  Proportional integral derivative (PID) controllers are important and widely
used tools in system control. Tuning of the controller gains is a laborious
task, especially for complex systems such as combustion engines. To minimize
the time of an engineer for tuning of the gains in a simulation software, we
propose to formulate a part of the problem as a black-box optimization task. In
this paper, we summarize the properties and practical limitations of tuning of
the gains in this particular application. We investigate the latest methods of
black-box optimization and conclude that the Covariance Matrix Adaptation
Evolution Strategy (CMA-ES) with bi-population restart strategy, elitist parent
selection and active covariance matrix adaptation is best suited for this task.
Details of the algorithm's experiment-based calibration are explained as well
as derivation of a suitable objective function. The method's performance is
compared with that of PSO and SHADE. Finally, its usability is verified on six
models of real engines.
