| Abstract | This paper presents an approach for constructingimproved visual representations of high dimensional objectivespaces using virtual reality. These spaces arise from the solutionof multi-objective optimization problems with more than 3objective functions which lead to high dimensional Paretofronts. The 3-D representations of m-dimensional Pareto fronts,or their approximations, are constructed via similarity structuremappings between the original objective spaces and the 3-Dspace. Alpha shapes are introduced for the representation andcompared with previous approaches based on convex hulls. Inaddition, the mappings minimizing a measure of the amount ofdissimilarity loss are obtained via genetic programming. Thisapproach is preliminarily investigated using both theoreticallyderived high dimensional Pareto fronts for a test problem(DTLZ2) and practically obtained objective spaces for the 4dimensional knapsack problem via multi-objective evolutionaryalgorithms like HLGA, NSGA, and VEGA. The improvedrepresentation captures more accurately the real nature ofthe m-dimensional objective spaces and the quality of themappings obtained with genetic programming is equivalent tothose computed with classical optimization algorithms. |
|---|
