Adaptation of the penalty function method to genetic algorithm in electromagnetic devices designing

Abstract

PurposeThe purpose of this paper is to elaborate the effective method of adaptation of the external penalty function to the genetic algorithm.Design/methodology/approachIn the case of solving the optimization tasks with constraints using the external penalty function, the penalty term has a larger value than the primary objective function. The sigmoidal transformation is introduced to solve this problem. A new method of determining the value of the penalty coefficient in subsequent iterations associated with the changing penalty has been proposed. The proposed approach has been applied to the optimization of an electromagnetic linear actuator, and the mathematical model of the devices contains equations of the magnetic field, by taking into account the nonlinearity of ferromagnetic material.FindingsThe proposed new approach of the penalty function method consists in the reduction of the external penalty function in successive penalty iterations instead of its increase as it is in the classical method. In addition, the method of normalization of constraints during the formulation of optimization problem has a significant impact on the obtained results of optimization calculations.Originality/valueThe proposed approach can be applied to solve constrained optimization tasks in designing of electromagnetic devices.