Lens design: Global optimization with escape function

The technique of using the 'escape function' for global optimization in lens design is described. This includes how to identify two solutions as independent; the threshold value for this criterion can be chosen to determine how to explore local solutions-rough or fine. Choice of appropriate values for two parameters in the escape function is most important, since this will affect the efficiency of the automatic global optimization process. There are two problems, i.e. giving default values at the beginning of the design, and determining a default rule to change them when the escape is unsuccessful. The latter was solved by assuming a 'saddle path' as the best route to escape. An exact solution for the former was not found, but a hint for finding a second best solution is shown based on the statistical study of local minima.