The Application of the Annealing Algorithm to the Construction of Exact Optimal Designs for Linear – Regression Models

Abstract

This article reports the application of the annealing algorithm to the construction of exact D−, I−, and G-optimal designs for polynomial regression of degree 5 on the interval [—1, l] and for the second-order model in two factors on the design space [—1, l] × [—1, 1]. Details of the perturbation scheme and the annealing schedules used are given, and the method of implementation is illustrated by means of a simple example. The algorithm is assessed by comparing its performance, in terms of computer time and effkiency, with the modified Fedorov procedure, and it is shown to be particularly effective in finding G-optimal designs. The salient features of the exact designs constructed in this study are also summarized.

KEY WORDS:

• Polynomial regression
• Second-order design