Designing faster mixed integer linear programming algorithm via learning the optimal path

Designing faster algorithms for solving Mixed-Integer Linear Programming (MILP) problems is highly desired across numerous practical domains, as a vast array of complex real-world challenges can be effectively modeled as MILP formulations. Solving these problems typically employs the branch-and-bound algorithm, the core of which can be conceived as searching for a path of nodes (or sub-problems) that contains the optimal solution to the original MILP problem. Traditional approaches to finding this path rely heavily on hand-crafted, intuition-based heuristic strategies, which often suffer from unstable and unpredictable performance across different MILP problem instances. To address this limitation, we introduce DeepBound, a deep learning-based node selection algorithm that automates the learning of such human intuition from data. The core of DeepBound lies in learning to prioritize nodes containing the optimal solution, thereby improving solving efficiency. DeepBound introduces a multi-level feature fusion network to capture the node representations. To tackle the inherent node imbalance in branch-and-bound trees, DeepBound employs a pairwise training paradigm that enhances the model's ability to discriminate between nodes. Extensive experiments on three NP-hard MILP benchmarks demonstrate that DeepBound achieves superior solving efficiency over conventional heuristic rules and existing learning-based approaches, obtaining optimal feasible solutions with significantly reduced computation time. Moreover, DeepBound demonstrates strong generalization capability on large and complex instances. The analysis of its learned features reveals that the method can automatically discover more flexible and robust feature selection, which may effectively improve and potentially replace human-designed heuristic rules.

Rethinking All Evidence: Enhancing Trustworthy Retrieval-Augmented Generation via Conflict-Driven Summarization

Retrieval-Augmented Generation (RAG) enhances large language models (LLMs) by integrating their parametric knowledge with external retrieved content. However, knowledge conflicts caused by internal inconsistencies or noisy retrieved content can severely undermine the generation reliability of RAG systems.In this work, we argue that LLMs should rethink all evidence, including both retrieved content and internal knowledge, before generating responses.We propose CARE-RAG (Conflict-Aware and Reliable Evidence for RAG), a novel framework that improves trustworthiness through Conflict-Driven Summarization of all available evidence.CARE-RAG first derives parameter-aware evidence by comparing parameter records to identify diverse internal perspectives. It then refines retrieved evidences to produce context-aware evidence, removing irrelevant or misleading content. To detect and summarize conflicts, we distill a 3B LLaMA3.2 model to perform conflict-driven summarization, enabling reliable synthesis across multiple sources.To further ensure evaluation integrity, we introduce a QA Repair step to correct outdated or ambiguous benchmark answers.Experiments on revised QA datasets with retrieval data show that CARE-RAG consistently outperforms strong RAG baselines, especially in scenarios with noisy or conflicting evidence.