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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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PeerJ Inc.
2022-07-01
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| Series: | PeerJ Computer Science |
| Subjects: | |
| Online Access: | https://peerj.com/articles/cs-960.pdf |
| _version_ | 1818189109591539712 |
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| author | Hassan Musafer Emre Tokgoz Ausif Mahmood |
| author_facet | Hassan Musafer Emre Tokgoz Ausif Mahmood |
| author_sort | Hassan Musafer |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-11T23:37:36Z |
| format | Article |
| id | doaj.art-2e4322386e0d48c8ae4d8bb77747df27 |
| institution | Directory Open Access Journal |
| issn | 2376-5992 |
| language | English |
| last_indexed | 2024-12-11T23:37:36Z |
| publishDate | 2022-07-01 |
| publisher | PeerJ Inc. |
| record_format | Article |
| series | PeerJ Computer Science |
| spelling | doaj.art-2e4322386e0d48c8ae4d8bb77747df272022-12-22T00:45:49ZengPeerJ Inc.PeerJ Computer Science2376-59922022-07-018e96010.7717/peerj-cs.960High-dimensional normalized data profiles for testing derivative-free optimization algorithmsHassan Musafer0Emre Tokgoz1Ausif Mahmood2School of Computer Science and Engineering, University of Bridgeport, Bridgeport, CT, United States of AmericaSchool of Engineering, Quinnipiac University, Hamden, CT, United States of AmericaSchool of Computer Science and Engineering, University of Bridgeport, Bridgeport, CT, United States of AmericaThis 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.https://peerj.com/articles/cs-960.pdfNormalized Data ProfilesDerivative-Free Optimization AlgorithmsNelder–Mead simplex algorithm (1965) |
| spellingShingle | Hassan Musafer Emre Tokgoz Ausif Mahmood High-dimensional normalized data profiles for testing derivative-free optimization algorithms PeerJ Computer Science Normalized Data Profiles Derivative-Free Optimization Algorithms Nelder–Mead simplex algorithm (1965) |
| 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 | Normalized Data Profiles Derivative-Free Optimization Algorithms Nelder–Mead simplex algorithm (1965) |
| url | https://peerj.com/articles/cs-960.pdf |
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