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Title: Robust simplex algorithm for online optimization

Abstract

A new optimization algorithm is introduced for online optimization applications. The algorithm was modified from the popular Nelder-Mead simplex method to make it noise aware and noise resistant. Simulation with an analytic function is used to demonstrate its performance. The algorithm has been successfully tested in experiments, which showed that the algorithm is robust for optimization problems with complex functional dependence, high cross-coupling between parameters, and high noise. Advantages of the new algorithm include high efficiency and that it does not require prior knowledge of the parameter space such as an initial conjugate direction set.

Authors:
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1477568
Alternate Identifier(s):
OSTI ID: 1490382
Report Number(s):
slac-pub-17288
Journal ID: ISSN 2469-9888; PRABCJ; 104601
Grant/Contract Number:  
AC02-76SF00515
Resource Type:
Published Article
Journal Name:
Physical Review Accelerators and Beams
Additional Journal Information:
Journal Name: Physical Review Accelerators and Beams Journal Volume: 21 Journal Issue: 10; Journal ID: ISSN 2469-9888
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
43 PARTICLE ACCELERATORS

Citation Formats

Huang, Xiaobiao. Robust simplex algorithm for online optimization. United States: N. p., 2018. Web. doi:10.1103/PhysRevAccelBeams.21.104601.
Huang, Xiaobiao. Robust simplex algorithm for online optimization. United States. doi:10.1103/PhysRevAccelBeams.21.104601.
Huang, Xiaobiao. Wed . "Robust simplex algorithm for online optimization". United States. doi:10.1103/PhysRevAccelBeams.21.104601.
@article{osti_1477568,
title = {Robust simplex algorithm for online optimization},
author = {Huang, Xiaobiao},
abstractNote = {A new optimization algorithm is introduced for online optimization applications. The algorithm was modified from the popular Nelder-Mead simplex method to make it noise aware and noise resistant. Simulation with an analytic function is used to demonstrate its performance. The algorithm has been successfully tested in experiments, which showed that the algorithm is robust for optimization problems with complex functional dependence, high cross-coupling between parameters, and high noise. Advantages of the new algorithm include high efficiency and that it does not require prior knowledge of the parameter space such as an initial conjugate direction set.},
doi = {10.1103/PhysRevAccelBeams.21.104601},
journal = {Physical Review Accelerators and Beams},
number = 10,
volume = 21,
place = {United States},
year = {2018},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevAccelBeams.21.104601

Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

Figures / Tables:

FIG. 1 FIG. 1: Minimum function values in 1000 evaluations for the Rosenbrock problem in 100 optimization runs (sorted) with the Nelder-Mead simplex algorithm (blue dashed line), Nelder-Mead with N = 3 averaging (red dash-dot line), the robust simplex algorithm without simplex rebuilding (RSim- plex w/o Rebuild, solid yellow line) and withmore » simplex rebuild- ing (RSimplex w/ Rebuild, solid magenta line).« less

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Works referenced in this record:

An Automatic Method for Finding the Greatest or Least Value of a Function
journal, March 1960


Multivariate optimization of a high brightness dc gun photoinjector
journal, March 2005

  • Bazarov, Ivan V.; Sinclair, Charles K.
  • Physical Review Special Topics - Accelerators and Beams, Vol. 8, Issue 3
  • DOI: 10.1103/PhysRevSTAB.8.034202

Multi-objective particle swarm and genetic algorithm for the optimization of the LANSCE linac operation
journal, March 2014

  • Pang, X.; Rybarcyk, L. J.
  • Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 741
  • DOI: 10.1016/j.nima.2013.12.042

Feasibility study of online tuning of the luminosity in a circular collider with the robust conjugate direction search method
journal, December 2015


Online optimization of storage ring nonlinear beam dynamics
journal, August 2015


A Simplex Method for Function Minimization
journal, January 1965


Experimental determination of storage ring optics using orbit response measurements
journal, March 1997

  • Safranek, J.
  • Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 388, Issue 1-2
  • DOI: 10.1016/S0168-9002(97)00309-4

Minimization of Betatron Oscillations of Electron Beam Injected Into a Time-Varying Lattice via Extremum Seeking
journal, January 2018

  • Scheinker, Alexander; Huang, Xiaobiao; Wu, Juhao
  • IEEE Transactions on Control Systems Technology, Vol. 26, Issue 1
  • DOI: 10.1109/TCST.2017.2664728

Stochastic Nelder–Mead simplex method – A new globally convergent direct search method for simulation optimization
journal, August 2012


Nelder-Mead Simplex Modifications for Simulation Optimization
journal, July 1996


A Revised Simplex Search Procedure for Stochastic Simulation Response Surface Optimization
journal, November 2000


Machine based optimization using genetic algorithms in a storage ring
journal, February 2014


An algorithm for online optimization of accelerators
journal, October 2013

  • Huang, Xiaobiao; Corbett, Jeff; Safranek, James
  • Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 726
  • DOI: 10.1016/j.nima.2013.05.046

    Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.