In the process of optimization, a variable glass body, initially a flat glass pane, is to be deformed so that a bundle of parallel light rays is focused on a screen. In addition, the resulting lens should have a minimal volume.
A (1, 10) Evolution Strategy is used: Starting from one parent lens, ten offspring lenses are produced, and the best of the offspring lenses becomes the next generation parent lens. The offspring lenses are created by copying the parent lens and then mutating the lens thickness at 25 given locations. Small changes are more likely than large ones. Thus, all offspring are similar to the parent lens. How strongly the offspring individuals deviate from the parents is determined by one or more step sizes, which are automatically adjusted. The smaller the step sizes, the more similar the individuals are in the population.
To determine the best of the ten offspring lenses, the quality of each offspring lens is calculated. Two objectives are given in the quality function: The lens should concentrate the incoming light and the volume of the lenses should be as small as possible. In the example, the focus has a high weight in the evaluation, so that the focus is very good, but at the same time a minimal volume is created under these circumstances.
When determining the best offspring, if the desired minimum volume is not taken into account in addition to the desired convergence of the light rays, it will only happen by chance that a thinner lens is also selected as the solution.
Often a compromise has to be found between the number of manipulated variables and the possibility of finding new innovative solutions. This becomes clear with lens optimization: initially, the thickness of the glass body was only changed in 25 places. This led to the result of the well-known convex lens. The 25 prisms, of which the lens is composed, merge into each other steplessly. If this condition is dropped and the upper and lower sides of the prisms are released for optimization, the result is the familiar Fresnel lens, a stepped lens that is used in studio spotlights, solar systems, lighthouses and rear walls of SLR cameras due to its small volume. In the example, the Fresnel lens has only about 20% of the volume of the convex lens.