# Boosting Combinatorial Problem Modeling with Machine Learning

arXiv: https://arxiv.org/abs/1807.05517 · HTML: https://mlsanity.com/paper/1807.05517/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jul 2018.

## Built on by (most cited first, 15 of 15)

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- [Artificial Intelligence for Operations Research: Revolutionizing the Operations Research Process](https://mlsanity.com/paper/2401.03244/) (2024)
- [PySCIPOpt-ML: Embedding Trained Machine Learning Models into Mixed-Integer Programs](https://mlsanity.com/paper/2312.08074/) (2023)
- [Efficient Multiple Constraint Acquisition](https://mlsanity.com/paper/2109.05920/) (2021)
- [Deep Neural Network Based Ensemble learning Algorithms for the healthcare system (diagnosis of chronic diseases)](https://mlsanity.com/paper/2103.08182/) (2021)
- [Enhancing Column Generation by Reinforcement Learning-Based Hyper-Heuristic for Vehicle Routing and Scheduling Problems](https://mlsanity.com/paper/2310.09686/) (2023)
- [Reinforcement learning with combinatorial actions for coupled restless bandits](https://mlsanity.com/paper/2503.01919/) (2025)
- [Learning to Learn in Interactive Constraint Acquisition](https://mlsanity.com/paper/2312.10795/) (2023)
- [Scaling Combinatorial Optimization Neural Improvement Heuristics with Online Search and Adaptation](https://mlsanity.com/paper/2412.10163/) (2024)
- [Machine Learning for Combinatorial Optimisation of Partially-Specified Problems: Regret Minimisation as a Unifying Lens](https://mlsanity.com/paper/2205.10157/) (2022)
- [Multi-Objective Linear Ensembles for Robust and Sparse Training of Few-Bit Neural Networks](https://mlsanity.com/paper/2212.03659/) (2022)
- [Integrating Symbolic Reasoning into Neural Generative Models for Design Generation](https://mlsanity.com/paper/2310.09383/) (2023)
- [Solving 0-1 Integer Programs with Unknown Knapsack Constraints Using Membership Oracles](https://mlsanity.com/paper/2405.14090/) (2024)
- [Digital Twin Applications in Urban Logistics: An Overview](https://mlsanity.com/paper/2302.00484/) (2023)
- [Mathematical Programming Algorithms for Convex Hull Approximation with a Hyperplane Budget](https://mlsanity.com/paper/2407.17341/) (2024)

## Abstract (arXiv)

In the past few years, the area of Machine Learning (ML) has witnessed tremendous advancements, becoming a pervasive technology in a wide range of applications. One area that can significantly benefit from the use of ML is Combinatorial Optimization. The three pillars of constraint satisfaction and optimization problem solving, i.e., modeling, search, and optimization, can exploit ML techniques to boost their accuracy, efficiency and effectiveness. In this survey we focus on the modeling component, whose effectiveness is crucial for solving the problem. The modeling activity has been traditionally shaped by optimization and domain experts, interacting to provide realistic results. Machine Learning techniques can tremendously ease the process, and exploit the available data to either create models or refine expert-designed ones. In this survey we cover approaches that have been recently proposed to enhance the modeling process by learning either single constraints, objective functions, or the whole model. We highlight common themes to multiple approaches and draw connections with related fields of research.