Motivated by the potential to capitalize on the varied performance of different algorithms across sets of different problem instances, the algorithm selection (AS) task targets the automated identification of a preferred optimization algorithm to solve a particular problem instance Kotthoff [2016], Kerschke et al. [2019]. Conventionally, AS is performed by taking into account the properties of the problem instance, which are typically described in the form of a numerical vector representation, also referred to as problem landscape features. Once a problem instance is represented in a vector form, Machine Learning (ML) models can be used to capture the relation between problem landscape features and algorithm performance, and further identify the best algorithm for a problem instance. In the field of single-objective continuous optimization, the most common choice of problem landscape features used to represent problem instances are the Exploratory Landscape Analysis (ELA) [Mersmann et al., 2011] features.

The selection of the most appropriate algorithm to solve a given problem instance, known as algorithm selection, is driven by the potential to capitalize on the complementary performance of different algorithms across sets of problem instances. However, determining the optimal algorithm for an unseen problem instance has been shown to be a challenging task, which has garnered significant attention from researchers in recent years. In this survey, we conduct an overview of the key contributions to algorithm selection in the field of single-objective continuous black-box optimization. We present ongoing work in representation learning of meta-features for optimization problem instances, algorithm instances, and their interactions. We also study machine learning models for automated algorithm selection, configuration, and performance prediction. Through this analysis, we identify gaps in the state of the art, based on which we present ideas for further development of meta-feature representations.

We propose a representation of optimization problem instances using a transformer-based neural network architecture trained for the task of problem classification of the 24 problem classes from the Black-box Optimization Benchmarking (BBOB) benchmark. We show that transformer-based methods can be trained to recognize problem classes with accuracies in the range of 70\%-80\% for different problem dimensions, suggesting the possible application of transformer architectures in acquiring representations for black-box optimization problems.

In many cases, a machine learning model must learn to correctly predict a few data points with particular values of interest in a broader range of data where many target values are zero. Zero-inflated data can be found in diverse scenarios, such as lumpy and intermittent demands, power consumption for home appliances being turned on and off, impurities measurement in distillation processes, and even airport shuttle demand prediction. The presence of zeroes affects the models' learning and may result in poor performance. Furthermore, zeroes also distort the metrics used to compute the model's prediction quality. This paper showcases two real-world use cases (home appliances classification and airport shuttle demand prediction) where a hierarchical model applied in the context of zero-inflated data leads to excellent results. In particular, for home appliances classification, the weighted average of Precision, Recall, F1, and AUC ROC was increased by 27%, 34%, 49%, and 27%, respectively. Furthermore, it is estimated that the proposed approach is also four times more energy efficient than the SOTA approach against which it was compared to. Two-fold models performed best in all cases when predicting airport shuttle demand, and the difference against other models has been proven to be statistically significant.

The application of machine learning (ML) models to the analysis of optimization algorithms requires the representation of optimization problems using numerical features. These features can be used as input for ML models that are trained to select or to configure a suitable algorithm for the problem at hand. Since in pure black-box optimization information about the problem instance can only be obtained through function evaluation, a common approach is to dedicate some function evaluations for feature extraction, e.g., using random sampling. This approach has two key downsides: (1) It reduces the budget left for the actual optimization phase, and (2) it neglects valuable information that could be obtained from a problem-solver interaction. In this paper, we propose a feature extraction method that describes the trajectories of optimization algorithms using simple descriptive statistics. We evaluate the generated features for the task of classifying problem classes from the Black Box Optimization Benchmarking (BBOB) suite. We demonstrate that the proposed DynamoRep features capture enough information to identify the problem class on which the optimization algorithm is running, achieving a mean classification accuracy of 95% across all experiments.