Machine Learning for Cutting Planes in Integer Programming: A Survey

• URL: http://arxiv.org/abs/2302.09166v2
• Date: Tue, 31 Oct 2023 15:57:05 GMT
• Title: Machine Learning for Cutting Planes in Integer Programming: A Survey
• Authors: Arnaud Deza and Elias B. Khalil
• Abstract summary: We present recent work on machine learning (ML) techniques for selecting cutting planes (or cuts) in mixed-integer linear programming (MILP) ML offers a promising approach for improving the cut selection process by using data to identify promising cuts that accelerate the solution of MILP instances. We analyze the empirical results in the literature in an attempt to quantify the progress that has been made and conclude by suggesting avenues for future research.
• Score: 21.567191691588643
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We survey recent work on machine learning (ML) techniques for selecting cutting planes (or cuts) in mixed-integer linear programming (MILP). Despite the availability of various classes of cuts, the task of choosing a set of cuts to add to the linear programming (LP) relaxation at a given node of the branch-and-bound (B&B) tree has defied both formal and heuristic solutions to date. ML offers a promising approach for improving the cut selection process by using data to identify promising cuts that accelerate the solution of MILP instances. This paper presents an overview of the topic, highlighting recent advances in the literature, common approaches to data collection, evaluation, and ML model architectures. We analyze the empirical results in the literature in an attempt to quantify the progress that has been made and conclude by suggesting avenues for future research.

Related papers

• Learning Cut Generating Functions for Integer Programming [1.1510009152620668]
  The branch-and-cut algorithm is the method of choice to solve large scale integer programming problems. Recent advances have employed a data-driven approach to select optimal cutting planes from a parameterized family. We show that the selected CGF can outperform the GMI cuts for certain distributions.
  arXiv  Detail & Related papers  (2024-05-22T20:56:34Z)
• Learning Cut Selection for Mixed-Integer Linear Programming via Hierarchical Sequence Model [81.56473654324328]
  We propose a novel hierarchical sequence model (HEM) to learn cut selection policies via reinforcement learning. HEM is the first method that can tackle (P1)-(P3) in cut selection simultaneously from a data-driven perspective. Experiments show that HEM significantly improves the efficiency of solving MILPs compared to human-designed and learning-based baselines.
  arXiv  Detail & Related papers  (2023-02-01T04:59:55Z)
• Branch Ranking for Efficient Mixed-Integer Programming via Offline Ranking-based Policy Learning [45.1011106869493]
  We formulate learning to branch as an offline reinforcement learning (RL) problem. We train a branching model named Branch Ranking via offline policy learning. Experiments on synthetic MIP benchmarks and real-world tasks demonstrate that Branch Rankink is more efficient and robust.
  arXiv  Detail & Related papers  (2022-07-26T15:34:10Z)
• Reinforcement Learning for Branch-and-Bound Optimisation using Retrospective Trajectories [72.15369769265398]
  Machine learning has emerged as a promising paradigm for branching. We propose retro branching; a simple yet effective approach to RL for branching. We outperform the current state-of-the-art RL branching algorithm by 3-5x and come within 20% of the best IL method's performance on MILPs with 500 constraints and 1000 variables.
  arXiv  Detail & Related papers  (2022-05-28T06:08:07Z)
• Structural Analysis of Branch-and-Cut and the Learnability of Gomory Mixed Integer Cuts [88.94020638263467]
  The incorporation of cutting planes within the branch-and-bound algorithm, known as branch-and-cut, forms the backbone of modern integer programming solvers. We conduct a novel structural analysis of branch-and-cut that pins down how every step of the algorithm is affected by changes in the parameters defining the cutting planes added to the input integer program. Our main application of this analysis is to derive sample complexity guarantees for using machine learning to determine which cutting planes to apply during branch-and-cut.
  arXiv  Detail & Related papers  (2022-04-15T03:32:40Z)
• Learning to Reformulate for Linear Programming [11.628932152805724]
  We propose a reinforcement learning-based reformulation method for linear programming (LP) to improve the performance of solving process. We implement the proposed method over two public research LP datasets and one large-scale LP dataset collected from practical production planning scenario.
  arXiv  Detail & Related papers  (2022-01-17T04:58:46Z)
• Memory-Based Optimization Methods for Model-Agnostic Meta-Learning and Personalized Federated Learning [56.17603785248675]
  Model-agnostic meta-learning (MAML) has become a popular research area. Existing MAML algorithms rely on the episode' idea by sampling a few tasks and data points to update the meta-model at each iteration. This paper proposes memory-based algorithms for MAML that converge with vanishing error.
  arXiv  Detail & Related papers  (2021-06-09T08:47:58Z)
• Sample Complexity of Tree Search Configuration: Cutting Planes and Beyond [98.92725321081994]
  State-of-the-art solvers integrate a myriad of cutting-plane techniques to speed up the underlying tree-search algorithm. We prove the first guarantees for learning high-performing cut-selection policies tailored to the instance distribution.
  arXiv  Detail & Related papers  (2021-06-08T00:57:59Z)
• Learning to Select Cuts for Efficient Mixed-Integer Programming [46.60355046375608]
  We propose a data-driven and generalizable cut selection approach, named Cut Ranking, in the settings of multiple instance learning. Cut Ranking has been deployed in an industrial solver for large-scale MIPs. It has achieved the average speedup ratio of 12.42% over the production solver without any accuracy loss of solution.
  arXiv  Detail & Related papers  (2021-05-28T07:48:34Z)
• A Scalable MIP-based Method for Learning Optimal Multivariate Decision Trees [17.152864798265455]
  We propose a novel MIP formulation, based on a 1-norm support vector machine model, to train a multivariate ODT for classification problems. We provide cutting plane techniques that tighten the linear relaxation of the MIP formulation, in order to improve run times to reach optimality. We demonstrate that our formulation outperforms its counterparts in the literature by an average of about 10% in terms of mean out-of-sample testing accuracy.
  arXiv  Detail & Related papers  (2020-11-06T14:17:41Z)
• A Survey on Large-scale Machine Learning [67.6997613600942]
  Machine learning can provide deep insights into data, allowing machines to make high-quality predictions. Most sophisticated machine learning approaches suffer from huge time costs when operating on large-scale data. Large-scale Machine Learning aims to learn patterns from big data with comparable performance efficiently.
  arXiv  Detail & Related papers  (2020-08-10T06:07:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.