Addressing the Multiplicity of Solutions in Optical Lens Design as a Niching Evolutionary Algorithms Computational Challenge. (arXiv:2105.10541v1 [cs.CE])

Optimal Lens Design constitutes a fundamental, long-standing real-world
optimization challenge. Potentially large number of optima, rich variety of
critical points, as well as solid understanding of certain optimal designs per
simple problem instances, provide altogether the motivation to address it as a
niching challenge. This study applies established Niching-CMA-ES heuristic to
tackle this design problem (6-dimensional Cooke triplet) in a simulation-based
fashion. The outcome of employing Niching-CMA-ES `out-of-the-box’ proves
successful, and yet it performs best when assisted by a local searcher which
accurately drives the search into optima. The obtained search-points are
corroborated based upon concrete knowledge of this problem-instance,
accompanied by gradient and Hessian calculations for validation. We extensively
report on this computational campaign, which overall resulted in (i) the
location of 19 out of 21 known minima within a single run, (ii) the discovery
of 540 new optima. These are new minima similar in shape to 21 theoretical
solutions, but some of them have better merit function value (unknown
heretofore), (iii) the identification of numerous infeasibility pockets
throughout the domain (also unknown heretofore). We conclude that niching
mechanism is well-suited to address this problem domain, and hypothesize on the
apparent multidimensional structures formed by the attained new solutions.



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