# A Sequential Deep Learning Algorithm for Sampled Mixed-integer Optimisation Problems

arXiv: https://arxiv.org/abs/2301.10703 · HTML: https://mlsanity.com/paper/2301.10703/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 46 references that are in the map.
- First posted on arXiv 25 Jan 2023.

## Builds on (most cited first, 10 of 10)

- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [Online Mixed-Integer Optimization in Milliseconds](https://mlsanity.com/paper/1907.02206/) (2019)
- [Learning for Constrained Optimization: Identifying Optimal Active Constraint Sets](https://mlsanity.com/paper/1802.09639/) (2018)
- [The Voice of Optimization](https://mlsanity.com/paper/1812.09991/) (2018)
- [On Repetitive Scenario Design](https://mlsanity.com/paper/1602.03796/) (2016)
- [Sequential Randomized Algorithms for Convex Optimization in the Presence of Uncertainty](https://mlsanity.com/paper/1304.2222/) (2013)
- [A Statistical Learning Theory Approach for Uncertain Linear and Bilinear Matrix Inequalities](https://mlsanity.com/paper/1305.4952/) (2013)
- [Randomized Constraints Consensus for Distributed Robust Linear Programming](https://mlsanity.com/paper/1706.00488/) (2017)
- [Algorithms for Optimal AC Power Flow in the Presence of Renewable Sources](https://mlsanity.com/paper/1811.05397/) (2018)

## Abstract (arXiv)

Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each iteration step of both algorithms, we first test the feasibility of a given test solution for each and every constraint associated with the sampled optimisation at hand, while also identifying those constraints that are violated. Subsequently, an optimisation problem is constructed with a constraint set consisting of the current basis -- namely, the smallest set of constraints that fully specifies the current test solution -- as well as constraints related to a limited number of the identified violating samples. We show that both algorithms exhibit finite-time convergence towards the optimal solution. Algorithm 2 features a neural network classifier that notably improves the computational performance compared to Algorithm 1. We quantitatively establish these algorithms' efficacy through three numerical tests: robust optimal power flow, robust unit commitment, and robust random mixed-integer linear program.