  Electric machine design optimization is a computationally expensive
multi-objective optimization problem. While the objectives require
time-consuming finite element analysis, optimization constraints can often be
based on mathematical expressions, such as geometric constraints. This article
investigates this optimization problem of mixed computationally expensive
nature by proposing an optimization method incorporated into a popularly-used
evolutionary multi-objective optimization algorithm - NSGA-II. The proposed
method exploits the inexpensiveness of geometric constraints to generate
feasible designs by using a custom repair operator. The proposed method also
addresses the time-consuming objective functions by incorporating surrogate
models for predicting machine performance. The article successfully establishes
the superiority of the proposed method over the conventional optimization
approach. This study clearly demonstrates how a complex engineering design can
be optimized for multiple objectives and constraints requiring heterogeneous
evaluation times and optimal solutions can be analyzed to select a single
preferred solution and importantly harnessed to reveal vital design features
common to optimal solutions as design principles.
