Faster S-metric calculation by considering dominated hypervolume as Klee s measure problem
| dc.contributor.author | Beume, Nicola | de |
| dc.contributor.author | Rudolph, Günter | de |
| dc.date.accessioned | 2009-05-12T16:00:52Z | |
| dc.date.available | 2009-05-12T16:00:52Z | |
| dc.date.issued | 2006-07 | de |
| dc.description.abstract | The dominated hypervolume (or S-metric) is a commonly accepted quality measure for comparing approximations of Pareto fronts generated by multi-objective optimizers. Since optimizers exist, namely evolutionary algorithms, that use the S-metric internally several times per iteration, a faster determination of the S-metric value is of essential importance. This paper describes how to consider the S-metric as a special case of a more general geometrical problem called Klee s measure problem (KMP). For KMP, an algorithm exists with run time O(n log n + n^(d/2) log n), for n points of d>= 3 dimensions. This complex algorithmis adapted to the special case of calculating the S-metric. Conceptual simplifications of the implementation are concerned that save on a factor of O(log n) and establish an upper bound of O(n log n + n^(d/2)) for the S-metric calculation, improving the previously known bound of O(n^(d-1)). | en |
| dc.identifier.uri | http://hdl.handle.net/2003/26124 | |
| dc.identifier.uri | http://dx.doi.org/10.17877/DE290R-12786 | |
| dc.language.iso | en | de |
| dc.relation.ispartofseries | Reihe CI; 216-06 | de |
| dc.subject | evolutionary algorithms | en |
| dc.subject | hypervolume | en |
| dc.subject | Klee s measure problem | en |
| dc.subject | multi-objective optimization | en |
| dc.subject | performance assessment | en |
| dc.subject | S-metric | en |
| dc.subject.ddc | 004 | de |
| dc.title | Faster S-metric calculation by considering dominated hypervolume as Klee s measure problem | en |
| dc.type | Text | de |
| dc.type.publicationtype | report | de |
| dcterms.accessRights | open access |
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