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High-dimensional normalized data profiles for testing derivative-free optimization algorithms

This article provides a new tool for examining the efficiency and robustness of derivative-free optimization algorithms based on high-dimensional normalized data profiles that test a variety of performance metrics. Unlike the traditional data profiles that examine a single dimension, the proposed da...

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Autores principales: Musafer, Hassan, Tokgoz, Emre, Mahmood, Ausif
Formato: Online Artículo Texto
Lenguaje:English
Publicado: PeerJ Inc. 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9454945/
https://www.ncbi.nlm.nih.gov/pubmed/36091977
http://dx.doi.org/10.7717/peerj-cs.960
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author Musafer, Hassan
Tokgoz, Emre
Mahmood, Ausif
author_facet Musafer, Hassan
Tokgoz, Emre
Mahmood, Ausif
author_sort Musafer, Hassan
collection PubMed
description This article provides a new tool for examining the efficiency and robustness of derivative-free optimization algorithms based on high-dimensional normalized data profiles that test a variety of performance metrics. Unlike the traditional data profiles that examine a single dimension, the proposed data profiles require several dimensions in order to analyze the relative performance of different optimization solutions. To design a use case, we utilize five sequences (solvers) of trigonometric simplex designs that extract different features of non-isometric reflections, as an example to show how various metrics (dimensions) are essential to provide a comprehensive evaluation about a particular solver relative to others. In addition, each designed sequence can rotate the starting simplex through an angle to designate the direction of the simplex. This type of features extraction is applied to each sequence of the triangular simplexes to determine a global minimum for a mathematical problem. To allocate an optimal sequence of trigonometric simplex designs, a linear model is used with the proposed data profiles to examine the convergence rate of the five simplexes. Furthermore, we compare the proposed five simplexes to an optimized version of the Nelder–Mead algorithm known as the Genetic Nelder–Mead algorithm. The experimental results demonstrate that the proposed data profiles lead to a better examination of the reliability and robustness for the considered solvers from a more comprehensive perspective than the existing data profiles. Finally, the high-dimensional data profiles reveal that the proposed solvers outperform the genetic solvers for all accuracy tests.
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spelling pubmed-94549452022-09-09 High-dimensional normalized data profiles for testing derivative-free optimization algorithms Musafer, Hassan Tokgoz, Emre Mahmood, Ausif PeerJ Comput Sci Algorithms and Analysis of Algorithms This article provides a new tool for examining the efficiency and robustness of derivative-free optimization algorithms based on high-dimensional normalized data profiles that test a variety of performance metrics. Unlike the traditional data profiles that examine a single dimension, the proposed data profiles require several dimensions in order to analyze the relative performance of different optimization solutions. To design a use case, we utilize five sequences (solvers) of trigonometric simplex designs that extract different features of non-isometric reflections, as an example to show how various metrics (dimensions) are essential to provide a comprehensive evaluation about a particular solver relative to others. In addition, each designed sequence can rotate the starting simplex through an angle to designate the direction of the simplex. This type of features extraction is applied to each sequence of the triangular simplexes to determine a global minimum for a mathematical problem. To allocate an optimal sequence of trigonometric simplex designs, a linear model is used with the proposed data profiles to examine the convergence rate of the five simplexes. Furthermore, we compare the proposed five simplexes to an optimized version of the Nelder–Mead algorithm known as the Genetic Nelder–Mead algorithm. The experimental results demonstrate that the proposed data profiles lead to a better examination of the reliability and robustness for the considered solvers from a more comprehensive perspective than the existing data profiles. Finally, the high-dimensional data profiles reveal that the proposed solvers outperform the genetic solvers for all accuracy tests. PeerJ Inc. 2022-07-22 /pmc/articles/PMC9454945/ /pubmed/36091977 http://dx.doi.org/10.7717/peerj-cs.960 Text en ©2022 Musafer et al. https://creativecommons.org/licenses/by/4.0/This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ Computer Science) and either DOI or URL of the article must be cited.
spellingShingle Algorithms and Analysis of Algorithms
Musafer, Hassan
Tokgoz, Emre
Mahmood, Ausif
High-dimensional normalized data profiles for testing derivative-free optimization algorithms
title High-dimensional normalized data profiles for testing derivative-free optimization algorithms
title_full High-dimensional normalized data profiles for testing derivative-free optimization algorithms
title_fullStr High-dimensional normalized data profiles for testing derivative-free optimization algorithms
title_full_unstemmed High-dimensional normalized data profiles for testing derivative-free optimization algorithms
title_short High-dimensional normalized data profiles for testing derivative-free optimization algorithms
title_sort high-dimensional normalized data profiles for testing derivative-free optimization algorithms
topic Algorithms and Analysis of Algorithms
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9454945/
https://www.ncbi.nlm.nih.gov/pubmed/36091977
http://dx.doi.org/10.7717/peerj-cs.960
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