# Mixed-Integer Nonlinear Programming for State-based Non-Intrusive Load Monitoring

arXiv: https://arxiv.org/abs/2106.09158 · HTML: https://mlsanity.com/paper/2106.09158/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 50 references that are in the map.
- First posted on arXiv 16 Jun 2021.

## Builds on (most cited first, 5 of 5)

- [Neural NILM: Deep Neural Networks Applied to Energy Disaggregation](https://mlsanity.com/paper/1507.06594/) (2015)
- [Sequence-to-point learning with neural networks for nonintrusive load monitoring](https://mlsanity.com/paper/1612.09106/) (2016)
- [SOS-SDP: an Exact Solver for Minimum Sum-of-Squares Clustering](https://mlsanity.com/paper/2104.11542/) (2021)
- [Non-Intrusive Energy Disaggregation Using Non-negative Matrix Factorization with Sum-to-k Constraint](https://mlsanity.com/paper/1704.07308/) (2017)
- [Load Disaggregation Based on Aided Linear Integer Programming](https://mlsanity.com/paper/1603.07417/) (2016)

## Built on by (most cited first, 1 of 1)

- [Global Optimization for Cardinality-constrained Minimum Sum-of-Squares Clustering via Semidefinite Programming](https://mlsanity.com/paper/2209.08901/) (2022)

## Abstract (arXiv)

Energy disaggregation, known in the literature as Non-Intrusive Load Monitoring (NILM), is the task of inferring the energy consumption of each appliance given the aggregate signal recorded by a single smart meter. In this paper, we propose a novel two-stage optimization-based approach for energy disaggregation. In the first phase, a small training set consisting of disaggregated power profiles is used to estimate the parameters and the power states by solving a mixed integer programming problem. Once the model parameters are estimated, the energy disaggregation problem is formulated as a constrained binary quadratic optimization problem. We incorporate penalty terms that exploit prior knowledge on how the disaggregated traces are generated, and appliance-specific constraints characterizing the signature of different types of appliances operating simultaneously. Our approach is compared with existing optimization-based algorithms both on a synthetic dataset and on three real-world datasets. The proposed formulation is computationally efficient, able to disambiguate loads with similar consumption patterns, and successfully reconstruct the signatures of known appliances despite the presence of unmetered devices, thus overcoming the main drawbacks of the optimization-based methods available in the literature.