Acceleration of Global Optimization Algorithm by Detecting Local Extrema Based on Machine Learning
This paper features the study of global optimization problems and numerical methods of their solution. Such problems are computationally expensive since the objective function can be multi-extremal, nondifferentiable, and, as a rule, given in the form of a “black box”. This study used a deterministi...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-09-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/10/1272 |
| _version_ | 1797514651422949376 |
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| author | Konstantin Barkalov Ilya Lebedev Evgeny Kozinov |
| author_facet | Konstantin Barkalov Ilya Lebedev Evgeny Kozinov |
| author_sort | Konstantin Barkalov |
| collection | DOAJ |
| description | This paper features the study of global optimization problems and numerical methods of their solution. Such problems are computationally expensive since the objective function can be multi-extremal, nondifferentiable, and, as a rule, given in the form of a “black box”. This study used a deterministic algorithm for finding the global extremum. This algorithm is based neither on the concept of multistart, nor nature-inspired algorithms. The article provides computational rules of the one-dimensional algorithm and the nested optimization scheme which could be applied for solving multidimensional problems. Please note that the solution complexity of global optimization problems essentially depends on the presence of multiple local extrema. In this paper, we apply machine learning methods to identify regions of attraction of local minima. The use of local optimization algorithms in the selected regions can significantly accelerate the convergence of global search as it could reduce the number of search trials in the vicinity of local minima. The results of computational experiments carried out on several hundred global optimization problems of different dimensionalities presented in the paper confirm the effect of accelerated convergence (in terms of the number of search trials required to solve a problem with a given accuracy). |
| first_indexed | 2024-03-10T06:34:37Z |
| format | Article |
| id | doaj.art-55fae30583604c84922812d5ac6ba8a3 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T06:34:37Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-55fae30583604c84922812d5ac6ba8a32023-11-22T18:10:27ZengMDPI AGEntropy1099-43002021-09-012310127210.3390/e23101272Acceleration of Global Optimization Algorithm by Detecting Local Extrema Based on Machine LearningKonstantin Barkalov0Ilya Lebedev1Evgeny Kozinov2Department of Mathematical Software and Supercomputing Technologies, Lobachevsky University, 603950 Nizhny Novgorod, RussiaDepartment of Mathematical Software and Supercomputing Technologies, Lobachevsky University, 603950 Nizhny Novgorod, RussiaDepartment of Mathematical Software and Supercomputing Technologies, Lobachevsky University, 603950 Nizhny Novgorod, RussiaThis paper features the study of global optimization problems and numerical methods of their solution. Such problems are computationally expensive since the objective function can be multi-extremal, nondifferentiable, and, as a rule, given in the form of a “black box”. This study used a deterministic algorithm for finding the global extremum. This algorithm is based neither on the concept of multistart, nor nature-inspired algorithms. The article provides computational rules of the one-dimensional algorithm and the nested optimization scheme which could be applied for solving multidimensional problems. Please note that the solution complexity of global optimization problems essentially depends on the presence of multiple local extrema. In this paper, we apply machine learning methods to identify regions of attraction of local minima. The use of local optimization algorithms in the selected regions can significantly accelerate the convergence of global search as it could reduce the number of search trials in the vicinity of local minima. The results of computational experiments carried out on several hundred global optimization problems of different dimensionalities presented in the paper confirm the effect of accelerated convergence (in terms of the number of search trials required to solve a problem with a given accuracy).https://www.mdpi.com/1099-4300/23/10/1272global optimizationlocal optimizationmultiextremal problemsnumerical methodsapproximationdecision trees |
| spellingShingle | Konstantin Barkalov Ilya Lebedev Evgeny Kozinov Acceleration of Global Optimization Algorithm by Detecting Local Extrema Based on Machine Learning Entropy global optimization local optimization multiextremal problems numerical methods approximation decision trees |
| title | Acceleration of Global Optimization Algorithm by Detecting Local Extrema Based on Machine Learning |
| title_full | Acceleration of Global Optimization Algorithm by Detecting Local Extrema Based on Machine Learning |
| title_fullStr | Acceleration of Global Optimization Algorithm by Detecting Local Extrema Based on Machine Learning |
| title_full_unstemmed | Acceleration of Global Optimization Algorithm by Detecting Local Extrema Based on Machine Learning |
| title_short | Acceleration of Global Optimization Algorithm by Detecting Local Extrema Based on Machine Learning |
| title_sort | acceleration of global optimization algorithm by detecting local extrema based on machine learning |
| topic | global optimization local optimization multiextremal problems numerical methods approximation decision trees |
| url | https://www.mdpi.com/1099-4300/23/10/1272 |
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