# Confidence Threshold Neural Diving

arXiv: https://arxiv.org/abs/2202.07506 · HTML: https://mlsanity.com/paper/2202.07506/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 16 references that are in the map.
- First posted on arXiv 15 Feb 2022.

## Builds on (most cited first, 11 of 11)

- [SelectiveNet: A Deep Neural Network with an Integrated Reject Option](https://mlsanity.com/paper/1901.09192/) (2019)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Solving Mixed Integer Programs Using Neural Networks](https://mlsanity.com/paper/2012.13349/) (2020)
- [Reinforcement Learning for Integer Programming: Learning to Cut](https://mlsanity.com/paper/1906.04859/) (2019)
- [Hybrid Models for Learning to Branch](https://mlsanity.com/paper/2006.15212/) (2020)
- [Parameterizing Branch-and-Bound Search Trees to Learn Branching Policies](https://mlsanity.com/paper/2002.05120/) (2020)
- [CombOptNet: Fit the Right NP-Hard Problem by Learning Integer Programming Constraints](https://mlsanity.com/paper/2105.02343/) (2021)
- [Learning to Select Cuts for Efficient Mixed-Integer Programming](https://mlsanity.com/paper/2105.13645/) (2021)
- [Learning a Large Neighborhood Search Algorithm for Mixed Integer Programs](https://mlsanity.com/paper/2107.10201/) (2021)
- [Learning Primal Heuristics for Mixed Integer Programs](https://mlsanity.com/paper/2107.00866/) (2021)
- [Smart Feasibility Pump: Reinforcement Learning for (Mixed) Integer Programming](https://mlsanity.com/paper/2102.09663/) (2021)

## Built on by (most cited first, 5 of 5)

- [Apollo-MILP: An Alternating Prediction-Correction Neural Solving Framework for Mixed-Integer Linear Programming](https://mlsanity.com/paper/2503.01129/) (2025)
- [PROPEL: Supervised and Reinforcement Learning for Large-Scale Supply Chain Planning](https://mlsanity.com/paper/2504.07383/) (2025)
- [RL-SPH: Learning to Achieve Feasible Solutions for Integer Linear Programs](https://mlsanity.com/paper/2411.19517/) (2024)
- [HyP-ASO: A Hybrid Policy-based Adaptive Search Optimization Framework for Large-Scale Integer Linear Programs](https://mlsanity.com/paper/2509.15828/) (2025)
- [Solving Integer Linear Programming with Parallel Tempering](https://mlsanity.com/paper/2605.29366/) (2026)

## Abstract (arXiv)

Finding a better feasible solution in a shorter time is an integral part of solving Mixed Integer Programs. We present a post-hoc method based on Neural Diving to build heuristics more flexibly. We hypothesize that variables with higher confidence scores are more definite to be included in the optimal solution. For our hypothesis, we provide empirical evidence that confidence threshold technique produces partial solutions leading to final solutions with better primal objective values. Our method won 2nd place in the primal task on the NeurIPS 2021 ML4CO competition. Also, our method shows the best score among other learning-based methods in the competition.