  Identifying optimal designs for generalized linear models with a binary
response can be a challenging task, especially when there are both continuous
and discrete independent factors in the model. Theoretical results rarely exist
for such models, and the handful that do exist come with restrictive
assumptions. This paper investigates the use of particle swarm optimization
(PSO) to search for locally $D$-optimal designs for generalized linear models
with discrete and continuous factors and a binary outcome and demonstrates that
PSO can be an effective method. We provide two real applications using PSO to
identify designs for experiments with mixed factors: one to redesign an odor
removal study and the second to find an optimal design for an electrostatic
discharge study. In both cases we show that the $D$-efficiencies of the designs
found by PSO are much better than the implemented designs. In addition, we show
PSO can efficiently find $D$-optimal designs on a prototype or an irregularly
shaped design space, provide insights on the existence of minimally supported
optimal designs, and evaluate sensitivity of the $D$-optimal design to
mis-specifications in the link function.
