２段階GA ``Solid EMO'' によるレンズ系設計

Abstract

This paper discusses evolutionary multi-objective optimization (EMO) method for lens system design problems that have properties of global and local multimodality, epistasis among parameters and ill-scaledness. Applying NSGA-II-like EMO to them, it faces some difficulties. To solve them, we present a two stage GA called Solid EMO that consists of a repeated ESO (Evolutionary Single-objective Optimization) and an augmented EMO. The repeated ESO searches seeds of Pareto optimal solutions through solving weighted sum minimization problems repeatedly by a real-coded GA using ISM that deals with global multi-modality well. The augmented EMO, that behaves like a kind of local search by k-nearest neighbor limitation in reproduction and crossover with an ability of explorative search, refines and expands the seeds found by the first stage GA. Solid EMO was applied to three and four element lens system design problems. As a result, the proposed method succeeded in finding highly precise solution sets that consist of well-known types, triplet-type and Lee-type lens systems, in the three-element and four-element lens system design problems, respectively.