Locating the local minima in lens design with machine learning

We applied an extended version of the Niching-CMA-ES heuristic to search for local minima of the Cooke triplet, a renowned photographic lens design, of which 21 local minima were already known. The considered problem is defined by 6 input (decision) variables, namely the curvatures of the three lenses present in the Cooke triplet, and is driven by a single objective function, that is the RMS spot size. The applied approach found: (i) 19 out of the 21 known minima in a single run; (ii) 540 new local minima with objective values lower/equal to those of the known 21 minima; (iii) a large number of infeasible designs.