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,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. © 2014 chang li and daniel c. coster.