A method for handling uncertainty in evolutionary optimization with an application to feedback control of combustion

  • Authors:

  • Nikolaus Hansen;André S. P. Niederberger;Lino Guzzella;Petros Koumoutsakos

  • Affiliations:

  • Institute of Computational Science, Swiss Federal Institute of Technology, Zurich, Switzerland;Measurement and Control Laboratory, Swiss Federal Institute of Technology, Zurich, Switzerland;Measurement and Control Laboratory, Swiss Federal Institute of Technology, Zurich, Switzerland;Institute of Computational Science, Swiss Federal Institute of Technology, Zurich, Switzerland

  • Venue:
  • IEEE Transactions on Evolutionary Computation - Special issue on computational finance and economics
  • Year:
  • 2009

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Abstract

We present a novel method for handling uncertainty in evolutionary optimization. The method entails quantification and treatment of uncertainty and relies on the rank based selection operator of evolutionary algorithms. The proposed uncertainty handling is implemented in the context of the covariance matrix adaptation evolution strategy (CMA-ES) and verified on test functions. The present method is independent of the uncertainty distribution, prevents premature convergence of the evolution strategy and is well suited for online optimization as it requires only a small number of additional function evaluations. The algorithm is applied in an experimental setup to the online optimization of feedback controllers of thermoacoustic instabilities of gas turbine combustors. In order to mitigate these instabilities, gain-delay or model-based H∞ controllers sense the pressure and command secondary fuel injectors. The parameters of these controllers are usually specified via a trial and error procedure. We demonstrate that their online optimization with the proposed methodology enhances, in an automated fashion, the online performance of the controllers, even under highly unsteady operating conditions, and it also compensates for uncertainties in the model-building and design process.