Integer Linear Optimization Models for Time Series Alignment

• Grant number: 25/28693-7
• Support Opportunities: Scholarships abroad - Research Internship - Scientific Initiation
• Start date: April 01, 2026
• End date: June 30, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Petra Maria Bartmeyer
• Grantee: Tiago Almeida Zanetti
• Supervisor: Dylan Francis Jones
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: University of Portsmouth, England
• Associated to the scholarship: 25/08234-8 - Blood Pressure Prediction Using Machine Learning, BP.IC

Abstract

This study focuses on the development of mathematical programming formulations for the optimal alignment of time series. The alignment process plays a fundamental role in time series analysis, as temporal 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, provide efficient heuristic alignments but lack a rigorous mathematical optimization foundation. As they are not based on linear or integer programming, these methods cannot guarantee global optimality and offer limited flexibility to include additional structural or physiological constraints.The proposed approach formulates the alignment problem as an optimization task, defining explicit decision variables, constraints, and objective functions that model the temporal correspondence between sequences. By expressing the problem in this framework, it becomes possible to obtain alignments that are mathematically optimal or near-optimal while preserving properties such as monotonicity and continuity. The implementation will involve the use of linear and integer programming solvers to evaluate model performance. The results are expected to demonstrate improvements in alignment accuracy, interpretability, and robustness when compared to heuristic methods, providing a stronger theoretical basis for future work in biomedical signal prediction and time series modeling. (AU)