• Title, Summary, Keyword: vector optimization

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ON SECOND ORDER NECESSARY OPTIMALITY CONDITIONS FOR VECTOR OPTIMIZATION PROBLEMS

  • Lee, Gue-Myung;Kim, Moon-Hee
    • Journal of the Korean Mathematical Society
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    • v.40 no.2
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    • pp.287-305
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    • 2003
  • Second order necessary optimality condition for properly efficient solutions of a twice differentiable vector optimization problem is given. We obtain a nonsmooth version of the second order necessary optimality condition for properly efficient solutions of a nondifferentiable vector optimization problem. Furthermore, we prove a second order necessary optimality condition for weakly efficient solutions of a nondifferentiable vector optimization problem.

Reliability-Based Topology Optimization Using Single-Loop Single-Vector Approach (단일루프 단일벡터 방법을 이용한 신뢰성기반 위상최적설계)

  • Bang Seung-Hyun;Min Seung-Jae
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.30 no.8
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    • pp.889-896
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    • 2006
  • The concept of reliability has been applied to the topology optimization based on a reliability index approach or a performance measure approach. Since these approaches, called double-loop single vector approach, require the nested optimization problem to obtain the most probable point in the probabilistic design domain, the time for the entire process makes the practical use infeasible. In this work, new reliability-based topology optimization method is proposed by utilizing single-loop single-vector approach, which approximates searching the most probable point analytically, to reduce the time cost. The results of design examples show that the proposed method provides efficiency curtailing the time for the optimization process and accuracy satisfying the specified reliability.

ON LINEARIZED VECTOR OPTIMIZATION PROBLEMS WITH PROPER EFFICIENCY

  • Kim, Moon-Hee
    • Journal of applied mathematics & informatics
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    • v.27 no.3_4
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    • pp.685-692
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    • 2009
  • We consider the linearized (approximated) problem for differentiable vector optimization problem, and then we establish equivalence results between a differentiable vector optimization problem and its associated linearized problem under the proper efficiency.

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GENERALIZATIONS OF ISERMANN'S RESULTS IN VECTOR OPTIMIZATION

  • Lee, Gue-Myung
    • Bulletin of the Korean Mathematical Society
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    • v.30 no.1
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    • pp.1-7
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    • 1993
  • Vector optimization problems consist of two or more objective functions and constraints. Optimization entails obtaining efficient solutions. Geoffrion [3] introduced the definition of the properly efficient solution in order to eliminate efficient solutions causing unbounded trade-offs between objective functions. In 1974, Isermann [7] obtained a necessary and sufficient condition for an efficient solution of a linear vector optimization problem with linear constraints and showed that every efficient solution is a properly efficient solution. Since then, many authors [1, 2, 4, 5, 6] have extended the Isermann's results. In particular, Gulati and Islam [4] derived a necessary and sufficient condition for an efficient solution of a linear vector optimization problem with nonlinear constraints, under certain assumptions. In this paper, we consider the following nonlinear vector optimization problem (NVOP): (Fig.) where for each i, f$_{i}$ is a differentiable function from R$^{n}$ into R and g is a differentiable function from R$^{n}$ into R$^{m}$ .

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Direction Vector for Efficient Structural Optimization with Genetic Algorithm (효율적 구조최적화를 위한 유전자 알고리즘의 방향벡터)

  • Lee, Hong-Woo
    • Journal of the Korean Association for Spatial Structures
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    • v.8 no.3
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    • pp.75-82
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    • 2008
  • In this study, the modified genetic algorithm, D-GA, is proposed. D-GA is a hybrid genetic algorithm combined a simple genetic algorithm and the local search algorithm using direction vectors. Also, two types of direction vectors, learning direction vector and random direction vector, are defined without the sensitivity analysis. The accuracy of D-GA is compared with that of simple genetic algorithm. It is demonstrated that the proposed approach can be an effective optimization technique through a minimum weight structural optimization of ten bar truss.

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Design of SVM-Based Polynomial Neural Networks Classifier Using Particle Swarm Optimization (입자군집 최적화를 이용한 SVM 기반 다항식 뉴럴 네트워크 분류기 설계)

  • Roh, Seok-Beom;Oh, Sung-Kwun
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.67 no.8
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    • pp.1071-1079
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    • 2018
  • In this study, the design methodology as well as network architecture of Support Vector Machine based Polynomial Neural Network, which is a kind of the dynamically generated neural networks, is introduced. The Support Vector Machine based polynomial neural networks is given as a novel network architecture redesigned with the aid of polynomial neural networks and Support Vector Machine. The generic polynomial neural networks, whose nodes are made of polynomials, are dynamically generated in each layer-wise. The individual nodes of the support vector machine based polynomial neural networks is constructed as a support vector machine, and the nodes as well as layers of the support vector machine based polynomial neural networks are dynamically generated as like the generation process of the generic polynomial neural networks. Support vector machine is well known as a sort of robust pattern classifiers. In addition, in order to enhance the structural flexibility as well as the classification performance of the proposed classifier, multi-objective particle swarm optimization is used. In other words, the optimization algorithm leads to sequentially successive generation of each layer of support vector based polynomial neural networks. The bench mark data sets are used to demonstrate the pattern classification performance of the proposed classifiers through the comparison of the generalization ability of the proposed classifier with some already studied classifiers.

PROPER EFFICIENCY FOR SET-VALUED OPTIMIZATION PROBLEMS AND VECTOR VARIATIONAL-LIKE INEQUALITIES

  • Long, Xian Jun;Quan, Jing;Wen, Dao-Jun
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.3
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    • pp.777-786
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    • 2013
  • The purpose of this paper is to establish some relationships between proper efficiency of set-valued optimization problems and proper efficiency of vector variational-like inequalities under the assumptions of generalized cone-preinvexity. Our results extend and improve the corresponding results in the literature.

VECTOR OPTIMIZATION INVOLVING GENERALIZED SEMILOCALLY PRE-INVEX FUNCTIONS

  • GUPTA, SUDHA;SHARMA, VANI;CHAUDHARY, MAMTA
    • Journal of applied mathematics & informatics
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    • v.33 no.3_4
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    • pp.235-246
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    • 2015
  • In this paper, a vector optimization problem over cones is considered, where the functions involved are $\eta$-semidifferentiable. Necessary and sufficient optimality conditions are obtained. A dual is formulated and duality results are proved using the concepts of cone $\rho$-semilocally preinvex, cone $\rho$-semilocally quasi-preinvex and cone $\rho$-semilocally pseudo-preinvex functions.

Optimal design of homogeneous earth dams by particle swarm optimization incorporating support vector machine approach

  • Mirzaei, Zeinab;Akbarpour, Abolfazl;Khatibinia, Mohsen;Siuki, Abbas Khashei
    • Geomechanics and Engineering
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    • v.9 no.6
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    • pp.709-727
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    • 2015
  • The main aim of this study is to introduce optimal design of homogeneous earth dams with oblique and horizontal drains based on particle swarm optimization (PSO) incorporating weighted least squares support vector machine (WLS-SVM). To achieve this purpose, the upstream and downstream slopes of earth dam, the length of oblique and horizontal drains and angle among the drains are considered as the design variables in the optimization problem of homogeneous earth dams. Furthermore, the seepage through dam body and the weight of dam as objective functions are minimized in the optimization process simultaneously. In the optimization procedure, the stability coefficient of the upstream and downstream slopes and the seepage through dam body as the hydraulic responses of homogeneous earth dam are required. Hence, the hydraulic responses are predicted using WLS-SVM approach. The optimal results of illustrative examples demonstrate the efficiency and computational advantages of PSO with WLS-SVM in the optimal design of homogeneous earth dams with drains.