Dynamic Hassan Nelder Mead with Simplex Free Selectivity for Unconstrained Optimization
We propose a free selective simplex for the downhill Nelder Mead simplex algorithm (1965), rather than the determinant simplex that forces its elements to perform a single operation, such as reflection. Unlike the Nelder-Mead algorithm, the elements of the proposed simplex select various operations...
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| Format: | Article |
| Language: | English |
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IEEE
2018-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/8409931/ |
| _version_ | 1819169210269433856 |
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| author | Hassan A. Musafer Ausif Mahmood |
| author_facet | Hassan A. Musafer Ausif Mahmood |
| author_sort | Hassan A. Musafer |
| collection | DOAJ |
| description | We propose a free selective simplex for the downhill Nelder Mead simplex algorithm (1965), rather than the determinant simplex that forces its elements to perform a single operation, such as reflection. Unlike the Nelder-Mead algorithm, the elements of the proposed simplex select various operations of the algorithm to form the next simplex. In this way, we allow non-isometric reflections similar to that of the Nelder Mead, triangle simplex, but with rotation through an angle, permitting the proposed algorithm to have more control over the simplex, to change its size and direction for better performance. As a consequence, the solution that comes from the proposed simplex is always dynamic adaptive in size and orientation to different landscapes of mathematical functions. The proposed algorithm is examined in a large collection of different structures and classes of optimization problems. Additionally, comparisons are made with two enhanced, up-to-date versions of the Nelder-Mead algorithm. The numerical results show that Hassan Nelder Mead is stable due to non-dependence on the number of parameters processed. It also performs a higher accuracy for high dimensions compared with the other algorithms and a faster convergence rate toward global minima with respect to the number of simplex gradient estimates. |
| first_indexed | 2024-12-22T19:15:53Z |
| format | Article |
| id | doaj.art-b2107b0eca3442d2a2d8ca910d7c159a |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-22T19:15:53Z |
| publishDate | 2018-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-b2107b0eca3442d2a2d8ca910d7c159a2022-12-21T18:15:31ZengIEEEIEEE Access2169-35362018-01-016390153902610.1109/ACCESS.2018.28550798409931Dynamic Hassan Nelder Mead with Simplex Free Selectivity for Unconstrained OptimizationHassan A. Musafer0https://orcid.org/0000-0003-1939-0224Ausif Mahmood1Faculty of Electrical and Electronic Engineering, University of Technology, Baghdad, IraqFaculty of Computer Science and Engineering, University of Bridgeport, Bridgeport, CT, USAWe propose a free selective simplex for the downhill Nelder Mead simplex algorithm (1965), rather than the determinant simplex that forces its elements to perform a single operation, such as reflection. Unlike the Nelder-Mead algorithm, the elements of the proposed simplex select various operations of the algorithm to form the next simplex. In this way, we allow non-isometric reflections similar to that of the Nelder Mead, triangle simplex, but with rotation through an angle, permitting the proposed algorithm to have more control over the simplex, to change its size and direction for better performance. As a consequence, the solution that comes from the proposed simplex is always dynamic adaptive in size and orientation to different landscapes of mathematical functions. The proposed algorithm is examined in a large collection of different structures and classes of optimization problems. Additionally, comparisons are made with two enhanced, up-to-date versions of the Nelder-Mead algorithm. The numerical results show that Hassan Nelder Mead is stable due to non-dependence on the number of parameters processed. It also performs a higher accuracy for high dimensions compared with the other algorithms and a faster convergence rate toward global minima with respect to the number of simplex gradient estimates.https://ieeexplore.ieee.org/document/8409931/Unconstrained optimizationselective simplexSpendley-Hext-Himsworth algorithmNelder-Mead algorithmdownhill simplex algorithm |
| spellingShingle | Hassan A. Musafer Ausif Mahmood Dynamic Hassan Nelder Mead with Simplex Free Selectivity for Unconstrained Optimization IEEE Access Unconstrained optimization selective simplex Spendley-Hext-Himsworth algorithm Nelder-Mead algorithm downhill simplex algorithm |
| title | Dynamic Hassan Nelder Mead with Simplex Free Selectivity for Unconstrained Optimization |
| title_full | Dynamic Hassan Nelder Mead with Simplex Free Selectivity for Unconstrained Optimization |
| title_fullStr | Dynamic Hassan Nelder Mead with Simplex Free Selectivity for Unconstrained Optimization |
| title_full_unstemmed | Dynamic Hassan Nelder Mead with Simplex Free Selectivity for Unconstrained Optimization |
| title_short | Dynamic Hassan Nelder Mead with Simplex Free Selectivity for Unconstrained Optimization |
| title_sort | dynamic hassan nelder mead with simplex free selectivity for unconstrained optimization |
| topic | Unconstrained optimization selective simplex Spendley-Hext-Himsworth algorithm Nelder-Mead algorithm downhill simplex algorithm |
| url | https://ieeexplore.ieee.org/document/8409931/ |
| work_keys_str_mv | AT hassanamusafer dynamichassanneldermeadwithsimplexfreeselectivityforunconstrainedoptimization AT ausifmahmood dynamichassanneldermeadwithsimplexfreeselectivityforunconstrainedoptimization |