Integer Linear Optimization Models for Time Series Alignment

With the advancement of wearable devices, it has become possible to simultaneously collect several biomedical signals through multiple devices, such as smartwatches and performance monitoring straps. A central challenge in this collection is the integration of this physiological data from independent sensors to create a unified database. These signals, characterized as time series, present noise and distortions resulting from physical factors (such as user movement or momentary interruptions in capture), which prevents the series from being identical or just outdated, requiring a robust alignment to ensure the fidelity of clinical and performance information.

This work proposes the development of mathematical programming formulations, specifically using goal programming, aimed at the optimal alignment of these time series. The alignment process plays a key role in time series analysis, as time distortions or sampling inconsistencies between signals can significantly degrade the performance of predictive models. Traditional methods, such as Dynamic Time Warping (DTW) and its approximations (including FastDTW), offer efficient heuristic alignments, but in some applications lack the customization allowed by mathematical programming techniques . Different from dynamic programming-based approaches (DTW
for example), which may present limitations in the inclusion of complex structural constraints, the use of mathematical programming allows for rigorous and flexible model customization