Evolving the structure of Evolution Strategies

Abstract

Abstract-Various variants of the well known Covariance Matrix Adaptation Evolution Strategy (CMA-ES) have been proposed recently, which improve the empirical performance of the original algorithm by structural modifications. However, in practice it is often unclear which variation is best suited to the specific optimization problem at hand. As one approach to tackle this issue, algorithmic mechanisms attached to CMA-ES variants are considered and extracted as functional modules, allowing for combinations of them. This leads to a configuration space over ES structures, which enables the exploration of algorithm structures and paves the way toward novel algorithm generation. Specifically, eleven modules are incorporated in this framework with two or three alternative configurations for each module, resulting in 4 608 algorithms. A self-adaptive Genetic Algorithm (GA) is used to efficiently evolve effective ES-structures for given classes of optimization problems, outperforming any classical CMA-ES variants from literature. The proposed approach is evaluated on noiseless functions from BBOB suite. Furthermore, such an observation is again confirmed on different function groups and dimensionality, indicating the feasibility of ES configuration on real-world problem classes.

Automated Algorithm Selection on Continuous Black-Box Problems by Combining Exploratory Landscape Analysis and Machine Learning

“…Hansen and Ostermeier (2001) introduced one of the most popular evolution strategies: the Covariance Matrix Adaption Evolution Strategy (CMA-ES) with cumulative step-size adaptation (CMA-CSA, Atamna, 2015). It led to a plethora of variants (van Rijn et al, 2016), including the following three solvers from our portfolio: (1) IPOP400D (Auger et al, 2013), a restart version of the CMA-ES with an increasing population size (IPOP-CMA-ES, Auger and Hansen, 2005) and a maximum of 400 × (d + 2) function evaluations.…”

Towards dynamic algorithm selection for numerical black-box optimization

“…e approach was then tested in [37], where it was shown that the predicted gains can indeed materialize, with the caveat that one has to ensure a su ciently accurate estimate for the median anytime performances of each algorithm. ese two works, however, focus on a single family of numerical black-box optimization techniques, the modular CMA-ES framework suggested in [36]. Here in this work, in contrast, we explicitly want to go one step further, and study combinations of heuristics that are potentially of very di erent structure, such as, for example combining a Di erential Evolution (DE) algorithm for the global exploration with a CMA-ES for the nal convergence.…”

Increasing Population (μ + λ)-CMA-ES with Centre and Elitism (IPOP!+)

“…Whenever a run of the (µ W , λ) -CMA-ES is terminated due to one of the five to six local stagnation criterion [2], the population size is increased by a factor η for the next independent run of the (µ W , λ) -CMA-ES restarted from the beginning. Elitism(IPOP+) is a version of IPOP that uses a (µ W + λ) CMA-ES [8,9]. Van Rijn found that, adding elitism to the system often shows a massive improvement over IPOP when tested on many test functions.…”

“…In order to use the µ parents within the selection routine, care has to be taken when updating the CMA-ES central model. Van Rijn [8] does not mention how he accounted for this. Here, when computing the model, if a member of the new µ -selected population comes originally from the parent, the error term from the center of the model used to generate that member is recomputed through measuring the Euclidean distance from that member to the center of the current model, the same as for the offspring(not the Euclidean distance from the center that had generated the parental member which may have been from the previous generation or perhaps even earlier if that member is specially fit and had survived across multiple generations).…”

“…Recently, Van Rijn isolated each feature that have been previously proposed and performed a massive study combining the features in various combination against a varied test width to see what combination of features work well together and if any dominate [9]. In doing so, Van Rijn added the ES style "+" selection operator which he called elitism [8,9] as one of the various features. While (µ + λ)-ES style selection is obviously not novel, applying it to CMA-ES was.…”