Hans-Georg Beyer
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Prof. Dr. rer. nat. habil. Hans-Georg Beyer

Recent Talks

1. Evolution Strategies are Not Gradient Followers

In order to explain the working principles of Evolution Strategies (ESs) in real-valued search spaces, sometimes the picture of a (stochastic) gradient approximating strategy is invoked. There are publications in the field of machine learning and evolutionary algorithms where this misleading picture is promoted. Therefore, I gave a talk at Dagstuhl, Seminar 19431 (Oct. 20 - 25, 2019), showing that this picture is not correct: ESs are much more explorative than gradient strategies, thus they have a certain chance of not being trapped in the next local attractor. The slides of that talk can be obtained here.
BTW, even the consideration of ESs as Monte-Carlo approximators of the so-called natural gradient does not hold for standard ESs such as the Covariance Matrix Adaptation ES. A discussion of that topic can be found in my paper Convergence Analysis of Evolutionary Algorithms That are Based on the Paradigm of Information Geometry. While the main part of that paper is rather technical, the Introduction and the Conclusions should be easy to follow.


2. Design Principles for Matrix Adaptation Evolution Strategies

In the paper Simplify Your Covariance Matrix Adaptation Evolution Strategy we have shown that one can simplify this well-performing ES by removing the covariance matrix totally from the CMA-ES without performance degradation. As a result one obtains simpler Evolution Strategies that allow for further algorithm engineering addressing high-dimensional search spaces and constrained optimization problems. Here are tutorial slides discussing these topics.
Matlab/Octave code of the basic algorithms can be found at Downloads


3. Invited Talk at GECCO 2025:
It is Time for a Revision of COCO BBOB (pdf)

This talk held in Malaga, Spain, at the GECCO 2025 AABOH Workshop on July 14th, 2025, takes a critical look at the well-established COCO BBOB benchmark suite.
After a short recap of the ideas behind ECDF plots (empirical cumulative distribution function) a couple of weaknesses of the COCO BBOB design are discussed:
  • The function value targets between 10-6 and 10-8
    • are far too precise for real-world applications. These only reflect the local convergence behavior of the algorithms evaluated.
  • Aggregating function value targets of different test functions in a single ECDF plot is scientific nonsense.
  • The transformations used to generate different instantiations of the test functions favor CMA-ES like algorithms.
  • The 24 test functions used need a renovation in order to reflect the developments of the last 15 years.
Regarding the last item of this bullet list, I've proposed a couple of simple, scale- and tunable, but challenging test functions that appear hard for CMA-ES like algorithms (and others). These are HappyCat-, HGBat-, ThreeButton-, and the Audi-function. The peculiarity of these functions is that (except for Audi) they have only one local minimum (being also the global one). In 2D one can easily locate the global minimizer visually. Yet, it is difficult for the algorithms to get close to the global minimizer.

For example, in the case of ThreeButton it takes the CMA-ES very long to get to the minimizer even in the case of a rather weak 2D version of this function. This can be seen in this mp4-video where the offspring population (pink dots) is displayed in the search space along with the contour lines of the ThreeButton function. Unlike most of the functions in the BBOB test suite where the CMA-ES has to learn the covariance matrix ones, in the case of ThreeButton it has to permanently learn and re-learn this matrix (note, in order to shorten the video, some generation intervals of the evolution process were skipped).

In the slides of this talk additional videos have been linked to show the evolution of the population in the HappyCat and HGBat landscape for 2D and 10D instances. For the higher-dimensional case a visualization trick has been invented to display the exploratory behavior of the offspring population. To this end, those two dimensions of the parent centroid that are most far apart from the minimizer are determined. These two dimensions (that can change from generation to generation) are used to display the offspring individuals. As an example, see the (simple) 10D HGBat case with β=1.

When thinking about scaleable test functions in a renovated BBOB test suite also examples from physics come into mind. Some of them are discussed in this talk: Thomson's and Tammes' problem as well as the Lennard-Jones energy minimization. All these problems are well-suited for large-scale optimization benchmarking.


last change: 22.02.2026