Automated algorithm performance prediction in numerical blackbox optimization often relies on problem characterizations, such as exploratory landscape analysis features. These features are typically used as inputs to machine learning models and are represented in a tabular format. However, such approaches often overlook algorithm configurations, a key factor influencing performance. The relationships between algorithm operators, parameters, problem characteristics, and performance outcomes form a complex structure best represented as a graph. This work explores the use of heterogeneous graph data structures and graph neural networks to predict the performance of optimization algorithms by capturing the complex dependencies between problems, algorithm configurations, and performance outcomes. We focus on two modular frameworks, modCMA-ES and modDE, which decompose two widely used derivative-free optimization algorithms: the covariance matrix adaptation evolution strategy (CMA-ES) and differential evolution (DE). We evaluate 324 modCMA-ES and 576 modDE variants on 24 BBOB problems across six runtime budgets and two problem dimensions. Achieving up to 36.6% improvement in MSE over traditional tabular-based methods, this work highlights the potential of geometric learning in black-box optimization.

The application of Large Language Models (LLMs) for Automated Algorithm Discovery (AAD), particularly for optimisation heuristics, is an emerging field of research. This emergence necessitates robust, standardised benchmarking practices to rigorously evaluate the capabilities and limitations of LLM-driven AAD methods and the resulting generated algorithms, especially given the opacity of their design process and known issues with existing benchmarks. To address this need, we introduce BLADE (Benchmark suite for LLM-driven Automated Design and Evolution), a modular and extensible framework specifically designed for benchmarking LLM-driven AAD methods in a continuous black-box optimisation context. BLADE integrates collections of benchmark problems (including MA-BBOB and SBOX-COST among others) with instance generators and textual descriptions aimed at capability-focused testing, such as generalisation, specialisation and information exploitation. It offers flexible experimental setup options, standardised logging for reproducibility and fair comparison, incorporates methods for analysing the AAD process (e.g., Code Evolution Graphs and various visualisation approaches) and facilitates comparison against human-designed baselines through integration with established tools like IOHanalyser and IOHexplainer. BLADE provides an `out-of-the-box' solution to systematically evaluate LLM-driven AAD approaches. The framework is demonstrated through two distinct use cases exploring mutation prompt strategies and function specialisation.

Surrogate models provide efficient alternatives to computationally demanding real-world processes but often require large datasets for effective training. A promising solution to this limitation is the transfer of pre-trained surrogate models to new tasks. Previous studies have investigated the transfer of differentiable and non-differentiable surrogate models, typically assuming an affine transformation between the source and target functions. This paper extends previous research by addressing a broader range of transformations, including linear and nonlinear variations. Specifically, we consider the combination of an unknown input warping, such as one modelled by the beta cumulative distribution function, with an unspecified affine transformation. Our approach achieves transfer learning by employing a limited number of data points from the target task to optimize these transformations, minimizing empirical loss on the transfer dataset. We validate the proposed method on the widely used Black-Box Optimization Benchmark (BBOB) testbed and a real-world transfer learning task from the automobile industry. The results underscore the significant advantages of the approach, revealing that the transferred surrogate significantly outperforms both the original surrogate and the one built from scratch using the transfer dataset, particularly in data-scarce scenarios.

The performance of automated algorithm selection (AAS) strongly depends on the portfolio of algorithms to choose from. Selecting the portfolio is a non-trivial task that requires balancing the trade-off between the higher flexibility of large portfolios with the increased complexity of the AAS task. In practice, probably the most common way to choose the algorithms for the portfolio is a greedy selection of the algorithms that perform well in some reference tasks of interest. We set out in this work to investigate alternative, data-driven portfolio selection techniques. Our proposed method creates algorithm behavior meta-representations, constructs a graph from a set of algorithms based on their meta-representation similarity, and applies a graph algorithm to select a final portfolio of diverse, representative, and non-redundant algorithms. We evaluate two distinct meta-representation techniques (SHAP and performance2vec) for selecting complementary portfolios from a total of 324 different variants of CMA-ES for the task of optimizing the BBOB single-objective problems in dimensionalities 5 and 30 with different cut-off budgets. We test two types of portfolios: one related to overall algorithm behavior and the `personalized' one (related to algorithm behavior per each problem separately). We observe that the approach built on the performance2vec-based representations favors small portfolios with negligible error in the AAS task relative to the virtual best solver from the selected portfolio, whereas the portfolios built from the SHAP-based representations gain from higher flexibility at the cost of decreased performance of the AAS. Across most considered scenarios, personalized portfolios yield comparable or slightly better performance than the classical greedy approach. They outperform the full portfolio in all scenarios.

Extending a recent suggestion to generate new instances for numerical black-box optimization benchmarking by interpolating pairs of the well-established BBOB functions from the COmparing COntinuous Optimizers (COCO) platform, we propose in this work a further generalization that allows multiple affine combinations of the original instances and arbitrarily chosen locations of the global optima. We demonstrate that the MA-BBOB generator can help fill the instance space, while overall patterns in algorithm performance are preserved. By combining the landscape features of the problems with the performance data, we pose the question of whether these features are as useful for algorithm selection as previous studies suggested. MA-BBOB is built on the publicly available IOHprofiler platform, which facilitates standardized experimentation routines, provides access to the interactive IOHanalyzer module for performance analysis and visualization, and enables comparisons with the rich and growing data collection available for the (MA-)BBOB functions.