Evolving expertise for automated lens optimization.

We present a process to locate the desired local optimum of high-dimensional design problems such as the optimization of freeform mirror systems. By encoding active design variables into a binary vector imitating DNA sequences, we are able to perform a genetic optimization of the optimization process itself. The end result is an optimization route that is effectively able to sidestep local minima by warping the variable space around them in a way that mimics the expertise of veteran designers. The generality of the approach is validated through the automated generation of high-performance designs for off-axis three- and four-mirror free-form systems.

[1]  Pierre-Jean Erard,et al.  Knowledge-based optical system design: some optical systems generated by the KBOSD , 1992 .

[2]  Robert Michael Lewis,et al.  Implementing Generating Set Search Methods for Linearly Constrained Minimization , 2007, SIAM J. Sci. Comput..

[3]  B. Welford.  Note on a Method for Calculating Corrected Sums of Squares and Products , 1962 .

[4]  Charles Audet,et al.  Analysis of Generalized Pattern Searches , 2000, SIAM J. Optim..

[5]  Scott Lerner.  Use of an expert system for optimization of optical systems , 2003, SPIE Optics + Photonics.

[6]  Eric Haines,et al.  Point in Polygon Strategies , 1994, Graphics Gems.

[7]  Yongtian Wang,et al.  Expert system for generating initial layouts of zoom systems with multiple moving lens groups , 2005 .

[8]  Lalit M. Patnaik,et al.  Adaptive probabilities of crossover and mutation in genetic algorithms , 1994, IEEE Trans. Syst. Man Cybern..

[9]  Jie Sun,et al.  Solution Methodologies for the Smallest Enclosing Circle Problem , 2003, Comput. Optim. Appl..

[10]  Alan W. Greynolds,et al.  Combination of global-optimization and expert-systems techniques in optical design , 1992 .

[11]  Ujjwal Maulik,et al.  Fuzzy partitioning using a real-coded variable-length genetic algorithm for pixel classification , 2003, IEEE Trans. Geosci. Remote. Sens..

[12]  Roy George,et al.  A variable-length genetic algorithm for clustering and classification , 1995, Pattern Recognit. Lett..

[13]  Jannick P Rolland,et al.  Starting geometry creation and design method for freeform optics , 2018, Nature Communications.