  Simulation-based optimal design techniques are a convenient tool for solving
a particular class of optimal design problems. The goal is to find the optimal
configuration of factor settings with respect to an expected utility criterion.
This criterion depends on the specified probability model for the data and on
the assumed prior distribution for the model parameters. We develop new
simulation-based optimal design methods which incorporate likelihood-free
approaches and utilize them in novel applications.
  Most simulation-based design strategies solve the intractable expected
utility integral at a specific design point by using Monte Carlo simulations
from the probability model. Optimizing the criterion over the design points is
carried out in a separate step. M\"uller (1999) introduces an MCMC algorithm
which simultaneously addresses the simulation as well as the optimization
problem. In principle, the optimal design can be found by detecting the utility
mode of the sampled design points. Several improvements have been suggested to
facilitate this task for multidimensional design problems (see e.g. Amzal et
al. 2006).
  We aim to extend this simulation-based design methodology to design problems
where the likelihood of the probability model is of an unknown analytical form
but it is possible to simulate from the probability model. We further assume
that prior observations are available. In such a setting it is seems natural to
employ approximate Bayesian computation (ABC) techniques in order to be able to
simulate from the conditional probability model. We provide a thorough review
of adjacent literature and we investigate the benefits and the limitations of
our design methodology for a particular paradigmatic example.
