• Title/Summary/Keyword: dual solutions

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Dual Response Surface Optimization using Multiple Objective Genetic Algorithms (다목적 유전 알고리즘을 이용한 쌍대반응표면최적화)

  • Lee, Dong-Hee;Kim, Bo-Ra;Yang, Jin-Kyung;Oh, Seon-Hye
    • Journal of Korean Institute of Industrial Engineers
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    • v.43 no.3
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    • pp.164-175
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    • 2017
  • Dual response surface optimization (DRSO) attempts to optimize mean and variability of a process response variable using a response surface methodology. In general, mean and variability of the response variable are often in conflict. In such a case, the process engineer need to understand the tradeoffs between the mean and variability in order to obtain a satisfactory solution. Recently, a Posterior preference articulation approach to DRSO (P-DRSO) has been proposed. P-DRSO generates a number of non-dominated solutions and allows the process engineer to select the most preferred solution. By observing the non-dominated solutions, the DM can explore and better understand the trade-offs between the mean and variability. However, the non-dominated solutions generated by the existing P-DRSO is often incomprehensive and unevenly distributed which limits the practicability of the method. In this regard, we propose a modified P-DRSO using multiple objective genetic algorithms. The proposed method has an advantage in that it generates comprehensive and evenly distributed non-dominated solutions.

PROXIMAL AUGMENTED LAGRANGIAN AND APPROXIMATE OPTIMAL SOLUTIONS IN NONLINEAR PROGRAMMING

  • Chen, Zhe;Huang, Hai Qiao;Zhao, Ke Quan
    • Journal of applied mathematics & informatics
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    • v.27 no.1_2
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    • pp.149-159
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    • 2009
  • In this paper, we introduce some approximate optimal solutions and an augmented Lagrangian function in nonlinear programming, establish dual function and dual problem based on the augmented Lagrangian function, discuss the relationship between the approximate optimal solutions of augmented Lagrangian problem and that of primal problem, obtain approximate KKT necessary optimality condition of the augmented Lagrangian problem, prove that the approximate stationary points of augmented Lagrangian problem converge to that of the original problem. Our results improve and generalize some known results.

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MULTIOBJECTIVE VARIATIONAL PROGRAMMING UNDER GENERALIZED VECTOR VARIATIONAL TYPE I INVEXITY

  • Kim, Moon-Hee
    • Communications of the Korean Mathematical Society
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    • v.19 no.1
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    • pp.179-196
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    • 2004
  • Mond-Weir type duals for multiobjective variational problems are formulated. Under generalized vector variational type I invexity assumptions on the functions involved, sufficient optimality conditions, weak and strong duality theorems are proved efficient and properly efficient solutions of the primal and dual problems.

A Method Identifying the Optimal Nonbasic Columns for the Problem Size Reduction in Affine Scaling Algorithm (애핀법에 있어서 문제 축소를 위한 최적비기저의 결정 방법)

  • ;;Park, Soondal
    • Journal of the Korean Operations Research and Management Science Society
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    • v.17 no.3
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    • pp.59-65
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    • 1992
  • A modified primal-dual affine scaling algorithm for linear programming is presented. This modified algorithm generates an elipsoid containing all optimal dual solutions at each iteration, then checks whether or not a dual hyperplane intersects this ellipsoid. If the dual hyperplane has no intersection with this ellipsoid, its corresponding column must be optimal nonbasic. By condensing these columns, the size of LP problem can be reduced.

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Resonance and Response of the Submerged Dual Buoy/Porous-Membrane Breakwaters in Oblique Seas

  • Kee, S.T.
    • Journal of Ocean Engineering and Technology
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    • v.15 no.2
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    • pp.22-32
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    • 2001
  • The numerical investigation of obliquely incident wave interactions with fully submerged dual buoy/porous-membrane floating breakwaters placed in parallel with spacing is studied based on linear potential theory and Darcy's law. The numerical solutions are obtained by using a discrete-membrane dynamic model and second-kind modified Bessel function distribution over the entire boundaries of fluid regions. First, numerical solutions for an idealized dual submerged system without buoys are obtained. Second, a more practical dual submerged system with membrane tension provided by buoys at its tops is investigated by the multi-domain boundary element method particularly devised for dual buoy/porous-membrane problems with gaps. The velocity potentials of wave motion are coupled with porous-membrane deformation, and solved simultaneously since the boundary condition on porous-membrane is not known in advance. The effects of varying permeability on membranes and wave characteristics are discussed for the optimum design parameters of systems previously studied. The inclusion of permeability on membrane eliminates the resonances that aggravate the breakwater performance. The system is highly efficient when waves generated by the buoys and membranes were mutually canceled and its energy at resonance frequency dissipates through fine pores on membranes.

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Dual Natural-Convective Flows of Air in a Horizontal Annulus with a Constant Heat Flux Cylinder (일정 열유속 실린더를 갖는 수평 환형 공간에서의 공기의 이중 자연대류 유동)

  • Yoo Joo-Sik
    • Journal of computational fluids engineering
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    • v.4 no.2
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    • pp.1-8
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    • 1999
  • Natural convection in a horizontal annulus with the inner cylinder heated by the application of a constant heat flux and the isothermally cooled outer cylinder is considered, and the transition of flows and the bifurcation phenomenon are numerically investigated for air with Pr=0.7. The zero initial condition always induces a crescent-sheped eddy flow. A bicellular flow in which the fluid descends along the vertical central plane of the annulus can be obtained at high Rayleigh number by introducing artificial numerical disturbances. Dual solutions are found above a certain critical Rayleigh number. Hysteresis phenomena have not been observed.

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Numerical Solutions of Multi-Dimensional Solidification/Melting Problems by the Dual Reciprocity Boundary Element Method

  • Jo, Jong-Chull;Shin, Won-Ky
    • Proceedings of the Korean Nuclear Society Conference
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    • 1997.10a
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    • pp.617-624
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    • 1997
  • This Paper Presents an effective and simple procedure for the simulation of the motion of the solid-liquid interfacial boundary and the transient temperature field during phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual reciprocity boundary element method. The dual reciprocity boundary element approach provided in this paper is much simpler than the usual boundary element method applying a reciprocity principle and an available technique for dealing with domain integral of boundary element formulation simultaneously. The effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of an example with its semi-analytical or other numerical solutions where available.

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Secure Password System against Imposter (타인의 관찰에 의한 패스워드 노출로부터 안전한 패스워드 시스템)

  • Park, Sung-Bae;Park, Seung-Bae;Kang, Moon-Seol
    • The KIPS Transactions:PartC
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    • v.10C no.2
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    • pp.141-144
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    • 2003
  • We present a new password system, called dual password system, with the user verification procedure. Dual password system is the first password system in the world preventing the exposure of secret information to imposter at the terminal. User of dual password system matches two alphabets at same location of first password and second password iteratively for inputting password. Therefore, the deriving method of first password and second password from the password is important in dual password system. Related to the deriving method of first password and second password from password, a new problem, called dual password derivation problem, is defined, and the evaluation factors for the solutions of the dual password derivation problem are presented.

A Posterior Preference Articulation Method to Dual-Response Surface Optimization: Selection of the Most Preferred Solution Using TOPSIS (쌍대반응표면최적화를 위한 사후선호도반영법: TOPSIS를 활용한 최고선호해 선택)

  • Jeong, In-Jun
    • Knowledge Management Research
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    • v.19 no.2
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    • pp.151-162
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    • 2018
  • Response surface methodology (RSM) is one of popular tools to support a systematic improvement of quality of design in the product and process development stages. It consists of statistical modeling and optimization tools. RSM can be viewed as a knowledge management tool in that it systemizes knowledge about a manufacturing process through a big data analysis on products and processes. The conventional RSM aims to optimize the mean of a response, whereas dual-response surface optimization (DRSO), a special case of RSM, considers not only the mean of a response but also its variability or standard deviation for optimization. Recently, a posterior preference articulation approach receives attention in the DRSO literature. The posterior approach first seeks all (or most) of the nondominated solutions with no articulation of a decision maker (DM)'s preference. The DM then selects the best one from the set of nondominated solutions a posteriori. This method has a strength that the DM can understand the trade-off between the mean and standard deviation well by looking around the nondominated solutions. A posterior method has been proposed for DRSO. It employs an interval selection strategy for the selection step. This strategy has a limitation increasing inefficiency and complexity due to too many iterations when handling a great number (e.g., thousands ~ tens of thousands) of nondominated solutions. In this paper, a TOPSIS-based method is proposed to support a simple and efficient selection of the most preferred solution. The proposed method is illustrated through a typical DRSO problem and compared with the existing posterior method.