组合优化问题的机器学习求解方法  

Machine learning method for combinatorial optimization problems

作　　者：郭田德 李安琪 韩丛英 Tiande Guo;Anqi Li;Congying Han

机构地区：[1]中国科学院大学数学科学学院,北京100049

出　　处：《中国科学:数学》2025年第2期451-480,共30页Scientia Sinica:Mathematica

基　　金：国家自然科学基金重大项目课题(批准号:11991022)资助项目。

摘　　要：最优化是一个非常经典的研究领域,许多工程、管理等领域的问题本质上都是最优化问题.目前,以深度学习、强化学习为代表的机器学习方法发展迅速,在诸多学科领域都带来了关键性的促进和发展.最优化是机器学习的重要支撑学科之一,机器学习归根到底都要转化成求解一个最优化问题,这属于科学智能(science for AI(artificial intelligence))的研究内容.反过来,人工智能技术(包括机器学习)已经对科学的发展产生了重大影响,并且将形成新的科学研究范式—智能科学(AI for science).最优化问题的人工智能求解方法就是利用人工智能的理论方法设计最优化问题快速高效的求解算法.本文总结了组合优化机器学习求解方法最近几年的研究进展,深入分析了组合优化问题求解的难点及其人工智能求解方法的瓶颈问题,结合图像处理、博弈论和强化学习等热门领域的研究现状,给出了一些重要的研究方向.Optimization is a very classical research field,and many problems in engineering,management,and other fields are essentially optimization problems.At present,the rapid development of machine learning methods represented by deep learning and reinforcement learning has brought key promotion and development in many subject areas.Optimization is one of the most important supporting disciplines of machine learning,and machine learning is ultimately transformed into solving an optimization problem,which belongs to the research content of science for AI(artificial intelligence).In turn,AI technologies,including machine learning,are already having a significant impact on the development of science and will form a new paradigm of scientific research—AI for science.The artificial intelligence method of optimization problems is to design a fast and efficient algorithm of optimization problems using the theory of artificial intelligence.In this paper,we summarize the research progress of machine learning methods for combinatorial optimization in recent years,and deeply analyze the difficulties of solving combinatorial optimization problems and the bottlenecks of artificial intelligence solving methods.Some important research directions are given based on the current research status of image processing,game theory,reinforcement learning,and other popular fields.

关 键 词：组合优化 机器学习 最优化 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程] O224[自动化与计算机技术—控制科学与工程]