Strategies of game theory for the automated optimal design in electromechanics

Classical microeconomics and game theory offer a conceptual frame to solve a design problem, characterized by multiple objective functions in mutual conflict. This viewpoint is largely accepted for the design of high-tech products as seen in aerospace engineering. However, for long-established products – like electromechanical and electromagnetic devices – the ongoing evolution in design strategies is not fully influenced by the impact of new design methodologies and software facilities. With this rationale, the shape design of a permanent-magnet three-phase motor is considered as an example of small actuator for house appliances; the analysis of the magnetic field is based on a finite-element model of the device. The design goal is to identify the magnet shape, such that the cogging torque of the motor is minimum for a given value of radial induction at the air-gap. More generally, the problem is cast in terms of multiobjective design: find the set of magnet shapes such that the torque is minimum and the induction is maximum, subject to the given constraints. Solutions in terms of Pareto front and Nash equilibrium are obtained by means of an evolutionary algorithm; during the automated search, discrete-valued design variables were considered, for the sake of a realistic design. The paper shows that the application of multi-objective optimisation in electromechanics gives a powerful design tool. Requirements in terms of timing and facilities are compatible with the resources of a research-and-development (R&D) centre of an industrial company in the area of electrical engineering.