Weighted Hypervolume Indicator: Implementation of hypervolume indicators for different weight distribution functions. Using the hypervolume of the dominated portion of the objective space as a measure for the quality of Pareto set approximations has received more and more attention in recent years. So far, the hypervolume indicator is the only measure known in the literature on evolutionary multiobjective optimization that possesses the following two properties. On the one hand, it is sensitive to any type of improvements, i.e., whenever an approximation set A dominates another approximation set B, then the measure yields a strictly better quality value for the former than for the latter set. On the other hand, the hypervolume measure guarantees that any approximation set A that achieves the maximally possible quality value for a particular problem contains all Pareto-optimal objective vectors. With the recently proposed approach of a weighted hypervolume indicator, these properties are not removed by simultaneously be able to incorporate various user preferences. According to [zbt2007a], three different hypervolume based indicators have been developed incorporating the following preferences: Focus on extreme points, Focus on the extremes of the second objective plus one additional extreme point for the first objective, Focus on a given reference point.

References in zbMATH (referenced in 29 articles )

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  1. Martí, Luis; García, Jesús; Berlanga, Antonio; Molina, José M.: Multi-objective optimization with an adaptive resonance theory-based estimation of distribution algorithm (2013)
  2. Stracquadanio, Giovanni; Romano, Vittorio; Nicosia, Giuseppe: Semiconductor device design using the \textscBiMADSalgorithm (2013)
  3. Auger, Anne; Bader, Johannes; Brockhoff, Dimo; Zitzler, Eckart: Hypervolume-based multiobjective optimization: theoretical foundations and practical implications (2012)
  4. Berghammer, Rudolf; Friedrich, Tobias; Neumann, Frank: Convergence of set-based multi-objective optimization, indicators and deteriorative cycles (2012)
  5. Reiter, Peter; Gutjahr, Walter J.: Exact hybrid algorithms for solving a bi-objective vehicle routing problem (2012)
  6. Vatolkin, Igor; Preuß, Mike; Rudolph, Günter; Eichhoff, Markus; Weihs, Claus: Multi-objective evolutionary feature selection for instrument recognition in polyphonic audio mixtures (2012) ioport
  7. Bechikh, Slim; Ben Said, Lamjed; Ghédira, Khaled: Searching for knee regions of the Pareto front using mobile reference points (2011) ioport
  8. Kampolis, I. C.; Trompoukis, X. S.; Asouti, V. G.; Giannakoglou, K. C.: CFD-based analysis and two-level aerodynamic optimization on graphics processing units (2010)
  9. Zitzler, Eckart; Brockhoff, Dimo; Thiele, Lothar: The hypervolume indicator revisited: On the design of Pareto-compliant indicators via weighted integration (2007) ioport