OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 20 — Sep. 27, 2010
  • pp: 20876–20886

Mutation operators in lens system optimization to jump out of local minima

Lei Li, Qiong-Hua Wang, Xiao-Qing Xu, and Da-Hai Li  »View Author Affiliations

Optics Express, Vol. 18, Issue 20, pp. 20876-20886 (2010)

View Full Text Article

Enhanced HTML    Acrobat PDF (1607 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



In lens system design, Damped Least Squares method is a traditionally used local search method. In this paper we apply mutation operators to control damping factor in Damped Least Squares. We study the mutation behavior in this method when the algorithm confronts with local minima. The proposed method can go beyond local minima by taking mutation operators to control damping factor. The proposed method was successfully applied to design problems. The result indicates that the mutation operators provide an effective and rapid way to jump out of poor local minima.

© 2010 OSA

OCIS Codes
(220.2740) Optical design and fabrication : Geometric optical design
(220.3620) Optical design and fabrication : Lens system design
(080.1753) Geometric optics : Computation methods

ToC Category:
Optical Design and Fabrication

Original Manuscript: June 8, 2010
Revised Manuscript: August 13, 2010
Manuscript Accepted: September 15, 2010
Published: September 17, 2010

Lei Li, Qiong-Hua Wang, Xiao-Qing Xu, and Da-Hai Li, "Mutation operators in lens system optimization to jump out of local minima," Opt. Express 18, 20876-20886 (2010)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math. 2, 164–168 (1944).
  2. M. Isshiki, H. Ono, K. Hiraga, J. Ishikawa, and S. Nakadate, “Lens design: global optimization with escape function,” Opt. Rev. 2(6), 463–470 (1995). [CrossRef]
  3. D. Vasiljevic, “Classical and evolutionary algorithms in the optimization of optical systems,” (Wiley, 2001).
  4. V. Yakovlev and G. Tempea, “Optimization of chirped mirrors,” Appl. Opt. 41(30), 6514–6520 (2002). [CrossRef] [PubMed]
  5. C. Gagné, J. Beaulieu, M. Parizeau, and S. Thibault, “Human-competitive lens system design with evolution strategies,” Appl. Soft Comput. 8(4), 1439–1452 (2008). [CrossRef]
  6. I. Ono, S. Kobayashi, and Y. Yoshida, “Optimal lens design by real-coded genetic algorithms using UNDX,” Comput. Methods Appl. Mech. Eng. 186(2-4), 483–497 (2000). [CrossRef]
  7. L. Li, Q. H. Wang, D. H. Li, and H. R. Peng, “Jump method for optical thin film design,” Opt. Express 17(19), 16920–16926 (2009). [CrossRef] [PubMed]
  8. L. Li, Q. H. Wang, X. Q. Xu, and D. H. Li, “Two-step method for lens system design,” Opt. Express 18(12), 13285–13300 (2010). [CrossRef] [PubMed]
  9. D. Shafer, “Global optimization in optical design,” Comput. Phys. 8, 188–195 (1994).
  10. M. van Turnhout and F. Bociort, “Chaotic behavior in an algorithm to escape from poor local minima in lens design,” Opt. Express 17(8), 6436–6450 (2009). [CrossRef] [PubMed]
  11. J. Meiron, “Damped Least-Squares method for automatic lens design,” J. Opt. Soc. Am. 55(9), 1105–1107 (1965). [CrossRef]
  12. H. E. Nusse and J. A. Yorke, “Basins of attraction,” Science 271(5254), 1376–1380 (1996). [CrossRef]
  13. H. P. Schwefel, “Numerical optimization of computer models,” (Wiley, 1981).
  14. J. M. Yang and C. Y. Kao, “A robust evolutionary algorithm for optical thin-film designs,” Evol. Comput. 2, 978–985 (2000).
  15. D. C. O’Shea, “The monochromatic quartet: a search for the global optimum,” Proc. SPIE 1354, 548–554 (1990). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited