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 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.

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.

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.

Traditional benchmarking methods are often used to evaluate algorithms in isolation, with a single algorithm configuration (hyper-parameter setting) or with a limited set of a few variations against a limited set of state-of-the-art algorithms, leading to limited insights into their comparative performance and practical applicability. This study addresses these challenges by employing modular optimization approaches and explainable AI techniques in order to derive insights into the algorithmic behaviour of a large set of algorithm components (modules) and their hyper-parameters. Modular optimization frameworks allow for the comparison of various modifications on a core algorithm, facilitating a deeper understanding of each component's influence on the algorithm's performance in different scenarios. There is already a wide variety of modular algorithm frameworks available, but their application for explicit explainability of the various algorithmic components and settings has been relatively unexplored. This paper aims to bridge this gap by providing a comprehensive framework for explainable benchmarking in iterative optimization heuristics and by providing a software library (IOH-Xplainer) to facilitate researchers to use the proposed framework.

We consider the problem of learning multiple tasks in a continual learning setting in which data from different tasks is presented to the learner in a streaming fashion. A key challenge in this setting is the so-called "catastrophic forgetting problem", in which the performance of the learner in an "old task" decreases when subsequently trained on a "new task". Existing continual learning methods, such as Averaged Gradient Episodic Memory (A-GEM) and Orthogonal Gradient Descent (OGD), address catastrophic forgetting by minimizing the loss for the current task without increasing the loss for previous tasks. However, these methods assume the learner knows when the task changes, which is unrealistic in practice. In this paper, we alleviate the need to provide the algorithm with information about task changes by using an online clustering-based approach on a dynamically updated finite pool of samples or gradients. We thereby successfully counteract catastrophic forgetting in one of the hardest settings, namely: domain-incremental learning, a setting for which the problem was previously unsolved. We showcase the benefits of our approach by applying these ideas to projection-based methods, such as A-GEM and OGD, which lead to task-agnostic versions of them. Experiments on real datasets demonstrate the effectiveness of the proposed strategy and its promising performance compared to state-of-the-art methods.