Chain‑of‑thought (CoT) prompting boosts Large Language Models accuracy on multi‑step tasks, yet whether the generated ``thoughts'' reflect the true internal reasoning process is unresolved. We present the first feature‑level causal study of CoT faithfulness. Combining sparse autoencoders with activation patching, we extract monosemantic features from Pythia‑70M and Pythia‑2.8B while they tackle GSM8K math problems under CoT and plain (noCoT) prompting. Swapping a small set of CoT‑reasoning features into a noCoT run raises answer log‑probabilities significantly in the 2.8B model, but has no reliable effect in 70M, revealing a clear contrast for these two scales. CoT also leads to significantly higher activation sparsity and feature interpretability scores in the larger model, signalling more modular internal computation. For example, the model's confidence in generating correct answers improves from 1.2 to 4.3. We introduce patch‑curves and random‑feature patching baselines, showing that useful CoT information is not only present in the top-K patches but widely distributed. Overall, our results indicate that CoT can induce more interpretable internal structures in high-capacity LLMs, validating its role as a structured prompting method.

Structural bias (SB) refers to systematic preferences of an optimisation algorithm for particular regions of the search space that arise independently of the objective function. While SB has been studied extensively in single-objective optimisation, its role in multi-objective optimisation remains largely unexplored. This is problematic, as dominance relations, diversity preservation and Pareto-based selection mechanisms may introduce or amplify structural effects.

Bayesian optimization (BO) is a 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 BBOB test suite from the 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. 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.

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 κ 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.

We present a novel approach for constructing discrete optimization benchmarks that enables fine-grained control over problem properties, and such benchmarks can facilitate analyzing discrete algorithm behaviors. We build benchmark problems based on a set of block functions, where each block function maps a subset of variables to a real value. Problems are instantiated through a set of block functions, weight factors, and an adjacency graph representing the dependency among the block functions. Through analyzing intermediate block values, our framework allows to analyze algorithm behavior not only in the objective space but also at the level of variable representations in the obtained solutions. This capacity is particularly useful for analyzing discrete heuristics in large-scale multi-modal problems, thereby enhancing the practical relevance of benchmark studies. We demonstrate how the proposed approach can inspire the related work in self-adaptation and diversity control in evolutionary algorithms. Moreover, we explain that the proposed benchmark design enables explicit control over problem properties, supporting research in broader domains such as dynamic algorithm configuration and multi-objective optimization.

The advent of Large Language Models (LLMs) has opened new frontiers in automated algorithm design, giving rise to numerous powerful methods. However, these approaches retain critical limitations: they require extensive evaluation of the target problem to guide the search process, making them impractical for real-world optimization tasks, where each evaluation consumes substantial computational resources. This research proposes an innovative and efficient framework that decouples algorithm discovery from high-cost evaluation. Our core innovation lies in combining a Genetic Programming (GP) function generator with an LLM-driven evolutionary algorithm designer. The evolutionary direction of the GP-based function generator is guided by the similarity between the landscape characteristics of generated proxy functions and those of real-world problems, ensuring that algorithms discovered via proxy functions exhibit comparable performance on real-world problems. Our method enables deep exploration of the algorithmic space before final validation while avoiding costly real-world evaluations. We validate the framework's efficacy across multiple real-world problems, demonstrating its ability to discover high-performance algorithms while substantially reducing expensive evaluations. This approach shows a path to apply LLM-based automated algorithm design to computationally intensive real-world optimization challenges.

The practical deployment of Federated Learning (FL) on resource-constrained devices is fundamentally limited by the high cost of training large models and the instability caused by heterogeneous (non-IID) client data. Conventional pruning methods often treat data heterogeneity as a problem to be mitigated. In this work, we introduce a paradigm shift: we reframe client diversity as a feature to be harnessed. We propose AutoFLIP, a framework that begins not with training, but with a one-time federated loss exploration. During this phase, clients collaboratively build a map of the collective loss landscape, using their diverse data to reveal the problem's essential structure. This shared intelligence then guides an adaptive pruning strategy that is dynamically refined by client agreement throughout training. This approach allows AutoFLIP to identify robust and efficient sub-networks from the outset. Our extensive experiments show that AutoFLIP reduces computational overhead by an average of 52% and communication costs by over 65% while simultaneously achieving state-of-the-art accuracy in challenging non-IID settings.

NWO

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.

Combining large language models with evolutionary computation algorithms represents a promising research direction leveraging the remarkable generative and in-context learning capabilities of LLMs with the strengths of evolutionary algorithms. In this work, we present EvoCAD, a method for generating computer-aided design (CAD) objects through their symbolic representations using vision language models and evolutionary optimization. Our method samples multiple CAD objects, which are then optimized using an evolutionary approach with vision language and reasoning language models. We assess our method using GPT-4V and GPT-4o, evaluating it on the CAD-Prompt benchmark dataset and comparing it to prior methods. Additionally, we introduce two new metrics based on topological properties defined by the Euler characteristic, which capture a form of semantic similarity between 3D objects. Our results demonstrate that EvoCAD outperforms previous approaches on multiple metrics, particularly in generating topologically correct objects, which can be efficiently evaluated using our two novel metrics that complement existing spatial metrics.

Combining natural language and geometric shapes is an emerging research area with multiple applications in robotics and language-assisted design. A crucial task in this domain is object referent identification, which involves selecting a 3D object given a textual description of the target. Variability in language descriptions and spatial relationships of 3D objects makes this a complex task, increasing the need to better understand the behavior of neural network models in this domain. However, limited research has been conducted in this area. Specifically, when a model makes an incorrect prediction despite being provided with a seemingly correct object description, practitioners are left wondering: "Why is the model wrong?". In this work, we present a method answering this question by generating counterfactual examples. Our method takes a misclassified sample, which includes two objects and a text description, and generates an alternative yet similar formulation that would have resulted in a correct prediction by the model. We have evaluated our approach with data from the ShapeTalk dataset along with three distinct models. Our counterfactual examples maintain the structure of the original description, are semantically similar and meaningful. They reveal weaknesses in the description, model bias and enhance the understanding of the models behavior. Theses insights help practitioners to better interact with systems as well as engineers to improve models.

We introduce Time-Conditioned Contraction Matching (TCCM), a novel method for semi-supervised anomaly detection in tabular data. TCCM is inspired by flow matching, a recent generative modeling framework that learns velocity fields between probability distributions and has shown strong performance compared to diffusion models and generative adversarial networks. Instead of directly applying flow matching as originally formulated, TCCM builds on its core idea—learning velocity fields between distributions—but simplifies the framework by predicting a time-conditioned contraction vector toward a fixed target (the origin) at each sampled time step. This design offers three key advantages: (1) a lightweight and scalable training objective that removes the need for solving ordinary differential equations during training and inference; (2) an efficient scoring strategy called one time-step deviation, which quantifies deviation from expected contraction behavior in a single forward pass, addressing the inference bottleneck of existing continuous-time models such as DTE (a diffusion-based model with leading anomaly detection accuracy but heavy inference cost); and (3) explainability and provable robustness, as the learned velocity field operates directly in input space, making the anomaly score inherently feature-wise attributable; moreover, the score function is Lipschitz-continuous with respect to the input, providing theoretical guarantees under small perturbations. Extensive experiments on the ADBench benchmark show that TCCM strikes a favorable balance between detection accuracy and inference cost, outperforming state-of-the-art methods—especially on high-dimensional and large-scale datasets. The source code is provided at https://github.com/ZhongLIFR/TCCM-NIPS.

Background: There is great interest in agentic LLMs, large language models that act as agents. Objectives: We review the growing body of work in this area and provide a research agenda. Methods: Agentic LLMs are LLMs that (1) reason, (2) act, and (3) interact. We organize the literature according to these three categories. Results: The research in the first category focuses on reasoning, reflection, and retrieval, aiming to improve decision making; the second category focuses on action models, robots, and tools, aiming for agents that act as useful assistants; the third category focuses on multi-agent systems, aiming for collaborative task solving and simulating interaction to study emergent social behavior. We find that works mutually benefit from results in other categories: retrieval enables tool use, reflection improves multi-agent collaboration, and reasoning benefits all categories. Conclusions: We discuss applications of agentic LLMs and provide an agenda for further research. Important applications are in medical diagnosis, logistics and financial market analysis. Meanwhile, self-reflective agents playing roles and interacting with one another augment the process of scientific research itself. Further, agentic LLMs provide a solution for the problem of LLMs running out of training data: inference-time behavior generates new training states, such that LLMs can keep learning without needing ever larger datasets. We note that there is risk associated with LLM assistants taking action in the real world—safety, liability and security are open problems—while agentic LLMs are also likely to benefit society.

Large language models (LLMs), such as GPT-4 have demonstrated their ability to understand natural language and generate complex code snippets. This article introduces a novel LLM evolutionary algorithm (LLaMEA) framework, leveraging GPT models for the automated generation and refinement of algorithms. Given a set of criteria and a task definition (the search space), LLaMEA iteratively generates, mutates, and selects algorithms based on performance metrics and feedback from runtime evaluations. This framework offers a unique approach to generating optimized algorithms without requiring extensive prior expertise. We show how this framework can be used to generate novel closed box metaheuristic optimization algorithms for box-constrained, continuous optimization problems automatically. LLaMEA generates multiple algorithms that outperform state-of-the-art optimization algorithms (covariance matrix adaptation evolution strategy and differential evolution) on the 5-D closed box optimization benchmark (BBOB). The algorithms also show competitive performance on the 10- and 20-D instances of the test functions, although they have not seen such instances during the automated generation process. The results demonstrate the feasibility of the framework and identify future directions for automated generation and optimization of algorithms via LLMs.

Artificial intelligence methods are being increasingly applied across various domains, but their often opaque nature has raised concerns about accountability and trust. In response, the field of explainable AI (XAI) has emerged to address the need for human-understandable AI systems. Evolutionary computation (EC), a family of powerful optimization and learning algorithms, offers significant potential to contribute to XAI, and vice versa. This article provides an introduction to XAI and reviews current techniques for explaining machine learning (ML) models. We then explore how EC can be leveraged in XAI and examine existing XAI approaches that incorporate EC techniques. Furthermore, we discuss the application of XAI principles within EC itself, investigating how these principles can illuminate the behavior and outcomes of EC algorithms, their (automatic) configuration, and the underlying problem landscapes they optimize. Finally, we discuss open challenges in XAI and highlight opportunities for future research at the intersection of XAI and EC. Our goal is to demonstrate EC’s suitability for addressing current explainability challenges and to encourage further exploration of these methods, ultimately contributing to the development of more understandable and trustworthy ML models and EC algorithms.

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 article presents a novel approach that we call explainable benchmarking. We introduce the IOHxplainer software library, for systematic analysing the performance of various optimization algorithms and the impact of their different components and hyperparameters. We showcase the methodology in the context of two modular optimization implementations. Through this library, 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, aiming to improve future benchmarking and algorithm design practices.

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 the 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.

Computer Systems, Imagery and Media

Abstract 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.

Abstract To guide the design of better iterative optimisation heuristics, it is imperative to understand how inherent structural biases within algorithm components affect the performance on a wide variety of search landscapes. This study explores the impact of structural bias in the modular Covariance Matrix Adaptation Evolution Strategy (modCMA), focusing on the roles of various modulars within the algorithm. Through an extensive investigation involving $$435\,456$$ 435 456 configurations of modCMA, we identified key modules that significantly influence structural bias of various classes. Our analysis utilized the Deep-BIAS toolbox for structural bias detection and classification, complemented by SHAP analysis for quantifying module contributions. The performance of these configurations was tested on a sequence of affine-recombined functions, maintaining fixed optimum locations while gradually varying the landscape features. Our results demonstrate an interplay between module-induced structural bias and algorithm performance across different landscape characteristics.

Solving real-world engineering optimization problems, such as automotive crashworthiness optimization, is extremely challenging, because the problem characteristics are oftentimes not well understood. Furthermore, typical hyperparameter optimization (HPO) approaches that require a large function evaluation budget are computationally hindered, if the function evaluation is expensive, for example, requires finite element (FE) simulation runs. In this article, we propose an approach to characterize real-world expensive black-box optimization problems using the exploratory landscape analysis (ELA). Based on these landscape characteristics, we can identify test functions that are fast-to-evaluate and representative for HPO purposes. Focusing on 20 problem instances from automotive crashworthiness optimization, our results reveal that these 20 crashworthiness problems exhibit landscape features different from classical optimization benchmark test suites, such as the widely-used black-box optimization benchmarking (BBOB) problem set. In fact, these 20 problem instances belong to problem classes that are distinct from the BBOB test functions based on the clustering results. Further analysis indicates that, as far as the ELA features concern, they are most similar to problem classes of tree-based test functions. By analyzing the performance of two optimization algorithms with different hyperparameters, namely the covariance matrix adaptation evolutionary strategy (CMA-ES) and Bayesian optimization (BO), we show that the tree-based test functions are indeed representative in terms of predicting the algorithm performances. Following this, such scalable and fast-to-evaluate tree-based test functions have promising potential for automated design of an optimization algorithm for specific real-world problem classes.

The objective value of an ill-conditioned function may significantly change with a minor shift of the argument in the search space. Ill-conditioned functions do not have at all or exhibit very few hints towards better solutions and, thus, they are usually difficult to optimize with randomized search heuristics. However, problems that emerge in practical applications are likely to be formulated as ill-conditioned functions, as often Euclidean metric is used to measure distance in the search space. At the same time, it may be possible to use domain-specific knowledge to define such a metric in the search space so that the function stops being ill-conditioned. We consider finite search spaces and propose two mutation operators that leverage such metric to optimize the function more efficiently. The first operator assumes prior knowledge about the distance, the second operator uses the distance as a black box. Those operators apply an estimation of distribution algorithm to find the best mutant according to the defined function, which employs the given metric. For pseudo-Boolean and integer optimization problems, we experimentally show that both mutation operators speed up the search on most of the functions when applied in considered evolutionary algorithms and random local search. Moreover, those operators can be applied in any randomized search heuristic which uses perturbations. However, our mutation operators increase wall-clock time and so are helpful in practice when distance is (much) cheaper to compute than the real objective function.

In this work We consider and discuss the problems which come with trying to explain human and machine intelligence.How explainable artificial intelligence research is being carried out, the pitfalls and limitations of current approaches and the bigger question of whether we need explanations for trusting inherently complex and large intelligent systems, whether artificial or not.

Thirty years, 1993-2023, is a huge time frame in science. We address some major developments in the field of evolutionary algorithms, with applications in parameter optimization, over these 30 years. These include the covariance matrix adaptation evolution strategy and some fast-growing fields such as multimodal optimization, surrogate-assisted optimization, multiobjective optimization, and automated algorithm design. Moreover, we also discuss particle swarm optimization and differential evolution, which did not exist 30 years ago, either. One of the key arguments made in the paper is that we need fewer algorithms, not more, which, however, is the current trend through continuously claiming paradigms from nature that are suggested to be useful as new optimization algorithms. Moreover, we argue that we need proper benchmarking procedures to sort out whether a newly proposed algorithm is useful or not. We also briefly discuss automated algorithm design approaches, including configurable algorithm design frameworks, as the proposed next step toward designing optimization algorithms automatically, rather than by hand.

Oftentimes the characteristics of real-world engineering optimization problems are not well understood. In this paper, we introduce an approach for characterizing highly nonlinear and Finite Element (FE) simulation-based engineering optimization problems, focusing on ten representative problem instances from automotive crashworthiness optimization. By computing characteristic Exploratory Landscape Analysis (ELA) features, we show that these ten crashworthiness problem instances exhibit landscape features different from classical optimization benchmark test suites, such as the widely-used Black-Box Optimization Benchmarking (BBOB) problem set. Using clustering approaches, we demonstrate that these ten problem instances are clearly distinct from the BBOB test functions. Further analysis of the crashworthiness problem instances reveal that, as far as ELA concerns, they are most similar to a class of artificially generated functions. We identify such artificially generated functions and propose to use them as scalable and fast-to-evaluate representatives of the real-world problems. Such artificially generated functions could be used for the automated design of an optimization algorithm for specific real-world problem classes.

Bayesian optimization is often used to optimize expensive black box optimization problems with long simulation times. Typically Bayesian optimization algorithms propose one solution per iteration. The downside of this strategy is the sub-optimal use of available computing power. To efficiently use the available computing power (or a number of licenses etc.) we introduce a multi-point acquisition function for parallel efficient multi-objective optimization algorithms. The multi-point acquisition function is based on the hypervolume contribution of multiple solutions simultaneously, leading to well spread solutions along the Pareto frontier. By combining this acquisition function with a constraint handling technique, multiple feasible solutions can be proposed and evaluated in parallel every iteration. The hypervolume and feasibility of the solutions can easily be estimated by using multiple cheap radial basis functions as surrogates with different configurations. The acquisition function can be used with different population sizes and even for one shot optimization. The strength and generalizability of the new acquisition function is demonstrated by optimizing a set of black box constraint multi-objective problem instances. The experiments show a huge time saving factor by using our novel multi-point acquisition function, while only marginally worsening the hypervolume after the same number of function evaluations.

The choice of design representations, as of search operators, is central to the performance of evolutionary optimization algorithms, in particular, for multitask problems. The multitask approach pushes further the parallelization aspect of these algorithms by solving simultaneously multiple optimization tasks using a single population. During the search, the operators implicitly transfer knowledge between solutions to the offspring, taking advantage of potential synergies between problems to drive the solutions to optimality. Nevertheless, in order to operate on the individuals, the design space of each task has to be mapped to a common search space, which is challenging in engineering cases without clear semantic overlap between parameters. Here, we apply a 3-D point cloud autoencoder to map the representations from the Cartesian to a unified design representation: the latent space of the autoencoder. The transfer of latent space features between design representations allows the reconstruction of shapes with interpolated characteristics and maintenance of common parts, which potentially improves the performance of the designs in one or more tasks during the optimization. Compared to traditional representations for shape optimization, such as free-form deformation, the latent representation enables more representative design modifications, while keeping the baseline characteristics of the learned classes of objects. We demonstrate the efficiency of our approach in an optimization scenario where we minimize the aerodynamic drag of two different car shapes with common underbodies for cost-efficient vehicle platform design.

Benchmarking heuristic algorithms is vital to understand under which conditions and on what kind of problems certain algorithms perform well. Most benchmarks are performance based, to test algorithm performance under a wide set of conditions. There is also resource- and behavior-based benchmarks to test the resource consumption and the behavior of algorithms. In this article, we propose a novel behavior-based benchmark toolbox: BIAS (Bias in algorithms, structural). This toolbox can detect structural bias (SB) per dimension and across dimension-based on 39 statistical tests. Moreover, it predicts the type of SB using a random forest model. BIAS can be used to better understand and improve existing algorithms (removing bias) as well as to test novel algorithms for SB in an early phase of development. Experiments with a large set of generated SB scenarios show that BIAS was successful in identifying bias. In addition, we also provide the results of BIAS on 432 existing state-of-the-art optimization algorithms showing that different kinds of SB are present in these algorithms, mostly toward the center of the objective space or showing discretization behavior. The proposed toolbox is made available open-source and recommendations are provided for the sample size and hyper-parameters to be used when applying the toolbox on other algorithms.

Methods for learning on 3D point clouds became ubiquitous due to the popularization of 3D scanning technology and advances of machine learning techniques. Among these methods, point-based deep neural networks have been utilized to explore 3D designs in optimization tasks. However, engineering computer simulations require high-quality meshed models, which are challenging to automatically generate from unordered point clouds. In this work, we propose Point2FFD: A novel deep neural network for learning compact geometric representations and generating simulation-ready meshed models. Built upon an autoencoder architecture, Point2FFD learns to compress 3D point clouds into a latent design space, from which the network generates 3D polygonal meshes by selecting and deforming simulation-ready mesh templates. Through benchmark experiments, we show that our proposed network achieves comparable shape-generative performance than existing state-of-the-art point-based generative models. In real world-inspired vehicle aerodynamic optimizations, we demonstrate that Point2FFD generates simulation-ready meshes of realistic car shapes and leads to better optimized designs than the benchmarked networks.

Methods for learning and compressing high-dimensional data allow designers to generate novel and low-dimensional design representations for shape optimization problems. By using compact design spaces, global optimization algorithms require less function evaluations to characterize the problem landscape. Furthermore, data-driven representations are often domain-agnostic and independent of the user expertise, and thus potentially capture more relevant design features than a human designer would suggest. However, more factors than the dimensionality play a role in the efficiency of design representations. In this paper, we perform a comparative analysis of design representations for 3D shape optimization problems obtained with principal component analysis, kernel-principal component analysis and a 3D point cloud autoencoder, which we apply on a benchmark data set of computer aided engineering car models. We evaluate the shape-generative capabilities of these methods and show that we can modify the geometries more locally with the autoencoder than with the remaining methods. In a vehicle aerodynamic optimization framework, we verify that this property of the autoencoder representation improves the optimization performance by enabling potentially complementary degrees of freedom for the optimizer. With our study, we provide insights on the qualitative properties and quantifiable measures on the efficiency of deep neural networks as shape generative models for engineering optimization problems, as well as analyses of geometric representations for engineering optimization with evolutionary algorithms.

In order to reduce the dimensionality of 3D point cloud representations, autoencoder architectures generate increasingly abstract, compressed features of the input data. Visualizing these features is central to understanding the learning process, however, while successful visualization techniques exist for neural networks applied to computer vision tasks, similar methods for geometric, especially non-Euclidean, input data are currently lacking. Hence, we propose a first-of-kind method to project the features learned by point cloud autoencoders into a 3D-space augmented with color maps. Our proposal explores the properties of 1D-convolutions, used in state-of-the art point cloud autoencoder architectures to handle the input data, which leads to an intuitive interpretation of the visualized features. Furthermore, we tackle the search for relevant co-activations in the feature space by clustering the input data in the latent space, where we explore the correspondence between network features and geometric characteristics of typical shapes of the clusters. We tested our approach with experiments on a benchmark data set, and with three different configurations of a point cloud autoencoder, where we show that the features learned by the autoencoder correlate with the occupancy of the input space by the training data.

Abstract KrigingorGaussian Process Regressionis applied in many fields as a non-linear regression model as well as a surrogate model in the field of evolutionary computation. However, the computational and space complexity of Kriging, that is cubic and quadratic in the number of data points respectively, becomes a major bottleneck with more and more data available nowadays. In this paper, we propose a general methodology for the complexity reduction, called cluster Kriging, where the whole data set is partitioned into smaller clusters and multiple Kriging models are built on top of them. In addition, four Kriging approximation algorithms are proposed as candidate algorithms within the new framework. Each of these algorithms can be applied to much larger data sets while maintaining the advantages and power of Kriging. The proposed algorithms are explained in detail and compared empirically against a broad set of existing state-of-the-art Kriging approximation methods on a well-defined testing framework. According to the empirical study, the proposed algorithms consistently outperform the existing algorithms. Moreover, some practical suggestions are provided for using the proposed algorithms.

Designing the architecture for an artificial neural network is a cumbersome task because of the numerous parameters to configure, including activation functions, layer types, and hyper-parameters. With the large number of parameters for most networks nowadays, it is intractable to find a good configuration for a given task by hand. In this paper the Mixed Integer Parallel Efficient Global Optimization (MIP-EGO) algorithm is proposed to automatically configure convolutional neural network architectures. It is shown that on several image classification tasks this approach is able to find competitive network architectures in terms of prediction accuracy, compared to the best hand-crafted ones in literature, when using only a fraction of the number of training epochs. Moreover, instead of the standard sequential evaluation in EGO, several candidate architectures are proposed and evaluated in parallel, which reduces the execution overhead significantly and leads to an efficient automation for deep neural network design.

Efficient Global Optimization (EGO) is an effective method to optimize expensive black-box functions and utilizes Kriging models (or Gaussian process regression) trained on a relatively small design data set. In real-world applications, such as experimental optimization, where a large data set is available, the EGO algorithm becomes computationally infeasible due to the time and space complexity of Kriging. Recently, the so-called Cluster Kriging methods have been proposed to reduce such complexities for the big data, where data sets are clustered and Kriging models are built on each cluster. Furthermore, Kriging models are combined in an optimal way for the prediction. In addition, we analyze the Cluster Kriging landscape to adopt the existing infill-criteria, e.g., the expected improvement. The approach is tested on selected global optimization problems. It is shown by the empirical studies that this approach significantly reduces the CPU time of the EGO algorithm while maintaining the convergence rate of the algorithm.

In the past years, quite a number of algorithmic extensions of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) have been proposed. These extensions define a large algorithm design space, but relatively little is known about the performance of most of these variations and the interaction between them.

Bayesian Optimization or Efficient Global Optimization (EGO) is a global search strategy that is designed for expensive black-box functions. In this algorithm, a statistical model (usually the Gaussian process model) is constructed on some initial data samples. The global optimum is approached by iteratively maximizing a so-called acquisition function, that balances the exploration and exploitation effect of the search. The performance of such an algorithm is largely affected by the choice of the acquisition function. Inspired by the usage of higher moments from the Gaussian process model, it is proposed to construct a novel acquisition function based on the moment-generating function (MGF) of the improvement, which is the stochastic gain over the current best fitness value by sampling at an unknown point. This MGF-based acquisition function takes all the higher moments into account and introduces an additional real-valued parameter to control the trade-off between exploration and exploitation. The motivation, rationale and closed-form expression of the proposed function are discussed in detail. In addition, we also illustrate its advantage over other acquisition functions, especially the so-called generalized expected improvement.

Outlier detection in high-dimensional data is a challenging yet important task, as it has applications in, e.g., fraud detection and quality control. State-of-the-art density-based algorithms perform well because they 1) take the local neighbourhoods of data points into account and 2) consider feature subspaces. In highly complex and high-dimensional data, however, existing methods are likely to overlook important outliers because they do not explicitly take into account that the data is often a mixture distribution of multiple components. We therefore introduce GLOSS, an algorithm that performs local subspace outlier detection using global neighbourhoods. Experiments on synthetic data demonstrate that GLOSS more accurately detects local outliers in mixed data than its competitors. Moreover, experiments on real-world data show that our approach identifies relevant outliers overlooked by existing methods, confirming that one should keep an eye on the global perspective even when doing local outlier detection.

Kriging or Gaussian Process Regression has been successfully applied in many fields. One of the major bottlenecks of Kriging is the complexity in both processing time (cubic) and memory (quadratic) in the number of data points. To overcome these limitations, a variety of approximation algorithms have been proposed. One of these approximation algorithms is Optimally Weighted Cluster Kriging (OWCK). In this paper, OWCK is extended and enhanced by the use of fuzzy clustering methods in order to increase the accuracy. Several options are proposed and evaluated against both the original OWCK and a variety of other Kriging approximation algorithms.