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Adaptive extremal optimization by detrended fluctuation analysis
Institution:1. INAOE, Department of Electronics, Luis Enrique Erro No. 1, Tonantzintla, Puebla 72840, Mexico;2. CINVESTAV, Computer Sciences Department, Av. IPN 2508, Mexico City 07360, México;3. SEMTECH/Snowbush Mexico Design Center, Mexico;1. College of Computer Science and Technology, Zhejiang University of Technology, Hangzhou, 310023, P.R. China;2. College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou, 310023, P.R. China;1. Clinical Assistant Professor, Department of Oral and Maxillofacial Surgery, Ewha Womans University Medical Center, Seoul, Korea;2. Resident, Department of Oral and Maxillofacial Surgery, Ninth People''s Hospital, College of Stomatology Shanghai Jiao Tong University School of Medicine, Shanghai, China;3. Professor, Department of Oral and Maxillofacial Surgery, Ninth People''s Hospital, College of Stomatology Shanghai Jiao Tong University School of Medicine, Shanghai, China;4. Professor, Department of Oral and Maxillofacial Surgery, Ninth People''s Hospital, College of Stomatology Shanghai Jiao Tong University School of Medicine, Shanghai, China;6. Associate Professor, Department of Oral and Maxillofacial Surgery, Ninth People''s Hospital, College of Stomatology Shanghai Jiao Tong University School of Medicine, Shanghai, China;5. Associate Professor, Department of Oral and Maxillofacial Surgery, Ninth People''s Hospital, College of Stomatology Shanghai Jiao Tong University School of Medicine, Shanghai, China
Abstract:Global optimization is one of the key challenges in computational physics as several problems, e.g. protein structure prediction, the low-energy landscape of atomic clusters, detection of community structures in networks, or model-parameter fitting can be formulated as global optimization problems. Extremal optimization (EO) has become in recent years one particular, successful approach to the global optimization problem. As with almost all other global optimization approaches, EO is driven by an internal dynamics that depends crucially on one or more parameters. Recently, the existence of an optimal scheme for this internal parameter of EO was proven, so as to maximize the performance of the algorithm. However, this proof was not constructive, that is, one cannot use it to deduce the optimal parameter itself a priori. In this study we analyze the dynamics of EO for a test problem (spin glasses). Based on the results we propose an online measure of the performance of EO and a way to use this insight to reformulate the EO algorithm in order to construct optimal values of the internal parameter online without any input by the user. This approach will ultimately allow us to make EO parameter free and thus its application in general global optimization problems much more efficient.
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