Sorting Pareto solutions: a principle of optimal design for electrical machines

Purpose – The purpose of the paper is to show that the a posteriori analysis of the Pareto front associated with a given design problem facilitates the task of the decision maker and possibly helps to identify innovative solutions. The idea is to investigate the similarities existing among non-dominated solutions. Design/methodology/approach – A permanent-magnet alternator for automotive applications is considered as case study. The design problem exhibits six design variables and two energy-related objective functions. A suitable sampling of the objective space is made and non-dominated solutions, located along an L-shaped front, are approximated. Results are assessed by means of a successive optimization using NSGA-II algorithm. Findings – From the approximated Pareto front, three optimal devices have been selected and remapped in the design space in order to compare their performance. This is done in terms of iron and copper losses, material costs, rated voltage, and air-gap induction. Moreover, making the NSGA-II start from the knee-point of the front, it is shown that a direct approximation of the two sub-fronts is possible. Originality/value – In this paper, a method to sort out the optimal solutions located along the Pareto front is proposed as a possible criterion of decision making; so doing, previously unpredicted solutions might be identified.