Design und Management komplexer technischer Prozesse und Systeme mit Methoden der Computational Intelligence Faster S-Metric Calculation by Considering Dominated Hypervolume as Klee‘s Measure Problem
نویسندگان
چکیده
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 logn + n logn), for n points of d ≥ 3 dimensions. This complex algorithm is adapted to the special case of calculating the S-metric. Conceptual simplifications of the implementation are concerned that save on a factor of O(logn) and establish an upper bound of O(n logn + n) for the S-metric calculation, improving the previously known bound of O(n).
منابع مشابه
Sonderforschungsbereich 531: Design und Management komplexer Prozesse und Systeme mit Methoden der Computational Intelligence
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