Thomas Bäck

Charles Moussa, Jan N. van Rijn, Thomas Bäck et al.

As restricted quantum computers are slowly becoming a reality, the search for meaningful first applications intensifies. In this domain, one of the more investigated approaches is the use of a special type of quantum circuit - a so-called quantum neural network -- to serve as a basis for a machine learning model. Roughly speaking, as the name suggests, a quantum neural network can play a similar role to a neural network. However, specifically for applications in machine learning contexts, very little is known about suitable circuit architectures, or model hyperparameters one should use to achieve good learning performance. In this work, we apply the functional ANOVA framework to quantum neural networks to analyze which of the hyperparameters were most influential for their predictive performance. We analyze one of the most typically used quantum neural network architectures. We then apply this to $7$ open-source datasets from the OpenML-CC18 classification benchmark whose number of features is small enough to fit on quantum hardware with less than $20$ qubits. Three main levels of importance were detected from the ranking of hyperparameters obtained with functional ANOVA. Our experiment both confirmed expected patterns and revealed new insights. For instance, setting well the learning rate is deemed the most critical hyperparameter in terms of marginal contribution on all datasets, whereas the particular choice of entangling gates used is considered the least important except on one dataset. This work introduces new methodologies to study quantum machine learning models and provides new insights toward quantum model selection.

Andrea Skolik, Michele Cattelan, Sheir Yarkoni et al.

Variational quantum algorithms are the leading candidate for advantage on near-term quantum hardware. When training a parametrized quantum circuit in this setting to solve a specific problem, the choice of ansatz is one of the most important factors that determines the trainability and performance of the algorithm. In quantum machine learning (QML), however, the literature on ansatzes that are motivated by the training data structure is scarce. In this work, we introduce an ansatz for learning tasks on weighted graphs that respects an important graph symmetry, namely equivariance under node permutations. We evaluate the performance of this ansatz on a complex learning task, namely neural combinatorial optimization, where a machine learning model is used to learn a heuristic for a combinatorial optimization problem. We analytically and numerically study the performance of our model, and our results strengthen the notion that symmetry-preserving ansatzes are a key to success in QML.

Patrick Echtenbruck, Martina Echtenbruck, Joost Batenburg et al.

Automated model selection is often proposed to users to choose which machine learning model (or method) to apply to a given regression task. In this paper, we show that combining different regression models can yield better results than selecting a single ('best') regression model, and outline an efficient method that obtains optimally weighted convex linear combination from a heterogeneous set of regression models. More specifically, in this paper, a heuristic weight optimization, used in a preceding conference paper, is replaced by an exact optimization algorithm using convex quadratic programming. We prove convexity of the quadratic programming formulation for the straightforward formulation and for a formulation with weighted data points. The novel weight optimization is not only (more) exact but also more efficient. The methods we develop in this paper are implemented and made available via github-open source. They can be executed on commonly available hardware and offer a transparent and easy to interpret interface. The results indicate that the approach outperforms model selection methods on a range of data sets, including data sets with mixed variable type from drug discovery applications.

Yash J. Patel, Sofiene Jerbi, Thomas Bäck et al.

Variational quantum algorithms such as the Quantum Approximation Optimization Algorithm (QAOA) in recent years have gained popularity as they provide the hope of using NISQ devices to tackle hard combinatorial optimization problems. It is, however, known that at low depth, certain locality constraints of QAOA limit its performance. To go beyond these limitations, a non-local variant of QAOA, namely recursive QAOA (RQAOA), was proposed to improve the quality of approximate solutions. The RQAOA has been studied comparatively less than QAOA, and it is less understood, for instance, for what family of instances it may fail to provide high quality solutions. However, as we are tackling $\mathsf{NP}$-hard problems (specifically, the Ising spin model), it is expected that RQAOA does fail, raising the question of designing even better quantum algorithms for combinatorial optimization. In this spirit, we identify and analyze cases where RQAOA fails and, based on this, propose a reinforcement learning enhanced RQAOA variant (RL-RQAOA) that improves upon RQAOA. We show that the performance of RL-RQAOA improves over RQAOA: RL-RQAOA is strictly better on these identified instances where RQAOA underperforms, and is similarly performing on instances where RQAOA is near-optimal. Our work exemplifies the potentially beneficial synergy between reinforcement learning and quantum (inspired) optimization in the design of new, even better heuristics for hard problems.

Diederick Vermetten, Furong Ye, Thomas Bäck et al.

Extending a recent suggestion to generate new instances for numerical black-box optimization benchmarking by interpolating pairs of the well-established BBOB functions from the COmparing COntinuous Optimizers (COCO) platform, we propose in this work a further generalization that allows multiple affine combinations of the original instances and arbitrarily chosen locations of the global optima. We demonstrate that the MA-BBOB generator can help fill the instance space, while overall patterns in algorithm performance are preserved. By combining the landscape features of the problems with the performance data, we pose the question of whether these features are as useful for algorithm selection as previous studies suggested. MA-BBOB is built on the publicly available IOHprofiler platform, which facilitates standardized experimentation routines, provides access to the interactive IOHanalyzer module for performance analysis and visualization, and enables comparisons with the rich and growing data collection available for the (MA-)BBOB functions.

David Von Dollen, Sheir Yarkoni, Daniel Weimer et al.

Genetic algorithms have unique properties which are useful when applied to black box optimization. Using selection, crossover, and mutation operators, candidate solutions may be obtained without the need to calculate a gradient. In this work, we study results obtained from using quantum-enhanced operators within the selection mechanism of a genetic algorithm. Our approach frames the selection process as a minimization of a binary quadratic model with which we encode fitness and distance between members of a population, and we leverage a quantum annealing system to sample low energy solutions for the selection mechanism. We benchmark these quantum-enhanced algorithms against classical algorithms over various black-box objective functions, including the OneMax function, and functions from the IOHProfiler library for black-box optimization. We observe a performance gain in average number of generations to convergence for the quantum-enhanced elitist selection operator in comparison to classical on the OneMax function. We also find that the quantum-enhanced selection operator with non-elitist selection outperform benchmarks on functions with fitness perturbation from the IOHProfiler library. Additionally, we find that in the case of elitist selection, the quantum-enhanced operators outperform classical benchmarks on functions with varying degrees of dummy variables and neutrality.

Frank Neumann, Aneta Neumann, Chao Qian et al.

Submodular functions play a key role in the area of optimization as they allow to model many real-world problems that face diminishing returns. Evolutionary algorithms have been shown to obtain strong theoretical performance guarantees for a wide class of submodular problems under various types of constraints while clearly outperforming standard greedy approximation algorithms. This paper introduces a setup for benchmarking algorithms for submodular optimization problems with the aim to provide researchers with a framework to enhance and compare the performance of new algorithms for submodular problems. The focus is on the development of iterative search algorithms such as evolutionary algorithms with the implementation provided and integrated into IOHprofiler which allows for tracking and comparing the progress and performance of iterative search algorithms. We present a range of submodular optimization problems that have been integrated into IOHprofiler and show how the setup can be used for analyzing and comparing iterative search algorithms in various settings.

Jiajie Fan, Laure Vuaille, Hao Wang et al.

Generative Engineering Design approaches driven by Deep Generative Models (DGM) have been proposed to facilitate industrial engineering processes. In such processes, designs often come in the form of images, such as blueprints, engineering drawings, and CAD models depending on the level of detail. DGMs have been successfully employed for synthesis of natural images, e.g., displaying animals, human faces and landscapes. However, industrial design images are fundamentally different from natural scenes in that they contain rich structural patterns and long-range dependencies, which are challenging for convolution-based DGMs to generate. Moreover, DGM-driven generation process is typically triggered based on random noisy inputs, which outputs unpredictable samples and thus cannot perform an efficient industrial design exploration. We tackle these challenges by proposing a novel model Self-Attention Adversarial Latent Autoencoder (SA-ALAE), which allows generating feasible design images of complex engineering parts. With SA-ALAE, users can not only explore novel variants of an existing design, but also control the generation process by operating in latent space. The potential of SA-ALAE is shown by generating engineering blueprints in a real automotive design task.

Veysel Kocaman, Ofer M. Shir, Thomas Bäck et al.

We propose an augmentation policy for Contrastive Self-Supervised Learning (SSL) in the form of an already established Salient Image Segmentation technique entitled Global Contrast based Salient Region Detection. This detection technique, which had been devised for unrelated Computer Vision tasks, was empirically observed to play the role of an augmentation facilitator within the SSL protocol. This observation is rooted in our practical attempts to learn, by SSL-fashion, aerial imagery of solar panels, which exhibit challenging boundary patterns. Upon the successful integration of this technique on our problem domain, we formulated a generalized procedure and conducted a comprehensive, systematic performance assessment with various Contrastive SSL algorithms subject to standard augmentation techniques. This evaluation, which was conducted across multiple datasets, indicated that the proposed technique indeed contributes to SSL. We hypothesize whether salient image segmentation may suffice as the only augmentation policy in Contrastive SSL when treating downstream segmentation tasks.

Lucas Correia, Jan-Christoph Goos, Philipp Klein et al.

Time-series anomaly detection plays an important role in engineering processes, like development, manufacturing and other operations involving dynamic systems. These processes can greatly benefit from advances in the field, as state-of-the-art approaches may aid in cases involving, for example, highly dimensional data. To provide the reader with understanding of the terminology, this survey introduces a novel taxonomy where a distinction between online and offline, and training and inference is made. Additionally, it presents the most popular data sets and evaluation metrics used in the literature, as well as a detailed analysis. Furthermore, this survey provides an extensive overview of the state-of-the-art model-based online semi- and unsupervised anomaly detection approaches for multivariate time-series data, categorising them into different model families and other properties. The biggest research challenge revolves around benchmarking, as currently there is no reliable way to compare different approaches against one another. This problem is two-fold: on the one hand, public data sets suffers from at least one fundamental flaw, while on the other hand, there is a lack of intuitive and representative evaluation metrics in the field. Moreover, the way most publications choose a detection threshold disregards real-world conditions, which hinders the application in the real world. To allow for tangible advances in the field, these issues must be addressed in future work.

Bas van Stein, Fu Xing Long, Moritz Frenzel et al.

We propose DoE2Vec, a variational autoencoder (VAE)-based methodology to learn optimization landscape characteristics for downstream meta-learning tasks, e.g., automated selection of optimization algorithms. Principally, using large training data sets generated with a random function generator, DoE2Vec self-learns an informative latent representation for any design of experiments (DoE). Unlike the classical exploratory landscape analysis (ELA) method, our approach does not require any feature engineering and is easily applicable for high dimensional search spaces. For validation, we inspect the quality of latent reconstructions and analyze the latent representations using different experiments. The latent representations not only show promising potentials in identifying similar (cheap-to-evaluate) surrogate functions, but also can significantly boost performances when being used complementary to the classical ELA features in classification tasks.

Lucas Correia, Jan-Christoph Goos, Philipp Klein et al.

A clear need for automatic anomaly detection applied to automotive testing has emerged as more and more attention is paid to the data recorded and manual evaluation by humans reaches its capacity. Such real-world data is massive, diverse, multivariate and temporal in nature, therefore requiring modelling of the testee behaviour. We propose a variational autoencoder with multi-head attention (MA-VAE), which, when trained on unlabelled data, not only provides very few false positives but also manages to detect the majority of the anomalies presented. In addition to that, the approach offers a novel way to avoid the bypass phenomenon, an undesirable behaviour investigated in literature. Lastly, the approach also introduces a new method to remap individual windows to a continuous time series. The results are presented in the context of a real-world industrial data set and several experiments are undertaken to further investigate certain aspects of the proposed model. When configured properly, it is 9% of the time wrong when an anomaly is flagged and discovers 67% of the anomalies present. Also, MA-VAE has the potential to perform well with only a fraction of the training and validation subset, however, to extract it, a more sophisticated threshold estimation method is required.

Mathieu Cherpitel, Janne Luijten, Thomas Bäck et al.

Automated analysis of needle electromyography (nEMG) signals is emerging as a tool to support the detection of neuromuscular diseases (NMDs), yet the signals' high and heterogeneous sampling rates pose substantial computational challenges for feature-based machine-learning models, particularly for near real-time analysis. Downsampling offers a potential solution, but its impact on diagnostic signal content and classification performance remains insufficiently understood. This study presents a workflow for systematically evaluating information loss caused by downsampling in high-frequency time series. The workflow combines shape-based distortion metrics with classification outcomes from available feature-based machine learning models and feature space analysis to quantify how different downsampling algorithms and factors affect both waveform integrity and predictive performance. We use a three-class NMD classification task to experimentally evaluate the workflow. We demonstrate how the workflow identifies downsampling configurations that preserve diagnostic information while substantially reducing computational load. Analysis of shape-based distortion metrics showed that shape-aware downsampling algorithms outperform standard decimation, as they better preserve peak structure and overall signal morphology. The results provide practical guidance for selecting downsampling configurations that enable near real-time nEMG analysis and highlight a generalisable workflow that can be used to balance data reduction with model performance in other high-frequency time-series applications as well.

Lucas Correia, Jan-Christoph Goos, Philipp Klein et al.

As attention to recorded data grows in the realm of automotive testing and manual evaluation reaches its limits, there is a growing need for automatic online anomaly detection. This real-world data is complex in many ways and requires the modelling of testee behaviour. To address this, we propose a temporal variational autoencoder (TeVAE) that can detect anomalies with minimal false positives when trained on unlabelled data. Our approach also avoids the bypass phenomenon and introduces a new method to remap individual windows to a continuous time series. Furthermore, we propose metrics to evaluate the detection delay and root-cause capability of our approach and present results from experiments on a real-world industrial data set. When properly configured, TeVAE flags anomalies only 6% of the time wrongly and detects 65% of anomalies present. It also has the potential to perform well with a smaller training and validation subset but requires a more sophisticated threshold estimation method.

Francesca Da Ros, Tarik Začiragić, Aske Plaat et al.

Reproducibility is an important requirement in evolutionary computation, where results largely depend on computational experiments. In practice, reproducibility relies on how algorithms, experimental protocols, and artifacts are documented and shared. Despite growing awareness, there is still limited empirical evidence on the actual reproducibility levels of published work in the field. In this paper, we study the reproducibility practices in papers published in the Evolutionary Combinatorial Optimization and Metaheuristics track of the Genetic and Evolutionary Computation Conference over a ten-year period. We introduce a structured reproducibility checklist and apply it through a systematic manual assessment of the selected corpus. In addition, we propose RECAP (REproducibility Checklist Automation Pipeline), an LLM-based system that automatically evaluates reproducibility signals from paper text and associated code repositories. Our analysis shows that papers achieve an average completeness score of 0.62, and that 36.90% of them provide additional material beyond the manuscript itself. We demonstrate that automated assessment is feasible: RECAP achieves substantial agreement with human evaluators (Cohen's k of 0.67). Together, these results highlight persistent gaps in reproducibility reporting and suggest that automated tools can effectively support large-scale, systematic monitoring of reproducibility practices.

Marios Kefalas, Juan de Santiago Rojo, Asteris Apostolidis et al.

Data-driven modeling is an imperative tool in various industrial applications, including many applications in the sectors of aeronautics and commercial aviation. These models are in charge of providing key insights, such as which parameters are important on a specific measured outcome or which parameter values we should expect to observe given a set of input parameters. At the same time, however, these models rely heavily on assumptions (e.g., stationarity) or are "black box" (e.g., deep neural networks), meaning that they lack interpretability of their internal working and can be viewed only in terms of their inputs and outputs. An interpretable alternative to the "black box" models and with considerably less assumptions is symbolic regression (SR). SR searches for the optimal model structure while simultaneously optimizing the model's parameters without relying on an a-priori model structure. In this work, we apply SR on real-life exhaust gas temperature (EGT) data, collected at high frequencies through the entire flight, in order to uncover meaningful algebraic relationships between the EGT and other measurable engine parameters. The experimental results exhibit promising model accuracy, as well as explainability returning an absolute difference of 3°C compared to the ground truth and demonstrating consistency from an engineering perspective.

Qi Huang, Sofoklis Kitharidis, Thomas Bäck et al.

In time-series classification, understanding model decisions is crucial for their application in high-stakes domains such as healthcare and finance. Counterfactual explanations, which provide insights by presenting alternative inputs that change model predictions, offer a promising solution. However, existing methods for generating counterfactual explanations for time-series data often struggle with balancing key objectives like proximity, sparsity, and validity. In this paper, we introduce TX-Gen, a novel algorithm for generating counterfactual explanations based on the Non-dominated Sorting Genetic Algorithm II (NSGA-II). TX-Gen leverages evolutionary multi-objective optimization to find a diverse set of counterfactuals that are both sparse and valid, while maintaining minimal dissimilarity to the original time series. By incorporating a flexible reference-guided mechanism, our method improves the plausibility and interpretability of the counterfactuals without relying on predefined assumptions. Extensive experiments on benchmark datasets demonstrate that TX-Gen outperforms existing methods in generating high-quality counterfactuals, making time-series models more transparent and interpretable.

Mathieu Cherpitel, Thomas Bäck, Martijn R. Tannemaat et al.

Unsupervised feature selection is commonly formulated as a multiobjective optimisation problem that jointly optimises subset quality and subset size. Yet the behaviour of this formulation depends critically on the choice of evaluation objective, the direction of subset-size regularisation, and the initialisation strategy. We study these factors in a controlled setting using a synthetic dataset with known informative, redundant, and irrelevant feature types. Six formulations are compared by combining three evaluation objectives: accuracy, silhouette score, and PCA reconstruction loss with subset-size minimisation or maximisation. The results show that formulation strongly affects both search dynamics and the quality of the resulting Pareto front. Silhouette-based formulations exhibit a strong bias toward trivial low-cardinality solutions and remain weak proxies for predictive performance. In contrast, the proposed PCA loss objective produces compact subsets with test accuracy comparable to subsets obtained by directly optimising supervised accuracy. Overall, the study shows that objective design is central to effective multiobjective unsupervised feature selection.

Alexander Zeiser, Bas van Stein, Thomas Bäck

Anomaly detection describes methods of finding abnormal states, instances or data points that differ from a normal value space. Industrial processes are a domain where predicitve models are needed for finding anomalous data instances for quality enhancement. A main challenge, however, is absence of labels in this environment. This paper contributes to a data-centric way of approaching artificial intelligence in industrial production. With a use case from additive manufacturing for automotive components we present a deep-learning-based image processing pipeline. Additionally, we integrate the concept of domain randomisation and synthetic data in the loop that shows promising results for bridging advances in deep learning and its application to real-world, industrial production processes.

Maarten C. Vonk, Anna V. Kononova, Thomas Bäck et al.

Western governments have adopted an assortment of counter-hybrid threat measures to defend against hostile actions below the conventional military threshold. The impact of these measures is unclear because of the ambiguity of hybrid threats, their cross-domain nature, and uncertainty about how countermeasures shape adversarial behavior. This paper offers a novel approach to clarifying this impact by unifying previously bifurcating hybrid threat modeling methods through a (multi-agent) influence diagram framework. The model balances the costs of countermeasures, their ability to dissuade the adversary from executing hybrid threats, and their potential to mitigate the impact of hybrid threats. We run 1000 semi-synthetic variants of a real-world-inspired scenario simulating the strategic interaction between attacking agent A and defending agent B over a cyber attack on critical infrastructure to explore the effectiveness of a set of five different counter-hybrid threat measures. Counter-hybrid measures range from strengthening resilience and denial of the adversary's ability to execute a hybrid threat to dissuasion through the threat of punishment. Our analysis primarily evaluates the overarching characteristics of counter-hybrid threat measures. This approach allows us to generalize the effectiveness of these measures and examine parameter impact sensitivity. In addition, we discuss policy relevance and outline future research avenues.

Qi Huang, Furong Ye, Ananta Shahane et al.

Large Language Models (LLMs) have already been widely adopted for automated algorithm design, demonstrating strong abilities in generating and evolving algorithms across various fields. Existing work has largely focused on examining their effectiveness in solving specific problems, with search strategies primarily guided by adaptive prompt designs. In this paper, through investigating the token-wise attribution of the prompts to LLM-generated algorithmic codes, we show that providing high-quality algorithmic code examples can substantially improve the performance of the LLM-driven optimization. Building upon this insight, we propose leveraging prior benchmark algorithms to guide LLM-driven optimization and demonstrate superior performance on two black-box optimization benchmarks: the pseudo-Boolean optimization suite (pbo) and the black-box optimization suite (bbob). Our findings highlight the value of integrating benchmarking studies to enhance both efficiency and robustness of the LLM-driven black-box optimization methods.

Ismail Labiad, Thomas Bäck, Pierre Fernandez et al.

In many cases, adversarial attacks are based on specialized algorithms specifically dedicated to attacking automatic image classifiers. These algorithms perform well, thanks to an excellent ad hoc distribution of initial attacks. However, these attacks are easily detected due to their specific initial distribution. We therefore consider other black-box attacks, inspired from generic black-box optimization tools, and in particular the log-normal algorithm. We apply the log-normal method to the attack of fake detectors, and get successful attacks: importantly, these attacks are not detected by detectors specialized on classical adversarial attacks. Then, combining these attacks and deep detection, we create improved fake detectors.

Niki van Stein, Anna V. Kononova, Lars Kotthoff et al.

Large language models have enabled automated algorithm design (AAD) by generating optimization algorithms directly from natural-language prompts. While evolutionary frameworks such as LLaMEA demonstrate strong exploratory capabilities across the algorithm design space, their search dynamics are entirely driven by fitness feedback, leaving substantial information about the generated code unused. We propose a mechanism for guiding AAD using feedback constructed from graph-theoretic and complexity features extracted from the abstract syntax trees of the generated algorithms, based on a surrogate model learned over an archive of evaluated solutions. Using explainable AI techniques, we identify features that substantially affect performance and translate them into natural-language mutation instructions that steer subsequent LLM-based code generation without restricting expressivity. We propose LLaMEA-SAGE, which integrates this feature-driven guidance into LLaMEA, and evaluate it across several benchmarks. We show that the proposed structured guidance achieves the same performance faster than vanilla LLaMEA in a small controlled experiment. In a larger-scale experiment using the MA-BBOB suite from the GECCO-MA-BBOB competition, our guided approach achieves superior performance compared to state-of-the-art AAD methods. These results demonstrate that signals derived from code can effectively bias LLM-driven algorithm evolution, bridging the gap between code structure and human-understandable performance feedback in automated algorithm design.

Iván Olarte Rodríguez, Anja Jankovic, Thomas Bäck et al.

Exploratory Landscape Analysis (ELA) provides numerical features for characterizing black-box optimization problems. In high-dimensional settings, however, ELA suffers from sparsity effects, high estimator variance, and the prohibitive cost of computing several feature classes. Dimensionality reduction has therefore been proposed as a way to make ELA applicable in such settings, but it remains unclear whether features computed in reduced spaces still reflect intrinsic properties of the original landscape. In this work, we investigate the robustness of ELA features under dimensionality reduction via Random Gaussian Embeddings (RGEs). Starting from the same sampled points and objective values, we compute ELA features in projected spaces and compare them to those obtained in the original search space across multiple sample budgets and embedding dimensions. Our results show that linear random projections often alter the geometric and topological structure relevant to ELA, yielding feature values that are no longer representative of the original problem. While a small subset of features remains comparatively stable, most are highly sensitive to the embedding. Moreover, robustness under projection does not necessarily imply informativeness, as apparently robust features may still reflect projection-induced artifacts rather than intrinsic landscape characteristics.

Jiajie Fan, Laure Vuaille, Thomas Bäck et al.

Deep Generative Models (DGMs) are widely used to create innovative designs across multiple industries, ranging from fashion to the automotive sector. In addition to generating images of high visual quality, the task of structural design generation imposes more stringent constrains on the semantic expression, e.g., no floating material or missing part, which we refer to as plausibility in this work. We delve into the impact of noise schedules of diffusion models on the plausibility of the outcome: there exists a range of noise levels at which the model's performance decides the result plausibility. Also, we propose two techniques to determine such a range for a given image set and devise a novel parametric noise schedule for better plausibility. We apply this noise schedule to the training and sampling of the well-known diffusion model EDM and compare it to its default noise schedule. Compared to EDM, our schedule significantly improves the rate of plausible designs from 83.4% to 93.5% and Fréchet Inception Distance (FID) from 7.84 to 4.87. Further applications of advanced image editing tools demonstrate the model's solid understanding of structure.

Fu Xing Long, Moritz Frenzel, Peter Krause et al.

In landscape-aware algorithm selection problem, the effectiveness of feature-based predictive models strongly depends on the representativeness of training data for practical applications. In this work, we investigate the potential of randomly generated functions (RGF) for the model training, which cover a much more diverse set of optimization problem classes compared to the widely-used black-box optimization benchmarking (BBOB) suite. Correspondingly, we focus on automated algorithm configuration (AAC), that is, selecting the best suited algorithm and fine-tuning its hyperparameters based on the landscape features of problem instances. Precisely, we analyze the performance of dense neural network (NN) models in handling the multi-output mixed regression and classification tasks using different training data sets, such as RGF and many-affine BBOB (MA-BBOB) functions. Based on our results on the BBOB functions in 5d and 20d, near optimal configurations can be identified using the proposed approach, which can most of the time outperform the off-the-shelf default configuration considered by practitioners with limited knowledge about AAC. Furthermore, the predicted configurations are competitive against the single best solver in many cases. Overall, configurations with better performance can be best identified by using NN models trained on a combination of RGF and MA-BBOB functions.

Zhong Li, Qi Huang, Lincen Yang et al.

In recent years, generative models have achieved remarkable performance across diverse applications, including image generation, text synthesis, audio creation, video generation, and data augmentation. Diffusion models have emerged as superior alternatives to Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs) by addressing their limitations, such as training instability, mode collapse, and poor representation of multimodal distributions. This success has spurred widespread research interest. In the domain of tabular data, diffusion models have begun to showcase similar advantages over GANs and VAEs, achieving significant performance breakthroughs and demonstrating their potential for addressing unique challenges in tabular data modeling. However, while domains like images and time series have numerous surveys summarizing advancements in diffusion models, there remains a notable gap in the literature for tabular data. Despite the increasing interest in diffusion models for tabular data, there has been little effort to systematically review and summarize these developments. This lack of a dedicated survey limits a clear understanding of the challenges, progress, and future directions in this critical area. This survey addresses this gap by providing a comprehensive review of diffusion models for tabular data. Covering works from June 2015, when diffusion models emerged, to December 2024, we analyze nearly all relevant studies, with updates maintained in a \href{https://github.com/Diffusion-Model-Leiden/awesome-diffusion-models-for-tabular-data}{GitHub repository}. Assuming readers possess foundational knowledge of statistics and diffusion models, we employ mathematical formulations to deliver a rigorous and detailed review, aiming to promote developments in this emerging and exciting area.

Jiajie Fan, Amal Trigui, Thomas Bäck et al.

A great interest has arisen in using Deep Generative Models (DGM) for generative design. When assessing the quality of the generated designs, human designers focus more on structural plausibility, e.g., no missing component, rather than visual artifacts, e.g., noises or blurriness. Meanwhile, commonly used metrics such as Fréchet Inception Distance (FID) may not evaluate accurately because they are sensitive to visual artifacts and tolerant to semantic errors. As such, FID might not be suitable to assess the performance of DGMs for a generative design task. In this work, we propose to encode the to-be-evaluated images with a Denoising Autoencoder (DAE) and measure the distribution distance in the resulting latent space. Hereby, we design a novel metric Fréchet Denoised Distance (FDD). We experimentally test our FDD, FID and other state-of-the-art metrics on multiple datasets, e.g., BIKED, Seeing3DChairs, FFHQ and ImageNet. Our FDD can effectively detect implausible structures and is more consistent with structural inspections by human experts. Our source code is publicly available at https://github.com/jiajie96/FDD_pytorch.

Matīss Kalnāre, Sofoklis Kitharidis, Thomas Bäck et al.

Transformer-based models have become state-of-the-art tools in various machine learning tasks, including time series classification, yet their complexity makes understanding their internal decision-making challenging. Existing explainability methods often focus on input-output attributions, leaving the internal mechanisms largely opaque. This paper addresses this gap by adapting various Mechanistic Interpretability techniques; activation patching, attention saliency, and sparse autoencoders, from NLP to transformer architectures designed explicitly for time series classification. We systematically probe the internal causal roles of individual attention heads and timesteps, revealing causal structures within these models. Through experimentation on a benchmark time series dataset, we construct causal graphs illustrating how information propagates internally, highlighting key attention heads and temporal positions driving correct classifications. Additionally, we demonstrate the potential of sparse autoencoders for uncovering interpretable latent features. Our findings provide both methodological contributions to transformer interpretability and novel insights into the functional mechanics underlying transformer performance in time series classification tasks.

Wenhu Li, Niki van Stein, Thomas Bäck et al.

Bayesian optimization (BO) is a powerful class of algorithms for optimizing expensive black-box functions, but designing effective BO algorithms remains a manual, expertise-driven task. Recent advancements in Large Language Models (LLMs) have opened new avenues for automating scientific discovery, including the automatic design of optimization algorithms. While prior work has used LLMs within optimization loops or to generate non-BO algorithms, we tackle a new challenge: Using LLMs to automatically generate full BO algorithm code. Our framework uses an evolution strategy to guide an LLM in generating Python code that preserves the key components of BO algorithms: An initial design, a surrogate model, and an acquisition function. The LLM is prompted to produce multiple candidate algorithms, which are evaluated on the established Black-Box Optimization Benchmarking (BBOB) test suite from the COmparing Continuous Optimizers (COCO) platform. Based on their performance, top candidates are selected, combined, and mutated via controlled prompt variations, enabling iterative refinement. Despite no additional fine-tuning, the LLM-generated algorithms outperform state-of-the-art BO baselines in 19 (out of 24) BBOB functions in dimension 5 and generalize well to higher dimensions, and different tasks (from the Bayesmark framework). This work demonstrates that LLMs can serve as algorithmic co-designers, offering a new paradigm for automating BO development and accelerating the discovery of novel algorithmic combinations. The source code is provided at https://github.com/Ewendawi/LLaMEA-BO.

Annie Wong, Thomas Bäck, Aske Plaat et al.

Large language models excel on static benchmarks, but their ability as self-learning agents in dynamic environments remains unclear. We evaluate three prompting strategies: self-reflection, heuristic mutation, and planning across dynamic tasks with open-source models. We find that larger models generally outperform smaller ones, but that strategic prompting can close this performance gap. Second, an overly long prompt can negatively impact smaller models on basic reactive tasks, while larger models show more robust behaviour. Third, advanced prompting techniques primarily benefit smaller models on complex games, but offer less improvement for already high-performing large language models. Yet, we find that advanced reasoning methods yield highly variable outcomes: while capable of significantly improving performance when reasoning and decision-making align, they also introduce instability and can lead to big performance drops. Compared to human performance, our findings reveal little evidence of true emergent reasoning. Instead, large language model performance exhibits persistent limitations in areas like planning and spatial coordination, suggesting that large language models still suffer fundamental shortcomings that may not be fully overcome through self-reflective prompting alone. Reasoning is a multi-faceted task, and while methods like Chain-of-thought improve multi-step reasoning on math word problems, our findings using dynamic benchmarks highlight important shortcomings in general reasoning capabilities, indicating a need to move beyond static benchmarks to capture the complexity of reasoning.

Zhong Li, Qi Huang, Yuxuan Zhu et al.

Optimization modeling translates real decision-making problems into mathematical optimization models and solver-executable implementations. Although language models are increasingly used to generate optimization formulations and solver code, existing benchmarks are almost entirely text-only. This omits many optimization-modeling tasks that arise in operational practice, where requirements are described in text but instance information is conveyed through visual artifacts such as tables, graphs, maps, schedules, and dashboards. We introduce multimodal optimization modeling, a benchmark setting in which models must construct both a mathematical formulation and executable solver code from a text-and-visual problem specification. To evaluate this setting, we develop a solver-grounded framework that generates structured optimization instances, verifies each with an exact solver, and builds both the model-facing inputs and hidden reference files from the same verified source. We instantiate the framework as MM-OptBench, a benchmark of 780 solver-verified instances spanning 6 optimization families, 26 subcategories, and 3 structural difficulty levels. We evaluate 9 multimodal large language models (MLLMs), including 6 frontier general-purpose models and 3 math-specialized models, with aggregate, family-level, difficulty-level, and failure-mode analyses. The results show that the task remains far from solved: the best two models reach 52.1% and 51.3% pass@1, while on average across the six general-purpose MLLMs, pass@1 is 43.4% on easy instances and 15.9% on hard instances. All three math-specialized MLLMs solve 0/780 instances. Failure attribution shows that errors arise both when extracting instance data from text and visuals and when turning extracted data into solver-correct formulations and code. MM-OptBench provides a testbed for solver-grounded, decision-oriented multimodal intelligence.

Hao Wang, Diederick Vermetten, Furong Ye et al.

Benchmarking and performance analysis play an important role in understanding the behaviour of iterative optimization heuristics (IOHs) such as local search algorithms, genetic and evolutionary algorithms, Bayesian optimization algorithms, etc. This task, however, involves manual setup, execution, and analysis of the experiment on an individual basis, which is laborious and can be mitigated by a generic and well-designed platform. For this purpose, we propose IOHanalyzer, a new user-friendly tool for the analysis, comparison, and visualization of performance data of IOHs. Implemented in R and C++, IOHanalyzer is fully open source. It is available on CRAN and GitHub. IOHanalyzer provides detailed statistics about fixed-target running times and about fixed-budget performance of the benchmarked algorithms with a real-valued codomain, single-objective optimization tasks. Performance aggregation over several benchmark problems is possible, for example in the form of empirical cumulative distribution functions. Key advantages of IOHanalyzer over other performance analysis packages are its highly interactive design, which allows users to specify the performance measures, ranges, and granularity that are most useful for their experiments, and the possibility to analyze not only performance traces, but also the evolution of dynamic state parameters. IOHanalyzer can directly process performance data from the main benchmarking platforms, including the COCO platform, Nevergrad, the SOS platform, and IOHexperimenter. An R programming interface is provided for users preferring to have a finer control over the implemented functionalities.

Niki van Stein, Diederick Vermetten, Anna V. Kononova et al.

Benchmarking heuristic algorithms is vital to understand under which conditions and on what kind of problems certain algorithms perform well. In most current research into heuristic optimization algorithms, only a very limited number of scenarios, algorithm configurations and hyper-parameter settings are explored, leading to incomplete and often biased insights and results. This paper presents a novel approach we call explainable benchmarking. Introducing the IOH-Xplainer software framework, for analyzing and understanding the performance of various optimization algorithms and the impact of their different components and hyper-parameters. We showcase the framework in the context of two modular optimization frameworks. Through this framework, we examine the impact of different algorithmic components and configurations, offering insights into their performance across diverse scenarios. We provide a systematic method for evaluating and interpreting the behaviour and efficiency of iterative optimization heuristics in a more transparent and comprehensible manner, allowing for better benchmarking and algorithm design.

Niki van Stein, Anna V. Kononova, Lars Kotthoff et al.

Large Language Models (LLMs) have demonstrated great promise in generating code, especially when used inside an evolutionary computation framework to iteratively optimize the generated algorithms. However, in some cases they fail to generate competitive algorithms or the code optimization stalls, and we are left with no recourse because of a lack of understanding of the generation process and generated codes. We present a novel approach to mitigate this problem by enabling users to analyze the generated codes inside the evolutionary process and how they evolve over repeated prompting of the LLM. We show results for three benchmark problem classes and demonstrate novel insights. In particular, LLMs tend to generate more complex code with repeated prompting, but additional complexity can hurt algorithmic performance in some cases. Different LLMs have different coding ``styles'' and generated code tends to be dissimilar to other LLMs. These two findings suggest that using different LLMs inside the code evolution frameworks might produce higher performing code than using only one LLM.

Niki van Stein, Anna V. Kononova, Haoran Yin et al.

The application of Large Language Models (LLMs) for Automated Algorithm Discovery (AAD), particularly for optimisation heuristics, is an emerging field of research. This emergence necessitates robust, standardised benchmarking practices to rigorously evaluate the capabilities and limitations of LLM-driven AAD methods and the resulting generated algorithms, especially given the opacity of their design process and known issues with existing benchmarks. To address this need, we introduce BLADE (Benchmark suite for LLM-driven Automated Design and Evolution), a modular and extensible framework specifically designed for benchmarking LLM-driven AAD methods in a continuous black-box optimisation context. BLADE integrates collections of benchmark problems (including MA-BBOB and SBOX-COST among others) with instance generators and textual descriptions aimed at capability-focused testing, such as generalisation, specialisation and information exploitation. It offers flexible experimental setup options, standardised logging for reproducibility and fair comparison, incorporates methods for analysing the AAD process (e.g., Code Evolution Graphs and various visualisation approaches) and facilitates comparison against human-designed baselines through integration with established tools like IOHanalyser and IOHexplainer. BLADE provides an `out-of-the-box' solution to systematically evaluate LLM-driven AAD approaches. The framework is demonstrated through two distinct use cases exploring mutation prompt strategies and function specialisation.

Qi Huang, Wei Chen, Thomas Bäck et al.

In this work, we propose a model-agnostic instance-based post-hoc explainability method for time series classification. The proposed algorithm, namely Time-CF, leverages shapelets and TimeGAN to provide counterfactual explanations for arbitrary time series classifiers. We validate the proposed method on several real-world univariate time series classification tasks from the UCR Time Series Archive. The results indicate that the counterfactual instances generated by Time-CF when compared to state-of-the-art methods, demonstrate better performance in terms of four explainability metrics: closeness, sensibility, plausibility, and sparsity.

Dikshit Chauhan, Bapi Dutta, Indu Bala et al.

Integrating Large Language Models (LLMs) and Evolutionary Computation (EC) represents a promising avenue for advancing artificial intelligence by combining powerful natural language understanding with optimization and search capabilities. This manuscript explores the synergistic potential of LLMs and EC, reviewing their intersections, complementary strengths, and emerging applications. We identify key opportunities where EC can enhance LLM training, fine-tuning, prompt engineering, and architecture search, while LLMs can, in turn, aid in automating the design, analysis, and interpretation of ECs. The manuscript explores the synergistic integration of EC and LLMs, highlighting their bidirectional contributions to advancing artificial intelligence. It first examines how EC techniques enhance LLMs by optimizing key components such as prompt engineering, hyperparameter tuning, and architecture search, demonstrating how evolutionary methods automate and refine these processes. Secondly, the survey investigates how LLMs improve EC by automating metaheuristic design, tuning evolutionary algorithms, and generating adaptive heuristics, thereby increasing efficiency and scalability. Emerging co-evolutionary frameworks are discussed, showcasing applications across diverse fields while acknowledging challenges like computational costs, interpretability, and algorithmic convergence. The survey concludes by identifying open research questions and advocating for hybrid approaches that combine the strengths of EC and LLMs.

Jiajie Fan, Babak Gholami, Thomas Bäck et al.

Boundary Representation (B-Rep) is the de facto representation of 3D solids in Computer-Aided Design (CAD). B-Rep solids are defined with a set of NURBS (Non-Uniform Rational B-Splines) surfaces forming a closed volume. To represent a surface, current works often employ the UV-grid approximation, i.e., sample points uniformly on the surface. However, the UV-grid method is not efficient in surface representation and sometimes lacks precision and regularity. In this work, we propose NeuroNURBS, a representation learning method to directly encode the parameters of NURBS surfaces. Our evaluation in solid generation and segmentation tasks indicates that the NeuroNURBS performs comparably and, in some cases, superior to UV-grids, but with a significantly improved efficiency: for training the surface autoencoder, GPU consumption is reduced by 86.7%; memory requirement drops by 79.9% for storing 3D solids. Moreover, adapting BrepGen for solid generation with our NeuroNURBS improves the FID from 30.04 to 27.24, and resolves the undulating issue in generated surfaces.

Niki van Stein, Haoran Yin, Anna V. Kononova et al.

We investigate the behaviour space of meta-heuristic optimisation algorithms automatically generated by Large Language Model driven algorithm discovery methods. Using the Large Language Evolutionary Algorithm (LLaMEA) framework with a GPT o4-mini LLM, we iteratively evolve black-box optimisation heuristics, evaluated on 10 functions from the BBOB benchmark suite. Six LLaMEA variants, featuring different mutation prompt strategies, are compared and analysed. We log dynamic behavioural metrics including exploration, exploitation, convergence and stagnation measures, for each run, and analyse these via visual projections and network-based representations. Our analysis combines behaviour-based projections, Code Evolution Graphs built from static code features, performance convergence curves, and behaviour-based Search Trajectory Networks. The results reveal clear differences in search dynamics and algorithm structures across LLaMEA configurations. Notably, the variant that employs both a code simplification prompt and a random perturbation prompt in a 1+1 elitist evolution strategy, achieved the best performance, with the highest Area Over the Convergence Curve. Behaviour-space visualisations show that higher-performing algorithms exhibit more intensive exploitation behaviour and faster convergence with less stagnation. Our findings demonstrate how behaviour-space analysis can explain why certain LLM-designed heuristics outperform others and how LLM-driven algorithm discovery navigates the open-ended and complex search space of algorithms. These findings provide insights to guide the future design of adaptive LLM-driven algorithm generators.

Shuaiqun Pan, Diederick Vermetten, Manuel López-Ibáñez et al.

Surrogate models are frequently employed as efficient substitutes for the costly execution of real-world processes. However, constructing a high-quality surrogate model often demands extensive data acquisition. A solution to this issue is to transfer pre-trained surrogate models for new tasks, provided that certain invariances exist between tasks. This study focuses on transferring non-differentiable surrogate models (e.g., random forests) from a source function to a target function, where we assume their domains are related by an unknown affine transformation, using only a limited amount of transfer data points evaluated on the target. Previous research attempts to tackle this challenge for differentiable models, e.g., Gaussian process regression, which minimizes the empirical loss on the transfer data by tuning the affine transformations. In this paper, we extend the previous work to the random forest and assess its effectiveness on a widely-used artificial problem set - Black-Box Optimization Benchmark (BBOB) testbed, and on four real-world transfer learning problems. The results highlight the significant practical advantages of the proposed method, particularly in reducing both the data requirements and computational costs of training surrogate models for complex real-world scenarios.

Lucas Correia, Jan-Christoph Goos, Thomas Bäck et al.

Benchmarking anomaly detection approaches for multivariate time series is a challenging task due to a lack of high-quality datasets. Current publicly available datasets are too small, not diverse and feature trivial anomalies, which hinders measurable progress in this research area. We propose a solution: a diverse, extensive, and non-trivial dataset generated via state-of-the-art simulation tools that reflects realistic behaviour of an automotive powertrain, including its multivariate, dynamic and variable-state properties. Additionally, our dataset represents a discrete-sequence problem, which remains unaddressed by previously-proposed solutions in literature. To cater for both unsupervised and semi-supervised anomaly detection settings, as well as time series generation and forecasting, we make different versions of the dataset available, where training and test subsets are offered in contaminated and clean versions, depending on the task. We also provide baseline results from a selection of approaches based on deterministic and variational autoencoders, as well as a non-parametric approach. As expected, the baseline experimentation shows that the approaches trained on the semi-supervised version of the dataset outperform their unsupervised counterparts, highlighting a need for approaches more robust to contaminated training data. Furthermore, results show that the threshold used can have a large influence on detection performance, hence more work needs to be invested in methods to find a suitable threshold without the need for labelled data.

Christian Internò, Elena Raponi, Niki van Stein et al.

As the era of connectivity and unprecedented data generation expands, collaborative intelligence emerges as a key driver for machine learning, encouraging global-scale model development. Federated learning (FL) stands at the heart of this transformation, enabling distributed systems to work collectively on complex tasks while respecting strict constraints on privacy and security. Despite its vast potential, specially in the age of complex models, FL encounters challenges such as elevated communication costs, computational constraints, and the heterogeneous data distributions. In this context, we present AutoFLIP, a novel framework that optimizes FL through an adaptive hybrid pruning approach, grounded in a federated loss exploration phase. By jointly analyzing diverse non-IID client loss landscapes, AutoFLIP efficiently identifies model substructures for pruning both at structured and unstructured levels. This targeted optimization fosters a symbiotic intelligence loop, reducing computational burdens and boosting model performance on resource-limited devices for a more inclusive and democratized model usage. Our extensive experiments across multiple datasets and FL tasks show that AutoFLIP delivers quantifiable benefits: a 48.8% reduction in computational overhead, a 35.5% decrease in communication costs, and a notable improvement in global accuracy. By significantly reducing these overheads, AutoFLIP offer the way for efficient FL deployment in real-world applications for a scalable and broad applicability.

Annie Wong, Jacob de Nobel, Thomas Bäck et al.

Although deep reinforcement learning methods can learn effective policies for challenging problems such as Atari games and robotics tasks, algorithms are complex, and training times are often long. This study investigates how Evolution Strategies perform compared to gradient-based deep reinforcement learning methods. We use Evolution Strategies to optimize the weights of a neural network via neuroevolution, performing direct policy search. We benchmark both deep policy networks and networks consisting of a single linear layer from observations to actions for three gradient-based methods, such as Proximal Policy Optimization. These methods are evaluated against three classical Evolution Strategies and Augmented Random Search, which all use linear policy networks. Our results reveal that Evolution Strategies can find effective linear policies for many reinforcement learning benchmark tasks, unlike deep reinforcement learning methods that can only find successful policies using much larger networks, suggesting that current benchmarks are easier to solve than previously assumed. Interestingly, Evolution Strategies also achieve results comparable to gradient-based deep reinforcement learning algorithms for higher-complexity tasks. Furthermore, we find that by directly accessing the memory state of the game, Evolution Strategies can find successful policies in Atari that outperform the policies found by Deep Q-Learning. Evolution Strategies also outperform Augmented Random Search in most benchmarks, demonstrating superior sample efficiency and robustness in training linear policy networks.

Kirill Antonov, Roman Kalkreuth, Kaifeng Yang et al.

Symbolic regression (SR) poses a significant challenge for randomized search heuristics due to its reliance on the synthesis of expressions for input-output mappings. Although traditional genetic programming (GP) algorithms have achieved success in various domains, they exhibit limited performance when tree-based representations are used for SR. To address these limitations, we introduce a novel SR approach called Fourier Tree Growing (FTG) that draws insights from functional analysis. This new perspective enables us to perform optimization directly in a different space, thus avoiding intricate symbolic expressions. Our proposed algorithm exhibits significant performance improvements over traditional GP methods on a range of classical one-dimensional benchmarking problems. To identify and explain limiting factors of GP and FTG, we perform experiments on a large-scale polynomials benchmark with high-order polynomials up to degree 100. To the best of the authors' knowledge, this work represents the pioneering application of functional analysis in addressing SR problems. The superior performance of the proposed algorithm and insights into the limitations of GP open the way for further advancing GP for SR and related areas of explainable machine learning.

Wei Liu, Yaoxin Wu, Yingqian Zhang et al.

Deep reinforcement learning (DRL) has shown great promise in addressing multi-objective combinatorial optimization problems (MOCOPs). Nevertheless, the robustness of these learning-based solvers has remained insufficiently explored, especially across diverse and complex problem distributions. In this paper, we propose a unified robustness-oriented framework for preference-conditioned DRL solvers for MOCOPs. Within this framework, we develop a preference-based adversarial attack to generate hard instances that expose solver weaknesses, and quantify the attack impact by the resulting degradation on Pareto-front quality. We further introduce a defense strategy that integrates hardness-aware preference selection into adversarial training to reduce overfitting to restricted preference regions and improve out-of-distribution performance. The experimental results on multi-objective traveling salesman problem (MOTSP), multi-objective capacitated vehicle routing problem (MOCVRP), and multi-objective knapsack problem (MOKP) verify that our attack method successfully learns hard instances for different solvers. Furthermore, our defense method significantly strengthens the robustness and generalizability of neural solvers, delivering superior performance on hard or out-of-distribution instances.

Urban Skvorc, Niki van Stein, Moritz Seiler et al.

Benchmarking in continuous black-box optimisation is hindered by the limited structural diversity of existing test suites such as BBOB. We explore whether large language models embedded in an evolutionary loop can be used to design optimisation problems with clearly defined high-level landscape characteristics. Using the LLaMEA framework, we guide an LLM to generate problem code from natural-language descriptions of target properties, including multimodality, separability, basin-size homogeneity, search-space homogeneity and globallocal optima contrast. Inside the loop we score candidates through ELA-based property predictors. We introduce an ELA-space fitness-sharing mechanism that increases population diversity and steers the generator away from redundant landscapes. A complementary basin-of-attraction analysis, statistical testing and visual inspection, verifies that many of the generated functions indeed exhibit the intended structural traits. In addition, a t-SNE embedding shows that they expand the BBOB instance space rather than forming an unrelated cluster. The resulting library provides a broad, interpretable, and reproducible set of benchmark problems for landscape analysis and downstream tasks such as automated algorithm selection.

Niki van Stein, Anna V. Kononova, Thomas Bäck

Automated algorithm design is entering a new phase: Large Language Models can now generate full optimisation (meta)heuristics, explore vast design spaces and adapt through iterative feedback. Yet this rapid progress is largely performance-driven and opaque. Current LLM-based approaches rarely reveal why a generated algorithm works, which components matter or how design choices relate to underlying problem structures. This paper argues that the next breakthrough will come not from more automation, but from coupling automation with understanding from systematic benchmarking. We outline a vision for explainable automated algorithm design, built on three pillars: (i) LLM-driven discovery of algorithmic variants, (ii) explainable benchmarking that attributes performance to components and hyperparameters and (iii) problem-class descriptors that connect algorithm behaviour to landscape structure. Together, these elements form a closed knowledge loop in which discovery, explanation and generalisation reinforce each other. We argue that this integration will shift the field from blind search to interpretable, class-specific algorithm design, accelerating progress while producing reusable scientific insight into when and why optimisation strategies succeed.

Robin van der Laag, Hao Wang, Thomas Bäck et al.

Stochastic multi-objective optimization (SMOOP) requires ranking multivariate distributions; yet, most empirical studies perform scalarization, which loses information and is unreliable. Based on the optimal transport theory, we introduce the center-outward q-dominance relation and prove it implies strong first-order stochastic dominance (FSD). Also, we develop an empirical test procedure based on q-dominance, and derive an explicit sample size threshold, $n^*(δ)$, to control the Type I error. We verify the usefulness of our approach in two scenarios: (1) as a ranking method in hyperparameter tuning; (2) as a selection method in multi-objective optimization algorithms. For the former, we analyze the final stochastic Pareto sets of seven multi-objective hyperparameter tuners on the YAHPO-MO benchmark tasks with q-dominance, which allows us to compare these tuners when the expected hypervolume indicator (HVI, the most common performance metric) of the Pareto sets becomes indistinguishable. For the latter, we replace the mean value-based selection in the NSGA-II algorithm with $q$-dominance, which shows a superior convergence rate on noise-augmented ZDT benchmark problems. These results establish center-outward q-dominance as a principled, tractable foundation for seeking truly stochastically dominant solutions for SMOOPs.

Sofoklis Kitharidis, Cor J. Veenman, Thomas Bäck et al.

In the context of algorithmic decision-making, fair machine learning methods often yield multiple models that balance predictive fairness and performance in varying degrees. This diversity introduces a challenge for stakeholders who must select a model that aligns with their specific requirements and values. To address this, we propose an interactive framework that assists in navigating and interpreting the trade-offs across a portfolio of models. Our approach leverages weakly supervised metric learning to learn a Mahalanobis distance that reflects similarity in fairness and performance outcomes, effectively structuring the feature importance space of the models according to stakeholder-relevant criteria. We then apply clustering technique (k-means) to group models based on their transformed representations of feature importances, allowing users to explore clusters of models with similar predictive behaviors and fairness characteristics. This facilitates informed decision-making by helping users understand how models differ not only in their fairness-performance balance but also in the features that drive their predictions.