• Title/Summary/Keyword: Mathematical Optimization

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ROBUST SEMI-INFINITE INTERVAL-VALUED OPTIMIZATION PROBLEM WITH UNCERTAIN INEQUALITY CONSTRAINTS

  • Jaichander, Rekha R.;Ahmad, Izhar;Kummari, Krishna
    • Korean Journal of Mathematics
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    • v.30 no.3
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    • pp.475-489
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    • 2022
  • This paper focuses on a robust semi-infinite interval-valued optimization problem with uncertain inequality constraints (RSIIVP). By employing the concept of LU-optimal solution and Extended Mangasarian-Fromovitz Constraint Qualification (EMFCQ), necessary optimality conditions are established for (RSIIVP) and then sufficient optimality conditions for (RSIIVP) are derived, by using the tools of convexity. Moreover, a Wolfe type dual problem for (RSIIVP) is formulated and usual duality results are discussed between the primal (RSIIVP) and its dual (RSIWD) problem. The presented results are demonstrated by non-trivial examples.

Optimization of Mass cultivation Media for the Production of Biomass and Natural Colourants from Two Marine Cyanobacteria by a Mathematical Design of Experiments

  • Sekar, S.;Priya, S.Sri Lavanya;Roy, P.Wesley
    • Journal of Plant Biotechnology
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    • v.2 no.3
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    • pp.157-163
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    • 2000
  • Optimization of chemicals in the large scale sea water medium and inoculum for biomass and natural colourants production in the marine cyanobacteria, Phomidium tenue BDU 46241 (phycoerythrin producer) and P.valderianum BDU 30501 (phycocyanin producer) was carried out by experiments in L8 orthogonal array. Mathematical analysis revealed the significance of these factors. The factor(s) that critically control the yield varied with the organism and the end-product further, the desirable level of these factors between the normal and a higher level tested was identified and improved media were evolved. In both cyanobacteria, higher level of $K_2$$HPO_4$, $NaNO_3$ and inoculum with normal level of ferric ammonium citrate was found to be desirable for biomass production and additionally, higher level of $MgSO_4$ for pigment production. The level of other factors varied with the organism and the end-product. Confirmation experiments showed that the clues obtained based on mathematical experimentation are valid. In P.tenue, the medium optimized for biomass production increased the yield of biomass by 495% and the medium optimized for phycoerythrin production increased the yield of biomass by 408% with 30% increase in phycoerythrin content of the biomass. Similarly in P.valderianum, the medium optimized for biomass production increased the yield of biomass by 224% and the medium optimized for phycocyanin production increased the yield of biomass by 143% with 44% increase in phycocyanin content of the biomass.

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SECOND ORDER DUALITY IN VECTOR OPTIMIZATION OVER CONES

  • Suneja, S.K.;Sharma, Sunila;Vani, Vani
    • Journal of applied mathematics & informatics
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    • v.26 no.1_2
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    • pp.251-261
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    • 2008
  • In this paper second order cone convex, second order cone pseudoconvex, second order strongly cone pseudoconvex and second order cone quasiconvex functions are introduced and their interrelations are discussed. Further a MondWeir Type second order dual is associated with the Vector Minimization Problem and the weak and strong duality theorems are established under these new generalized convexity assumptions.

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A modeling of manufacturing system and a model analysis by a SIMAN language (생산공정의 모델링과 SIMAN 언어에 의한 모델분석)

  • 이만형;김경천;한성현
    • 제어로봇시스템학회:학술대회논문집
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    • 1987.10b
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    • pp.300-306
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    • 1987
  • This paper deals with a modeling of manufacturing system and a model analysis by a SIMAN language. A flow of production process is analyzed, and a mathematical model on the basis of the analyzed data is simulated by a SIMAN language. An object of this study is to achieve an optimization of production a reduction of cost, and an improvement of quality by a applicable line-balancing technique and an optimization technique in a real factor induced an analysis and synthesis of the result of simulation.

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The Motion Transformation of Character Included Contrained Optimization Problem (구속조건을 고려한 캐릭터의 움직임 변경)

  • 이지홍;이원희;조인성
    • Proceedings of the IEEK Conference
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    • 2002.06c
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    • pp.223-226
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    • 2002
  • If one can easily modify the existing motion data to a new motion in making an animation movie, he can save a lot of time for graphic design. To implement this kind of system, we propose a PC-based system composed of low cost commercial animation tool (3D Studio Max) for visualization of the animation and motion editing module that handles optimization process during the motion transform. Researchers studying advanced motion transform techniques only have to focus on the mathematical manipulation of the motion data

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Shape Optimization of the H-shape Spacer Grid Spring Structure

  • Yoon, Kyung-Ho;Kim, Hyung-Kyu;Kang, Heung-Seok;Song, Kee-Nam;Park, Ki-Jong
    • Nuclear Engineering and Technology
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    • v.33 no.5
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    • pp.547-555
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    • 2001
  • In pressurized light water reactor fuel assembly, spacer grids support nuclear fuel rods both laterally and vertically. The fuel rods are supported by spacer grid springs and grid dimples that are located in the grid cell. The support system allows for some thermal expansion and imbalance of the fuel rods. The imbalance is absorbed by elastic energy to prevent coolant flow- induced vibration damage. Design requirements are defined and a design process is established. The design process includes mathematical optimization as well as practical design method. The shape of the grid spring is designed to maintain its function during the lifetime of the fuel assembly. A structural optimization method is employed for the shape design. Since the optimization is carried out in the linear range of finite element analysis, the optimum solution is verified by nonlinear analysis. A good design is found and the final design is compared with the initial conceptual design. Commercial codes are utilized for structural analysis and optimization.

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Shape Optimization of a Heat Exchanger with Internally Finned Tube (내부핀이 부착된 원형관 열교환기의 형상 최적화)

  • Lee, Ju-Hee;Lee, Sang-Hwan;Park, Kyoung-Woo;Choi, Dong-Hoon
    • Proceedings of the KSME Conference
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    • 2004.04a
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    • pp.1418-1423
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    • 2004
  • Optimization of a heat exchanger with internally finned circular tubes has been performed for three-dimensional periodically fully developed turbulent flow and heat transfer. The design variables of fin number N, fin width ($d_1,d_2$) and fin height(H), are numerically optimized for the limiting conditions of $N=22{\sim}37$, $d_1=0.5{\sim}1.5$ mm, $d_2=0.5{\sim}1.5$ mm, $H=0.1{\sim}1.5$. Due to the periodic boundary conditions along main flow direction, the three layers of meshes are considered. The CFD and the mathematical optimization are coupled to optimize the heat exchanger. The flow and thermal fields are predicted using the finite volume method and the optimization is carried out by using the sequential quadratic programming (SQP) method which is widely used in the constrained nonlinear optimization problem.

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Minimization of a Cogging Torque for an Interior Permanent Magnet Synchronous Machine using a Novel Hybrid Optimization Algorithm

  • Kim, Il-Woo;Woo, Dong-Kyun;Lim, Dong-Kuk;Jung, Sang-Yong;Lee, Cheol-Gyun;Ro, Jong-Suk;Jung, Hyun-Kyo
    • Journal of Electrical Engineering and Technology
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    • v.9 no.3
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    • pp.859-865
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    • 2014
  • Optimization of an electric machine is mainly a nonlinear multi-modal problem. For the optimization of the multi-modal problem, many function calls are required with much consumption of time. To address this problem, this paper proposes a novel hybrid algorithm in which function calls are less than conventional methods. Specifically, the proposed method uses the kriging metamodel and the fill-blank technique to find an approximated solution in a whole problem region. To increase the convergence speed in local peaks, a parallel gradient assisted simplex method is proposed and combined with the kriging meta-model. The correctness and usefulness of the proposed hybrid algorithm is verified through a mathematical test function and applied into the practical optimization as the cogging torque minimization for an interior permanent magnet synchronous machine.

Flow/Heat Transfer Analysis and Shape Optimization of a Heat Exchanger with Internally Finned Tube (내부휜이 부착된 원형관 열교환기의 열/유동 해석 및 최적설계)

  • Lee Juhee;Lee Sanghwan;Lim Hyo-Jae;Park Kyoungwoo
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.29 no.4 s.235
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    • pp.460-468
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    • 2005
  • Analyses of flow and heat transfer characteristics and shape optimization of internally finned circular tubes have been performed for three-dimensional periodically fully developed turbulent flow and heat transfer. CFD and mathematical optimization are coupled in order to optimize the shape of heat exchanger. The design variables such as fin widths $(d_{1},\;d_{2})$ and fin height (h) are numerically optimized by minimizing the pressure loss and maximizing the heat transfer rate for limiting conditions of $d_{1}=0.2\~1.5\;mm,\;d_{2}=0.2\~1.5\;mm,$ and $h=0.2\~1.5mm$. Due to the periodic boundary conditions along main flow direction, the three layers of meshes are considered. The flow and thermal fields are predicted using the finite volume method and the optimization is carried out by means of the sequential quadratic programming (SQP) method which is widely used in the constrained nonlinear optimization problem.

A comparative study of multi-objective evolutionary metaheuristics for lattice girder design optimization

  • Talaslioglu, Tugrul
    • Structural Engineering and Mechanics
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    • v.77 no.3
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    • pp.417-439
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    • 2021
  • The geometric nonlinearity has been successfully integrated with the design of steel structural system. Thus, the tubular lattice girder, one application of steel structural systems have already been optimized to obtain an economic design following the completion of computationally expensive design procedure. In order to decrease its computing cost, this study proposes to employ five multi-objective metaheuristics for the design optimization of geometrically nonlinear tubular lattice girder. Then, the employed multi-objective optimization algorithms (MOAs), NSGAII, PESAII, SPEAII, AbYSS and MoCell are evaluated considering their computing performances. For an unbiased evaluation of their computing performance, a tubular lattice girder with varying size-shape-topology and a benchmark truss design with 17 members are not only optimized considering the geometrically nonlinear behavior, but three benchmark mathematical functions along with the four benchmark linear design problems are also included for the comparison purpose. The proposed experimental study is carried out by use of an intelligent optimization tool named JMetal v5.10. According to the quantitative results of employed quality indicators with respect to a statistical analysis test, MoCell is resulted with an achievement of showing better computing performance compared to other four MOAs. Consequently, MoCell is suggested as an optimization tool for the design of geometrically nonlinear tubular lattice girder than the other employed MOAs.