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北山, 哲士 ; 荒川, 雅生 ; 山崎, 光悦 ; Kitayama, Satoshi ; Arakawa, Masao ; Yamazaki, Koetsu
概要:
金沢大学理工研究域機械工学系<br />This paper proposes a new method which is called as Adaptive Range Particle Swarm Optimization (ARPS
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O), based on Adaptive Range Genetic Algorithm. That is, the search domain is determined by using the mean and standard deviation of each design variable. At the initial search stage it is preferable to explore the design domain widely, and is also preferable to explore the small design domain as the search goes on. To achieve this objective, new parameter which determines the search domain is introduced. Through numerical examples, the effectiveness and validity of proposed method are examined.<br />本講演では,連続型多峰性関数の大域的最適解を求めるために開発されたParticle Swarm Optimizationをさらに発展させ,設計変数の平均と標準偏差を用いて探索領域を適宜変更させる領域適応型Particle Swarm Optimizationを提案する.本論文で提案する方法の有効性を数値計算例を通じて検討する.<br />出版者照会後に全文公開
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Kitayama, Satoshi ; Yamazaki, Koetsu
概要:
This paper presents a simple method to estimate the width of Gaussian kernel based on an adaptive scaling technique. The
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Gaussian kernel is widely employed in radial basis function (RBF) network, support vector machine (SVM), least squares support vector machine (LS-SVM), Kriging models, and so on. It is widely known that the width of the Gaussian kernel in these machine learning techniques plays an important role. Determination of the optimal width is a time-consuming task. Therefore, it is preferable to determine the width with a simple manner. In this paper, we first examine a simple estimate of the width proposed by Nakayama et al. Through the examination, four sufficient conditions for the simple estimate of the width are described. Then, a new simple estimate for the width is proposed. In order to obtain the proposed estimate of the width, all dimensions are equally scaled. A simple technique called the adaptive scaling technique is also developed. It is expected that the proposed simple method to estimate the width is applicable to wide range of machine learning techniques employing the Gaussian kernel. Through examples, the validity of the proposed simple method to estimate the width is examined. © 2011 Elsevier B.V. All rights reserved.
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Kitayama, Satoshi ; Arakawa, Masao ; Yamazaki, Koetsu
概要:
金沢大学理工研究域機械工学系<br />This paper presents a Sequential Approximate Optimization (SAO) procedure that uses the Radial Basis
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Function (RBF) network. If the objective and constraints are not known explicitly but can be evaluated through a computationally intensive numerical simulation, the response surface, which is often called meta-modeling, is an attractive method for finding an approximate global minimum with a small number of function evaluations. An RBF network is used to construct the response surface. The Gaussian function is employed as the basis function in this paper. In order to obtain the response surface with good approximation, the width of this Gaussian function should be adjusted. Therefore, we first examine the width. Through this examination, some sufficient conditions are introduced. Then, a simple method to determine the width of the Gaussian function is proposed. In addition, a new technique called the adaptive scaling technique is also proposed. The sufficient conditions for the width are satisfied by introducing this scaling technique. Second, the SAO algorithm is developed. The optimum of the response surface is taken as a new sampling point for local approximation. In addition, it is necessary to add new sampling points in the sparse region for global approximation. Thus, an important issue for SAO is to determine the sparse region among the sampling points. To achieve this, a new function called the density function is constructed using the RBF network. The global minimum of the density function is taken as the new sampling point. Through the sampling strategy proposed in this paper, the approximate global minimum can be found with a small number of function evaluations. Through numerical examples, the validities of the width and sampling strategy are examined in this paper. © 2010 Springer Science+Business Media, LLC.
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Srirat, Jirasak ; Yamazaki, Koetsu ; Kitayama, Satoshi
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Optimum segmented blank holder shape and its variable blank holder gaps (VBHGs) are determined by a sequential approximate optimization (SAO) with radial basis function network. In deep drawing, wrinkling and tearing of blank sheet are
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major defects. The optimum segmented blank holder shape and its VBHGs are determined to avoid these defects. The Forming Limit Diagram (FLD) is employed to evaluate quantitatively the wrinkling and the tearing. In the numerical examples, a square cup deep drawing is handled. The objective is to minimize the thickness deviation after sheet forming. The wrinkling and the tearing are separately evaluated as the constraints. The dimensions of the segmented blank holder shape and the BHGs are taken as the design variables. The optimization result shows that simultaneous optimization of both the segmented blank holder shape and the VBHGs is one of the effective approaches for improving product quality.
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Kawamoto, Kiichiro ; Yoneyama, Takeshi ; Okada, Masato ; Kitayama, Satoshi ; Chikahisa, Junpei
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This study focused on utilizing a servo die cushion (in conjunction with a servo press) as a "back-pressure load generator," to determine its effect on shape accuracy of the formed part and total forming load in forward extrusion during
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cold forging. The effect of back-pressure load application was confirmed in experiments, and the optimum setting pattern of back-pressure load was considered to minimize both shape accuracy of the formed part and back-pressure energy, which was representative of forming energy using a sequential approximate optimization. The precise back-pressure load control by the servo die cushion enabled the ideal load-pattern setting for optimization to be achieved.
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Kitayama, Satoshi ; Arakawa, Masao ; Yamazaki, Koetsu
概要:
金沢大学大学院自然科学研究科知的システム創成<br />In practical applications, it is important to reduce the function evaluations in the simulat
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ion, and obtain the approximate optimum with high accuracy. To achieve these objectives, the integrative optimization system using the RBF Network (RBFN) and the Generalized Random Tunneling Algorithm (GRTA) is proposed in this paper. This system consists of three parts. (1) Construction of the response surface, (2) Optimization by the GRTA, and (3) Adding the sampling points. The RBFN is used to construct the response surface. The radius on RBFN, which affects the accuracy of response surface, is an important parameter. Firstly new equation for the radius is proposed, based on the examination of existing equation. Secondly a simple sampling strategy to obtain an optimum with high accuracy is also proposed. In general, the objective function and the constraints are approximated, separately. However, the optimum of response surface will often violate the constraints. To avoid such situations, the augmented objective function is utilized in this paper. Then the proposed sampling strategy is applied. Through typical benchmark problems, the validity and effectiveness are examined.
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Kitayama, Satoshi ; Arakawa, Masao ; Yamazaki, Koetsu
概要:
金沢大学大学院自然科学研究科知的システム創成<br />金沢大学工学部<br />This paper proposes a new method which is called as Adaptive Range Particle Swa
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rm Optimization (ARPSO), based on Adaptive Range Genetic Algorithm. That is, the active search domain is determined by using the mean and standard deviation of each design variable. In general, multipoints methods are utilized in the field of evolutionary computation. At the initial search stage it is preferable to explore the search domain widely, and is also preferable to explore the smaller search domain as the search goes on. To achieve this objective, new parameter which determines the active search domain is introduced. This new parameter gradually increases as the search goes on. Finally it is possible to shrink the search domain. The way to determine the maximum value of this new parameter is also shown in this paper. The optimum solution with high accuracy and a. little number of function calls is obtained by proposed method in compared with original Particle Swarm Optimization. Through numerical examples, the effectiveness and validity of proposed method are examined.
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Kitayama, Satoshi ; Arakawa, Masao ; Yamazaki, Koetsu
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In this paper, a simple method for the multi-objective optimization problems by the Particle Swarm Optimization (PSO) is proposed. The objectives of the Multi Objective Evolutionary Algorithms (MOEA) are summarized as follows : (1) To find
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the pareto optimal solutions, (2) To find the pareto optimal solutions as diverse as possible. To achieve these objectives by the PSO for the single objective problems, we propose how to define the g-best in this swarm without introducing some new parameters. That is, one particle among the non-inferior solutions is selected as the g-best to achieve the diversity among the non inferior solutions. The relative distance in the objective space is utilized to select the gbest among the non-inferior solutions. Additionally, some particles among the non inferior solutions are also selected as the gbest of the inferior solutions to find the pareto optimal solutions. The absolute distance in the objective space is utilized to select the g-best of the inferior solutions. We also show the geometric interpretation about the movement of particles. The validity of proposed approach is examined through typical numerical examples.
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Kitayama, Satoshi ; Arakawa, Masao ; Yamazaki, Koetsu
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金沢大学理工研究域機械工学系<br />In this paper, the basic characteristics of the differential evolution (DE) are examined. Thus, one
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is the meta-heuristics, and the other is the global optimization technique. It is said that DE is the global optimization technique, and also belongs to the meta-heuristics. Indeed, DE can find the global minimum through numerical experiments. However, there are no proofs and useful investigations with regard to such comments. In this paper, the DE is compared with the generalized random tunneling algorithm (GRTA) and the particle swarm optimization (PSO) that are the global optimization techniques for continuous design variables. Through the examinations, some common characteristics as the global optimization technique are clarified in this paper. Through benchmark test problems including structural optimization problems, the search ability of DE as the global optimization technique is examined. © 2011 Elsevier B.V. All rights reserved.
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Kitayama, Satoshi ; Hamano, Satoshi ; Yamazaki, Koetsu ; Kubo, Tatsuo ; Nishikawa, Hikaru ; Kinoshita, Hiroshi
概要:
金沢大学理工研究域機械工学系<br />In deep drawing, a low blank holder force (BHF) can cause wrinkling, while a high BHF can lead to te
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aring. Thus, it is important to determine the appropriate BHF to be utilized in the forming process. In this study, a variable blank holder force (VBHF) approach to deep drawing is employed, and a simple closed-loop type algorithm is developed to obtain the VBHF trajectory. The proposed algorithm is divided into two phases. The objective of the first phase is to check wrinkling and tearing. In this phase, a low BHF, which is the cause of wrinkling, is used as the initial BHF; it is then increased to prevent wrinkling. The algorithm is terminated when tearing occurs. In a numerical simulation, the distance between the die and the blank holder is used to measure wrinkling. On the other hand, the thickness of the blank is used to determine the tearing. Next, in the second phase, the deviations in thickness are examined. Wrinkles are also checked in the second phase. By iterating the above two phases, the VBHF trajectory can be obtained. One of the advantages of the VBHF is that it reduces the forming energy. The validity of the proposed algorithm is examined through both a numerical simulation and experiment. © 2010 Springer-Verlag London Limited.
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