Empirical Convergence Theory of Harmony Search Algorithm for Box-Constrained Discrete Optimization of Convex Function
The harmony search (HS) algorithm is an evolutionary computation technique, which was inspired by music improvisation. So far, it has been applied to various scientific and engineering optimization problems including project scheduling, structural design, energy system operation, car lane detection,...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/5/545 |
| _version_ | 1797414287114764288 |
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| author | Jin Hee Yoon Zong Woo Geem |
| author_facet | Jin Hee Yoon Zong Woo Geem |
| author_sort | Jin Hee Yoon |
| collection | DOAJ |
| description | The harmony search (HS) algorithm is an evolutionary computation technique, which was inspired by music improvisation. So far, it has been applied to various scientific and engineering optimization problems including project scheduling, structural design, energy system operation, car lane detection, ecological conservation, model parameter calibration, portfolio management, banking fraud detection, law enforcement, disease spread modeling, cancer detection, astronomical observation, music composition, fine art appreciation, and sudoku puzzle solving. While there are many application-oriented papers, only few papers exist on how HS performs for finding optimal solutions. Thus, this preliminary study proposes a new approach to show how HS converges on an optimal solution under specific conditions. Here, we introduce a distance concept and prove the convergence based on the empirical probability. Moreover, a numerical example is provided to easily explain the theorem. |
| first_indexed | 2024-03-09T05:30:52Z |
| format | Article |
| id | doaj.art-f7f642468aee4ec19ab8f9181c6ec26c |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T05:30:52Z |
| publishDate | 2021-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-f7f642468aee4ec19ab8f9181c6ec26c2023-12-03T12:33:29ZengMDPI AGMathematics2227-73902021-03-019554510.3390/math9050545Empirical Convergence Theory of Harmony Search Algorithm for Box-Constrained Discrete Optimization of Convex FunctionJin Hee Yoon0Zong Woo Geem1Department of Mathematics and Statistics, Sejong University, Seoul 05006, KoreaCollege of IT Convergence, Gachon University, Seongnam 13120, KoreaThe harmony search (HS) algorithm is an evolutionary computation technique, which was inspired by music improvisation. So far, it has been applied to various scientific and engineering optimization problems including project scheduling, structural design, energy system operation, car lane detection, ecological conservation, model parameter calibration, portfolio management, banking fraud detection, law enforcement, disease spread modeling, cancer detection, astronomical observation, music composition, fine art appreciation, and sudoku puzzle solving. While there are many application-oriented papers, only few papers exist on how HS performs for finding optimal solutions. Thus, this preliminary study proposes a new approach to show how HS converges on an optimal solution under specific conditions. Here, we introduce a distance concept and prove the convergence based on the empirical probability. Moreover, a numerical example is provided to easily explain the theorem.https://www.mdpi.com/2227-7390/9/5/545harmony searchconvergenceempirical probabilityoptimizationmetaheuristics |
| spellingShingle | Jin Hee Yoon Zong Woo Geem Empirical Convergence Theory of Harmony Search Algorithm for Box-Constrained Discrete Optimization of Convex Function Mathematics harmony search convergence empirical probability optimization metaheuristics |
| title | Empirical Convergence Theory of Harmony Search Algorithm for Box-Constrained Discrete Optimization of Convex Function |
| title_full | Empirical Convergence Theory of Harmony Search Algorithm for Box-Constrained Discrete Optimization of Convex Function |
| title_fullStr | Empirical Convergence Theory of Harmony Search Algorithm for Box-Constrained Discrete Optimization of Convex Function |
| title_full_unstemmed | Empirical Convergence Theory of Harmony Search Algorithm for Box-Constrained Discrete Optimization of Convex Function |
| title_short | Empirical Convergence Theory of Harmony Search Algorithm for Box-Constrained Discrete Optimization of Convex Function |
| title_sort | empirical convergence theory of harmony search algorithm for box constrained discrete optimization of convex function |
| topic | harmony search convergence empirical probability optimization metaheuristics |
| url | https://www.mdpi.com/2227-7390/9/5/545 |
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