optimization solver configuration

This work addresses the high sensitivity of constraint programming solver performance to hyperparameter configurations and the prohibitive cost of manual tuning. The authors propose a resource-aware, two-phase auto-tuning framework that, within a limited time budget, first explores promising configurations and then solves the target problem using the best identified configuration. Innovatively integrating Bayesian optimization with Hamming distance-based search within a unified framework, the approach is implemented using CPMpy. Experimental evaluation on 114 combinatorial optimization instances demonstrates that the method outperforms the default configurations on 25.4% and 38.6% of instances for the ACE and Choco solvers, respectively, significantly surpassing either search strategy in isolation.

Automated reasoning systems often struggle to adapt solving strategies to unique, challenging problem instances due to reliance on static or benchmark-dependent configuration. Method: We propose the first purely online, single-instance-driven adaptive tuning paradigm. It dynamically decomposes problems into subtasks via a divide-and-conquer structure and employs online reinforcement learning to optimize strategy selection in real time—without any historical benchmarks or offline pretraining. Feedback signals are derived solely from the current instance, and the framework integrates a SAT solver with a neural network verification module to enable closed-loop optimization. Contribution/Results: Our approach enables fully online policy evolution, discovering non-standard solving paths. Experiments demonstrate significant improvements in solving efficiency and success rates on both SAT solving and neural network formal verification tasks, validating the effectiveness and cross-task generalizability of single-instance adaptive tuning.

This work addresses the limitations of existing large language model (LLM)-driven heuristic design, which often relies solely on end-point evaluation while neglecting solution process efficiency and incurs high re-adaptation costs under distribution shifts. To overcome these issues, the authors propose DASH, a novel framework that introduces a convergence-dynamics-aware evaluation mechanism to jointly optimize search strategies and runtime scheduling. DASH further incorporates a profiled library retrieval module that enables efficient reuse across heterogeneous problem instances through solver profiling. Experimental results demonstrate that DASH achieves over a fourfold improvement in runtime efficiency across four combinatorial optimization problems and outperforms state-of-the-art methods in overall performance. Moreover, under distribution shift scenarios, DASH significantly reduces solution quality degradation and lowers LLM re-adaptation costs by approximately 90%.

Many optimization problems in manufacturing, logistics, and healthcare remain reliant on manual heuristics due to the high modeling barrier for Mixed-Integer Linear Programming (MILP). Method: This paper proposes the first end-to-end MILP automation framework driven by natural language descriptions. It introduces a modular large language model (LLM) architecture integrating natural language understanding, program synthesis, code debugging, solution quality verification, and feedback-driven iterative refinement. Additionally, it establishes NLP4LP—the first long-horizon, complex LP benchmark dataset derived from natural language problem specifications. Contribution/Results: Experiments demonstrate that our framework achieves an accuracy gain of +12.3% over state-of-the-art methods on easy instances and +8.7% on hard instances—including those in NLP4LP—significantly advancing automated modeling and efficient solving of large-scale real-world optimization problems.

Configuring Mixed-Integer Linear Programming (MILP) solver parameters—particularly for cutting-plane separation—is challenging due to high-dimensional, problem-dependent search spaces; existing machine learning approaches suffer from poor generalization, heavy reliance on large-scale labeled data, and difficulty integrating into solver pipelines. Method: We propose the first LLM-driven zero-shot cutting-plane separator configuration framework. It leverages large language models to jointly parse natural-language problem descriptions and LaTeX-based MILP formulations, augmented by literature-informed prompt engineering and semantic modeling of separators—requiring no custom interfaces or extensive retraining. A lightweight, performance-driven clustering ensemble strategy ensures both robustness and real-time responsiveness. Results: On benchmark combinatorial optimization instances and real-world datasets, our method matches state-of-the-art performance while reducing training data requirements by over 90% and generating configurations in under one second.

This work addresses the critical challenge that modern GPU-accelerated linear programming solvers—such as cuPDLP, which is based on the primal-dual hybrid gradient (PDHG) algorithm—exhibit performance highly sensitive to hyperparameters, yet lack tuning methods with provable generalization guarantees. For the first time, this study establishes structural relationships between hyperparameters and solution trajectories for multiple adaptive techniques in complex first-order LP solvers, including preconditioning, restart strategies, and smoothed weight updates. By integrating convergence analysis of PDHG with a model of structural sensitivity, the authors propose a data-driven hyperparameter learning framework that offers theoretical generalization guarantees under polynomial sample complexity. Experimental results demonstrate that the framework significantly enhances solver efficiency across diverse problem instances.

This work addresses the interoperability challenges arising from inconsistent interfaces among numerical solvers by proposing and implementing MaRDI—a standardized, open interface tailored for nonlinear optimization. Designed with a modular architecture, MaRDI establishes a generic solver adapter layer that enables seamless integration of diverse optimizers and embeds naturally within physics-informed neural network (PINN) training pipelines. Its efficacy is demonstrated through application to the viscous Burgers equation, where it substantially reduces the development overhead and benchmarking costs associated with solver-specific bindings. By abstracting low-level implementation details, MaRDI allows researchers to focus on core algorithmic innovation while significantly enhancing the efficiency and reproducibility of cross-solver experimentation.

Existing optimization modeling benchmarks are confined to purely textual inputs, rendering them inadequate for real-world decision-making scenarios that often involve multimodal (text-and-image) information. This work proposes and constructs MOptBench, the first solver-grounded multimodal optimization modeling benchmark, encompassing six problem categories, 26 subcategories, and three difficulty levels. The benchmark ensures correctness through structured instance generation and rigorous validation via exact solvers, enabling fine-grained evaluation and error attribution. Evaluation of nine multimodal large language models on 780 verified instances reveals that the best-performing model achieves a pass@1 rate of 52.1%, while general-purpose models succeed on only 15.9% of hard instances, and math-specialized models fail entirely—highlighting significant limitations in current models’ capacity for complex multimodal reasoning.

This study addresses the lack of systematic guidance for selecting optimizers in software configuration tuning under varying time budgets. Through a large-scale empirical evaluation across 22 real-world configurable systems, the authors compare eight prominent optimization approaches, including model-based methods such as SMAC and model-free techniques like genetic algorithms. The results reveal that model-based optimizers generally outperform others under low time budgets, whereas model-free methods dominate when budgets are high. Notably, FLASH demonstrates consistently strong performance across all budget regimes. This robustness stems from the prevalence of high-quality local optima with large basins of attraction in most systems, offering practitioners a reliable, budget-agnostic choice for configuration optimization.