A New Approach to the Construction of Optimal Designs(*)

R. H. Harding and N. J. A. Sloane (**)

AT&T Bell Laboratories 
Murray Hill, New Jersey 07974 

(**) Present address:
Information Sciences Research
AT&T Shannon Lab
Florham Park, NJ 07932-0971 USA
Email: njas@research.att.com

(*) A different version of this paper appeared in the 
Journal of Statistical Planning and Inferenceg, Vol. 37 (1993), 339-369.
It is also DIMACS Technical Report 93-47, August 1993.

ABSTRACT

By combining a modified version of Hooke and Jeeves' pattern search
with exact or Monte Carlo moment calculations, it is possible to find
I-, D- and A-optimal (or nearly optimal) designs for a wide range of
response-surface problems.

The algorithm routinely handles problems involving the minimization of functions of 1000 variables,
and so for example can construct designs for a full quadratic response-surface 
depending on 12 continuous process variables.
The algorithm handles continuous or discrete variables, linear equality or
inequality constraints, and a response surface that is any low degree polynomial.

The design may be required to include a specified set of points,
so a sequence of designs can be obtained, each optimal given that the earlier
runs have been made.

The modeling region need not coincide with the measurement region.

The algorithm has been implemented in a program called gos,
which has been used to compute extensive tables of designs.
Many of these are more efficient than the best designs previously known.



For the full version see
http://NeilSloane.com/doc/design.pdf (pdf) or
http://NeilSloane.com/doc/design.ps (ps)