Learning to Select Cuts for Efficient Mixed-Integer Programming

@article{Huang2021LearningTS,
  title={Learning to Select Cuts for Efficient Mixed-Integer Programming},
  author={Zeren Huang and Kerong Wang and Furui Liu and Hui-Ling Zhen and Weinan Zhang and Min jie Yuan and Jianye Hao and Yong Yu and Jun Wang},
  journal={ArXiv},
  year={2021},
  volume={abs/2105.13645}
}
Cutting plane methods play a significant role in modern solvers for tackling mixed-integer programming (MIP) problems. Proper selection of cuts would remove infeasible solutions in the early stage, thus largely reducing the computational burden without hurting the solution accuracy. However, the major cut selection approaches heavily rely on heuristics, which strongly depend on the specific problem at hand and thus limit their generalization capability. In this paper, we propose a data-driven… Expand

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References

SHOWING 1-10 OF 55 REFERENCES
Learning to Branch in Mixed Integer Programming
TLDR
This work proposes a machine learning (ML) framework for variable branching in MIP, and observes the decisions made by Strong Branching, a time-consuming strategy that produces small search trees, collecting features that characterize the candidate branching variables at each node of the tree. Expand
Reinforcement Learning for Integer Programming: Learning to Cut
TLDR
Across a wide range of IP tasks, it is shown that the trained RL agent significantly outperforms human-designed heuristics, and effectively generalizes to 10X larger instances and across IP problem classes. Expand
Learning to Branch
TLDR
It is shown how to use machine learning to determine an optimal weighting of any set of partitioning procedures for the instance distribution at hand using samples from the distribution, and it is proved that this reduction can even be exponential. Expand
Learning to Run Heuristics in Tree Search
TLDR
This work gives a theoretical framework for analyzing this decision-making process in a simplified setting, proposes a ML approach for modeling heuristic success likelihood, and design practical rules that leverage the ML models to dynamically decide whether to run a heuristic at each node of the search tree. Expand
Solving Mixed Integer Programs Using Neural Networks
TLDR
This paper applies learning to the two key sub-tasks of a MIP solver, generating a high-quality joint variable assignment, and bounding the gap in objective value between that assignment and an optimal one. Expand
Learning to Search in Branch and Bound Algorithms
TLDR
This work addresses the key challenge of learning an adaptive node searching order for any class of problem solvable by branch-and-bound by applying its algorithm to linear programming based branch- and-bound for solving mixed integer programs (MIP). Expand
Attention, Learn to Solve Routing Problems!
TLDR
A model based on attention layers with benefits over the Pointer Network is proposed and it is shown how to train this model using REINFORCE with a simple baseline based on a deterministic greedy rollout, which is more efficient than using a value function. Expand
Reinforcement Learning for Solving the Vehicle Routing Problem
TLDR
This work presents an end-to-end framework for solving the Vehicle Routing Problem (VRP) using reinforcement learning, and demonstrates how this approach can handle problems with split delivery and explore the effect of such deliveries on the solution quality. Expand
Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon
TLDR
A main point of the paper is seeing generic optimization problems as data points and inquiring what is the relevant distribution of problems to use for learning on a given task. Expand
Branch-and-Cut Algorithms for Combinatorial Optimization Problems
Branch-and-cut methods are very successful techniques for solving a wide variety of integer programming problems, and they can provide a guarantee of optimality. We describe how a branch-and-cutExpand
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