Dynamic Pareto fronts and optimal control of geometry in a problem of transient magnetic diffusion

The feasibility of dynamic multi-objective optimisation in computational electromagnetism is proved and a relevant benchmark of inverse magnetic diffusion is defined and solved. Accordingly, the optimal control of the geometry of a magnetic pole under step excitation has been proposed as a dynamic optimisation problem, characterised by two constrained objective functions that are both time- and field-dependent; the non-dominated solutions at steady state are to be determined. The benchmark has been solved numerically as a problem of transient magnetic diffusion, whereas the associated Pareto front has been identified by means of an enumerative search method in the time domain. In particular, the effect of a time-dependent energy constraint on the front at steady state has been determined. The theory of dynamic multi-objective optimisation in electromagnetism is discussed.