# Automating Personnel Rostering by Learning Constraints Using Tensors

arXiv: https://arxiv.org/abs/1805.11375 · HTML: https://mlsanity.com/paper/1805.11375/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2018.

## Built on by (most cited first, 6 of 6)

- [Optimization with Constraint Learning: A Framework and Survey](https://mlsanity.com/paper/2110.02121/) (2021)
- [Inverse Mixed-Integer Programming: Learning Constraints then Objective Functions](https://mlsanity.com/paper/2510.04455/) (2025)
- [Easy, adaptable and high-quality Modelling with domain-specific Constraint Patterns](https://mlsanity.com/paper/2206.02479/) (2022)
- [Machine Learning and Constraint Programming for Efficient Healthcare Scheduling](https://mlsanity.com/paper/2409.07547/) (2024)
- [A study on constraint extraction and exception exclusion in care worker scheduling](https://mlsanity.com/paper/2512.24853/) (2025)
- [Learning Size Independent Constraint Models from Input Data and Positive and Negative Example Solutions](https://mlsanity.com/paper/2610.13640/) (2026)

## Abstract (arXiv)

Many problems in operations research require that constraints be specified in the model. Determining the right constraints is a hard and laborsome task. We propose an approach to automate this process using artificial intelligence and machine learning principles. So far there has been only little work on learning constraints within the operations research community. We focus on personnel rostering and scheduling problems in which there are often past schedules available and show that it is possible to automatically learn constraints from such examples. To realize this, we adapted some techniques from the constraint programming community and we have extended them in order to cope with multidimensional examples. The method uses a tensor representation of the example, which helps in capturing the dimensionality as well as the structure of the example, and applies tensor operations to find the constraints that are satisfied by the example. To evaluate the proposed algorithm, we used constraints from the Nurse Rostering Competition and generated solutions that satisfy these constraints; these solutions were then used as examples to learn constraints. Experiments demonstrate that the proposed algorithm is capable of producing human readable constraints that capture the underlying characteristics of the examples.