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Journal of Applied Mathematics
Volume 2014, Article ID 746914, 6 pages
Research Article

A Simulated Annealing Algorithm for D-Optimal Design for 2-Way and 3-Way Polynomial Regression with Correlated Observations

1Business School, Shandong University of Political Science and Law, 63 East Jiefang Road, Jinan, Shandong 250014, China
2Department of Mathematics and Statistics, Utah State University, Logan, UT 84341, USA

Received 10 November 2013; Revised 1 March 2014; Accepted 1 March 2014; Published 26 March 2014

Academic Editor: Li Weili

Copyright © 2014 Chang Li and Daniel C. Coster. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.