  Forecast combination involves using multiple forecasts to create a single,
more accurate prediction. Recently, feature-based forecasting has been employed
to either select the most appropriate forecasting models or to optimize the
weights of their combination. In this paper, we present a multi-task
optimization paradigm that focuses on solving both problems simultaneously and
enriches current operational research approaches to forecasting. In essence, it
incorporates an additional learning and optimization task into the standard
feature-based forecasting approach, focusing on the identification of an
optimal set of forecasting methods. During the training phase, an optimization
model with linear constraints and quadratic objective function is employed to
identify accurate and diverse methods for each time series. Moreover, within
the training phase, a neural network is used to learn the behavior of that
optimization model. Once training is completed the candidate set of methods is
identified using the network. The proposed approach elicits the essential role
of diversity in feature-based forecasting and highlights the interplay between
model combination and model selection when optimizing forecasting ensembles.
Experimental results on a large set of series from the M4 competition dataset
show that our proposal enhances point forecast accuracy compared to
state-of-the-art methods.
