Optimal lens design by real-coded genetic algorithms using UNDX

This paper presents new lens optimization methods based on real-coded genet ic algorithms (GAs). We take advantage of GA's capability of global optimiz ation and multi-objective optimization against two serious problems in conv entional lens optimization techniques: (1) choosing a starting point by tri al and error, and (2) combining multiple criteria to a single criterion. In this paper, two criteria for lenses, the resolution and the distortion, ar e considered. First, we propose a real-coded GA that optimizes a single cri terion, a weighted sum of the resolution and the distortion. To overcome a problem of the difficulty in generating feasible lenses especially in large -scale problems, we introduce a feasibility enforcement operator to modify an infeasible solution into a feasible one. By applying the proposed method to some small-scale problems, we show that the proposed method can find em pirically optimal and suboptimal lenses. We also apply the proposed method to some relatively large-scale problems and show that the proposed method c an effectively work under large-scale problems. Next, regarding the lens de sign problem as a multi-objective optimization problem, we propose a real-c oded multi-objective GA that explicitly optimizes the two criteria, the res olution and the distortion. We show the effectiveness of the proposed metho d in multi-objective lens optimization by applying it to a three-element le ns design problem. (C) 2000 Published by Elsevier Science S.A. All rights r eserved.