Design space exploration and optimization using self-organizing maps
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RESEARCH PAPER
Design space exploration and optimization using self-organizing maps Sidhant Pravinkumar Thole1
· Palaniappan Ramu1
Received: 16 March 2020 / Revised: 23 May 2020 / Accepted: 18 June 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Identifying regions of interest (RoI) in the design space is extremely useful while building metamodels with limited computational budget. Self-organizing maps (SOM) are used as a visualization technique for design space exploration that permits identifying RoI. Conventional implementation of SOM is susceptible to folds or intersections that hinder visualizing the design space. This work proposes a modified SOM algorithm whose maps are interpretable and that does not fold and allows smoother input and performance space visualization. The modified algorithm enables identification of RoI and additional sampling in the identified RoI allows building accurate Kriging metamodel, which is then used for optimization. The proposed approach is demonstrated on benchmark nonlinear analytical examples and two practical engineering design examples. Results show that the proposed approach is highly efficient in identifying the RoI and in obtaining the optima with less samples. Keywords Design space exploration · Self-organizing maps · Design of experiments
1 Introduction In the context of design optimization that involves expensive computer models, metamodels are used to alleviate the prohibitive computational expense. In order to build an accurate metamodel, information to some degree about the true function’s nonlinearity in the design space is required. This information influences the choice of basis functions, kernels, and the minimum sample size required. For the same sample size, the accuracy of the metamodel deteriorates with the increase in the size of the design space and dimensions (Wang and Simpson 2004b). Therefore, metamodel accuracy, number of samples, size of design space, and number of dimensions are always a tradeoff. For a given sample size, researchers address the above challenges using dimension reduction techniques (Chowdhury et al. 2009; Constantine et al. 2014; Berguin Responsible Editor: Axel Schumacher Palaniappan Ramu
[email protected] Sidhant Pravinkumar Thole [email protected] 1
Department of Engineering Design, Indian Institute of Technology Madras, Tamil Nadu, India
and Mavris 2015; Diez et al. 2015) and reduction of the design space by decomposing it into multiple regions of interest (RoI) (Wang and Shan 2004a, b; Missoum et al. 2007; Tseng et al. 2014). In the dimension reduction techniques, the underlying idea is to identify major factors and express the function in terms of these factors. Though these techniques are helpful in reducing computational time, the reverse mapping of the low dimension to original higher dimension is not possible. Hence, design space reduction techniques are an attractive alternate. The prime idea in design space reduction is to identify the “sweet spots” or RoI within the design spac
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