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» Multiplicative approximations and the hypervolume indicator
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FOGA
2011
12 years 8 months ago
The logarithmic hypervolume indicator
It was recently proven that sets of points maximizing the hypervolume indicator do not give a good multiplicative approximation of the Pareto front. We introduce a new “logarith...
Tobias Friedrich, Karl Bringmann, Thomas Voß...
PPSN
2010
Springer
13 years 3 months ago
Tight Bounds for the Approximation Ratio of the Hypervolume Indicator
The hypervolume indicator is widely used to guide the search and to evaluate the performance of evolutionary multi-objective optimization algorithms. It measures the volume of the ...
Karl Bringmann, Tobias Friedrich
GECCO
2009
Springer
148views Optimization» more  GECCO 2009»
13 years 11 months ago
Multiplicative approximations and the hypervolume indicator
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 alg...
Tobias Friedrich, Christian Horoba, Frank Neumann
EMO
2006
Springer
158views Optimization» more  EMO 2006»
13 years 9 months ago
The Hypervolume Indicator Revisited: On the Design of Pareto-compliant Indicators Via Weighted Integration
The design of quality measures for approximations of the Pareto-optimal set is of high importance not only for the performance assessment, but also for the construction of multiobj...
Eckart Zitzler, Dimo Brockhoff, Lothar Thiele
GECCO
2010
Springer
187views Optimization» more  GECCO 2010»
13 years 10 months ago
The maximum hypervolume set yields near-optimal approximation
In order to allow a comparison of (otherwise incomparable) sets, many evolutionary multiobjective optimizers use indicator functions to guide the search and to evaluate the perfor...
Karl Bringmann, Tobias Friedrich