Comparative Analysis of Indicators for Multiobjective Diversity Optimization

Indicator-based (multiobjective) diversity optimization aims at finding a set of near (Pareto-)optimal solutions that maximizes a diversity indicator, where diversity is typically interpreted as the number of essentially different solutions. Whereas, in the first diversity-oriented evolutionary multiobjective optimization algorithm, the NOAH algorithm by Ulrich and Thiele, the Solow Polasky Diversity (also related to Magnitude) served as a metric, other diversity indicators might be considered, such as the parameter-free Max-Min Diversity, and the Riesz s-Energy, which features uniformly distributed solution sets. In this paper, focusing on multiobjective diversity optimization, we discuss different diversity indicators from the perspective of indicator-based evolutionary algorithms (IBEA) with multiple objectives. We examine theoretical, computational, and practical properties of these indicators, such as monotonicity in species, twinning, monotonicity in distance, strict monotonicity in distance, uniformity of maximizing point sets, computational effort for a set of size~n, single-point contributions, subset selection, and submodularity. We present new theorems -- including a proof of the NP-hardness of the Riesz s-Energy Subset Selection Problem -- and consolidate existing results from the literature. In the second part, we apply these indicators in the NOAH algorithm and analyze search dynamics through an example. We examine how optimizing with one indicator affects the performance of others and propose NOAH adaptations specific to the Max-Min indicator.

TX-Gen: Multi-Objective Optimization for Sparse Counterfactual Explanations for Time-Series Classification

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.

Landscape-Aware Automated Algorithm Configuration using Multi-output Mixed Regression and Classification

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.

Online Model-based Anomaly Detection in Multivariate Time Series: Taxonomy, Survey, Research Challenges and Future Directions

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.

TeVAE: A Variational Autoencoder Approach for Discrete Online Anomaly Detection in Variable-state Multivariate Time-series Data

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.

LLaMEA: A Large Language Model Evolutionary Algorithm for Automatically Generating Metaheuristics

Large Language Models (LLMs) such as GPT-4 have demonstrated their ability to understand natural language and generate complex code snippets. This paper introduces a novel Large Language Model 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 black-box metaheuristic optimization algorithms automatically. LLaMEA generates multiple algorithms that outperform state-of-the-art optimization algorithms (Covariance Matrix Adaptation Evolution Strategy and Differential Evolution) on the five dimensional black box optimization benchmark (BBOB). The algorithms also show competitive performance on the 10- and 20-dimensional 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.

Evolving Reliable Differentiating Constraints for the Chance-constrained Maximum Coverage Problem

Chance-constrained problems involve stochastic components in the constraints which can be violated with a small probability. We investigate the impact of different types of chance constraints on the performance of iterative search algorithms and study the classical maximum coverage problem in graphs with chance constraints. Our goal is to evolve reliable chance constraint settings for a given graph where the performance of algorithms differs significantly not just in expectation but with high confidence. This allows to better learn and understand how different types of algorithms can deal with different types of constraint settings and supports automatic algorithm selection. We develop an evolutionary algorithm that provides sets of chance constraints that differentiate the performance of two stochastic search algorithms with high confidence. We initially use traditional approximation ratio as the fitness function of (1+1)~EA to evolve instances, which shows inadequacy to generate reliable instances. To address this issue, we introduce a new measure to calculate the performance difference for two algorithms, which considers variances of performance ratios. Our experiments show that our approach is highly successful in solving the instability issue of the performance ratios and leads to evolving reliable sets of chance constraints with significantly different performance for various types of algorithms.

Automated Federated Learning via Informed Pruning

Federated learning (FL) represents a pivotal shift in machine learning (ML) as it enables collaborative training of local ML models coordinated by a central aggregator, all without the need to exchange local data. However, its application on edge devices is hindered by limited computational capabilities and data communication challenges, compounded by the inherent complexity of Deep Learning (DL) models. Model pruning is identified as a key technique for compressing DL models on devices with limited resources. Nonetheless, conventional pruning techniques typically rely on manually crafted heuristics and demand human expertise to achieve a balance between model size, speed, and accuracy, often resulting in sub-optimal solutions. In this study, we introduce an automated federated learning approach utilizing informed pruning, called AutoFLIP, which dynamically prunes and compresses DL models within both the local clients and the global server. It leverages a federated loss exploration phase to investigate model gradient behavior across diverse datasets and losses, providing insights into parameter significance. Our experiments showcase notable enhancements in scenarios with strong non-IID data, underscoring AutoFLIP's capacity to tackle computational constraints and achieve superior global convergence.

Avoiding Redundant Restarts in Multimodal Global Optimization

Na\"ive restarts of global optimization solvers when operating on multimodal search landscapes may resemble the Coupon's Collector Problem, with a potential to waste significant function evaluations budget on revisiting the same basins of attractions. In this paper, we assess the degree to which such ``duplicate restarts'' occur on standard multimodal benchmark functions, which defines the \textit{redundancy potential} of each particular landscape. We then propose a repelling mechanism to avoid such wasted restarts with the CMA-ES and investigate its efficacy on test cases with high redundancy potential compared to the standard restart mechanism.

Empirical Analysis of the Dynamic Binary Value Problem with IOHprofiler

Optimization problems in dynamic environments have recently been the source of several theoretical studies. One of these problems is the monotonic Dynamic Binary Value problem, which theoretically has high discriminatory power between different Genetic Algorithms. Given this theoretical foundation, we integrate several versions of this problem into the IOHprofiler benchmarking framework. Using this integration, we perform several large-scale benchmarking experiments to both recreate theoretical results on moderate dimensional problems and investigate aspects of GA's performance which have not yet been studied theoretically. Our results highlight some of the many synergies between theory and benchmarking and offer a platform through which further research into dynamic optimization problems can be performed.