  Many chemical and biological experiments involve multiple treatment factors
and often it is convenient to fit a nonlinear model in these factors. This
nonlinear model can be mechanistic, empirical or a hybrid of the two. Motivated
by experiments in chemical engineering, we focus on D-optimal design for
multifactor nonlinear response surfaces in general. In order to find and study
optimal designs, we first implement conventional point and coordinate exchange
algorithms. Next, we develop a novel multiphase optimisation method to
construct D-optimal designs with improved properties. The benefits of this
method are demonstrated by application to two experiments involving nonlinear
regression models. The designs obtained are shown to be considerably more
informative than designs obtained using traditional design optimality
algorithms.
