A Simulated Annealing Algorithm for D-Optimal Design for 2-Way and 3-Way Polynomial Regression with Correlated Observations
Much of the previous work in D-optimal design for regression models with correlated errors focused on polynomial models with a single predictor variable, in large part because of the intractability of an analytic solution. In this paper, we present a modified, improved simulated annealing algorithm,...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/746914 |
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| author | Chang Li Daniel C. Coster |
| author_facet | Chang Li Daniel C. Coster |
| author_sort | Chang Li |
| collection | DOAJ |
| description | Much of the previous work in D-optimal design for regression models with correlated errors focused on polynomial models with a single predictor variable, in large part because of the intractability of an analytic solution. In this paper, we present a modified, improved simulated annealing algorithm, providing practical approaches to specifications of the annealing cooling parameters, thresholds, and search neighborhoods for the perturbation scheme, which finds approximate D-optimal designs for 2-way and 3-way polynomial regression for a variety of specific correlation structures with a given correlation coefficient. Results in each correlated-errors case are compared with traditional simulated annealing algorithm, that is, the SA algorithm without our improvement. Our improved simulated annealing results had generally higher D-efficiency than traditional simulated annealing algorithm, especially when the correlation parameter was well away from 0. |
| format | Article |
| id | doaj-art-e6f8bc0863494ee6ab563bb21b49e94d |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-e6f8bc0863494ee6ab563bb21b49e94d2025-02-03T01:27:16ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/746914746914A Simulated Annealing Algorithm for D-Optimal Design for 2-Way and 3-Way Polynomial Regression with Correlated ObservationsChang Li0Daniel C. Coster1Business School, Shandong University of Political Science and Law, 63 East Jiefang Road, Jinan, Shandong 250014, ChinaDepartment of Mathematics and Statistics, Utah State University, Logan, UT 84341, USAMuch of the previous work in D-optimal design for regression models with correlated errors focused on polynomial models with a single predictor variable, in large part because of the intractability of an analytic solution. In this paper, we present a modified, improved simulated annealing algorithm, providing practical approaches to specifications of the annealing cooling parameters, thresholds, and search neighborhoods for the perturbation scheme, which finds approximate D-optimal designs for 2-way and 3-way polynomial regression for a variety of specific correlation structures with a given correlation coefficient. Results in each correlated-errors case are compared with traditional simulated annealing algorithm, that is, the SA algorithm without our improvement. Our improved simulated annealing results had generally higher D-efficiency than traditional simulated annealing algorithm, especially when the correlation parameter was well away from 0.http://dx.doi.org/10.1155/2014/746914 |
| spellingShingle | Chang Li Daniel C. Coster A Simulated Annealing Algorithm for D-Optimal Design for 2-Way and 3-Way Polynomial Regression with Correlated Observations Journal of Applied Mathematics |
| title | A Simulated Annealing Algorithm for D-Optimal Design for 2-Way and 3-Way Polynomial Regression with Correlated Observations |
| title_full | A Simulated Annealing Algorithm for D-Optimal Design for 2-Way and 3-Way Polynomial Regression with Correlated Observations |
| title_fullStr | A Simulated Annealing Algorithm for D-Optimal Design for 2-Way and 3-Way Polynomial Regression with Correlated Observations |
| title_full_unstemmed | A Simulated Annealing Algorithm for D-Optimal Design for 2-Way and 3-Way Polynomial Regression with Correlated Observations |
| title_short | A Simulated Annealing Algorithm for D-Optimal Design for 2-Way and 3-Way Polynomial Regression with Correlated Observations |
| title_sort | simulated annealing algorithm for d optimal design for 2 way and 3 way polynomial regression with correlated observations |
| url | http://dx.doi.org/10.1155/2014/746914 |
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