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Non‐monotonicity of Observed Hypervolume in 1‐Greedy S ‐Metric Selection
Author(s) -
Judt Leonard,
Mersmann Olaf,
Naujoks Boris
Publication year - 2012
Publication title -
journal of multi‐criteria decision analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.462
H-Index - 47
eISSN - 1099-1360
pISSN - 1057-9214
DOI - 10.1002/mcda.1485
Subject(s) - monotonic function , mathematics , intuition , mathematical optimization , selection (genetic algorithm) , metric (unit) , population , computer science , mathematical analysis , artificial intelligence , economics , philosophy , operations management , demography , epistemology , sociology
The progression of the dominated hypervolume in the course of the optimization process, with respect to a global reference point, is thought to be monotonically increasing. This intuition is based on the observation that in each iteration, the solution that contributes the least to the dominated hypervolume is eliminated. Derived from results of multiple optimization runs with incorporated reference point adaptation, we show that this does not always hold for two‐dimensional and three‐dimensional objective spaces. For the two‐dimensional case, this is because the two boundary solutions are always retained in the population regardless of their hypervolume contribution. For the three‐dimensional case, we are able to show that the cause of the drop in dominated hypervolume is the continuous adaption of the reference point during selection. Copyright © 2012 John Wiley & Sons, Ltd.