Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/66827
Citations | ||
Scopus | Web of Science® | Altmetric |
---|---|---|
?
|
?
|
Type: | Conference paper |
Title: | Multiplicative approximations and the hypervolume indicator |
Author: | Friedrich, T. Horoba, C. Neumann, F. |
Citation: | Proceedings of the 11th Annual Conference on Genetic and Evolutionary Computation: GECCO '09, pp.571-578 |
Publisher: | ACM Press |
Publisher Place: | New York |
Issue Date: | 2009 |
ISBN: | 9781605583259 |
Conference Name: | Genetic and Evolutionary Computation Conference (11th : 2009 : Montreal, Canada) |
Editor: | Rothlauf, F. |
Statement of Responsibility: | Tobias Friedrich, Christian Horoba, Frank Neumann |
Abstract: | Indicator-based algorithms have become a very popular approach to solve multi-objective optimization problems. In this paper, we contribute to the theoretical understanding of algorithms maximizing the hypervolume for a given problem by distributing μ points on the Pareto front. We examine this common approach with respect to the achieved multiplicative approximation ratio for a given multi-objective problem and relate it to a set of μ points on the Pareto front that achieves the best possible approximation ratio. For the class of linear fronts and a class of concave fronts, we prove that the hypervolume gives the best possible approximation ratio. In addition, we examine Pareto fronts of different shapes by numerical calculations and show that the approximation computed by the hypervolume may differ from the optimal approximation ratio. |
Keywords: | Approximation evolutionary algorithms hypervolume indicator indicator-based algorithms multi-objective optimization |
Rights: | Copyright 2009 ACM |
DOI: | 10.1145/1569901.1569981 |
Published version: | http://dx.doi.org/10.1145/1569901.1569981 |
Appears in Collections: | Aurora harvest 5 Computer Science publications |
Files in This Item:
There are no files associated with this item.
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.