Dynamic MOSD

Abstract

Usually, in problems of shape design of electromagnetic devices, objectives and constraints do not depend on time: various methods of static multiobjective optimisation have been presented in Chapter 5 and used in Chapter 7. However, when either the objectives or the constraints, or both of them, depend on time, the PF is time dependent too; if this happens, it is not possible to identify the PF by exploring the objective space at steady state, but the time evolution is to be taken into account, resorting to dynamic multiobjective optimisation.

When considering a single-objective design problem in dynamic conditions, genetic algorithms have been adopted with major modifications to the basic operators, in order to track the time evolution of the optimum in a cost-effective way (Eiben et al. 1999). Also the exploitation of the concept of artificial life has given a good paradigm to mimic the natural search in a dynamic environment (Adami 1998) and (Thimbledy et al. 1995). However, when considering a multiobjective design problem in dynamic conditions, very few studies are available. In classical control theory, for instance, dynamic optimisation is a well known approach to the design of time-dependent systems; dynamic multiobjective optimisation has been developed e.g. for the synthesis of a closed-loop controller and applied to the design of a combustion process (Farina et al. 2004). In computational electromagnetism this stream of research is at the early beginning; here, an introduction to dynamic multiobjective optimisation is presented and applied to a shape design problem, characterized by objective functions which are both time and field dependent.