Global and multi-objective optimization for lens design by real-coded genetic algorithms

Abstract

This paper presents new lens optimization methods based on real-coded genetic algorithms (GAs). We take advantage of GA's capability of global optimization and multi-objective optimization against two serious problems in conventional lens optimization techniques: (1) choosing a starting point by trial and error, and (2) combining plural criteria to a single criterion. In this paper, two criteria for lenses, the resolution and the distortion, are considered. First, we propose a real-coded GA that optimizes a single criterion, 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 an 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 empirically optimal and suboptimal lenses. We also apply the proposed method to some relatively large-scale problems and show that the proposed method can effectively work under large-scale problems. Next, regarding the lens design problem as a multi-objective optimization problem, we propose a real-coded multi-objective GA that explicitly optimizes the two criteria. We show that effectiveness of the proposed method in multi-objective lens optimization by applying it to a three-element lens design problem.