Virtual Reality High Dimensional Objective Spaces for
Multi-Objective Optimization: An Improved
Representation
J. Valdes, A. Barton, and R. Orchard. 2007 IEEE Congress on Evolutionary Computation, page 4191--4198. Singapore, IEEE Computational Intelligence Society, IEEE Press, (25-28 September 2007)
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.
%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
}