On the interrelationships between knees and aggregate objective functions

Abstract

Optimizing several objectives that are often at odds with each other provides difficult challenges that are not encountered if having only one goal at hand. One intuitive way to solve a multi-objective problem is to aggregate the objectives and reformulate it as an optimization problem having just a single goal. This goal can be a designer specific aggregation of the objectives or a characterization of knees, trade-offs, utilities, stronger optimality concepts or preferences. This paper examines the theoretical relationships between two knee concepts and aggregate objective functions methods. The changes in the fitness landscape by utilizing different aggregations is also discussed.