Qi Huang, Furong Ye, Ananta Shahane, Thomas Bäck, Niki van Stein
Large Language Models (LLMs) have already been widely adopted for automated algorithm design, demonstrating strong abilities in generating and evolving algorithms across various fields. Existing work has largely focused on examining their effectiveness in solving specific problems, with search strategies primarily guided by adaptive prompt designs. In this paper, through investigating the token-wise attribution of the prompts to LLM-generated algorithmic code, we show that the embedded code examples and their associated strategy instructions have the strongest influence on the generated algorithms. Building upon this insight, we propose leveraging existing benchmark algorithms as strong priors to guide LLM-driven optimization. We evaluate this approach with three LLMs on two black-box optimization benchmarks: the pseudo-Boolean optimization suite (pbo) and the black-box optimization suite (bbob). Despite relying on a simple (1+1) elitist search, it obtains the best average rank in five of six benchmark--LLM settings against six state-of-the-art LLM-driven methods, including more sophisticated search strategies. Our findings highlight the value of integrating benchmarking studies to enhance both efficiency and robustness of the LLM-driven black-box optimization methods.
Zhong Li, Qi Huang, Yuxuan Zhu, Mohammad Mohammadi Amiri, Niki van Stein, Thomas Bäck, Matthijs van Leeuwen, Zaiwen Wen 等 9 位作者
Optimization modeling translates real decision-making problems into mathematical optimization models and solver-executable implementations. Although language models are increasingly used to generate optimization formulations and solver code, existing benchmarks for this capability are almost entirely text-only. This omits many optimization-modeling tasks that arise in operational practice, where requirements are described in text but essential instance information is often conveyed through visual artifacts such as tables, graphs, maps, schedules, and planning dashboards. We introduce multimodal optimization modeling, a benchmark setting where models must construct both a mathematical formulation and executable solver code from a text-and-visual problem specification. To evaluate this setting, we develop a solver-grounded framework that generates structured optimization instances, verifies each instance with an exact solver, and builds both model-facing inputs and hidden reference files from the same verified source. We instantiate it as MM-OptBench, a benchmark of 780 solver-verified instances spanning 6 optimization families, 26 subcategories, and 3 structural difficulty levels. We evaluate 9 multimodal large language models (MLLMs), including 6 frontier general-purpose and 3 math-specialized models, with aggregate, family-level, difficulty-level, and failure-mode analyses. The task remains far from solved: the best two models reach 52.1% and 51.3% pass@1, while on average across the six general-purpose MLLMs, pass@1 is 43.4% on easy and 15.9% on hard instances. All three math-specialized MLLMs solve 0/780 instances. Post-hoc extraction diagnostics and oracle-reading evaluation reveal difficulties in both multimodal grounding and downstream solver-artifact generation. MM-OptBench provides a concrete testbed for solver-grounded, decision-oriented multimodal intelligence.
Lincen Yang, Qi Huang, Niki van Stein, Thomas Bäck, Matthijs van Leeuwen, Zhong Li
Subgroup discovery aims to identify regions of the feature space where a target variable deviates from its marginal distribution. A fundamental challenge in this problem is the trade-off between a subgroup's deviation and its support: small subgroups can be highly deviating but statistically meaningless, while large ones cannot deviate much by construction. Existing methods tackle this challenge by collapsing the two into a single scalar quality measure, implicitly committing to one particular trade-off and making it difficult to recover the most deviating subgroup under a user-specified support constraint. We instead provide the first theoretical and structural characterization of optimal subgroups with maximum Kullback-Leibler (KL) divergence under arbitrary support constraints. Under a partition-based generative model, where the feature space decomposes into regions of homogeneous conditional distributions of the target variable called atoms, we prove that every point on the deviation-support Pareto front is a union of whole atoms together with at most one fractional atom. This reduces an uncountable search to a finite combinatorial problem. Guided by this theory, we propose a simple two-step recipe: learn a homogeneous partition, then select atoms greedily. Across 19 benchmark datasets, it finds the most deviating subgroups at a range of support thresholds, and reliably improves subgroups returned by existing methods when applied as a post-processing step. These results empirically validate the sufficiency and necessity of our theoretical contributions.