Gaussian Process Surrogate Models for the CMA Evolution Strategy.

This article deals with Gaussian process surrogate models for the Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES)-several already existing and two by the authors recently proposed models are presented. The work discusses different variants of surrogate model exploitation and focuses on the benefits of employing the Gaussian process uncertainty prediction, especially during the selection of points for the evaluation with a surrogate model. The experimental part of the article thoroughly compares and evaluates the five presented Gaussian process surrogate and six other state-of-the-art optimizers on the COCO benchmarks. The algorithm presented in most detail, DTS-CMA-ES, which combines cheap surrogate-model predictions with the objective function evaluations in every iteration, is shown to approach the function optimum at least comparably fast and often faster than the state-of-the-art black-box optimizers for budgets of roughly 25-100 function evaluations per dimension, in 10- and less-dimensional spaces even for 25-250 evaluations per dimension.

Optimization of catalysts using specific, description-based genetic algorithms.

This paper deals with the key optimization task that has to be solved when improving the performance of many chemical processes--optimization of the catalysts used in the reaction via the optimization of its composition and preparation. A novel approach is presented that allows for the preservation of the advantages of genetic algorithms developed specifically for the optimization of catalytic materials but avoids the disadvantageous necessity to reimplement the algorithm when the scope of the optimized materials changes. Its main idea is to automatically generate problem-tailored implementations from requirements concerning the materials with a program generator. For the specification of such requirements, a formal description language, called catalyst description language, has been developed.

Piecewise-linear neural networks and their relationship to rule extraction from data.

This article addresses the topic of extracting logical rules from data by means of artificial neural networks. The approach based on piecewise linear neural networks is revisited, which has already been used for the extraction of Boolean rules in the past, and it is shown that this approach can be important also for the extraction of fuzzy rules. Two important theoretical properties of piecewise-linear neural networks are proved, allowing an elaboration of the basic ideas of the approach into several variants of an algorithm for the extraction of Boolean rules. That algorithm has already been used in two real-world applications. Finally, a connection to the extraction of rules of the Lukasiewicz logic is established, relying on recent results about rational McNaughton functions. Based on one of the constructive proofs of the McNaughton theorem, an algorithm is formulated that in principle allows extracting a particular kind of formulas of the Lukasiewicz predicate logic from piecewise-linear neural networks trained with rational data.

Efficient discovery of nonlinear dependencies in a combinatorial catalyst data set.

Exploration of a complex catalyst system using Genetic Algorithm methods and combinatorial experimentation efficiently removes noncontributing elements and generates data that can be used to model the remaining system. In particular the combined methods effectively navigate and optimize systems with highly nonlinear dependencies (3-way and higher interactions).