Determination of Initial Variable Derivative Increments Using Genetic Algorithm in Damped Least-Squares Automatic Lens Design Problem

Abstract

An important factor in performing effective optimization with the damped least-squares method is to establish appropriate initial values for the variable derivative increments prior to starting the optimization process. It is shown first that the determination of these increments can be treated as a combinatorial problem. Then, a novel method of determining optimum variable derivative increments is developed using a genetic algorithm and the characteristics of the eigenvalues of the Jacobian matrix. Some numerical experiments to show the effectiveness of this method are also presented. The proposed method reduces the number of optimization reiterations required to reach a stationary point.