Aggregation Trees for visualization and dimension reduction in many-objective optimization

This paper introduces the concept of Aggregation Trees for the visualization of the results of high-dimensional multi-objective optimization problems, or many-objective problems and as a means of performing dimension reduction. The high dimensionality of many-objective optimization makes it difficult to represent the relationship between objectives and solutions in such problems and most approaches in the literature are based on the representation of solutions in lower dimensions. The method of Aggregation Trees proposed here is based on an iterative aggregation of objectives that are represented in a tree. The location of conflict is also calculated and represented on the tree. Thus, the tree can represent which objectives and groups of objectives are the most harmonic, what sort of conflict is present between groups of objectives, and which aggregations would be helpful in order to reduce the problem dimension. (C) 2014 Elsevier Inc. All rights reserved.