%0 Conference Paper %1 Valdes:2007:cec %A Valdes, Julio J. %A Barton, Alan J. %A Orchard, Robert %B 2007 IEEE Congress on Evolutionary Computation %C Singapore %D 2007 %E Srinivasan, Dipti %E Wang, Lipo %I IEEE Press %K algorithms, genetic programming %P 4191--4198 %T Virtual Reality High Dimensional Objective Spaces for Multi-Objective Optimization: An Improved Representation %X This paper presents an approach for constructing improved visual representations of high dimensional objective spaces using virtual reality. These spaces arise from the solution of multi-objective optimisation problems with more than 3 objective functions which lead to high dimensional Pareto fronts. The 3-D representations of m-dimensional Pareto fronts, or their approximations, are constructed via similarity structure mappings between the original objective spaces and the 3-D space. Alpha shapes are introduced for the representation and compared with previous approaches based on convex hulls. In addition, the mappings minimising a measure of the amount of dissimilarity loss are obtained via genetic programming. 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 improved representation captures more accurately the real nature of the m-dimensional objective spaces and the quality of the mappings obtained with genetic programming is equivalent to those computed with classical optimization algorithms. %@ 1-4244-1340-0

@inproceedings{Valdes:2007:cec, abstract = {This paper presents an approach for constructing improved visual representations of high dimensional objective spaces using virtual reality. These spaces arise from the solution of multi-objective optimisation problems with more than 3 objective functions which lead to high dimensional Pareto fronts. The 3-D representations of m-dimensional Pareto fronts, or their approximations, are constructed via similarity structure mappings between the original objective spaces and the 3-D space. Alpha shapes are introduced for the representation and compared with previous approaches based on convex hulls. In addition, the mappings minimising a measure of the amount of dissimilarity loss are obtained via genetic programming. 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 improved representation captures more accurately the real nature of the m-dimensional objective spaces and the quality of the mappings obtained with genetic programming is equivalent to those computed with classical optimization algorithms.}, added-at = {2008-06-19T17:35:00.000+0200}, address = {Singapore}, author = {Valdes, Julio J. and Barton, Alan J. and Orchard, Robert}, biburl = {https://www.bibsonomy.org/bibtex/248415e3783a1e96c9fb8716cb36e4ba1/brazovayeye}, booktitle = {2007 IEEE Congress on Evolutionary Computation}, editor = {Srinivasan, Dipti and Wang, Lipo}, file = {1796.pdf}, interhash = {923fe64a18b5bb0cadbded3428840142}, intrahash = {48415e3783a1e96c9fb8716cb36e4ba1}, isbn = {1-4244-1340-0}, keywords = {algorithms, genetic programming}, month = {25-28 September}, notes = {CEC 2007 - A joint meeting of the IEEE, the EPS, and the IET. IEEE Catalog Number: 07TH8963C}, organization = {IEEE Computational Intelligence Society}, pages = {4191--4198}, publisher = {IEEE Press}, timestamp = {2008-06-19T17:53:28.000+0200}, title = {Virtual Reality High Dimensional Objective Spaces for Multi-Objective Optimization: An Improved Representation}, year = 2007 }