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Purpose This paper aims to further improve the efficiency of multi-objective optimization design of synchronous reluctance motors (SynRMs) using the level set (LS) method, which has the advantage of obtaining a practical shape. The solutions obtained by gradient methods tend to be local ones due to the multi-modality of the objective function, especially when multiple objective functions. A huge number of trial calculations are required to obtain a high-quality and broadly distributed Pareto front. Therefore, it is indispensable to effectively get out of the local solutions in the optimization process with the LS method. Design/methodology/approach The authors propose a novel method appropriately switching multiple objective functions with high independence of sensitivity information. The authors adopt highly independent mathematical expressions for the objective functions of the average torque and torque ripple. In addition, the authors repeatedly perform the optimization while appropriately selecting the sensitivity information of one objective function from multiple ones, which enables the authors to effectively break out of local solutions in the optimization process. Findings The proposed method was applied to the shape optimization of SynRM flux barriers and successfully searched a more extensive and advanced Pareto front in comparison with the conventional method. Originality/value The proposed method adopts search spaces with mathematical high independence for average torque and torque ripple. In the optimization process, when the solution search is judged to get stuck by several criteria, the search space is alternately switched to effectively get out of local solutions.

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This paper describes the relaxation-based algorithm for the harmonic analysis of nonlinear circuits. First, we present Iterated Spectrum Analysis based on the harmonic balance method, where the harmonic balance method is applied to every node independently. As a result, we can avoid dealing with large scale Jacobian matrices and reduce the total simulation time, compared with the previous method based on the standard Newton-Raphson method. Furthermore, we refer to the algorithm with two types of latency. One is the iteration latency and the other is the frequency domain latency. And we propose the multirate-sampling technique based on the consideration of the frequency domain latency. Finally, we apply the present algorithm to the simple analogue circuit simulation and verify its availability for the harmonic analysis.