Injecting External Solutions Into CMA-ES

Nikolaus Hansen 1, 2, 3
1 TAO - Machine Learning and Optimisation
LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8623
Abstract : This report considers how to inject external candidate solutions into the CMA-ES algorithm. The injected solutions might stem from a gradient or a Newton step, a surrogate model optimizer or any other oracle or search mechanism. They can also be the result of a repair mechanism, for example to render infeasible solutions feasible. Only small modifications to the CMA-ES are necessary to turn injection into a reliable and effective method: too long steps need to be tightly renormalized. The main objective of this report is to reveal this simple mechanism. Depending on the source of the injected solutions, interesting variants of CMA-ES arise. When the best-ever solution is always (re-)injected, an elitist variant of CMA-ES with weighted multi-recombination arises. When \emph{all} solutions are injected from an \emph{external} source, the resulting algorithm might be viewed as \emph{adaptive encoding} with step-size control. In first experiments, injected solutions of very good quality lead to a convergence speed twice as fast as on the (simple) sphere function without injection. This means that we observe an impressive speed-up on otherwise difficult to solve functions. Single bad injected solutions on the other hand do no significant harm.
Type de document :
[Research Report] RR-7748, INRIA. 2011
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Contributeur : Nikolaus Hansen <>
Soumis le : mercredi 19 octobre 2011 - 00:59:39
Dernière modification le : jeudi 5 avril 2018 - 12:30:12
Document(s) archivé(s) le : vendredi 20 janvier 2012 - 10:25:29


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  • HAL Id : inria-00628254, version 1
  • ARXIV : 1110.4181



Nikolaus Hansen. Injecting External Solutions Into CMA-ES. [Research Report] RR-7748, INRIA. 2011. 〈inria-00628254〉



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