Thomas Bartz-Beielstein

Thomas Bartz-Beielstein

This document provides a comprehensive guide to hyperparameter tuning using spotPython for scikit-learn, PyTorch, and river. The first part introduces spotPython's surrogate model-based optimization process, while the second part focuses on hyperparameter tuning. Several case studies are presented, including hyperparameter tuning for sklearn models such as Support Vector Classification, Random Forests, Gradient Boosting (XGB), and K-nearest neighbors (KNN), as well as a Hoeffding Adaptive Tree Regressor from river. The integration of spotPython into the PyTorch and PyTorch Lightning training workflow is also discussed. With a hands-on approach and step-by-step explanations, this cookbook serves as a practical starting point for anyone interested in hyperparameter tuning with Python. Highlights include the interplay between Tensorboard, PyTorch Lightning, spotPython, and river. This publication is under development, with updates available on the corresponding webpage.

Jens U. Brandt, Noah C. Puetz, Jobel Jose George et al.

Virtual sensing aims to infer hard-to-measure quantities from accessible measurements and is central to perception and control in physical systems. Despite rapid progress from first-principle and hybrid models to modern data-driven methods research remains siloed, leaving no established default approach that transfers across processes, modalities, and sensing configurations. We introduce MuViS, a domain-agnostic benchmarking suite for multimodal virtual sensing that consolidates diverse datasets into a unified interface for standardized preprocessing and evaluation. Using this framework, we benchmark established approaches spanning gradient-boosted decision trees and deep neural network (NN) architectures, and show that none of these provides a universal advantage, underscoring the need for generalizable virtual sensing architectures. MuViS is released as an open-source, extensible platform for reproducible comparison and future integration of new datasets and model classes.

Thomas Bartz-Beielstein

The `spotoptim` package implements surrogate-model-based optimization of expensive black-box functions in Python. Building on two decades of Sequential Parameter Optimization (SPO) methodology, it provides a Kriging-based optimization loop with Expected Improvement, support for continuous, integer, and categorical variables, noise-aware evaluation via Optimal Computing Budget Allocation (OCBA), and multi-objective extensions. A steady-state parallelization strategy overlaps surrogate search with objective evaluation on multi-core hardware, and a success-rate-based restart mechanism detects stagnation while preserving the best solution found. The package returns scipy-compatible `OptimizeResult` objects and accepts any scikit-learn-compatible surrogate model. Built-in TensorBoard logging provides real-time monitoring of convergence and surrogate quality. This report describes the architecture and module structure of spotoptim, provides worked examples including neural network hyperparameter tuning, and compares the framework with BoTorch, Optuna, Ray Tune, BOHB, SMAC, and Hyperopt. The package is open-source.

Vekil Bekmyradov, Noah C. Pütz, Thomas Bartz-Beielstein

Large Language Models (LLMs) have achieved impressive results on public benchmarks, often leading to claims of advanced reasoning and understanding. However, recent research in cognitive science reveals that these models sometimes rely on shallow heuristics and memorization, taking shortcuts rather than demonstrating genuine cognitive abilities. This paper investigates LLM behavior in automated test generation for software, contrasting performance on an open-source system (LevelDB) with SAP HANA, one of the most widely deployed commercial database systems worldwide, whose proprietary codebase is guaranteed to be absent from training data. We combine cognitive evaluation principles, drawing on Mitchell's mechanism-focused assessment methodology, with empirical software testing, employing mutation score and iterative compiler-feedback repair loops to assess both accuracy and underlying reasoning strategies. Results show that LLMs excel on familiar, open-source benchmarks but struggle with unseen, complex domains, often prioritizing compilability over semantic effectiveness. These findings provide independent software engineering evidence for the broader claim that current LLMs lack robust reasoning, and highlight the need for evaluation frameworks that penalize trivial shortcuts and reward true generalization.

Julian Hatzky, Thomas Bartz-Beielstein, A. E. Eiben et al.

Multi-task optimization is a powerful approach for solving a large number of tasks in parallel. However, existing algorithms face distinct limitations: Population-based methods scale poorly and remain underexplored for large task sets. Approaches that do scale beyond a thousand tasks are mostly MAP-Elites variants and rely on a fixed, discretized archive that disregards the topology of the task space. We introduce MONET (Multi-Task Optimization over Networks of Tasks), a multi-task optimization algorithm that models the task space as a graph: tasks are nodes, and edges connect tasks in the task parameter space. This representation enables knowledge transfer between tasks and remains tractable for high-dimensional problems while exploiting the topology of the task space. MONET combines social learning, which generates candidates from neighboring nodes via crossover, with individual learning, which refines a node's own solution independently via mutation. We evaluate MONET on four domains (archery, arm, and cartpole with 5,000 tasks each; hexapod with 2,000 tasks) and show that it matches or exceeds the performance of existing MAP-Elites-based baselines across all four domains.

Thomas Bartz-Beielstein, Eva Bartz

With spotforecast2-safe we present an integrated Compliance-by-Design approach to Python-based point forecasting of time series in safety-critical environments. A review of the relevant open-source tooling shows that existing compliance solutions operate consistently outside of the library to be used - e.g. as scanners, templates, or runtime layers. spotforecast2-safe takes the inverse approach and anchors the requirements of Regulation (EU) 2024/1689 (the EU AI Act, in German: KI-VO), of IEC 61508, of the ISA/IEC 62443 standards series, and of the Cyber Resilience Act within the library: in application-programming-interface contracts, persistence formats, and continuous-integration gates. The approach is operationalised by four non-negotiable code-development rules (zero dead code, deterministic processing, fail-safe handling, minimal dependencies) together with the corresponding process rules (model card, executable docstrings, CI workflows, Common-Platform-Enumeration (CPE) identifier, REUSE-conformant licensing, release pipeline). Interactive visualisation, hyperparameter tuning and automated machine learning (AutoML), as well as deep-learning and large-language-model backends are deliberately excluded, because each of these components either enlarges the attack surface, introduces non-determinism, or impairs reproducibility. A bidirectional traceability matrix maps every regulatory provision onto the corresponding mechanism in the code; an end-to-end example of European-market electricity generation, transmission, and consumption forecasting demonstrates the application. The package is open-source and available under Affero General Public License (AGPL) 3.0-or-later.

Abdul-Malik Akiev, Danyal Ergür, Alexander Schirger et al.

Speedlines in compressor performance maps (CPMs) are critical for understanding and predicting compressor behavior under various operating conditions. We investigate a physics-based method for reconstructing compressor performance maps from sparse measurements by fitting each speedline with a superellipse and encoding it as a compact, interpretable vector (surge, choke, curvature, and shape parameters). Building on the formulation of Llamas et al., we develop a robust two-stage fitting pipeline that couples global search with local refinement. The approach is validated on industrial data-sets for different turbocharger types. We discuss prediction quality for inter- and extrapolation, metric sensitivities and outline opportunities for physics-informed constraints, alternative function families, and hybrid physics-ML mappings to improve boundary behavior and, ultimately, enable full CPM reconstruction from limited data.

Alexander Hinterleitner, Thomas Bartz-Beielstein, Richard Schulz et al.

Research in Explainable Artificial Intelligence (XAI) is increasing, aiming to make deep learning models more transparent. Most XAI methods focus on justifying the decisions made by Artificial Intelligence (AI) systems in security-relevant applications. However, relatively little attention has been given to using these methods to improve the performance and robustness of deep learning algorithms. Additionally, much of the existing XAI work primarily addresses classification problems. In this study, we investigate the potential of feature attribution methods to filter out uninformative features in input data for regression problems, thereby improving the accuracy and stability of predictions. We introduce a feature selection pipeline that combines Integrated Gradients with k-means clustering to select an optimal set of variables from the initial data space. To validate the effectiveness of this approach, we apply it to a real-world industrial problem - blade vibration analysis in the development process of turbo machinery.

Thomas Bartz-Beielstein

The goal of this article is to provide an introduction to the desirability function approach to multi-objective optimization (direct and surrogate model-based), and multi-objective hyperparameter tuning. This work is based on the paper by Kuhn (2016). It presents a `Python` implementation of Kuhn's `R` package `desirability`. The `Python` package `spotdesirability` is available as part of the `sequential parameter optimization` framework. After a brief introduction to the desirability function approach is presented, three examples are given that demonstrate how to use the desirability functions for classical optimization, surrogate-model based optimization, and hyperparameter tuning.

Alexander Hinterleitner, Thomas Bartz-Beielstein

Despite the growing interest in Explainable Artificial Intelligence (XAI), explainability is rarely considered during hyperparameter tuning or neural architecture optimization, where the focus remains primarily on minimizing predictive loss. In this work, we introduce the novel concept of XAI consistency, defined as the agreement among different feature attribution methods, and propose new metrics to quantify it. For the first time, we integrate XAI consistency directly into the hyperparameter tuning objective, creating a multi-objective optimization framework that balances predictive performance with explanation robustness. Implemented within the Sequential Parameter Optimization Toolbox (SPOT), our approach uses both weighted aggregation and desirability-based strategies to guide model selection. Through our proposed framework and supporting tools, we explore the impact of incorporating XAI consistency into the optimization process. This enables us to characterize distinct regions in the architecture configuration space: one region with poor performance and comparatively low interpretability, another with strong predictive performance but weak interpretability due to low \gls{xai} consistency, and a trade-off region that balances both objectives by offering high interpretability alongside competitive performance. Beyond introducing this novel approach, our research provides a foundation for future investigations into whether models from the trade-off zone-balancing performance loss and XAI consistency-exhibit greater robustness by avoiding overfitting to training performance, thereby leading to more reliable predictions on out-of-distribution data.

Thomas Bartz-Beielstein, Axel Wellendorf, Noah Pütz et al.

The increasing shortage of nursing staff and the acute risk of falls in nursing homes pose significant challenges for the healthcare system. This study presents the development of an automated fall detection system integrated into care beds, aimed at enhancing patient safety without compromising privacy through wearables or video monitoring. Mechanical vibrations transmitted through the bed frame are processed using a short-time Fourier transform, enabling robust classification of distinct human fall patterns with a convolutional neural network. Challenges pertaining to the quantity and diversity of the data are addressed, proposing the generation of additional data with a specific emphasis on enhancing variation. While the model shows promising results in distinguishing fall events from noise using lab data, further testing in real-world environments is recommended for validation and improvement. Despite limited available data, the proposed system shows the potential for an accurate and rapid response to falls, mitigating health implications, and addressing the needs of an aging population. This case study was performed as part of the ZIM Project. Further research on sensors enhanced by artificial intelligence will be continued in the ShapeFuture Project.

Thomas Bartz-Beielstein

Batch Machine Learning (BML) reaches its limits when dealing with very large amounts of streaming data. This is especially true for available memory, handling drift in data streams, and processing new, unknown data. Online Machine Learning (OML) is an alternative to BML that overcomes the limitations of BML. OML is able to process data in a sequential manner, which is especially useful for data streams. The `river` package is a Python OML-library, which provides a variety of online learning algorithms for classification, regression, clustering, anomaly detection, and more. The `spotRiver` package provides a framework for hyperparameter tuning of OML models. The `spotRiverGUI` is a graphical user interface for the `spotRiver` package. The `spotRiverGUI` releases the user from the burden of manually searching for the optimal hyperparameter setting. After the data is provided, users can compare different OML algorithms from the powerful `river` package in a convenient way and tune the selected algorithms very efficiently.

Thomas Bartz-Beielstein

The goal of hyperparameter tuning (or hyperparameter optimization) is to optimize the hyperparameters to improve the performance of the machine or deep learning model. spotPython (``Sequential Parameter Optimization Toolbox in Python'') is the Python version of the well-known hyperparameter tuner SPOT, which has been developed in the R programming environment for statistical analysis for over a decade. PyTorch is an optimized tensor library for deep learning using GPUs and CPUs. This document shows how to integrate the spotPython hyperparameter tuner into the PyTorch training workflow. As an example, the results of the CIFAR10 image classifier are used. In addition to an introduction to spotPython, this tutorial also includes a brief comparison with Ray Tune, a Python library for running experiments and tuning hyperparameters. This comparison is based on the PyTorch hyperparameter tuning tutorial. The advantages and disadvantages of both approaches are discussed. We show that spotPython achieves similar or even better results while being more flexible and transparent than Ray Tune.

Jörg Stork, Philip Wenzel, Severin Landwein et al.

We have built a novel system for the surveillance of drinking water reservoirs using underwater sensor networks. We implement an innovative AI-based approach to detect, classify and localize underwater events. In this paper, we describe the technology and cognitive AI architecture of the system based on one of the sensor networks, the hydrophone network. We discuss the challenges of installing and using the hydrophone network in a water reservoir where traffic, visitors, and variable water conditions create a complex, varying environment. Our AI solution uses an autoencoder for unsupervised learning of latent encodings for classification and anomaly detection, and time delay estimates for sound localization. Finally, we present the results of experiments carried out in a laboratory pool and the water reservoir and discuss the system's potential.

Eva Bartz, Martin Zaefferer, Olaf Mersmann et al.

Machine learning algorithms such as random forests or xgboost are gaining more importance and are increasingly incorporated into production processes in order to enable comprehensive digitization and, if possible, automation of processes. Hyperparameters of these algorithms used have to be set appropriately, which can be referred to as hyperparameter tuning or optimization. Based on the concept of tunability, this article presents an overview of theoretical and practical results for popular machine learning algorithms. This overview is accompanied by an experimental analysis of 30 hyperparameters from six relevant machine learning algorithms. In particular, it provides (i) a survey of important hyperparameters, (ii) two parameter tuning studies, and (iii) one extensive global parameter tuning study, as well as (iv) a new way, based on consensus ranking, to analyze results from multiple algorithms. The R package mlr is used as a uniform interface to the machine learning models. The R package SPOT is used to perform the actual tuning (optimization). All additional code is provided together with this paper.

Margarita Rebolledo, Daan Zeeuwe, Thomas Bartz-Beielstein et al.

Most evolutionary robotics studies focus on evolving some targeted behavior without taking the energy usage into account. This limits the practical value of such systems because energy efficiency is an important property for real-world autonomous robots. In this paper, we mitigate this problem by extending our simulator with a battery model and taking energy consumption into account during fitness evaluations. Using this system we investigate how energy awareness affects the evolution of robots. Since our system is to evolve morphologies as well as controllers, the main research question is twofold: (i) what is the impact on the morphologies of the evolved robots, and (ii) what is the impact on the behavior of the evolved robots if energy consumption is included in the fitness evaluation? The results show that including the energy consumption in the fitness in a multi-objective fashion (by NSGA-II) reduces the average size of robot bodies while at the same time reducing their speed. However, robots generated without size reduction can achieve speeds comparable to robots from the baseline set.

Thomas Bartz-Beielstein, Frederik Rehbach, Amrita Sen et al.

A surrogate model based hyperparameter tuning approach for deep learning is presented. This article demonstrates how the architecture-level parameters (hyperparameters) of deep learning models that were implemented in Keras/tensorflow can be optimized. The implementation of the tuning procedure is 100% accessible from R, the software environment for statistical computing. With a few lines of code, existing R packages (tfruns and SPOT) can be combined to perform hyperparameter tuning. An elementary hyperparameter tuning task (neural network and the MNIST data) is used to exemplify this approach

Jörg Stork, Martin Zaefferer, Nils Eisler et al.

In addition to their undisputed success in solving classical optimization problems, neuroevolutionary and population-based algorithms have become an alternative to standard reinforcement learning methods. However, evolutionary methods often lack the sample efficiency of standard value-based methods that leverage gathered state and value experience. If reinforcement learning for real-world problems with significant resource cost is considered, sample efficiency is essential. The enhancement of evolutionary algorithms with experience exploiting methods is thus desired and promises valuable insights. This work presents a hybrid algorithm that combines topology-changing neuroevolutionary optimization with value-based reinforcement learning. We illustrate how the behavior of policies can be used to create distance and loss functions, which benefit from stored experiences and calculated state values. They allow us to model behavior and perform a directed search in the behavior space by gradient-free evolutionary algorithms and surrogate-based optimization. For this purpose, we consolidate different methods to generate and optimize agent policies, creating a diverse population. We exemplify the performance of our algorithm on standard benchmarks and a purpose-built real-world problem. Our results indicate that combining methods can enhance the sample efficiency and learning speed for evolutionary approaches.

Thomas Bartz-Beielstein, Marcel Dröscher, Alpar Gür et al.

Crises like the COVID-19 pandemic pose a serious challenge to health-care institutions. They need to plan the resources required for handling the increased load, for instance, hospital beds and ventilators. To support the resource planning of local health authorities from the Cologne region, BaBSim.Hospital, a tool for capacity planning based on discrete event simulation, was created. The predictive quality of the simulation is determined by 29 parameters. Reasonable default values of these parameters were obtained in detailed discussions with medical professionals. We aim to investigate and optimize these parameters to improve BaBSim.Hospital. First approaches with "out-of-the-box" optimization algorithms failed. Implementing a surrogate-based optimization approach generated useful results in a reasonable time. To understand the behavior of the algorithm and to get valuable insights into the fitness landscape, an in-depth sensitivity analysis was performed. The sensitivity analysis is crucial for the optimization process because it allows focusing the optimization on the most important parameters. We illustrate how this reduces the problem dimension without compromising the resulting accuracy. The presented approach is applicable to many other real-world problems, e.g., the development of new elevator systems to cover the last mile or simulation of student flow in academic study periods.

Margarita Rebolledo, Sowmya Chandrasekaran, Thomas Bartz-Beielstein

Drinking water supply and distribution systems are critical infrastructure that has to be well maintained for the safety of the public. One important tool in the maintenance of water distribution systems (WDS) is flushing. Flushing is a process carried out in a periodic fashion to clean sediments and other contaminants in the water pipes. Given the different topographies, water composition and supply demand between WDS no single flushing strategy is suitable for all of them. In this report a non-exhaustive overview of optimization methods for flushing in WDS is given. Implementation of optimization methods for the flushing procedure and the flushing planing are presented. Suggestions are given as a possible option to optimise existing flushing planing frameworks.

Thomas Bartz-Beielstein, Frederik Rehbach, Olaf Mersmann et al.

We present a resource-planning tool for hospitals under special consideration of the COVID-19 pandemic, called babsim.hospital. It provides many advantages for crisis teams, e.g., comparison with their own local planning, simulation of local events, simulation of several scenarios (worst / best case). There are benefits for medical professionals, e.g, analysis of the pandemic at local, regional, state and federal level, the consideration of special risk groups, tools for validating the length of stays and transition probabilities. Finally, there are potential advantages for administration, management, e.g., assessment of the situation of individual hospitals taking local events into account, consideration of relevant resources such as beds, ventilators, rooms, protective clothing, and personnel planning, e.g., medical and nursing staff. babsim.hospital combines simulation, optimization, statistics, and artificial intelligence processes in a very efficient way. The core is a discrete, event-based simulation model.

Jan Strohschein, Andreas Fischbach, Andreas Bunte et al.

This paper presents the cognitive module of the cognitive architecture for artificial intelligence (CAAI) in cyber-physical production systems (CPPS). The goal of this architecture is to reduce the implementation effort of artificial intelligence (AI) algorithms in CPPS. Declarative user goals and the provided algorithm-knowledge base allow the dynamic pipeline orchestration and configuration. A big data platform (BDP) instantiates the pipelines and monitors the CPPS performance for further evaluation through the cognitive module. Thus, the cognitive module is able to select feasible and robust configurations for process pipelines in varying use cases. Furthermore, it automatically adapts the models and algorithms based on model quality and resource consumption. The cognitive module also instantiates additional pipelines to test algorithms from different classes. CAAI relies on well-defined interfaces to enable the integration of additional modules and reduce implementation effort. Finally, an implementation based on Docker, Kubernetes, and Kafka for the virtualization and orchestration of the individual modules and as messaging-technology for module communication is used to evaluate a real-world use case.

Sowmya Chandrasekaran, Margarita Rebolledo, Thomas Bartz-Beielstein

EventDetectR: An efficient Event Detection System (EDS) capable of detecting unexpected water quality conditions. This approach uses multiple algorithms to model the relationship between various multivariate water quality signals. Then the residuals of the models were utilized in constructing the event detection algorithm, which provides a continuous measure of the probability of an event at every time step. The proposed framework was tested for water contamination events with industrial data from automated water quality sensors. The results showed that the framework is reliable with better performance and is highly suitable for event detection.

Tom Peetz, Sebastian Vogt, Martin Zaefferer et al.

Testing new, innovative technologies is a crucial task for safety and acceptance. But how can new systems be tested if no historical real-world data exist? Simulation provides an answer to this important question. Classical simulation tools such as event-based simulation are well accepted. But most of these established simulation models require the specification of many parameters. Furthermore, simulation runs, e.g., CFD simulations, are very time consuming. Generative Adversarial Networks (GANs) are powerful tools for generating new data for a variety of tasks. Currently, their most frequent application domain is image generation. This article investigates the applicability of GANs for imitating simulations. We are comparing the simulation output of a technical system with the output of a GAN. To exemplify this approach, a well-known multi-car elevator system simulator was chosen. Our study demonstrates the feasibility of this approach. It also discusses pitfalls and technical problems that occurred during the implementation. Although we were able to show that in principle, GANs can be used as substitutes for expensive simulation runs, we also show that they cannot be used "out of the box". Fine tuning is needed. We present a proof-of-concept, which can serve as a starting point for further research.

Thomas Bartz-Beielstein, Carola Doerr, Daan van den Berg et al.

This survey compiles ideas and recommendations from more than a dozen researchers with different backgrounds and from different institutes around the world. Promoting best practice in benchmarking is its main goal. The article discusses eight essential topics in benchmarking: clearly stated goals, well-specified problems, suitable algorithms, adequate performance measures, thoughtful analysis, effective and efficient designs, comprehensible presentations, and guaranteed reproducibility. The final goal is to provide well-accepted guidelines (rules) that might be useful for authors and reviewers. As benchmarking in optimization is an active and evolving field of research this manuscript is meant to co-evolve over time by means of periodic updates.

Andreas Fischbach, Jan Strohschein, Andreas Bunte et al.

This paper introduces CAAI, a novel cognitive architecture for artificial intelligence in cyber-physical production systems. The goal of the architecture is to reduce the implementation effort for the usage of artificial intelligence algorithms. The core of the CAAI is a cognitive module that processes declarative goals of the user, selects suitable models and algorithms, and creates a configuration for the execution of a processing pipeline on a big data platform. Constant observation and evaluation against performance criteria assess the performance of pipelines for many and varying use cases. Based on these evaluations, the pipelines are automatically adapted if necessary. The modular design with well-defined interfaces enables the reusability and extensibility of pipeline components. A big data platform implements this modular design supported by technologies such as Docker, Kubernetes, and Kafka for virtualization and orchestration of the individual components and their communication. The implementation of the architecture is evaluated using a real-world use case.

Frederik Rehbach, Martin Zaefferer, Boris Naujoks et al.

Surrogate-based optimization relies on so-called infill criteria (acquisition functions) to decide which point to evaluate next. When Kriging is used as the surrogate model of choice (also called Bayesian optimization), one of the most frequently chosen criteria is expected improvement. We argue that the popularity of expected improvement largely relies on its theoretical properties rather than empirically validated performance. Few results from the literature show evidence, that under certain conditions, expected improvement may perform worse than something as simple as the predicted value of the surrogate model. We benchmark both infill criteria in an extensive empirical study on the `BBOB' function set. This investigation includes a detailed study of the impact of problem dimensionality on algorithm performance. The results support the hypothesis that exploration loses importance with increasing problem dimensionality. A statistical analysis reveals that the purely exploitative search with the predicted value criterion performs better on most problems of five or higher dimensions. Possible reasons for these results are discussed. In addition, we give an in-depth guide for choosing the infill criteria based on prior knowledge about the problem at hand, its dimensionality, and the available budget.

Thomas Bartz-Beielstein

Artificial intelligence is considered as a key technology. It has a huge impact on our society. Besides many positive effects, there are also some negative effects or threats. Some of these threats to society are well-known, e.g., weapons or killer robots. But there are also threats that are ignored. These unknown-knowns or blind spots affect privacy, and facilitate manipulation and mistaken identities. We cannot trust data, audio, video, and identities any more. Democracies are able to cope with known threats, the known-knowns. Transforming unknown-knowns to known-knowns is one important cornerstone of resilient societies. An AI-resilient society is able to transform threats caused by new AI tecchnologies such as generative adversarial networks. Resilience can be seen as a positive adaptation of these threats. We propose three strategies how this adaptation can be achieved: awareness, agreements, and red flags. This article accompanies the TEDx talk "Why we urgently need an AI-resilient society", see https://youtu.be/f6c2ngp7rqY.

Jörg Stork, Martin Zaefferer, Thomas Bartz-Beielstein et al.

In the last years, reinforcement learning received a lot of attention. One method to solve reinforcement learning tasks is Neuroevolution, where neural networks are optimized by evolutionary algorithms. A disadvantage of Neuroevolution is that it can require numerous function evaluations, while not fully utilizing the available information from each fitness evaluation. This is especially problematic when fitness evaluations become expensive. To reduce the cost of fitness evaluations, surrogate models can be employed to partially replace the fitness function. The difficulty of surrogate modeling for Neuroevolution is the complex search space and how to compare different networks. To that end, recent studies showed that a kernel based approach, particular with phenotypic distance measures, works well. These kernels compare different networks via their behavior (phenotype) rather than their topology or encoding (genotype). In this work, we discuss the use of surrogate model-based Neuroevolution (SMB-NE) using a phenotypic distance for reinforcement learning. In detail, we investigate a) the potential of SMB-NE with respect to evaluation efficiency and b) how to select adequate input sets for the phenotypic distance measure in a reinforcement learning problem. The results indicate that we are able to considerably increase the evaluation efficiency using dynamic input sets.

Jörg Stork, Martin Zaefferer, Thomas Bartz-Beielstein

In NeuroEvolution, the topologies of artificial neural networks are optimized with evolutionary algorithms to solve tasks in data regression, data classification, or reinforcement learning. One downside of NeuroEvolution is the large amount of necessary fitness evaluations, which might render it inefficient for tasks with expensive evaluations, such as real-time learning. For these expensive optimization tasks, surrogate model-based optimization is frequently applied as it features a good evaluation efficiency. While a combination of both procedures appears as a valuable solution, the definition of adequate distance measures for the surrogate modeling process is difficult. In this study, we will extend cartesian genetic programming of artificial neural networks by the use of surrogate model-based optimization. We propose different distance measures and test our algorithm on a replicable benchmark task. The results indicate that we can significantly increase the evaluation efficiency and that a phenotypic distance, which is based on the behavior of the associated neural networks, is most promising.

Jörg Stork, A. E. Eiben, Thomas Bartz-Beielstein

Surrogate-based optimization, nature-inspired metaheuristics, and hybrid combinations have become state of the art in algorithm design for solving real-world optimization problems. Still, it is difficult for practitioners to get an overview that explains their advantages in comparison to a large number of available methods in the scope of optimization. Available taxonomies lack the embedding of current approaches in the larger context of this broad field. This article presents a taxonomy of the field, which explores and matches algorithm strategies by extracting similarities and differences in their search strategies. A particular focus lies on algorithms using surrogates, nature-inspired designs, and those created by design optimization. The extracted features of components or operators allow us to create a set of classification indicators to distinguish between a small number of classes. The features allow a deeper understanding of components of the search strategies and further indicate the close connections between the different algorithm designs. We present intuitive analogies to explain the basic principles of the search algorithms, particularly useful for novices in this research field. Furthermore, this taxonomy allows recommendations for the applicability of the corresponding algorithms.

Jörg Stork, Martin Zaefferer, Thomas Bartz-Beielstein

The topology optimization of artificial neural networks can be particularly difficult if the fitness evaluations require expensive experiments or simulations. For that reason, the optimization methods may need to be supported by surrogate models. We propose different distances for a suitable surrogate model, and compare them in a simple numerical test scenario.

Martin Zaefferer, Thomas Bartz-Beielstein, Günter Rudolph

Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a new kernel may require too much time and effort for users who simply aim at practical usage. Furthermore, designing definite distances or kernels may be equally intricate. Finally, models can be enabled to use indefinite kernels. This may deteriorate the accuracy or computational cost of the model. Hence, an efficient method to determine definiteness is required. We propose an empirical approach. We show that sampling as well as optimization with an evolutionary algorithm may be employed to determine definiteness. We provide a proof-of-concept with 16 different distance measures for permutations. Our approach allows to disprove definiteness if a respective counter-example is found. It can also provide an estimate of how likely it is to obtain indefinite kernel matrices. This provides a simple, efficient tool to decide whether additional effort should be spent on designing/selecting a more suitable kernel or algorithm.

Martin Zaefferer, Jörg Stork, Oliver Flasch et al.

Surrogate models are a well established approach to reduce the number of expensive function evaluations in continuous optimization. In the context of genetic programming, surrogate modeling still poses a challenge, due to the complex genotype-phenotype relationships. We investigate how different genotypic and phenotypic distance measures can be used to learn Kriging models as surrogates. We compare the measures and suggest to use their linear combination in a kernel. We test the resulting model in an optimization framework, using symbolic regression problem instances as a benchmark. Our experiments show that the model provides valuable information. Firstly, the model enables an improved optimization performance compared to a model-free algorithm. Furthermore, the model provides information on the contribution of different distance measures. The data indicates that a phenotypic distance measure is important during the early stages of an optimization run when less data is available. In contrast, genotypic measures, such as the tree edit distance, contribute more during the later stages.

Thomas Bartz-Beielstein, Martin Zaefferer, Frederik Rehbach

The performance of optimization algorithms relies crucially on their parameterizations. Finding good parameter settings is called algorithm tuning. The sequential parameter optimization (SPOT) package for R is a toolbox for tuning and understanding simulation and optimization algorithms. Model-based investigations are common approaches in simulation and optimization. Sequential parameter optimization has been developed, because there is a strong need for sound statistical analysis of simulation and optimization algorithms. SPOT includes methods for tuning based on classical regression and analysis of variance techniques; tree-based models such as CART and random forest; Gaussian process models (Kriging), and combinations of different meta-modeling approaches. Using a simple simulated annealing algorithm, we will demonstrate how optimization algorithms can be tuned using SPOT. The underling concepts of the SPOT approach are explained. This includes key techniques such as exploratory fitness landscape analysis and sensititvity analysis. Many examples illustrate how SPOT can be used for understanding the performance of algorithms and gaining insight into algorithm's behavior. Furthermore, we demonstrate how SPOT can be used as an optimizer and how a sophisticated ensemble approach is able to combine several meta models via stacking. This article exemplifies how SPOT can be used for automatic and interactive tuning.