Reconfigurable devices are of paramount importance in many applications, and their multiobjective optimal design is an interesting area of research. Usually, the result of a multiobjective optimization process is a Pareto-optimal front, and the device corresponding to a specific solution on the front is assumed to be non-reconfigurable. This means that if the shape, supply, or material is altered, the updated configuration, in general, is no longer optimal.
The challenge is to develop a method inspired by multi-objective optimization that can generate a sequence of device configurations, each representing the best trade-off among design criteria, with a variable parameter that characterizes the design.
Accordingly, an original concept of a Pareto meta-front in a two-dimensional objective space is presented: given a family of fronts parameterized by a variable, the meta-front is defined as the curve that joins all points closest to utopia. In other words, the curve describes the variation in the best combinations of two conflicting design criteria as a function of a parameter, e.g., a magnetic material property or an electrical supply condition.
The case study considered to prove the validity of the proposed method is twofold: first, the attention is focused on a class of small inductors, the design of which asks for low power loss, small core volume, and high saturation current across a broad range of prescribed inductance, i.e., the variable parameter.
Next, the optimal shape design of an interior permanent-magnet motor is considered: it is assumed that the motor is magnetically reconfigurable, meaning that the variable parameter indexes a set of several permanent-magnet materials, each of which is characterized by its own demagnetization curve for a given supply frequency. Conversely, the supply frequency can be assumed to be the variable parameter, given a permanent magnet material. Whatever the parameter, running torque maximization and cogging torque minimization are the two design criteria.
More generally, the curve of meta-optimal solutions lays the ground for an innovative and fruitful interpretation of Pareto optimality. The proposed method is highly generalizable and could be readily applied to the design of complex electromagnetic devices that require the simultaneous optimization of multiple, interdependent quantities.
