TY - GEN
T1 - Theoretically investigating optimal μ-distributions for the hypervolume indicator
T2 - 11th International Conference on Parallel Problem Solving from Nature, PPSN 2010
AU - Auger, Anne
AU - Bader, Johannes
AU - Brockhoff, Dimo
PY - 2010/11/12
Y1 - 2010/11/12
N2 - Several indicator-based evolutionary multiobjective optimization algorithms have been proposed in the literature. The notion of optimal μ -distributions formalizes the optimization goal of such algorithms: find a set of μ solutions that maximizes the underlying indicator among all sets with μ solutions. In particular for the often used hypervolume indicator, optimal μ-distributions have been theoretically analyzed recently. All those results, however, cope with bi-objective problems only. It is the main goal of this paper to extend some of the results to the 3-objective case. This generalization is shown to be not straight-forward as a solution's hypervolume contribution has not a simple geometric shape anymore in opposition to the bi-objective case where it is always rectangular. In addition, we investigate the influence of the reference point on optimal μ-distributions and prove that also in the 3-objective case situations exist for which the Pareto front's extreme points cannot be guaranteed in optimal μ-distributions.
AB - Several indicator-based evolutionary multiobjective optimization algorithms have been proposed in the literature. The notion of optimal μ -distributions formalizes the optimization goal of such algorithms: find a set of μ solutions that maximizes the underlying indicator among all sets with μ solutions. In particular for the often used hypervolume indicator, optimal μ-distributions have been theoretically analyzed recently. All those results, however, cope with bi-objective problems only. It is the main goal of this paper to extend some of the results to the 3-objective case. This generalization is shown to be not straight-forward as a solution's hypervolume contribution has not a simple geometric shape anymore in opposition to the bi-objective case where it is always rectangular. In addition, we investigate the influence of the reference point on optimal μ-distributions and prove that also in the 3-objective case situations exist for which the Pareto front's extreme points cannot be guaranteed in optimal μ-distributions.
U2 - 10.1007/978-3-642-15844-5_59
DO - 10.1007/978-3-642-15844-5_59
M3 - Conference contribution
AN - SCOPUS:78149264729
SN - 3642158439
SN - 9783642158438
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 586
EP - 596
BT - Parallel Problem Solving from Nature, PPSN XI - 11th International Conference, Proceedings
Y2 - 11 September 2010 through 15 September 2010
ER -