The design of genetic or protein networks that satisfy a given set of behavioural specifications is one of the main challenges of synthetic biology. Model-based design is a natural choice in this respect. Here we consider the problem of tuning parameters of a stochastic model to force one or more behavioural goals to hold. In particular, we consider several objectives specified by signal temporal logic formulae, and we look for a parameter set making their satisfaction probability as large as possible. This formalisation results in a multi-objective optimisation problem, which we solve by considering an optimisation scheme combining satisfaction probability and average robustness of STL properties, leveraging state of the art multi-objective optimisation routines.
