A multi-recombinative active matrix adaptation evolution strategy for constrained optimization

  • Patrick SpettelEmail author
  • Hans-Georg Beyer


This paper presents the multi-recombinative constraint active matrix adaptation evolution strategy (Constraint Active-MA-ES). It extends the MA-ES recently introduced by Beyer and Sendhoff in order to handle constrained black-box optimization problems. The active covariance matrix adaptation approach for constraint handling similar to the method proposed by Arnold and Hansen for the \((1+1)\) covariance matrix adaptation evolution strategy is used. As a first step toward constraint handling, active covariance matrix adaptation is incorporated into the MA-ES and evaluated on unconstrained problems (Active-MA-ES). As the second step, constraint handling based on active covariance matrix adaptation for the MA-ES is proposed (Constraint Active-MA-ES). The algorithm has been tested on different test functions and it has been compared to other methods. The experiments show that for cases where directional sampling of the offspring mutations is beneficial, the Active-MA-ES can reach the target faster than the MA-ES. In particular, the Active-MA-ES reaches the final target precision on average by a factor of 1.4 generations (Ellipsoid), a factor of 1.6 generations (Different Powers), and a factor of 2.0 generations (Tablet) faster than the MA-ES. The experiments for the Constraint Active-MA-ES reveal that it achieves 80% of the considered targets with about \(N \times 10^5\) function and constraint evaluations. With this result, it is the best method among the compared approaches.


Constrained optimization Active matrix adaptation evolution strategy Black-box optimization benchmarking 



This work was supported by the Austrian Science Fund FWF under Grant P29651-N32.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Research Center Process and Product EngineeringVorarlberg University of Applied SciencesDornbirnAustria

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