Optical Design with Epsilon-Dominated Multi-objective Evolutionary Algorithm

  • Shaine Joseph
  • Hyung W. Kang
  • Uday K. Chakraborty
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4431)


Significant improvement over a patented lens design is achieved using multi-objective evolutionary optimization. A comparison of the results obtained from NSGA2 and ε-MOEA is done. In our current study, ε-MOEA converged to essentially the same Pareto-optimal solutions as the one with NSGA2, but ε-MOEA proved to be better in providing reasonably good solutions, comparable to the patented design, with lower number of lens evaluations. ε-MOEA is shown to be computationally more efficient and practical than NSGA2 to obtain the required initial insight into the objective function trade-offs while optimizing large and complex optical systems.


Design Variable Optical Design Single Objective Optimization Code Versus Lens Evaluation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Kidger, M.J.: Intermediate Optical Design. SPIE Press, Bellingham (2004)Google Scholar
  2. 2.
    Vasiljevic, D.: Classical and Evolutionary Algorithms in the Optimization of Optical Sytems. Kluwer Academic Publishers, Dordrecht (2002)Google Scholar
  3. 3.
    Cheng, X., Wang, Y., Hao, Q., Sasian, J.: Automatic element addition and deletion in lens optimization. Applied Optics 42(7), 1309–1317 (2003)CrossRefGoogle Scholar
  4. 4.
    Koza, J.R., Al-Sakran, S.H., Jones, L.W.: Automated re-invention of six patented optical lens systems using genetic programming. In: Proc. GECCO, New York, pp. 1953–1960 (2005)Google Scholar
  5. 5.
    Bociort, F., Driel, E., Serebriakov, A.: Network structure of the set of local minima in optical system optimization. In: Proc. of SPIE, vol. 5174, pp. 26–34 (2003)Google Scholar
  6. 6.
    Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. John Wiley & Sons, Chichester (2003)Google Scholar
  7. 7.
    Deb, K., Mohan, M., Mishra, S.: A Fast Multi-objective Evolutionary Algorithm for Finding Well-Spread Pareto-Optimal Solutions. KanGAL Report no. 2003002 (2003)Google Scholar
  8. 8.
    Ono, I., Kobayashi, S., Yoshida, K.: Global and Multi-objective Optimization for Lens Design by Real-coded Genetic Algorithms. In: Proc. of SPIE, vol. 3482, pp. 110–121 (1998)Google Scholar
  9. 9.
    Joseph, S.: Lens Design and Optimization Using Multi-Objective Evolutionary Algorithms. Ph.D. dissertation, University of Missouri-Rolla (2005)Google Scholar
  10. 10.
    Joseph, S., Kang, H.W., Chakraborty, U.K.: Lens Optimization In A Classical-Evolutionary Hybrid Framework. In: Proc. MENDEL: 12th International Conference on Soft Computing, Brno, Czech Republic, EU (2006)Google Scholar
  11. 11.
    Coello Coello, C.A., et al.: Evolutionary Algorithms for Solving Multi-Objective Problems. Kluwer Academic Publishers, Dordrecht (2002)zbMATHGoogle Scholar
  12. 12.

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Shaine Joseph
    • 1
  • Hyung W. Kang
    • 1
  • Uday K. Chakraborty
    • 1
  1. 1.Department of Mathematics and Computer Science, University of Missouri, St. Louis, One University Blvd., St. Louis, MO 63121USA

Personalised recommendations