In many recent works, the potential of Exploratory Landscape Analysis (ELA) features to numerically characterize, in particular, single-objective continuous optimization problems has been demonstrated. These numerical features provide the input for all kinds of machine learning tasks on continuous optimization problems, ranging, i.a., from High-level Property Prediction to Automated Algorithm Selection and Automated Algorithm Configuration. Without ELA features, analyzing and understanding the characteristics of single-objective continuous optimization problems would be impossible. Yet, despite their undisputed usefulness, ELA features suffer from several drawbacks. These include, in particular, (1.) a strong correlation between multiple features, as well as (2.) its very limited applicability to multi-objective continuous optimization problems. As a remedy, recent works proposed deep learning-based approaches as alternatives to ELA. In these works, e.g., point-cloud transformers were used to characterize an optimization problem's fitness landscape. However, these approaches require a large amount of labeled training data. Within this work, we propose a hybrid approach, Deep-ELA, which combines (the benefits of) deep learning and ELA features. Specifically, we pre-trained four transformers on millions of randomly generated optimization problems to learn deep representations of the landscapes of continuous single- and multi-objective optimization problems. Our proposed framework can either be used out-of-the-box for analyzing single- and multi-objective continuous optimization problems, or subsequently fine-tuned to various tasks focussing on algorithm behavior and problem understanding.

Hyperparameter optimization (HPO) is a key component of machine learning models for achieving peak predictive performance. While numerous methods and algorithms for HPO have been proposed over the last years, little progress has been made in illuminating and examining the actual structure of these black-box optimization problems. Exploratory landscape analysis (ELA) subsumes a set of techniques that can be used to gain knowledge about properties of unknown optimization problems. In this paper, we evaluate the performance of five different black-box optimizers on 30 HPO problems, which consist of two-, three- and five-dimensional continuous search spaces of the XGBoost learner trained on 10 different data sets. This is contrasted with the performance of the same optimizers evaluated on 360 problem instances from the black-box optimization benchmark (BBOB). We then compute ELA features on the HPO and BBOB problems and examine similarities and differences. A cluster analysis of the HPO and BBOB problems in ELA feature space allows us to identify how the HPO problems compare to the BBOB problems on a structural meta-level. We identify a subset of BBOB problems that are close to the HPO problems in ELA feature space and show that optimizer performance is comparably similar on these two sets of benchmark problems. We highlight open challenges of ELA for HPO and discuss potential directions of future research and applications.

Multimodality is one of the biggest difficulties for optimization as local optima are often preventing algorithms from making progress. This does not only challenge local strategies that can get stuck. It also hinders meta-heuristics like evolutionary algorithms in convergence to the global optimum. In this paper we present a new concept of gradient descent, which is able to escape local traps. It relies on multiobjectivization of the original problem and applies the recently proposed and here slightly modified multi-objective local search mechanism MOGSA. We use a sophisticated visualization technique for multi-objective problems to prove the working principle of our idea. As such, this work highlights the transfer of new insights from the multi-objective to the single-objective domain and provides first visual evidence that multiobjectivization can link single-objective local optima in multimodal landscapes.

The Traveling Salesperson Problem (TSP) is a classical N P-hard optimization problem of utmost relevance, e.g., in transportation logistics, bioinformatics or circuit board fabrication. The goal is to route a salesperson through a set of cities such that each city is visited exactly once and the tour is of minimal length. In the past decades tremendous progress has been made in the development of high-performing heuristic TSP solvers. The local search-based Lin-Kernigham Heuristic (LKH) [14] and the genetic algorithm Edge-Assembly-Crossover (EAX) [35], along with their respective restart versions introduced in Kotthoff et al. [25], undeniably pose the state-of-the-art in inexact TSP solving. Automated Algorithm Selection (AS), originally proposed by Rice [39] back in 1976, is a powerful framework to predict the best-performing solver(s) from a portfolio of candidate solvers by means of machine learning. It has been successfully applied to a wide spectrum of challenging optimization problems in both the combinatorial [24, 29, 30, 40, 48] and continuous domain [21, 4] with partly astonishing performance gains - see the recent survey by Kerschke et al. [19] for a comprehensive overview. In particular, the TSP was subject to several successful ASstudies [25, 20, 33, 34, 37] which exploited the complementary performance profiles of simple heuristics on the one hand and the state-of-the-art solvers LKH and EAX on classical TSP benchmark sets on the other hand.

Routing of multiple vehicles is an important and difficult problem with applications in the logistic domain [1], especially in the area of customer servicing [2]. In postal services, after-sales services, and in business to business delivery or pick up services one or more vehicles have to be efficiently routed towards customers. If customers can request services over time, the problem becomes dynamic: besides a set of fixed customers, new requests can appear at any point in time. Of course, it is desirable that as many customers as possible are serviced while the tour of any vehicle is kept short. However, it is usually infeasible (due to human resources, labor regulations, or other constraints) to service all customer requests. And clearly, the less customers are left unserviced, the longer the tours become. Thus, the problem is inherently multi-objective. Any efficient solution (smallest maximum tour across all vehicles) is a compromise between the desire to service as many customers as possible (e.g.

The Traveling-Salesperson-Problem (TSP) is arguably one of the best-known NP-hard combinatorial optimization problems. The two sophisticated heuristic solvers LKH and EAX and respective (restart) variants manage to calculate close-to optimal or even optimal solutions, also for large instances with several thousand nodes in reasonable time. In this work we extend existing benchmarking studies by addressing anytime behaviour of inexact TSP solvers based on empirical runtime distributions leading to an increased understanding of solver behaviour and the respective relation to problem hardness. It turns out that performance ranking of solvers is highly dependent on the focused approximation quality. Insights on intersection points of performances offer huge potential for the construction of hybridized solvers depending on instance features. Moreover, instance features tailored to anytime performance and corresponding performance indicators will highly improve automated algorithm selection models by including comprehensive information on solver quality.

Artificial neural networks in general and deep learning networks in particular established themselves as popular and powerful machine learning algorithms. While the often tremendous sizes of these networks are beneficial when solving complex tasks, the tremendous number of parameters also causes such networks to be vulnerable to malicious behavior such as adversarial perturbations. These perturbations can change a model's classification decision. Moreover, while single-step adversaries can easily be transferred from network to network, the transfer of more powerful multi-step adversaries has - usually -- been rather difficult. In this work, we introduce a method for generating strong ad-versaries that can easily (and frequently) be transferred between different models. This method is then used to generate a large set of adversaries, based on which the effects of selected defense methods are experimentally assessed. At last, we introduce a novel, simple, yet effective approach to enhance the resilience of neural networks against adversaries and benchmark it against established defense methods. In contrast to the already existing methods, our proposed defense approach is much more efficient as it only requires a single additional forward-pass to achieve comparable performance results.

The detection of orchestrated and potentially manipulative campaigns in social media is far more meaningful than analyzing single account behaviour but also more challenging in terms of pattern recognition, data processing, and computational complexity. While supervised learning methods need an enormous amount of reliable ground truth data to find rather inflexible patterns, classical unsupervised learning techniques need a lot of computational power to handle large amount of data. This makes them infeasible for real-time analysis. In this work, we demonstrate the applicability of text stream clustering for the real-time detection of coordinated campaigns.

It has long been observed that for practically any computational problem that has been intensely studied, different instances are best solved using different algorithms. This is particularly pronounced for computationally hard problems, where in most cases, no single algorithm defines the state of the art; instead, there is a set of algorithms with complementary strengths. This performance complementarity can be exploited in various ways, one of which is based on the idea of selecting, from a set of given algorithms, for each problem instance to be solved the one expected to perform best. The task of automatically selecting an algorithm from a given set is known as the per-instance algorithm selection problem and has been intensely studied over the past 15 years, leading to major improvements in the state of the art in solving a growing number of discrete combinatorial problems, including propositional satisfiability and AI planning. Per-instance algorithm selection also shows much promise for boosting performance in solving continuous and mixed discrete/continuous optimisation problems. This survey provides an overview of research in automated algorithm selection, ranging from early and seminal works to recent and promising application areas. Different from earlier work, it covers applications to discrete and continuous problems, and discusses algorithm selection in context with conceptually related approaches, such as algorithm configuration, scheduling or portfolio selection. Since informative and cheaply computable problem instance features provide the basis for effective per-instance algorithm selection systems, we also provide an overview of such features for discrete and continuous problems. Finally, we provide perspectives on future work in the area and discuss a number of open research challenges.

In this paper, we build upon previous work on designing informative and efficient Exploratory Landscape Analysis features for characterizing problems' landscapes and show their effectiveness in automatically constructing algorithm selection models in continuous black-box optimization problems. Focussing on algorithm performance results of the COCO platform of several years, we construct a representative set of high-performing complementary solvers and present an algorithm selection model that manages to outperform the single best solver out of the portfolio by factor two. Acting on the assumption that the function set of the Black-Box Optimization Benchmark is representative enough for practical applications the model allows for selecting the best suited optimization algorithm within the considered set for unseen problems prior to the optimization itself based on a small sample of function evaluations. Note that such a sample can even be reused for the initial algorithm population so that feature costs become negligible.