A visualisation of the machines is

A visualisation of the machines is depicted in Fig. 2. One seesthat the size of the PM has decreased substantially whilemaintaining the desired EMF. For the settings with nominaloptimisation the three methods result in comparable PM sizes. Thevolume has been reduced by more than 50%, which indicates avery good improvement (and that the initial guess was poor). Sincethe offline phase for the construction of the reduced basis takes234 s, there is no MOR applied for Nominal (i), Linearised (i) andLinearised (ii). The UQ deterministic settings on the other handrequire many more evaluations of the FEM model. Alternatively,this extra computational cost can be reduced by using SQ. Only forthe MC procedure it pays off to use MOR, which is shown bycomparing the times for the offline and online phase. The initialnumber of unknowns (8128) has been reduced to a basis of size 27.The difference in optimised volume for the various combinationsof MOR and SQ is less than 0.1%. The application of PSO and GAto the robust stochastic formulation results in smaller magnets, buthas a computational cost that is more than 10 times higher than forRobust (i), even though the computations have been acceleratedusing parallelisation. In contrast to SQP the PSO and GAalgorithms do not make use of derivative information and thusevaluate much more machine models at every iteration step.Consequently, MOR is particularly beneficial in this case to speedup the computations, i.e. in the case of PSO the online costs arereduced by one order of magnitude, see Robust (iii) and (vii) inTable 2. All procedures terminated by reaching the desiredaccuracy.