Machine Learning Augmented Branch and Bound for Mixed Integer Linear Programming

Machine Learning Augmented Branch and Bound for Mixed Integer Linear Programming

8 Feb 2024 | Lara Scavuzzo, Karen Aardal, Andrea Lodi, Neil Yorke-Smith
This paper presents a survey on the integration of machine learning (ML) with Mixed Integer Linear Programming (MILP) solvers, focusing on enhancing the branch-and-bound (B&B) algorithm. MILP is a key area in mathematical optimization, used in various applications. Modern MILP solvers use B&B as their main component, and recent years have seen significant progress in using ML to improve B&B tasks like primal heuristics, branching, cutting planes, node selection, and solver configuration. The paper discusses how ML can automatically optimize B&B efficiency metrics and how to represent MILPs for learning algorithms, benchmarks, and software. The paper introduces the B&B algorithm, which systematically explores the feasible region by partitioning it into sub-MILPs and using LP relaxations to bound the solution. Key components of B&B include preprocessing, branching, cutting planes, and primal heuristics. The paper also defines evaluation metrics for MILP, such as the optimality gap, primal gap, and primal-dual integral. The paper then provides an overview of machine learning concepts, including supervised learning, reinforcement learning, and neural networks. It discusses how ML can be applied to various B&B tasks, such as improving primal heuristics, learning to branch, and scheduling heuristics. The paper highlights methods like using ML to predict solutions, improve neighborhood selection, and schedule heuristics based on past performance. The paper also covers different approaches to learning within B&B, including online and offline learning, and discusses the challenges of generalizing ML models to different MILP instances. It presents case studies and experiments showing the effectiveness of ML in improving B&B performance, particularly in reducing the optimality gap and improving solution quality. The paper concludes with future directions, emphasizing the need for further research to integrate ML with MILP solvers effectively.This paper presents a survey on the integration of machine learning (ML) with Mixed Integer Linear Programming (MILP) solvers, focusing on enhancing the branch-and-bound (B&B) algorithm. MILP is a key area in mathematical optimization, used in various applications. Modern MILP solvers use B&B as their main component, and recent years have seen significant progress in using ML to improve B&B tasks like primal heuristics, branching, cutting planes, node selection, and solver configuration. The paper discusses how ML can automatically optimize B&B efficiency metrics and how to represent MILPs for learning algorithms, benchmarks, and software. The paper introduces the B&B algorithm, which systematically explores the feasible region by partitioning it into sub-MILPs and using LP relaxations to bound the solution. Key components of B&B include preprocessing, branching, cutting planes, and primal heuristics. The paper also defines evaluation metrics for MILP, such as the optimality gap, primal gap, and primal-dual integral. The paper then provides an overview of machine learning concepts, including supervised learning, reinforcement learning, and neural networks. It discusses how ML can be applied to various B&B tasks, such as improving primal heuristics, learning to branch, and scheduling heuristics. The paper highlights methods like using ML to predict solutions, improve neighborhood selection, and schedule heuristics based on past performance. The paper also covers different approaches to learning within B&B, including online and offline learning, and discusses the challenges of generalizing ML models to different MILP instances. It presents case studies and experiments showing the effectiveness of ML in improving B&B performance, particularly in reducing the optimality gap and improving solution quality. The paper concludes with future directions, emphasizing the need for further research to integrate ML with MILP solvers effectively.
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