Nested multi-level structures are frequently encountered in many real-world optimization problems. Decomposition techniques are a commonly applied approach used to handle nested multi-level structures; however, the typical problem-specific focus of such techniques has led to numerous specialized formulations and solution methods. This lack of generalized results for nested multi-level optimization problems is addressed in this paper with the proposal of a theoretical framework for their formulation and the application of decomposition techniques. The developed theoretical framework will be used to highlight the prevalence of general multi-level structures within a wide range of application areas. Further, state-of-the-art solution methods for nested multi-level optimization problems will be described in the context of the proposed framework. The discussion in this paper will highlight the broad applicability of the general formulation and solution methodologies developed for this important class of real-world optimization problems.
University of Exeter, United Kingdom, October 2021