Exploratory landscape analysis and fitness landscape analysis in general have given valuable insight into problem hardness understanding as well as facilitating algorithm design and endeavors such as automated algorithm selection and configuration. These techniques have largely been limited to search spaces of a single domain. In this work, we provide the means to compute exploratory landscape features for mixed-variable problems where the decision space is a mixture of continuous, binary, integer, and categorical variables. This is achieved by introducing a preprocessing scheme which needs to be incorporated into the process of exploratory landscape analysis feature generation. To highlight the merit of our approach for practical applications, we design and conduct an automated algorithm selection study based on a hyperparameter optimization benchmark suite and our preprocessing scheme. Our trained algorithm selector is able to close the gap between the single best and the virtual best solver by 57.5% over all benchmark problems.

The herein proposed Python package pflacco provides a set of numerical features to characterize single-objective continuous and constrained optimization problems. Thereby, pflacco addresses two major challenges in the area optimization. Firstly, it provides the means to develop an understanding of a given problem instance, which is crucial for designing, selecting, or configuring optimization algorithms in general. Secondly, these numerical features can be utilized in the research streams of automated algorithm selection and configuration. While the majority of these landscape features is already available in the R package flacco, our Python implementation offers these tools to an even wider audience and thereby promotes research interests and novel avenues in the area of optimization.

Exploratory landscape analysis (ELA) is a well-established tool to characterize optimization problems via numerical features. ELA is used for problem comprehension, algorithm design, and applications such as automated algorithm selection and configuration. Until recently, however, ELA was limited to search spaces with either continuous or discrete variables, neglecting problems with mixed variable types. This gap was addressed in a recent study that uses an approach based on target-encoding to compute exploratory landscape features for mixedvariable problems. In this work, we investigate an alternative encoding scheme based on SHAP values. While these features do not lead to better results in the algorithm selection setting considered in previous work, the two different encoding mechanisms exhibit complementary performance. Combining both feature sets into a hybrid approach outperforms each encoding mechanism individually. Finally, we experiment with two different ways of meta-selecting between the two feature sets. Both approaches are capable of taking advantage of the performance complementarity of the models trained on target-encoded and SHAP-encoded feature sets, respectively.

Artificial benchmark functions are commonly used in optimization research because of their ability to rapidly evaluate potential solutions, making them a preferred substitute for real-world problems. However, these benchmark functions have faced criticism for their limited resemblance to real-world problems. In response, recent research has focused on automatically generating new benchmark functions for areas where established test suites are inadequate. These approaches have limitations, such as the difficulty of generating new benchmark functions that exhibit exploratory landscape analysis (ELA) features beyond those of existing benchmarks. The objective of this work is to develop a method for generating benchmark functions for single-objective continuous optimization with user-specified structural properties. Specifically, we aim to demonstrate a proof of concept for a method that uses an ELA feature vector to specify these properties in advance. To achieve this, we begin by generating a random sample of decision space variables and objective values. We then adjust the objective values using CMA-ES until the corresponding features of our new problem match the predefined ELA features within a specified threshold. By iteratively transforming the landscape in this way, we ensure that the resulting function exhibits the desired properties. To create the final function, we use the resulting point cloud as training data for a simple neural network that produces a function exhibiting the target ELA features. We demonstrate the effectiveness of this approach by replicating the existing functions of the well-known BBOB suite and creating new functions with ELA feature values that are not present in BBOB.

Optimization is ubiquitous in our daily lives. In the past, (sub-)optimal solutions to any problem have been derived by trial and error, sheer luck, or the expertise of knowledgeable individuals. In our contemporary age, there thankfully exists a plethora of different algorithms that can find solutions more reliably than ever before. Yet, choosing an appropriate algorithm for any given problem is challenging in itself. The field of automated algorithm selection provides various approaches to tackle this latest problem. This is done by delegating the selection of a suitable algorithm for a given problem to a complex computer model. This computer model is generated through the use of Artificial Intelligence. Many of these computer models rely on some sort of information about the problem to make a reasonable selection. Various methods exist to provide this informative input to the computer model in the form of numerical data. In this cumulative dissertation, I propose several improvements to the different variants of informative inputs. This in turn enhances and refines the current state-of-the-art of automated algorithm selection. Specifically, I identify and address current issues with the existing body of work to strengthen the foundation that future work builds upon. Furthermore, the rise of deep learning offers ample opportunities for automated algorithm selection. In several joint works, my colleagues and I developed and evaluated several different methods that replace the existing methods to extract an informative input. Lastly, automated algorithm selection approaches have been restricted to certain types of problems. I propose a method to extend the generation of informative inputs to other problem types and provide an outlook on further promising research directions.

Exploratory landscape analysis (ELA) in single-objective black-box optimization relies on a comprehensive and large set of numerical features characterizing problem instances. Those foster problem understanding and serve as basis for constructing automated algorithm selection models choosing the best suited algorithm for a problem at hand based on the aforementioned features computed prior to optimization. This work specifically points to the sensitivity of a substantial proportion of these features to absolute objective values, i.e., we observe a lack of shift and scale invariance. We show that this unfortunately induces bias within automated algorithm selection models, an overfitting to specific benchmark problem sets used for training and thereby hinders generalization capabilities to unseen problems. We tackle these issues by presenting an appropriate objective normalization to be used prior to ELA feature computation and empirically illustrate the respective effectiveness focusing on the BBOB benchmark set.

Exploratory landscape analysis has been at the forefront of characterizing single-objective continuous optimization problems. Other variants, which can be summarized under the term landscape analysis, have been used in the domain of combinatorial problems. However, none to little has been done in this research area for mixed-integer problems. In this work, we evaluate the current state of existing exploratory landscape analysis features and their applicability on a subset of mixed-integer problems.

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.

Exploratory Landscape Analysis is a powerful technique for numerically characterizing landscapes of single-objective continuous optimization problems. Landscape insights are crucial both for problem understanding as well as for assessing benchmark set diversity and composition. Despite the irrefutable usefulness of these features, they suffer from their own ailments and downsides. Hence, in this work we provide a collection of different approaches to characterize optimization landscapes. Similar to conventional landscape features, we require a small initial sample. However, instead of computing features based on that sample, we develop alternative representations of the original sample. These range from point clouds to 2D images and, therefore, are entirely feature-free. We demonstrate and validate our devised methods on the BBOB testbed and predict, with the help of Deep Learning, the high-level, expert-based landscape properties such as the degree of multimodality and the existence of funnel structures. The quality of our approaches is on par with methods relying on the traditional landscape features. Thereby, we provide an exciting new perspective on every research area which utilizes problem information such as problem understanding and algorithm design as well as automated algorithm configuration and selection.

In recent years, feature-based automated algorithm selection using exploratory landscape analysis has demonstrated its great potential in single-objective continuous black-box optimization. However, feature computation is problem-specific and can be costly in terms of computational resources. This paper investigates feature-free approaches that rely on state-of-the-art deep learning techniques operating on either images or point clouds. We show that point-cloud-based strategies, in particular, are highly competitive and also substantially reduce the size of the required solver portfolio. Moreover, we highlight the effect and importance of cost-sensitive learning in automated algorithm selection models.

We propose a novel method for automated algorithm selection in the domain of single-objective continuous black-box optimization. In contrast to existing methods, we use convolutional neural networks as the selection apparatus which bases its decision on a so-called ‘fitness map’. This fitness map is a 2D representation of a two dimensional search space where different gray scales indicate the quality of found solutions in certain areas. Our devised approach uses a modular CMA-ES framework which offers the option to create the conventional CMA-ES, CMA-ES with the alternate step-size adaptation and many other variants proposed over the years. In total, 4 608 different configurations are possible where most configurations are of complementary nature. In this proof-of-concept work, we consider a subset of 32 possible configurations. The developed method is evaluated against an excerpt of BBOB functions and its performance is compared against baselines that are commonly used in automated algorithm selection - the best standalone algorithm (configuration) and the best obtainable sequence of configurations. While the results indicate that the use of the fitness map is not superior on every benchmark problem, it indubitably shows its merit on more hard-to-solve problems. This offers a promising perspective for generalizing to other types of optimization problems and problem domains.

In this paper, we rely on previous work proposing a modularized version of CMA-ES, which captures several alterations to the conventional CMA-ES developed in recent years. Each alteration provides significant advantages under certain problem properties, e.g., multi-modality, high conditioning. These distinct advancements are implemented as modules which result in 4608 unique versions of CMA-ES. Previous findings illustrate the competitive advantage of enabling and disabling the aforementioned modules for different optimization problems. Yet, this modular CMA-ES is lacking a method to automatically determine when the activation of specific modules is auspicious and when it is not. We propose a well-performing instance-specific algorithm configuration model which selects an (almost) optimal configuration of modules for a given problem instance. In addition, the structure of this configuration model is able to capture inter-dependencies between modules, e.g., two (or more) modules might only be advantageous in unison for some problem types, making the orchestration of modules a crucial task. This is accomplished by chaining multiple random forest classifiers together into a so-called Classifier Chain based on a set of numerical features extracted by means of Exploratory Landscape Analysis (ELA) to describe the given problem instances.

Procedural Content Generation of game content has been vastly improved over the last years and is more and more adopted also in the game industry. It relies mostly on evolutionary and related optimization methods but usually only treats a single of the many available facets as visuals, levels, audio, etc. The problem of how to combine several facets of generation is largely unsolved, but nevertheless very important. One of its subproblems is that we currently do not know in advance how users will react to machine-generated combinations. Based on a simple maze game with exchangeable visuals and audio styles we test how users receive ‘usual’ and ‘unusual’ facet compositions by means of rank trace based annotations of their own play-throughs. By means of machine learning techniques, we establish a model in order to learn and predict user reactions. Understanding the effects of facet composition on the user is fundamental if we want to rise evolutionary generation of content to the next level.