Visualizing High Dimensional Objective Spaces for Multi-objective Optimization: A Virtual Reality Approach

This paper presents an approach for constructing visual representations of high dimensional objective spaces using virtual reality. These spaces arise from the solution of multi-objective optimization problems with more than 3 objective functions which lead to high dimensional Pareto fronts which are difficult to use. This approach is preliminarily investigated using both theoretically derived high dimensional Pareto fronts for a test problem (DTLZ2) and practically obtained objective spaces for the 4 dimensional knapsack problem via multi-objective evolutionary algorithms like HLGA, NSGA, and VEGA. The expected characteristics of the high dimensional fronts in terms of relative sizes, sequencing, embedding and asymmetry were systematically observed in the constructed virtual reality spaces.