Large language models (LLMs) show potential for multi-interest analysis of users in recommender systems, going beyond heuristic assumptions in existing methods, e.g., co-occurring items indicate the same interest. Despite the effectiveness, two key challenges remain. First, the granularity of raw generation of LLMs for multi-interests is agnostic, possibly leading to overly fine or coarse interest grouping. Second, adopting LLM to analyze individual user behaviors lacks a global perspective on how items relate across users. In this paper, we propose an LLM-driven adaptive and representative multi-interest modeling framework to address these challenges. At the user-individual level, we exploit LLM analysis and alleviate the agnostic granularity by adaptively aggregating semantic clusters to collaborative multi-interests. At the user-crowd level, to mitigate the limited insights in individual behaviors, we formulate a max covering problem to expand the scope of LLM analysis with compactness and representativeness, disentangling interest representations from global perspectives. Experiments on real-world datasets show that our approach outperforms various baselines.

Mixed-integer programming (MIP) lies at the core of operations research and industrial optimization. While large language models (LLMs) have recently shown promise in automated MIP modeling from natural language, they prioritize semantic correctness but overlook formulation strength, severely bottlenecking the efficiency of downstream solvers. We propose FormuEvo, an LLM-guided evolutionary framework for automated discovery of solver-efficient MIP formulations. FormuEvo frames MIP formulation design as evolutionary optimization over the symbolic space of MIP formulations, represented as executable modeling programs, by iteratively generating, evaluating, and selecting stronger candidates via LLM-driven crossover, mutation, and repair operations. To move beyond blind exploration, FormuEvo introduces a solver-informed diagnosis mechanism that exploits fine-grained solver statistics as verbal gradients for targeted refinement. Additionally, a structured memory abstracts prior experience into reusable modeling strategies, avoiding redundant exploration while enabling zero-shot transfer to unseen problems and bootstrapping smaller LLMs. Experiments across diverse linear and non-linear problems demonstrate that FormuEvo discovers formulations that significantly outperform both expert-designed formulations and existing LLM-based approaches, accelerating solvers by up to 5.5×, with distilled knowledge transferring effectively across problems and model scales.