arXiv subjects

Minshuo Li

Publications and source records attributed to Minshuo Li.

3 recordsLinked to original sources

arXiv2026

Towards Solving Polynomial-Objective Integer Programming with Hypergraph Neural Networks

Complex real-world optimization problems often involve both discrete decisions and nonlinear relationships between variables. Many such problems can be modeled as polynomial-objective integer programs, encompassing cases with quadratic and higher-degree variable interactions. Nonlinearity makes them more challenging than their linear counterparts. In this paper, we propose a hypergraph neural network (HNN) based method to solve polynomial-objective integer programming (POIP). Besides presenting a high-degree-term-aware hypergraph representation to capture both high-degree information and variable-constraint interdependencies, we also propose a hypergraph neural network, which integrates convolution between variables and high-degree terms alongside convolution between variables and constraints, to predict solution values. Finally, a search process initialized from the predicted solutions is performed to further refine the results. Comprehensive experiments across a range of benchmarks demonstrate that our method consistently outperforms both existing learning-based approaches and state-of-the-art solvers, delivering superior solution quality with favorable efficiency. Note that our experiments involve both polynomial objectives and constraints, demonstrating our HNN's versatility for general POIP problems and highlighting its advancement over the existing literature.

cs.NE↗

arXiv2025

Large Language Models as End-to-end Combinatorial Optimization Solvers

Combinatorial optimization (CO) problems, central to decision-making scenarios like logistics and manufacturing, are traditionally solved using problem-specific algorithms requiring significant domain expertise. While large language models (LLMs) have shown promise in automating CO problem solving, existing approaches rely on intermediate steps such as code generation or solver invocation, limiting their generality and accessibility. This paper introduces a novel framework that empowers LLMs to serve as end-to-end CO solvers by directly mapping natural language problem descriptions to solutions. We propose a two-stage training strategy: supervised fine-tuning (SFT) imparts LLMs with solution generation patterns from domain-specific solvers, while a feasibility-and-optimality-aware reinforcement learning (FOARL) process explicitly mitigates constraint violations and refines solution quality. Evaluation across seven NP-hard CO problems shows that our method achieves a high feasibility rate and reduces the average optimality gap to 1.03-8.20% by tuning a 7B-parameter LLM, surpassing both general-purpose LLMs (e.g., GPT-4o), reasoning models (e.g., DeepSeek-R1), and domain-specific heuristics. Our method establishes a unified language-based pipeline for CO without extensive code execution or manual architectural adjustments for different problems, offering a general and language-driven alternative to traditional solver design while maintaining relative feasibility guarantees.

cs.AI↗

arXiv2024

Accelerate Solving Expensive Scheduling by Leveraging Economical Auxiliary Tasks

To fully leverage the multi-task optimization paradigm for accelerating the solution of expensive scheduling problems, this study has effectively tackled three vital concerns. The primary issue is identifying auxiliary tasks that closely resemble the original expensive task. We suggested a sampling strategy based on job importance, creating a compact matrix by extracting crucial rows from the entire problem specification matrix of the expensive task. This matrix serves as an economical auxiliary task. Mathematically, we proved that this economical auxiliary task bears similarity to its corresponding expensive task. The subsequent concern revolves around making auxiliary tasks more cost-effective. We determined the sampling proportions for the entire problem specification matrix through factorial design experiments, resulting in a more compact auxiliary task. With a reduced search space and shorter function evaluation time, it can rapidly furnish high-quality transferable information for the primary task. The last aspect involves designing transferable deep information from auxiliary tasks. We regarded the job priorities in the (sub-) optimal solutions to the economical auxiliary task as transferable invariants. By adopting a partial solution patching strategy, we augmented specificity knowledge onto the common knowledge to adapt to the target expensive task. The strategies devised for constructing task pairs and facilitating knowledge transfer, when incorporated into various evolutionary multitasking algorithms, were utilized to address expensive instances of permutation flow shop scheduling. Extensive experiments and statistical comparisons have validated that, with the collaborative synergy of these strategies, the performance of evolutionary multitasking algorithms is significantly enhanced in handling expensive scheduling tasks.

math.OC↗