Optimization is Not Enough: Why Problem Formulation Deserves Equal Attention

Black-box optimization is increasingly used in engineering design problems where simulation-based evaluations are costly and gradients are unavailable. In this context, the optimization community has largely analyzed algorithm performance in context-free setups, while not enough attention has been devoted to how problem formulation and domain knowledge may affect the optimization outcomes. We address this gap through a case study in the topology optimization of laminated composite structures, formulated as a black-box optimization problem. Specifically, we consider the design of a cantilever beam under a volume constraint, intending to minimize compliance while optimizing both the structural topology and fiber orientations. To assess the impact of problem formulation, we explicitly separate topology and material design variables and compare two strategies: a concurrent approach that optimizes all variables simultaneously without leveraging physical insight, and a sequential approach that optimizes variables of the same nature in stages. Our results show that context-agnostic strategies consistently lead to suboptimal or non-physical designs. In contrast, the sequential strategy yields better-performing and more interpretable solutions. These findings underscore the value of incorporating, when available, domain knowledge into the optimization process and motivate the development of new black-box benchmarks that reward physically informed and context-aware optimization strategies.

Landscape-aware Automated Algorithm Design: An Efficient Framework for Real-world Optimization

The advent of Large Language Models (LLMs) has opened new frontiers in automated algorithm design, giving rise to numerous powerful methods. However, these approaches retain critical limitations: they require extensive evaluation of the target problem to guide the search process, making them impractical for real-world optimization tasks, where each evaluation consumes substantial computational resources. This research proposes an innovative and efficient framework that decouples algorithm discovery from high-cost evaluation. Our core innovation lies in combining a Genetic Programming (GP) function generator with an LLM-driven evolutionary algorithm designer. The evolutionary direction of the GP-based function generator is guided by the similarity between the landscape characteristics of generated proxy functions and those of real-world problems, ensuring that algorithms discovered via proxy functions exhibit comparable performance on real-world problems. Our method enables deep exploration of the algorithmic space before final validation while avoiding costly real-world evaluations. We validated the framework's efficacy across multiple real-world problems, demonstrating its ability to discover high-performance algorithms while substantially reducing expensive evaluations. This approach shows a path to apply LLM-based automated algorithm design to computationally intensive real-world optimization challenges.

LLaMEA-SAGE: Guiding Automated Algorithm Design with Structural Feedback from Explainable AI

Large language models have enabled automated algorithm design (AAD) by generating optimization algorithms directly from natural-language prompts. While evolutionary frameworks such as LLaMEA demonstrate strong exploratory capabilities across the algorithm design space, their search dynamics are entirely driven by fitness feedback, leaving substantial information about the generated code unused. We propose a mechanism for guiding AAD using feedback constructed from graph-theoretic and complexity features extracted from the abstract syntax trees of the generated algorithms, based on a surrogate model learned over an archive of evaluated solutions. Using explainable AI techniques, we identify features that substantially affect performance and translate them into natural-language mutation instructions that steer subsequent LLM-based code generation without restricting expressivity. We propose LLaMEA-SAGE, which integrates this feature-driven guidance into LLaMEA, and evaluate it across several benchmarks. We show that the proposed structured guidance achieves the same performance faster than vanilla LLaMEA in a small controlled experiment. In a larger-scale experiment using the MA-BBOB suite from the GECCO-MA-BBOB competition, our guided approach achieves superior performance compared to state-of-the-art AAD methods. These results demonstrate that signals derived from code can effectively bias LLM-driven algorithm evolution, bridging the gap between code structure and human-understandable performance feedback in automated algorithm design.

Investigating the Interplay of Parameterization and Optimizer in Gradient-Free Topology Optimization: A Cantilever Beam Case Study

Gradient-free black-box optimization (BBO) is widely used in engineering design and provides a flexible framework for topology optimization (TO), enabling the discovery of high-performing structural designs without requiring gradient information from simulations. Yet, its success depends on two key choices: the geometric parameterization defining the search space and the optimizer exploring it. This study investigates this interplay through a compliance minimization problem for a cantilever beam subject to a connectivity constraint. We benchmark three geometric parameterizations, each combined with three representative BBO algorithms: differential evolution, covariance matrix adaptation evolution strategy, and heteroscedastic evolutionary Bayesian optimization, across 10D, 20D, and 50D design spaces. Results reveal that parameterization quality has a stronger influence on optimization performance than optimizer choice: a well-structured parameterization enables robust and competitive performance across algorithms, whereas weaker representations increase optimizer dependency. Overall, this study highlights the dominant role of geometric parameterization in practical BBO-based TO and shows that algorithm performance and selection cannot be fairly assessed without accounting for the induced design space.

LLM Driven Design of Continuous Optimization Problems with Controllable High-level Properties

Benchmarking in continuous black-box optimisation is hindered by the limited structural diversity of existing test suites such as BBOB. We explore whether large language models embedded in an evolutionary loop can be used to design optimisation problems with clearly defined high-level landscape characteristics. Using the LLaMEA framework, we guide an LLM to generate problem code from natural-language descriptions of target properties, including multimodality, separability, basin-size homogeneity, search-space homogeneity and globallocal optima contrast. Inside the loop we score candidates through ELA-based property predictors. We introduce an ELA-space fitness-sharing mechanism that increases population diversity and steers the generator away from redundant landscapes. A complementary basin-of-attraction analysis, statistical testing and visual inspection, verifies that many of the generated functions indeed exhibit the intended structural traits. In addition, a t-SNE embedding shows that they expand the BBOB instance space rather than forming an unrelated cluster. The resulting library provides a broad, interpretable, and reproducible set of benchmark problems for landscape analysis and downstream tasks such as automated algorithm selection.

How does downsampling affect needle electromyography signals? A generalisable workflow for understanding downsampling effects on high-frequency time series

Automated analysis of needle electromyography (nEMG) signals is emerging as a tool to support the detection of neuromuscular diseases (NMDs), yet the signals' high and heterogeneous sampling rates pose substantial computational challenges for feature-based machine-learning models, particularly for near real-time analysis. Downsampling offers a potential solution, but its impact on diagnostic signal content and classification performance remains insufficiently understood. This study presents a workflow for systematically evaluating information loss caused by downsampling in high-frequency time series. The workflow combines shape-based distortion metrics with classification outcomes from available feature-based machine learning models and feature space analysis to quantify how different downsampling algorithms and factors affect both waveform integrity and predictive performance. We use a three-class NMD classification task to experimentally evaluate the workflow. We demonstrate how the workflow identifies downsampling configurations that preserve diagnostic information while substantially reducing computational load. Analysis of shape-based distortion metrics showed that shape-aware downsampling algorithms outperform standard decimation, as they better preserve peak structure and overall signal morphology. The results provide practical guidance for selecting downsampling configurations that enable near real-time nEMG analysis and highlight a generalisable workflow that can be used to balance data reduction with model performance in other high-frequency time-series applications as well.

Adversarial Instance Generation and Robust Training for Neural Combinatorial Optimization with Multiple Objectives

Deep reinforcement learning (DRL) has shown great promise in addressing multi-objective combinatorial optimization problems (MOCOPs). Nevertheless, the robustness of these learning-based solvers has remained insufficiently explored, especially across diverse and complex problem distributions. In this paper, we propose a unified robustness-oriented framework for preference-conditioned DRL solvers for MOCOPs. Within this framework, we develop a preference-based adversarial attack to generate hard instances that expose solver weaknesses, and quantify the attack impact by the resulting degradation on Pareto-front quality. We further introduce a defense strategy that integrates hardness-aware preference selection into adversarial training to reduce overfitting to restricted preference regions and improve out-of-distribution performance. The experimental results on multi-objective traveling salesman problem (MOTSP), multi-objective capacitated vehicle routing problem (MOCVRP), and multi-objective knapsack problem (MOKP) verify that our attack method successfully learns hard instances for different solvers. Furthermore, our defense method significantly strengthens the robustness and generalizability of neural solvers, delivering superior performance on hard or out-of-distribution instances.

Center-Outward q-Dominance: A Sample-Computable Proxy for Strong Stochastic Dominance in Multi-Objective Optimisation

Stochastic multi-objective optimization (SMOOP) requires ranking multivariate distributions; yet, most empirical studies perform scalarization, which loses information and is unreliable. Based on the optimal transport theory, we introduce the center-outward q-dominance relation and prove it implies strong first-order stochastic dominance (FSD). Also, we develop an empirical test procedure based on q-dominance, and derive an explicit sample size threshold, $n^*(δ)$, to control the Type I error. We verify the usefulness of our approach in two scenarios: (1) as a ranking method in hyperparameter tuning; (2) as a selection method in multi-objective optimization algorithms. For the former, we analyze the final stochastic Pareto sets of seven multi-objective hyperparameter tuners on the YAHPO-MO benchmark tasks with q-dominance, which allows us to compare these tuners when the expected hypervolume indicator (HVI, the most common performance metric) of the Pareto sets becomes indistinguishable. For the latter, we replace the mean value-based selection in the NSGA-II algorithm with $q$-dominance, which shows a superior convergence rate on noise-augmented ZDT benchmark problems. These results establish center-outward q-dominance as a principled, tractable foundation for seeking truly stochastically dominant solutions for SMOOPs.

Benchmarking that Matters: Rethinking Benchmarking for Practical Impact

Benchmarking has driven scientific progress in Evolutionary Computation, yet current practices fall short of real-world needs. Widely used synthetic suites such as BBOB and CEC isolate algorithmic phenomena but poorly reflect the structure, constraints, and information limitations of continuous and mixed-integer optimization problems in practice. This disconnect leads to the misuse of benchmarking suites for competitions, automated algorithm selection, and industrial decision-making, despite these suites being designed for different purposes. We identify key gaps in current benchmarking practices and tooling, including limited availability of real-world-inspired problems, missing high-level features, and challenges in multi-objective and noisy settings. We propose a vision centered on curated real-world-inspired benchmarks, practitioner-accessible feature spaces and community-maintained performance databases. Real progress requires coordinated effort: A living benchmarking ecosystem that evolves with real-world insights and supports both scientific understanding and industrial use.

MECHBench: A Set of Black-Box Optimization Benchmarks originated from Structural Mechanics

Benchmarking is essential for developing and evaluating black-box optimization algorithms, providing a structured means to analyze their search behavior. Its effectiveness relies on carefully selected problem sets used for evaluation. To date, most established benchmark suites for black-box optimization consist of abstract or synthetic problems that only partially capture the complexities of real-world engineering applications, thereby severely limiting the insights that can be gained for application-oriented optimization scenarios and reducing their practical impact. To close this gap, we propose a new benchmarking suite that addresses it by presenting a curated set of optimization benchmarks rooted in structural mechanics. The current implemented benchmarks are derived from vehicle crashworthiness scenarios, which inherently require the use of gradient-free algorithms due to the non-smooth, highly non-linear nature of the underlying models. Within this paper, the reader will find descriptions of the physical context of each case, the corresponding optimization problem formulations, and clear guidelines on how to employ the suite.