Genetic Algorithms: An Evolutionary Approach to Optical Engineering

Abstract

We present a Genetic Algorithm that we developed to address optimization problems in optical engineering. Our objective is to determine the global optimum of a problem ideally by a single run of the genetic algorithm. We want also to achieve this objective with a reasonable use of computational resources. In order to accelerate the convergence of the algorithm, we establish generation after generation a quadratic approximation of the fitness in the close neighborhood of the best-so-far individual. We then inject in the population an individual that corresponds to the optimum of this approximation. We also use randomly-shifted Gray codes when applying mutations in order to achieve a better exploration of the parameter space. We provide automatic settings for the technical parameters of our algorithm and apply it to typical benchmark problems in 5, 10 and 20 dimensions. We show that the global optimum of these problems can be determined with a probability of success in one run of the order of 95-97 % and an average number of fitness evaluations of the order of 400-750×n, where n refers to the number of parameters to determine. We finally comment some applications of this algorithm to real-world engineering problems.