Robust Optimization Over Time: A Critical Review

Abstract

Robust optimization over time (ROOT) is the combination of robust optimization and dynamic optimization. In ROOT, frequent changes to deployed solutions are undesirable, which can be due to the high cost of switching between deployed solutions, limitations on the resources required to deploy new solutions, and/or the system's inability to tolerate frequent changes in the deployed solutions. ROOT is dedicated to the study and development of algorithms capable of dealing with the implications of deploying or maintaining solutions over longer time horizons involving multiple environmental changes. This paper presents an in-depth review of the research on ROOT. The overarching aim of this survey is to help researchers gain a broad perspective on the current state of the field, what has been achieved so far, and the existing challenges and pitfalls. This survey also aims to improve accessibility and clarity by standardizing terminology and unifying mathematical notions used across the field, providing explicit mathematical formulations of definitions, and improving many existing mathematical descriptions. Moreover, we classify ROOT problems based on two ROOT-specific criteria: the requirements for changing or keeping deployed solutions and the number of deployed solutions. This classification helps researchers gain a better understanding of the characteristics and requirements of ROOT problems, which is crucial to systematic algorithm design and benchmarking. Additionally, we classify ROOT methods based on the approach they use for finding robust solutions and provide a comprehensive

Robust Optimization over Time Problems—Characterization and Literature Review

“…In [7], the authors briefly review the literature on ROOT published up to 2019, while [8,9] surveyed the literature on evolutionary dynamic optimization up to 2021. More recently, the review of [10] organized the literature around a classification for ROOT problems based on two criteria: the requirements for changing or keeping deployed solutions and the number of deployed solutions. While these studies are useful to obtain an overview of what has and has not been carried out, we believe there is still room to make this overview more complete and comprehensive.…”