Tuning Parameters in the Genetic Algorithm Optimization of Electrostatic Electron Lenses

Abstract

The design of electrostatic electron lenses involves the choice of many geometrical parameters for the lens electrodes as well as the choice of voltages applied to the electrodes. The purpose of the design is to focus the electrons at a specific point and to minimize the aberrations of the lens. In a previous study, genetic algorithm optimization was introduced to aid the designer. For speeding up the electrostatic field calculations, new methods for analytical approximations of the field near the optical axis were introduced. In this paper, the influence of the main tuning parameters of the Genetic Algorithms is analyzed. The analysis is performed on a typical electrostatic lens systems including 6 electrodes. Different combinations of population sizes and number of generations are taken and the quality of the optimized lens system is compared. It is seen that within a constant computational effort (time or total number of system evaluations), a lower population size with a larger number of generations can achieve better results compared to having larger population size and fewer generations. The combination of Crossover Heuristic with Mutation Gaussian showed significantly better results compared to all other combinations of Mutations and Crossovers. Crossover Fraction is also evaluated to find the most suited values of this parameter.