• Title/Summary/Keyword: Mathematical Optimization

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Mathematical Modeling of Scheduling Problems for the Fusion Fuel Cycle (핵융합 공정주기에서의 생산 계획 최적화)

  • Lee, Suh-Young;Ha, Jin-Kuk;Lee, In-Beum;Lee, Euy Soo
    • Korean Chemical Engineering Research
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    • v.58 no.4
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    • pp.596-603
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    • 2020
  • In this study, a mathematical model for optimal operation of the fusion fuel cycle is developed based on scheduling approach. The fusion fuel cycle consists of a system for storing and supplying deuterium and tritium, and receiving and separating process after the fusion reaction. Except that tritium is a radioactive material, most of these processes consist of catalytic reactions and separation process. For these reasons, it is possible to apply scheduling approach which is also widely utilized to chemical plants to derive the optimal operating scenarios. The developed model determined the optimal regeneration cycle to minimize the amount of tritium inside the vacuum pumps. Based on the characteristics of various device in the fusion reactor, the optimal tritium plant operation scenario is evaluated. The formulated model was applied to the actual tokamak scenario and utilized to analyze the fuel flow and balance of ITER fuel cycle.

A Study on an Efficient Double-fleet Operation of the Korean High Speed Rail (한국 고속철도의 효율적 중련편성 운영방법에 대한 연구)

  • Oh, Seog-Moon;Sohn, Moo-Sung;Choi, In-Chan
    • Journal of the Korean Society for Railway
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    • v.10 no.6
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    • pp.742-750
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    • 2007
  • This paper presents a mathematical model for a double-fleet operation in Korean high speed rail (HSR). KORAIL has a plan to launch new HSR units in 2010, which are composed of 10 railcars. The double-fleet operation assigns a single-unit or two-unit fleet to a segment, accommodating demand fluctuation. The proposed model assumes stochastic demand and uses chance-constrained constraints to assure a preset service level. It can be used in the tactical planning stage of the rail management as it includes several real-world conditions, such as the capacities of the infra-structures and operational procedures. In the solution approach, the expected revenue in the objective function is linearized by using expected marginal revenue, and the chance-constrained constraints are linearized by assuming that demands are normally distributed. Subsequently, the model can be solved by a mixed-integer linear programming solver fur small size problems. The test results of the model applied to Friday morning train schedules for one month sample data from KTX operation in 2004 shows that the proposed model could be utilized to determine the effectiveness of double-fleet operation, which could significantly increase the expected profit and seat utilization rates when properly maneuvered.

Study on Support Vector Machines Using Mathematical Programming (수리계획법을 이용한 서포트 벡터 기계 방법에 관한 연구)

  • Yoon, Min;Lee, Hak-Bae
    • The Korean Journal of Applied Statistics
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    • v.18 no.2
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    • pp.421-434
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    • 2005
  • Machine learning has been extensively studied in recent years as effective tools in pattern classification problem. Although there have been several approaches to machine learning, we focus on the mathematical programming (in particular, multi-objective and goal programming; MOP/GP) approaches in this paper. Among them, Support Vector Machine (SVM) is gaining much popularity recently. In pattern classification problem with two class sets, the idea is to find a maximal margin separating hyperplane which gives the greatest separation between the classes in a high dimensional feature space. However, the idea of maximal margin separation is not quite new: in 1960's the multi-surface method (MSM) was suggested by Mangasarian. In 1980's, linear classifiers using goal programming were developed extensively. This paper proposes a new family of SVM using MOP/GP techniques, and discusses its effectiveness throughout several numerical experiments.

An Experimental and Modeling Study on the Oxidation Kinetics of Nitric Oxide over Platinum-based Catalysts (백금계 촉매상에서 산화질소(NO)의 산화반응속도에 관한 실험 및 모델링 연구)

  • Kim, Young-Deuk;Jeong, Soo-Jin;Kim, Woo-Seung
    • Transactions of the Korean Society of Automotive Engineers
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    • v.20 no.5
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    • pp.71-80
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    • 2012
  • To improve the $NO_X$ conversion over a SCR (selective catalytic reduction) catalyst, the DOC (diesel oxidation catalyst) is usually placed upstream of the SCR catalyst to enhance the fast SCR reaction ($4NH_3+2NO+2NO_2{\rightarrow}4N_2+6H_2O$) using equimolar amounts of NO and $NO_2$. Here, a ratio of $NO_2/NO_X$ above 50% should be avoided, because the reaction with $NO_2$ only ($4NH_3+4NO+O_2{\rightarrow}4N_2+6H_2O$) is slower than the standard SCR reaction ($4NH_3+4NO+O_2{\rightarrow}4N_2+6H_2O$). In order to accurately predict the performance characteristics of SCR catalysts, it is therefore desired to develop a more simple and reliable mathematical and kinetic models on the oxidation kinetics of nitric oxide over a DOC. In the present work, the prediction accuracy and limit of three different chemical reaction kinetics models are presented to describe the chemicophysical characteristics and conversion performance of DOCs. Steady-state experiments with DOCs mounted on a light-duty four-cylinder 2.0-L turbocharged diesel engine then are performed, using an engine-dynamometer system to calibrate the kinetic parameters such as activation energies and preexponential factors of heterogeneous reactions. The reaction kinetics for NO oxidation over Pt-based catalysts is determined in conjunction with a transient one-dimensional (1D) heterogeneous plug flow reactor (PFR) model with diesel exhaust gas temperatures in the range of 115~$525^{\circ}C$ and space velocities in the range of $(0.4{\sim}6.5){\times}10^5\;h^{-1}$.

Instrumental Genesis of Computer Algebra System(CAS) in Mathematical Problem Solving among High School Students (고등학교 수학 문제해결에서 CAS의 도구발생)

  • Han, Se-Ho;Chang, Kyung-Yoon
    • School Mathematics
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    • v.11 no.3
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    • pp.527-546
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    • 2009
  • This study was designed to gain insights into instrumental genesis process of CAS in Korean high school students and to explore its practical potentials in secondary mathematics education. Two activities, such as Concept-Centered Mathematics Activity based on CAS and Problem Solving Activities, were constructed and executed to 10th Grade seven students for twelve class hours. The finding on the students' activities are as follows : it is meaningful in mathematics education, especially in algebra education, in that the CAS based concept centered mathematics activity offers great opportunities to deal with high-qualified application problems. The problem solving activities based on the instrumented CAS may have an influence on the sequence of mathematics curriculum, e.g. the optimization problems may precede the calculus problems such as derivatives in high school. The results of this study to investigate the instrumental genesis of CAS in mathematical activities will give insights into the secondary mathematics curriculum to prepare the CAS in Korea.

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Modelling of effluent and GHGs for wastewater treatment plants using by MS Excel simulator(PKES) (MS Excel 시뮬레이터(PKES)를 이용한 하수처리장 유출수 및 온실가스 모델링)

  • Bin, Jung-In;Lee, Byung-Hun
    • Journal of Korean Society of Water and Wastewater
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    • v.28 no.6
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    • pp.735-745
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    • 2014
  • This paper presents PKES(PuKyung -Excel based Simulator) for WWTPs(wastewater treatment plants) by using MS Excel and VBA(Visual Basic for Application). PKES is a user-friendly simulator for the design and optimization of the whole plant including biological and physico-chemical processes for the wastewater and sludge treatment. PKES calculates the performance under steady or dynamic state and allows changing the mathematical model by the user. Mathematical model implemented in PKES is a improved integration model based on ASM2d and ADM1 for simulation of AS(activated sludge) and AD(anaerobic digestion). Gaseous components of $N_2$, $N_2O$, $CO_2$ and $CH_4$ are added for estimation of GHGs(greenhouse gases) emission. The simulation results for comparison between PKES and Aquasim(EAWAG) showed about the same effluent concentrations. As a result of verification using by measured data of BOD, TSS, TN and TP for 2 years of operation, calculated effluent concentrations were similar to measured effluent concentrations. The values of average RMSE(root mean square error) were 1.9, 0.8, 1.6 and 0.2 mg/L for BOD, TSS, TN and TP, respectively. Total GHGs emission of WWTP calculated by PKES was 138.5 ton-$CO_2$/day and GHGs emissions of $N_2O$, $CO_2$ and $CH_4$ were calculated at 21.7, 28.9 and 87.9 ton-$CO_2$/day, respectively. GHGs emission of activated sludge was 32.5 % and that of anaerobic digestion was 67.5 %.

An Experiment Study for S/N Ratio of Bead Geometry for Guaranteeing the Welding Quality in Bellows Weld Joint (벨로우즈 용접부의 품질확보를 위한 비드형상 S/N비에 관한 실험적 연구)

  • Lee, Jong-Pyo;Kim, Ill-Soo;Park, Min-Ho;Jin, Byeong-Ju;Kim, In-Ju;Kim, Ji-Sun
    • Journal of Welding and Joining
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    • v.35 no.2
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    • pp.43-51
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    • 2017
  • The automatic welding systems, have received much attention in recent years, because they are highly suitable not only to increase the quality and productivity, but also to decrease manufacturing time and cost for a given product. Automatic welding work in semiconductor or space industry to be carried out in pipe line and butt joint mostly and plasma arc welding(PAW) is actively applied. To get the desired quality welds in automated welding system is challenging, a mathematical model is needed that has complete control over the relevant process parameters in order to obtain the required mechanical properties. However, In various industries the welding process mathematical model is not fully formulated for the process parameter and on the welding conditions, therefore only partial variables can be predicted. Therefore, this paper investigates the interaction between the welding parameters and mechanical properties for predicting the weld bead geometry by analyzing the S/N ratio.

On Design Intelligent Control System by Fussionf of Fuzzy Logic and Genetic Algorithms (퍼지논리와 유전자 알고리즘 융합에 의한 지능형 제어 시스템)

  • Lee, Mal-Rye;Kim, Tae-Eun
    • The Transactions of the Korea Information Processing Society
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    • v.6 no.4
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    • pp.952-958
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    • 1999
  • This paper presented the application of GAs as a means of finding optimal solutions over a parameter space in the controller design for a fuzzy control system. The performance can involve a weighted combination of various performance characteristics such as rise-time, settling-time, settling-time, overshoot. The results obtained here are compared with those for a traditional design obtained using the root-locus method. In contrast to traditional methods, the GA-based method does not require the usual mathematical processess or mathematical model of the system. In this paper, the Ga-based Fuzzy control system combining Fuzzy control theory with the GA, that is known to be very effective in the optimization problem, will be proposed The effectiveness of the proposed control system will be demonstrated by computer simulations using task tracking position system in stable and unstable linear systems. It is shown that the GA-based controller is better than the traditional controller used It stable and unstable linear systems.

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Optimal Scheduling of Detection and Tracking Parameters in Phased Array Radars (위상배열 레이다 검출 및 추적 매개변수의 최적 스케쥴링)

  • Jung, Young-Hun;Kim, Hyun-Soo;Hong, Sun-Mog
    • Journal of the Korean Institute of Telematics and Electronics S
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    • v.36S no.7
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    • pp.50-61
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    • 1999
  • \In this paper, we consider the optimal scheduling of detection and tracking parameters in phased array radars to minimize the radar energy required for track maintenance in a cluttered environment. We develop a mathematical model of target detection induced by a search process in phased array radars. In the mathematical development, we take into account the effect of unwanted measurements that may have originated from clutter or false alarms in the detection process. We use and analytic approximation of the modified Riccati equation of the probabilistic data association (PDA) filter to take into account the effect of clutter interference in tracking. Based on the search process and the tracking models, we formulate the optimal scheduling problem into a nonlinear optimal control problem. We solve a constrained nonlinear optimization problem to obtain the solution of the optimal control problem.

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Characteristics of Lactose Hydrolysis by Immobilized β-Galactosidase on Chitosan Bead (Chitosan 담체에 고정화된 β-galactosidase에 의한 유당 분해 특성)

  • Kang, Byung-Chul
    • Journal of Life Science
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    • v.21 no.1
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    • pp.127-133
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    • 2011
  • ${\beta}$-Galactosidase was immobilized on chitosan bead by covalent bonding using glutaraldehyde. The characteristics of the immobilized enzyme were investigated. Maximum immobilization yield of 75% was obtained on chitosan bead. Optimum pH and temperature for the immobilized enzyme was 7.0 and $50^{\circ}C$, respectively. The immobilized enzyme showed a broader range of pH and temperature compared to a free one. A mathematical model for the operation of the immobilized enzyme in a packed-bed reactor was established and solved numerically. Under different inlet lactose concentrations and feed flow rate conditions, lactose conversion was measured in a packed-bed reactor. The experimental results of continuous operation in a packed-bed reactor were compared to theoretic results using Michaelis-Menten kinetics with competitive product inhibition and external mass transfer resistance. The model predicted the experimental data with errors less than 5%. Process optimization of continuous operation in a packed-bed reactor was also conducted. In a recirculation packed-bed operation, conversion of lactose was 97% in 3 hours. In a continuous packed-bed operation, the effect of flow rate and initial lactose concentration was investigated. Increasing flow rates and initial lactose concentration decreased the conversion of substrate.