Existing global optimization benchmark suites are of a moderate size and are based on a small number of analytical functions that date back even to the 1970s. This causes a risk of biasing the development of global optimization methods. We argue that the tasks related to the black-box adversarial attack (BBAA) can serve as valuable global optimization benchmark in many-dimensional space. We demonstrate the efficiency of several types of evolutionary algorithms and other metaheuristics in solving example BBAA problems. Thus, we take a step towards convergence of global optimization methods to the challenges and needs that arise in the modern machine learning field.
Consensus-based optimization (CBO) has established itself as an efficient gradient-free optimization scheme, with attractive mathematical properties, such as mean-field convergence results for non-convex loss functions. In this work, we study CBO in the context of closed-box adversarial attacks, which are imperceptible input perturbations that aim to fool a classifier, without accessing its gradient. Our contribution is to establish a connection between the so-called consensus hopping as introduced by Riedl et al. and natural evolution strategies (NES) commonly applied in the context of adversarial attacks and to rigorously relate both methods to gradient-based optimization schemes. Beyond that, we provide a comprehensive experimental study that shows that despite the conceptual similarities, CBO can outperform NES and other evolutionary strategies in certain scenarios.
Optimization benchmarks play a fundamental role in assessing algorithm performance; however, existing artificial benchmarks often fail to capture the diversity and irregularity of real-world problem structures, while benchmarks derived from real-world problems are costly and difficult to construct. To address these challenges, we propose an evolutionary automatic benchmark generation framework that leverages a large language model (LLM) as a generative operator, termed the LLM-driven evolutionary benchmark generator (LLM-EBG). In this framework, the LLM serves as an evolutionary operator that generates and evolves benchmark problems within a flexible, expressive representation space. As a case study, we generate unconstrained single-objective continuous minimization problems represented as mathematical expressions designed to induce significant performance differences between a genetic algorithm (GA) and differential evolution (DE). Experimental results show that LLM-EBG successfully produces benchmark problems in which the designated target algorithm consistently outperforms the comparative algorithm in more than 80% of trials. Furthermore, exploratory landscape analysis reveals that benchmarks favoring GA are highly sensitive to variable scaling, demonstrating that the proposed framework can generate problems with distinct geometric characteristics that reflect the intrinsic search behaviors of different optimization algorithms.
Probabilistic smoothing is a standard tool for global optimization, but existing methods rely on Gaussian kernels and specific transforms, often resulting in strong hyperparameter sensitivity and limited robustness. We propose a general smoothing framework that combines flexible symmetric unimodal kernels with monotonic ratio-based transformations. Under mild conditions, we show that the smoothed objective preserves the global maximizer and that all stationary points concentrate near the true optimum for sufficiently large amplification, without requiring a decreasing smoothing schedule. We further provide explicit complexity bounds for stochastic gradient ascent and show that a leave-one-out baseline provably reduces variance. Experiments on high-dimensional benchmarks and black-box adversarial attacks demonstrate improved robustness and competitive performance.