- author = "Julio J. Valdes and Alan J. Barton and Robert Orchard",
- title = "Virtual Reality High Dimensional Objective Spaces for Multi-Objective Optimization: An Improved Representation",
- booktitle = "2007 IEEE Congress on Evolutionary Computation",
- year = "2007",
- editor = "Dipti Srinivasan and Lipo Wang",
- pages = "4191--4198",
- address = "Singapore",
- month = "25-28 " # sep,
- organization = "IEEE Computational Intelligence Society",
- publisher = "IEEE Press",
- ISBN = "1-4244-1340-0",
- file = "1796.pdf",
- keywords = "genetic algorithms, genetic programming",
-
DOI = "
doi:10.1109/CEC.2007.4425018",
- 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.",
-
notes = "CEC 2007 - A joint meeting of the IEEE, the EPS, and
the IET.
IEEE Catalog Number: 07TH8963C",
