A survey for solving mixed integer programming via machine learning - Zhang, Jiayi; Liu, Chang; Li, Xijun; Zhen, Hui-Ling; Yuan, Mingxuan; Li, Yawen; Yan, Junchi (Neurocomputing (Amsterdam), 2023)
Machine learning (ML) has been recently introduced to solving optimization problems, especially for combinatorial optimization (CO) tasks. In this paper, we survey the trend of leveraging ML to solve the mixed-integer programming problem (MIP). Theoretically, MIP is an NP-hard problem, and most CO problems can be formulated as MIP. Like other CO problems, the human-designed heuristic algorithms for MIP rely on good initial solutions and cost a lot of computational resources. Therefore, researchers consider applying machine learning methods to solve MIP since ML-enhanced approaches can provide the solution based on the typical patterns from the training data. Specifically, we first introduce the formulation and preliminaries of MIP and representative traditional solvers. Then, we show the integration of machine learning and MIP with detailed discussions on related learning-based methods, which can be further classified into exact and heuristic algorithms. Finally, we propose the outlook for learning-based MIP solvers, the direction toward more combinatorial optimization problems beyond MIP, and the mutual embrace of traditional solvers and ML components. We maintain a list of papers that utilize machine learning technologies to solve combinatorial optimization problems, which is available athttps://github.com/Thinklab-SJTU/awesome-ml4co.