Typical formulations for fuzzy optimization utilize piecewise linear membership functions, which introduces regions of no differentiability and prevents the employment of deterministic methods. We propose the utilization of continuously differentiable membership functions, which permit the use of gradient-based methods. We present a general expression for the gradient of the decision degree function. Then, a stochastic method can be used to find a good starting point for the deterministic technique, in a hybrid approach. The formulation is applied to the optimization of an electrostatic micromotor. The average torque is maximized subject to a fuzzy constraint for the torque ripple. The results show the validity of the methodology in electromagnetic design.
- Electromagnetic design
- Fuzzy optimization