An algorithm for the simultaneous construction of D-optimal experimental designs

Abstract

Construction of optimal multiresponse designs when the responses are measured simultaneously for the same settings of the input variables have been studied. However, in some experiments, the response variables can be measured at different time points and also defined in the same experimental space. The response variables are assumed to be uncorrelated. In this case, simultaneous construction of more than one $D-$optimal design is required. We present an algorithm for the simultaneous construction of $D-$optimal designs for these kind of experiments. The algorithm operates on two parallel platforms. On one, the same support points are selected for the response functions. The starting point of the search, direction vector, and step length are computed. On the other, the choice of initial design and exchange of design points are carried out. Examples are given to illustrate the construction of optimal designs using the algorithm. The algorithm converges rapidly and is more economical than constructing $D-$optimal design for one response function at-a-time.

Keywords:

• D−optimal design
• Exchange algorithm
• Line search method
• Multiresponse

MATHEMATICAL SUBJECT CLASSIFICATION:

• 40A05
• 62K05