Virtual Reality High Dimensional Objective Spaces for Multi-Objective Optimization: An Improved Representation

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ConferenceProceedings of the IEEE Congress on Evolutionary Computation, September 25-28, 2007., Singapore
AbstractThis 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.
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AffiliationNRC Institute for Information Technology; National Research Council Canada
Peer reviewedNo
NRC number49364
NPARC number8913246
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Record identifierc81f9835-9374-4364-8099-3dad4cc41c94
Record created2009-04-22
Record modified2016-05-09
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