On data-driven chance constraint learning for mixed-integer optimization problems

When dealing with real-world optimization problems, decision-makers usually face high levels of uncertainty associated with partial information, unknown parameters, or complex relationships between these and the problem decision variables. In this work, we develop a novel Chance Constraint Learning (CCL) methodology with a focus on mixed-integer linear optimization problems which combines ideas from the chance constraint and constraint learning literature. Chance constraints set a probabilistic confidence level for a single or a set of constraints to be fulfilled, whereas the constraint learning methodology aims to model the functional relationship between the problem variables through predictive models. One of the main issues when establishing a learned constraint arises when we need to set further bounds for its response variable: the fulfillment of these is directly related to the accuracy of the predictive model and its probabilistic behaviour. In this sense, CCL makes use of linearizable machine learning models to estimate conditional quantiles of the learned variables, providing a data-driven solution for chance constraints. An open-access software has been developed to be used by practitioners. Furthermore, benefits from CCL have been tested in two real-world case studies, proving how robustness is added to optimal solutions when probabilistic bounds are set for learned constraints.

Hierarchical Clustering for Smart Meter Electricity Loads based on Quantile Autocovariances

In order to improve the efficiency and sustainability of electricity systems, most countries worldwide are deploying advanced metering infrastructures, and in particular household smart meters, in the residential sector. This technology is able to record electricity load time series at a very high frequency rates, information that can be exploited to develop new clustering models to group individual households by similar consumptions patterns. To this end, in this work we propose three hierarchical clustering methodologies that allow capturing different characteristics of the time series. These are based on a set of "dissimilarity" measures computed over different features: quantile auto-covariances, and simple and partial autocorrelations. The main advantage is that they allow summarizing each time series in a few representative features so that they are computationally efficient, robust against outliers, easy to automatize, and scalable to hundreds of thousands of smart meters series. We evaluate the performance of each clustering model in a real-world smart meter dataset with thousands of half-hourly time series. The results show how the obtained clusters identify relevant consumption behaviors of households and capture part of their geo-demographic segmentation. Moreover, we apply a supervised classification procedure to explore which features are more relevant to define each cluster.

A Single Scalable LSTM Model for Short-Term Forecasting of Disaggregated Electricity Loads

As a powerful tool to improve their efficiency and sustainability, most electricity systems worldwide are deploying advanced metering infrastructures to collect relevant operational data. In particular, smart meters play a key role in this transformation as they allow tracking electricity load consumption at a very disaggregated level and at high frequency rates. This data opens the possibility of developing new forecasting models with a potential positive impact in both electricity distribution and retailing activities. In this work, we present a general methodology that is able to process and forecast a large number of smart meter time series. Instead of using traditional and univariate approaches for each time series, we develop a single but complex recurrent neural network model with long short-term memory that is able to capture individual consumption patterns and also the cross-sectional relations among different households. The resulting model can accurately predict future loads (short-term) of individual consumers, even if these were not included in the original training set (out-of-sample consumers). This entails a great potential for large scale applications (Big Data) as once the single network is trained, accurate individual forecast for new consumers can be obtained at almost no computational cost. The performance of the proposed model is tested under a large set of numerical experiments by using a real world dataset with thousands of disaggregated electricity consumption time series. Furthermore, we exploit the considered dataset to explore how geo-demographic segmentation of consumers can improve the forecasting accuracy of the proposed model.