Visualization of Pareto-Sets in Evolutionary Multi-Objective Optimization

In this paper, a method for the visualization of the population of an evolutionary multi-objective optimization (EMO) algorithm is presented. The main characteristic of this approach is the preservation of Pareto-dominance relations among the individuals as good as possible. It will be shown that in general, a Pareto- dominance preserving mapping from higher- to lower- dimensional spaces does not exist. Thus, the demand is to find a mapping with as few wrongly indicated dominance relations as possible, which gives one more objective in addition to other mapping objectives like preserving nearest neighbor relations. Therefore, such a mapping poses a multi-objective optimization problem by itself, which is also handled by an EMO algorithm (NSGA-II in this case). The resulting mappings are shown for the run of a NSGA-II version on the 15 objective DTLZ2 problem as an example. From such plots, some insights into evolutionary dynamics can be obtained.