• Title/Summary/Keyword: polynomial optimization

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Tolerance Optimization of Lower Arm Used in Automobile Parts Considering Six Sigma Constraints (식스시그마 제약조건을 고려한 로워암의 공차 최적설계)

  • Lee, Kwang-Ki;Han, Seung-Ho
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.35 no.10
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    • pp.1323-1328
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    • 2011
  • In the current design process for the lower arm used in automobile parts, an optimal solution of its various design variables should be found through exploration of the design space approximated using the response surface model formulated with a first- or second-order polynomial equation. In this study, a multi-level computational DOE (design of experiment) was carried out to explore the design space showing nonlinear behavior, in terms of factors such as the total weight and applied stress of the lower arm, where a fractional-factorial orthogonal array based on the artificial neural network model was introduced. In addition, the tolerance robustness of the optimal solution was estimated using a tolerance optimization with six sigma constraints, taking into account the tolerances occurring in the design variables.

Effect of Various Regression Functions on Structural Optimizations Using the Central Composite Method (중심합성법에 의한 구조최적화에서 회귀함수변화의 영향)

  • Park, Jung-Sun;Jeon, Yong-Sung;Im, Jong-Bin
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.33 no.1
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    • pp.26-32
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    • 2005
  • In this paper, the effect of various regression models is investigated on structural optimization using the central composite method. Three bar truss and the upper platform of a satellite are optimized using various regression models that are polynomial, exponential and log functions. Response surface method is non-gradient, semi-global, discrete and fast converging in optimization problem. Sampling points are extracted by the design of experiments using the central composite method. Response surface is generated using the various regression functions. Structural analysis for calculating constraints is executed to find static and dynamic responses. From this study, it is verified that the response surface method has advantage in optimum value and computation time in comparison to other optimization methods.

Effects of Strawberry Puree and Red Pepper Powder Contents on Physicochemical Properties of Kochujang Analyzed Using Response Surface Methodology

  • Lee, Jun-Ho;Kim, Hui-Jeong
    • Preventive Nutrition and Food Science
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    • v.13 no.3
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    • pp.231-236
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    • 2008
  • Response surface methodology (RSM) was used for the analysis and optimization of the production process of strawberry Kochujang. Experiments were carried out according to a central composite design, selecting strawberry puree content and red pepper powder content as independent variables and soluble solids content, moisture content, water activity, color characteristics ($L^*-$, $a^*-$, and $b^*$-values) as response variables. The polynomial models developed by RSM were highly effective for describing the relationships between the study factors and the responses. Kochujang containing a higher amount of red pepper powder had a higher soluble solids content; on the contrary, soluble solids content decreased with the increase in the strawberry puree content in the sample. Moisture content increased with increased strawberry puree content but decreased with increased red pepper powder content. Water activity increased with the increase in strawberry puree content in the sample but was less affected by the amount of red pepper powder content. Decreases in $L^*$-values with increasing amount of red pepper powder were noted. $a^*$-values decreased with the increases in red pepper powder content but increased with the increase in strawberry puree content in the Kochujang formulation. $b^*$-values decreased with the increases in red pepper powder content but was less affected by the strawberry puree content. Overall optimization, conducted by overlaying the contour plots under investigation, was able to point out an optimal range of the independent variables within which the six responses were simultaneously optimized. The point chosen as representative of this optimal area corresponded to strawberry puree content=14.36% and red pepper powder content=11.33%, conditions under which the model predicted soluble solids content=$59.31^{\circ}Brix$, moisture content=45.30% (w.b.), water activity=0.758, $L^*$-value=24.81, $a^*$-value=7.250, and $b^*$-value=10.19.

Improved Valve-Point Optimization Algorithm for Economic Load Dispatch Problem with Non-convex Fuel Cost Function (비볼록 발전비용함수 경제급전문제의 개선된 밸브지점 최적화 알고리즘)

  • Lee, Sang-Un
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.15 no.6
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    • pp.257-266
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    • 2015
  • There is no polynomial-time algorithm that can be obtain the optimal solution for economic load dispatch problem with non-convex fuel cost functions. Therefore, electrical field uses quadratic fuel cost function unavoidably. This paper proposes a valve-point optimization (VPO) algorithm for economic load dispatch problem with non-convex fuel cost functions. This algorithm sets the initial values to maximum powers $P_i{\leftarrow}P_i^{max}$ for each generator. It then reduces the generation power of generator i with an average power cost of $_{max}\bar{c}_i$ to a valve point power $P_{ik}$. The proposed algorithm has been found to perform better than the extant heuristic methods when applied to 13 and 40-generator benchmark data. This paper consequently proves that the optimal solution to economic load dispatch problem with non-convex fuel cost functions converges to the valve-point power of each generator.

Optimization for the Sugaring Process of Yam for Snack Food Using Response Surface Methodology (마스낵 제조를 위한 당절임 공정의 최적화)

  • 한주영;김남우;황성희;윤광섭;신승렬
    • Food Science and Preservation
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    • v.10 no.3
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    • pp.320-325
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    • 2003
  • This study was conducted to optimize sugaring process of yam for development of new snack product and enhancement acceptability. Three variables by five level central composite design and response surface methodology were used to determine optimum conditions for sugaring time, temperature and concentration. Optimization of the process was conducted using the combination of the moisture content, solid content, color and rehydration ratio. The regression polynomial model was suitable (P>0.05) model by Lack-of-Fit analysis with highly significant. To optimize the process, based on surface response and contour plots, superimposing the individual contour plots for the response variables. The optimum conditions for this process were 5.5 hours and 58% at 40$^{\circ}C$ under the optimum of restricted variables as moisture content was 66 to 70, solid content was 25 to 30%, L value was above 75, a value was -2.1 to -2.4, b value was above 5 and rehydration ratio was 200 to 250.

A Study for searching optimized combination of Spent light water reactor fuel to reuse as heavy water reactor fuel by using evolutionary algorithm (진화 알고리즘을 이용한 경수로 폐연료의 중수로 재사용을 위한 최적 조합 탐색에 관한 연구)

  • 안종일;정경숙;정태충
    • Journal of Intelligence and Information Systems
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    • v.3 no.2
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    • pp.1-9
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    • 1997
  • These papers propose an evolutionary algorithm for re-using output of waste fuel of light water reactor system in nuclear power plants. Evolutionary algorithm is useful for optimization of the large space problem. The wastes contain several re-useable elements, and they should be carefully selected and blended to satisfy requirements as input material to the heavy water nuclear reactor system. This problem belongs to a NP-hard like the 0/1 Knapsack problem. Two evolutionary strategies are used as a, pp.oximation algorithms in the highly constrained combinatorial optimization problem. One is the traditional strategy, using random operator with evaluation function, and the other is heuristic based search that uses the vector operator reducing between goal and current status. We also show the method, which performs the feasible teat and solution evaluation by using the vectorized data in problem. Finally, We compare the simulation results of using random operator and vector operator for such combinatorial optimization problems.

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The Optimum Design of Airfoil Shape with Parallel Computation (병렬연산을 이용한 익형의 최적 설계)

  • Jo,Jang-Geun;Park,Won-Gyu
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.31 no.1
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    • pp.1-7
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    • 2003
  • The aerodynamic optimization method for airfoil design was described in this paper. The Navier-Stokes equations were solved to consider the viscous flow information around an airfoil. The Modified Method of Feasible Direction(MMFD) was used for sensitivity analysis and the polynomial interpolation was used for distance calculation of the minimization. The Message Passing Interface(MPI) library of parallel computation was adopted to reduce the computation time of flow solver by decomposing the entire computational domain into 8 sub-domains and one-to-one allocating 8 processors to 8 sub-domains. The parallel computation was also used to compute the sensitivity analysis by allocating each search direction to each processor. The present optimization reduced the drag of airfoil while the lift is maintained at the tolerable design value.

An Evaluation of Multiple-input Dual-output Run-to-Run Control Scheme for Semiconductor Manufacturing

  • Fan, Shu-Kai-S.;Lin, Yen
    • Industrial Engineering and Management Systems
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    • v.4 no.1
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    • pp.54-67
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    • 2005
  • This paper provides an evaluation of an optimization-based, multiple-input double-output (MIDO) run-to-run (R2R) control scheme for general semiconductor manufacturing processes. The controller in this research, termed adaptive dual response optimizing controller (ADROC), can serve as a process optimizer as well as a recipe regulator between consecutive runs of wafer fabrication. In evaluation, it is assumed that the equipment model could be appropriately described by a pair of second-order polynomial functions in terms of a set of controllable variables. Of practical relevance is to consider a drifting effect in the equipment model since in common semiconductor practice the process tends to drift due to machine aging and tool wearing. We select a typical application of R2R control to chemical mechanical planarization (CMP) in semiconductor manufacturing in this evaluation, and there are five different CMP process scenarios demonstrated, including mean shift, variance increase, and IMA disturbances. For the controller, ADROC, an on-line estimation technique is implemented in a self-tuning (ST) control manner for the adaptation purpose. Subsequently, an ad hoc global optimization algorithm based on the dual response approach, arising from the response surface methodology (RSM) literature, is used to seek the optimum recipe within the acceptability region for the execution of next run. The main components of ADROC are described and its control performance is assessed. It reveals from the evaluation that ADROC can provide excellent control actions for the MIDO R2R situations even though the process exhibits complicated, nonlinear interaction effects between control variables, and the drifting disturbances.

An Optimum Design of Steel Frames by Second Order Elastic Analysis (2차 탄성해석법에 의한 강뼈대 구조물의 최적설계)

  • Park, Moon-Ho;Jang, Chun-Ho;Kim, Ki-Wook
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.10 no.2
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    • pp.123-133
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    • 2006
  • The main objective of this study is to develop an optimization algorithm of framed structures with rigid and various semi-rigid connections using the multilevel dynamic programming and the sequential unconstrained minimization techniques (SUMT). The second-order elastic analysis is performed for steel framed structures. The second order elastic analysis is developed based on nonlinear beam-column theory considering the bowing effect. The following semi-rigid connections are considered; double web angle, top-seat angle and top-seat angle with web angle. We considered the three connection models, such as modified exponential, polynomial and three parameter model. The total weight of the structural steel is used as the objective function in the optimization process. The dimensions of steel cross section are selected as the design variables. The design constraints consist of strength requirements for axial, shear and flexural resistance and serviceability requirements.

A New Tree Representation for Evolutionary Algorithms (진화 알고리듬을 위한 새로운 트리 표현 방법)

  • Soak, Sang-Moon;Ahn, Byung-Ha
    • Journal of Korean Institute of Industrial Engineers
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    • v.31 no.1
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    • pp.10-19
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    • 2005
  • The minimum spanning tree (MST) problem is one of the traditional optimization problems. Unlike the MST, the degree constrained minimum spanning tree (DCMST) of a graph cannot, in general, be found using a polynomial time algorithm. So, finding the DCMST of a graph is a well-known NP-hard problem of importance in communications network design, road network design and other network-related problems. So, it seems to be natural to use evolutionary algorithms for solving DCMST. Especially, when applying an evolutionary algorithm to spanning tree problems, a representation and search operators should be considered simultaneously. This paper introduces a new tree representation scheme and a genetic operator for solving combinatorial tree problem using evolutionary algorithms. We performed empirical comparisons with other tree representations on several test instances and could confirm that the proposed method is superior to other tree representations. Even it is superior to edge set representation which is known as the best algorithm.