应用数学青年讨论班(午餐会)-- Learning-Based Methods for Combinatorial Optimization: Feasibility, Efficiency, and Optimality
报告人: 邹海军（中国科学院数学与系统科学研究院）
时间: 2026-11-3 12:15-13:00
地点: 智华楼-109
摘要: Learning-based methods have emerged as a promising approach to solving challenging combinatorial optimization problems, offering the potential to achieve high-quality solutions with remarkable computational efficiency. Despite recent advances, transforming learned models into effective optimization solvers remains challenging. Complex constraints can compromise solution feasibility, limited exploration can hinder solution quality, and mismatches between decision and solution spaces may introduce inherent optimality gaps. Moreover, sequential decision-making can accumulate suboptimality that is difficult to identify and correct. Addressing these challenges requires a deeper understanding of how learning interacts with the structure of optimization problems and their solution processes.
In this talk, I will present four studies that investigate these challenges across different combinatorial optimization problems. For constrained routing, we explore how to effectively handle complex constraints while maintaining feasibility and solution quality. For the quadratic assignment problem, we investigate how learning-based approaches can achieve metaheuristic-level solution quality with high computational efficiency. For heterogeneous DAG scheduling, we characterize the optimality gaps arising from the mismatch between decision and solution spaces, and address the challenge of modeling heterogeneous task–resource interactions. Finally, for flexible job-shop scheduling, we analyze the failure modes of autoregressive solvers and explore selective local correction to mitigate suboptimality. Together, these studies provide insights into the design of more effective, efficient, and generalizable learning-based optimization methods.
报告人简介：邹海军，中国科学院数学与系统科学研究院博士生，导师为袁亚湘研究员。他于2024年获得北京大学数学科学学院学士学位。其研究兴趣在于最优化理论与算法，目前聚焦于求解组合优化问题的学习优化方法和基于概率采样的优化算法。
