Learning to Understand the Problem Structure

This chapter focuses on an important aspect of learning the preference structure of the objectives, inherent in multi- and many-objective optimization problem formulations. This involves identifying the non-essential (redundant) objectives, and also determining the relative importance of the essential objectives. Such an approach to knowledge discovery is based on the following rationale. Modeling an optimization problem, analytically or through experiments, involves a lot of time and physical resources, possibly from multiple disciplines, in conjunction or isolation from each other. Often, it can be intriguing for analysts or decision makers (DMs) to know if the developed model represents the underlying problem in a minimal form or is marked by redundancy. Any redundancy among objectives, if revealed, could shed insightful light on the physics of the underlying problem, in addition to reducing its complexity and promising greater search efficiency for evolutionary multi- and many-objective optimization algorithms (EMâOAs). Furthermore, the revelation of the relative preferences among the essential objectives that are inherent in the problem models could also be significantly useful, as highlighted below.