Post-analysis of multi-objective optimization solutions using decision trees

Evolutionary algorithms are often applied to solve multi-objective optimization problems. Such algorithms effectively generate solutions of wide spread, and have good convergence properties. However, they do not provide any characteristics of the found optimal solutions, something which may be very valuable to decision makers. By performing a post-analysis of the solution set from multi-objective optimization, relationships between the input space and the objective space can be identified. In this study, decision trees are used for this purpose. It is demonstrated that they may effectively capture important characteristics of the solution sets produced by multi-objective optimization methods. It is furthermore shown that the discovered relationships may be used for improving the search for additional solutions. Two multi-objective problems are considered in this paper; a well-studied benchmark function problem with on a beforehand known optimal Pareto front, which is used for verification purposes, and a multi-objective optimization problem of a real-world production system. The results show that useful relationships may be identified by employing decision tree analysis of the solution sets from multi-objective optimizations.