Addressing the Multiplicity of Solutions in Optical Lens Design as a Niching Evolutionary Algorithms Computational Challenge

Optimal Lens Design constitutes a fundamental, long-standing real-world\noptimization challenge. Potentially large number of optima, rich variety of\ncritical points, as well as solid understanding of certain optimal designs per\nsimple problem instances, provide altogether the motivation to address it as a\nniching challenge. This study applies established Niching-CMA-ES heuristic to\ntackle this design problem (6-dimensional Cooke triplet) in a simulation-based\nfashion. The outcome of employing Niching-CMA-ES `out-of-the-box' proves\nsuccessful, and yet it performs best when assisted by a local searcher which\naccurately drives the search into optima. The obtained search-points are\ncorroborated based upon concrete knowledge of this problem-instance,\naccompanied by gradient and Hessian calculations for validation. We extensively\nreport on this computational campaign, which overall resulted in (i) the\nlocation of 19 out of 21 known minima within a single run, (ii) the discovery\nof 540 new optima. These are new minima similar in shape to 21 theoretical\nsolutions, but some of them have better merit function value (unknown\nheretofore), (iii) the identification of numerous infeasibility pockets\nthroughout the domain (also unknown heretofore). We conclude that niching\nmechanism is well-suited to address this problem domain, and hypothesize on the\napparent multidimensional structures formed by the attained new solutions.\n