Holger Ulmer, Felix Streichert, and Andreas Zell

Optimization by Gaussian Processes assisted Evolution Strategies

Selected Papers of the International Conference on Operations Research (OR 2003)

Abstract

Evolutionary Algorithms (EA) are excellent optimization tools for complex high-dimensional multimodal problems. However, they require a very large number of problem function evaluations. In many engineering optimization problems, like high throughput material science or design optimization, a single fitness evaluation is very expensive or time consuming. Therefore, standard evolutionary computation methods are not practical for such applications. Applying models as a surrogate of the real fitness function is a quite popular approach to handle this restriction. We propose a Model Assisted Evolution Strategy (MAES), which uses a Gaussian Process (GP) approximation model. The purpose of the Gaussian Process model is to preselect the most promising solutions, which are then actually evaluated by the real problem function. To refine the preselection process the likelihood of each individual to improve the overall best found solution is determined. Numerical results from extensive simulations on high dimensional test functions and one material optimization problem are presented. MAES has a much better convergence rate and achieves better results than standard evolutionary optimization approaches with less fitness evaluations.

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BibTeX 

@inproceedings{ulmer03optimization,
  author 		= "Holger Ulmer and Felix Streichert and Andreas Zell ",
  title 		= "Optimization by Gaussian Processes assisted Evolution Strategies",
  booktitle 		= "Selected Papers of the International Conference on Operations Research (OR 2003)",
  pages 		= "434-442",
  year 			= "2003",
  month 		= "3-5 September",
  address 		= {Heidelberg, Germany},
  publisher 		= {Springer Verlag},
  publisher_address 	= {Berlin},  
  abstract 		= {Evolutionary Algorithms (EA) are excellent optimization tools for complex
high-dimensional multimodal problems. However, they require a very large
number of problem function evaluations. In many engineering optimization
problems, like high throughput material science or design
optimization, a single fitness evaluation is very expensive or time
consuming. Therefore, standard evolutionary computation methods are not
practical for such applications. Applying models as a surrogate of the real
fitness function is a quite popular approach to handle this restriction. We
propose a Model Assisted Evolution Strategy (MAES), which uses a Gaussian
Process (GP) approximation model. The purpose of the Gaussian Process model
is to preselect the most promising solutions, which are then actually
evaluated by the real problem function. To refine the preselection process
the likelihood of each individual to improve the overall best found solution
is determined. Numerical results from extensive simulations on high
dimensional test functions and one material optimization problem are
presented. MAES has a much better convergence rate and achieves better
results than standard evolutionary optimization approaches with less fitness
evaluations.}
}