On the relationships between sub problems in the hierarchical optimization framework

Abstract

In many optimization problems there may exist multiple ways in which a particular hierarchical optimization problem can be modeled. In addition, the diversity of hierarchical optimization problems requires different types of multilevel relations between sub-problems. Thus, the approximate and accurate representations and solutions can be integrated. That is, to address the how partial solutions of sub-problems can be reintegrated to build a solution for the main problem. The nature of relations between components differs from one decomposition strategy to another. In this paper, we will investigate the possible links and relationships that may appear between sub-problems.