Fuzzy-logic adaptive genetic algorithm (FLAGA) in optical design

摘要

The problem of multiextremum optimization is very general in optical design. Many efforts have been applied to finding approaches to its solution, but optical software developers are still far from finding a universal and reliable method. Solving the problem of finding the optimal angles of rotation of real components is a good way to test different approaches to the problem of multiextremum optimization. Compared with the general approach to optical-system design, multiextremum optimization is unconstrained optimization with an analytical test for the optimization criterion: the mean-square wavefront deformation. Finding optimal angles of rotation shares many specific features with the general problem of optical-system design, such as having a large number of minimums. In addition, these minimums have a special character: they look like a "ravines". The common optimization methods (gradient or Newtonian) easily can find the local minimums associated with an initial point, but they lack the ability to jump to another minimum. A genetic algorithm can find some point in the zone of attraction to another minimum, but it gets stuck in a "ravine" bottom line. An adaptive genetic algorithm together with local optimization methods can find a major number of minimums.