A study of problems with multiple interdependent components - Part I
This work addresses the formal modeling of complex real-world optimization problems, such as in logistics and supply chain management, but appears incremental as it builds on existing decomposability concepts.
The paper tackles the challenge of modeling problems with multiple interdependent components by proposing a reverse perspective, defining components first and then their connections, and provides formal definitions and classifications for dependencies in such problems.
Recognising that real-world optimisation problems have multiple interdependent components can be quite easy. However, providing a generic and formal model for dependencies between components can be a tricky task. In fact, a PMIC can be considered simply as a single optimisation problem and the dependencies between components could be investigated by studying the decomposability of the problem and the correlations between the sub-problems. In this work, we attempt to define PMICs by reasoning from a reverse perspective. Instead of considering a decomposable problem, we model multiple problems (the components) and define how these components could be connected. In this document, we introduce notions related to problems with mutliple interndependent components. We start by introducing realistic examples from logistics and supply chain management to illustrate the composite nature and dependencies in these problems. Afterwards, we provide our attempt to formalise and classify dependency in multi-component problems.