Online Mixed-Integer Optimization in Milliseconds
Name
1907.02206.pdf
Description
Submitted version
Size
524.56 KB
Format
Adobe PDF
Checksum (MD5)
ff1008e1871282f31060fbc06906b100
Author(s)
Bertsimas, Dimitris
Stellato, Bartolomeo
Date Issued
April 8, 2022
Journal
INFORMS Journal on Computing
Publisher
Institute for Operations Research and the Management Sciences (INFORMS)
Citation
Bertsimas, Dimitris and Stellato, Bartolomeo. 2022. "Online Mixed-Integer Optimization in Milliseconds." INFORMS Journal on Computing.
Version
Original manuscript
Abstract
We propose a method to approximate the solution of online mixed-integer optimization (MIO) problems at very high speed using machine learning. By exploiting the repetitive nature of online optimization, we can greatly speed up the solution time. Our approach encodes the optimal solution into a small amount of information denoted as strategy using the voice of optimization framework. In this way, the core part of the optimization routine becomes a multiclass classification problem that 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. We propose an extremely fast online optimization method consisting of a feedforward neural network evaluation and a linear system solution where the matrix has already been factorized. Therefore, this online approach does not require any solver or 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 required to completely recover the optimal solution as a function of the problem dimensions. Compared with 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 up to two to three orders of magnitude speedups on examples from fuel cell energy management, sparse portfolio optimization, and motion planning with obstacle avoidance. Summary of Contribution: We propose a technique to approximate the solution of online optimization problems at high speed using machine learning. By exploiting the repetitive nature of online optimization, we learn the mapping between the key problem parameters and an encoding of the optimal solution to greatly speed up the solution time. This allows us to significantly improve the computation time and resources needed to solve online mixed-integer optimization problems. We obtain a simple method with a very low computing time variance, which is crucial in online settings.
MIT Department
Sloan School of Management
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1287/ijoc.2022.1181
