: Exponential Bandwidth Harmony Search with Centralized Global Search)

  • Kim, Young Nam;Lee, Eui Hoon
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.21 no.2
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    • pp.8-18
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    • 2020
  • An Exponential Bandwidth Harmony Search with Centralized Global Search (EBHS-CGS) was developed to enhance the performance of a Harmony Search (HS). EBHS-CGS added two methods to improve the performance of HS. The first method is an improvement of bandwidth (bw) that enhances the local search. This method replaces the existing bw with an exponential bw and reduces the bw value as the iteration proceeds. This form of bw allows for an accurate local search, which enables the algorithm to obtain more accurate values. The second method is to reduce the search range for an efficient global search. This method reduces the search space by considering the best decision variable in Harmony Memory (HM). This process is carried out separately from the global search of the HS by the new parameter, Centralized Global Search Rate (CGSR). The reduced search space enables an effective global search, which improves the performance of the algorithm. The proposed algorithm was applied to a representative optimization problem (math and engineering), and the results of the application were compared with the HS and better Improved Harmony Search (IHS).