# Online Mixed-Integer Optimization in Milliseconds

arXiv: https://arxiv.org/abs/1907.02206 · HTML: https://mlsanity.com/paper/1907.02206/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jul 2019.

## Built on by (most cited first, 30 of 38)

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- [Expressive Power of Graph Neural Networks for (Mixed-Integer) Quadratic Programs](https://mlsanity.com/paper/2406.05938/) (2024)
- [PILOT: Efficient Planning by Imitation Learning and Optimisation for Safe Autonomous Driving](https://mlsanity.com/paper/2011.00509/) (2020)
- [Learning to Optimize for Mixed-Integer Non-linear Programming with Feasibility Guarantees](https://mlsanity.com/paper/2410.11061/) (2024)
- [Learning-Guided Rolling Horizon Optimization for Long-Horizon Flexible Job-Shop Scheduling](https://mlsanity.com/paper/2502.15791/) (2025)
- [An actor-critic algorithm with policy gradients to solve the job shop scheduling problem using deep double recurrent agents](https://mlsanity.com/paper/2110.09076/) (2021)
- [Learning Optimal Solutions via an LSTM-Optimization Framework](https://mlsanity.com/paper/2207.02937/) (2022)
- [Taking the human out of decomposition-based optimization via artificial intelligence: Part II. Learning to initialize](https://mlsanity.com/paper/2310.07082/) (2023)
- [Improving Computational Efficiency for Powered Descent Guidance via Transformer-based Tight Constraint Prediction](https://mlsanity.com/paper/2311.05135/) (2023)
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- [Accelerating process control and optimization via machine learning: A review](https://mlsanity.com/paper/2412.18529/) (2024)
- [An Expandable Machine Learning-Optimization Framework to Sequential Decision-Making](https://mlsanity.com/paper/2311.06972/) (2023)
- [NeuralQP: A General Hypergraph-based Optimization Framework for Large-scale QCQPs](https://mlsanity.com/paper/2410.03720/) (2024)
- [A Machine Learning Approach to Two-Stage Adaptive Robust Optimization](https://mlsanity.com/paper/2307.12409/) (2023)
- [Differentiable Cutting-plane Layers for Mixed-integer Linear Optimization](https://mlsanity.com/paper/2311.03350/) (2023)
- [Generative deep learning for decision making in gas networks](https://mlsanity.com/paper/2102.02125/) (2021)
- [An analysis of optimization problems involving ReLU neural networks](https://mlsanity.com/paper/2502.03016/) (2025)
- [Constraint Matters: Multi-Modal Representation for Reducing Mixed-Integer Linear programming](https://mlsanity.com/paper/2508.18742/) (2025)
- [Graph-Based Imitation and Reinforcement Learning for Efficient Benders Decomposition](https://mlsanity.com/paper/2511.11870/) (2025)
- [Sub-millisecond Video Synchronization of Multiple Android Smartphones](https://mlsanity.com/paper/2107.00987/) (2021)
- [Optimal Control of Multiclass Fluid Queueing Networks: A Machine Learning Approach](https://mlsanity.com/paper/2307.12405/) (2023)
- [Deep learning enhanced mixed integer optimization: Learning to reduce model dimensionality](https://mlsanity.com/paper/2401.09556/) (2024)
- [Robotic warehousing operations: a learn-then-optimize approach to large-scale neighborhood search](https://mlsanity.com/paper/2408.16890/) (2024)
- [ID-PaS+ : Identity-Aware Predict-and-Search for General Mixed-Integer Linear Programs](https://mlsanity.com/paper/2512.10211/) (2025)
- [Parametric Nonconvex Optimization via Convex Surrogates](https://mlsanity.com/paper/2604.05640/) (2026)
- [A Sequential Deep Learning Algorithm for Sampled Mixed-integer Optimisation Problems](https://mlsanity.com/paper/2301.10703/) (2023)
- [Unit Commitment Predictor With a Performance Guarantee: A Support Vector Machine Classifier](https://mlsanity.com/paper/2310.08601/) (2023)

## Abstract (arXiv)

We propose a method to solve online mixed-integer optimization (MIO) problems at very high speed using machine learning. By exploiting the repetitive nature of online optimization, we are able to greatly speedup the solution time. Our approach encodes the optimal solution into a small amount of information denoted as strategy using the Voice of Optimization framework proposed in [BS21]. In this way the core part of the optimization algorithm becomes a multiclass classification problem which can be solved very quickly. In this work, we extend that framework to real-time and high-speed applications focusing on parametric mixed-integer quadratic optimization (MIQO). We propose an extremely fast online optimization algorithm consisting of a feedforward neural network (NN) evaluation and a linear system solution where the matrix has already been factorized. Therefore, this online approach does not require any solver nor iterative algorithm. We show the speed of the proposed method both in terms of total computations required and measured execution time. We estimate the number of floating point operations (flops) required to completely recover the optimal solution as a function of the problem dimensions. Compared to state-of-the-art MIO routines, the online running time of our method is very predictable and can be lower than a single matrix factorization time. We benchmark our method against the state-of-the-art solver Gurobi obtaining from two to three orders of magnitude speedups on examples from fuel cell energy management, sparse portfolio optimization and motion planning with obstacle avoidance.