Enhancement of the downhill simplex method of optimization

Research output: Chapter in Book/Report/Conference proceedingConference contribution

18 Citations (Scopus)

Abstract

The downhill simplex method of optimization is a "geometric" method to achieve function minimization. The standard algorithm uses arbitrary values for the deterministic factors that describe the "movement" of the simplex in the merit space. While it is a robust method of optimization, it is relatively slow to converge to local minima. However, its stability and the lack of use of derivates make it useful for optical design optimization, especially for the field of illumination. This paper describes preliminary efforts of optimizing the performance of the simplex optimizer. This enhancement is accomplished by optimizing the various control factors: alpha (reflection), beta (contraction), and gamma (expansion). This effort is accomplished by investigating the "end game" of optimal design, i.e., the shape of the figure of merit space is parabolic in N-dimensions near local minima. The figure of merit for the control factor optimization is the number of iterations to achieve a solution in comparison to the same case using the standard control factors. This optimization is done for parabolic wells of order N = 2 to 15. In this study it is shown that with the correct choice of the control factors, one can achieve up to a 35% improvement in convergence. Techniques using gradient weighting and the inclusion of additional control factors are proposed.

Original languageEnglish (US)
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
EditorsP.K. Manhart, J.M. Sasian
Pages270-282
Number of pages13
Volume4832
DOIs
StatePublished - 2002
Externally publishedYes
EventInternational Optical Design Conference 2002 - Tucson, AZ, United States
Duration: Jun 3 2002Jun 5 2002

Other

OtherInternational Optical Design Conference 2002
CountryUnited States
CityTucson, AZ
Period6/3/026/5/02

Fingerprint

simplex method
optimization
augmentation
figure of merit
Optical design
design optimization
games
Lighting
contraction
iteration
illumination
inclusions
gradients
expansion

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Condensed Matter Physics

Cite this

Koshel, R. J. (2002). Enhancement of the downhill simplex method of optimization. In P. K. Manhart, & J. M. Sasian (Eds.), Proceedings of SPIE - The International Society for Optical Engineering (Vol. 4832, pp. 270-282) https://doi.org/10.1117/12.486465

Enhancement of the downhill simplex method of optimization. / Koshel, Richard John.

Proceedings of SPIE - The International Society for Optical Engineering. ed. / P.K. Manhart; J.M. Sasian. Vol. 4832 2002. p. 270-282.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Koshel, RJ 2002, Enhancement of the downhill simplex method of optimization. in PK Manhart & JM Sasian (eds), Proceedings of SPIE - The International Society for Optical Engineering. vol. 4832, pp. 270-282, International Optical Design Conference 2002, Tucson, AZ, United States, 6/3/02. https://doi.org/10.1117/12.486465
Koshel RJ. Enhancement of the downhill simplex method of optimization. In Manhart PK, Sasian JM, editors, Proceedings of SPIE - The International Society for Optical Engineering. Vol. 4832. 2002. p. 270-282 https://doi.org/10.1117/12.486465
Koshel, Richard John. / Enhancement of the downhill simplex method of optimization. Proceedings of SPIE - The International Society for Optical Engineering. editor / P.K. Manhart ; J.M. Sasian. Vol. 4832 2002. pp. 270-282
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