• Title/Summary/Keyword: global optimization

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A B-spline based Branch & Bound Algorithm for Global Optimization (전역 최적화를 위한 B-스플라인 기반의 Branch & Bound알고리즘)

  • Park, Sang-Kun
    • Korean Journal of Computational Design and Engineering
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    • v.15 no.1
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    • pp.24-32
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    • 2010
  • This paper introduces a B-spline based branch & bound algorithm for global optimization. The branch & bound is a well-known algorithm paradigm for global optimization, of which key components are the subdivision scheme and the bound calculation scheme. For this, we consider the B-spline hypervolume to approximate an objective function defined in a design space. This model enables us to subdivide the design space, and to compute the upper & lower bound of each subspace where the bound calculation is based on the LHS sampling points. We also describe a search tree to represent the searching process for optimal solution, and explain iteration steps and some conditions necessary to carry out the algorithm. Finally, the performance of the proposed algorithm is examined on some test problems which would cover most difficulties faced in global optimization area. It shows that the proposed algorithm is complete algorithm not using heuristics, provides an approximate global solution within prescribed tolerances, and has the good possibility for large scale NP-hard optimization.

Individual and Global Optimization of Switched Flux Permanent Magnet Motors

  • Zhu, Z.Q.;Liu, X.
    • Journal of international Conference on Electrical Machines and Systems
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    • v.1 no.1
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    • pp.32-39
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    • 2012
  • With the aid of genetic algorithm (GA), global optimization with multiple geometry parameters is feasible in the design of switched flux permanent magnet (SFPM) machines. To investigate the advantages of global optimization over individual optimization, which has been used extensively for the design of SFPM machines, a comparison between the two approaches is carried out for the case of fixed copper loss and volume. In the case of individual parameter optimization, the sequence in which the individual parameters are optimized is very important. In the global optimization a better design can always be achieved although the corresponding torque density is found to be only slightly better than that of individually optimized with correct design sequence. By using the obtained global optimization results, the performance in machines having two types of stator and rotor pole combinations, i.e. 12/10 and 12/14, are compared, and it is shown that higher torque is exhibited in the 12/14 SFPM machine. Finally, this paper also demonstrates that global optimization, with the restriction of equal pole width, magnet thickness and slot opening, can maximize the torque density without significantly sacrificing other performance, such as cogging torque and overload capability.

Efficient Adaptive Global Optimization for Constrained Problems (구속조건이 있는 문제의 적응 전역최적화 효율 향상에 대한 연구)

  • Ahn, Joong-Ki;Lee, Ho-Il;Lee, Sung-Mhan
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.38 no.6
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    • pp.557-563
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    • 2010
  • This paper addresses the issue of adaptive global optimization using Kriging metamodel known as EGO(Efficient Global Optimization). The algorithm adaptively chooses where to generate subsequent samples based on an explicit trade-off between reduction of global uncertainty and exploration of the region of the interest. A strategy that saves the computational cost by using expectations derived from probabilistic nature of approximate model is proposed. At every iteration, a candidate test point that seems to be feasible/inactive or has little possibility to improve for minimum is identified and excluded from updating approximate models. By doing that the computational cost is saved without loss of accuracy.

Hull Form Optimization using Parametric Modification Functions and Global Optimization (전역 최적화기법과 파라메트릭 변환함수를 이용한 선형 최적화)

  • Kim, Hee-Jung;Chun, Ho-Hwan;An, Nam-Hyun
    • Journal of the Society of Naval Architects of Korea
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    • v.45 no.6
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    • pp.590-600
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    • 2008
  • This paper concerns the development of a designer friendly hull form parameterization and its coupling with advanced global optimization algorithms. As optimization algorithms, we choose the Partial Swarm Optimization(PSO) recently introduced to solve global optimization problems. Most general-purpose optimization softwares used in industrial applications use gradient-based algorithms, mainly due to their convergence properties and computational efficiency when a relatively few number of variables are considered. However, local optimizers have difficulties with local minima and non-connected feasible regions. Because of the increase of computer power and of the development of efficient Global Optimization (GO) methods, in recent years nongradient-based algorithms have attracted much attention. Furthermore, GO methods provide several advantages over local approaches. In the paper, the derivative-based SQP and the GO approach PSO are compared with their relative performances in solving some typical ship design optimization problem focusing on their effectiveness and efficiency.

Design of Two-group Zoom Lens System with Wide Angle of View Using Global Structure Function (전역구조함수를 사용한 광각 2군 줌 렌즈의 설계)

  • Kwon, Hyuk-Joon;Rim, Cheon-Seog
    • Korean Journal of Optics and Photonics
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    • v.20 no.6
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    • pp.319-327
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    • 2009
  • We introduce a new design technique by treating a two-group zoom lens system with a wide angle of view. First, the concept of the global optimization is introduced in the initial design stage, and from this, the global design technique is completed by analyzing and summarizing large quantities of modern design data. That is, we define the global structure function to achieve a new conceptual design technique for global optimization. And the function is put in a simple form by referring lots of patent data, manipulated with other algebraic equations, and solved finally such that we obtain the global solution region. The global solution region corresponds to the global optimization and suggests insightful systematized directions for the design of two-group zoom lens systems. These directions are attractive compared to global optimization.

A NOVEL FILLED FUNCTION METHOD FOR GLOBAL OPTIMIZATION

  • Lin, Youjiang;Yang, Yongjian;Zhang, Liansheng
    • Journal of the Korean Mathematical Society
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    • v.47 no.6
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    • pp.1253-1267
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    • 2010
  • This paper considers the unconstrained global optimization with the revised filled function methods. The minimization sequence could leave from a local minimizer to a better minimizer of the objective function through minimizing an auxiliary function constructed at the local minimizer. Some promising numerical results are also included.

Global Optimization Using Differential Evolution Algorithm (차분진화 알고리듬을 이용한 전역최적화)

  • Jung, Jae-Joon;Lee, Tae-Hee
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.27 no.11
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    • pp.1809-1814
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    • 2003
  • Differential evolution (DE) algorithm is presented and applied to global optimization in this research. DE suggested initially fur the solution to Chebychev polynomial fitting problem is similar to genetic algorithm(GA) including crossover, mutation and selection process. However, differential evolution algorithm is simpler than GA because it uses a vector concept in populating process. And DE turns out to be converged faster than CA, since it employs the difference information as pseudo-sensitivity In this paper, a trial vector and its control parameters of DE are examined and unconstrained optimization problems of highly nonlinear multimodal functions are demonstrated. To illustrate the efficiency of DE, convergence rates and robustness of global optimization algorithms are compared with those of simple GA.

A Global Optimization Method of Radial Basis Function Networks for Function Approximation (함수 근사화를 위한 방사 기저함수 네트워크의 전역 최적화 기법)

  • Lee, Jong-Seok;Park, Cheol-Hoon
    • The KIPS Transactions:PartB
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    • v.14B no.5
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    • pp.377-382
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    • 2007
  • This paper proposes a training algorithm for global optimization of the parameters of radial basis function networks. Since conventional training algorithms usually perform only local optimization, the performance of the network is limited and the final network significantly depends on the initial network parameters. The proposed hybrid simulated annealing algorithm performs global optimization of the network parameters by combining global search capability of simulated annealing and local optimization capability of gradient-based algorithms. Via experiments for function approximation problems, we demonstrate that the proposed algorithm can find networks showing better training and test performance and reduce effects of the initial network parameters on the final results.

A STUDY ON CONSTRAINED EGO METHOD FOR NOISY CFD DATA (Noisy 한 CFD 결과에 대한 구속조건을 고려한 EGO 방법 연구)

  • Bae, H.G.;Kwon, J.H.
    • Journal of computational fluids engineering
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    • v.17 no.4
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    • pp.32-40
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    • 2012
  • Efficient Global Optimization (EGO) method is a global optimization technique which can select the next sample point automatically by infill sampling criteria (ISC) and search for the global minimum with less samples than what the conventional global optimization method needs. ISC function consists of the predictor and mean square error (MSE) provided from the kriging model which is a stochastic metamodel. Also the constrained EGO method can minimize the objective function dealing with the constraints under EGO concept. In this study the constrained EGO method applied to the RAE2822 airfoil shape design formulated with the constraint. But the noisy CFD data caused the kriging model to fail to depict the true function. The distorted kriging model would make the EGO deviate from the correct search. This distortion of kriging model can be handled with the interpolation(p=free) kriging model. With the interpolation(p=free) kriging model, however, the search of EGO solution was stalled in the narrow feasible region without the chance to update the objective and constraint functions. Then the accuracy of EGO solution was not good enough. So the three-step search method was proposed to obtain the accurate global minimum as well as prevent from the distortion of kriging model for the noisy constrained CFD problem.