Theory of the hypervolume indicator: optimal μ-distributions and the choice of the reference point
By Anne Auger, Johannes Bader, Dimo Brockhoff, Eckart Zitzler. Foundations of Genetic Algorithms, 2009
432 citations recorded by the source corpus.
Subfields: Artificial Intelligence, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/ad93bf18c563c25ffb8f00bb77a284affd03daf4
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Citations in the corpus
- A Fast Way of Calculating Exact Hypervolumes (2012, neutral): “1.”
- Shift-Based Density Estimation for Pareto-Based Algorithms in Many-Objective Optimization (2014, background): “How would the Pareto-based algorithms, when integrated with SDE, compare with other state-of-the-art algorithms designed specially for many-objective problems?”
- Multi-objective training of Generative Adversarial Networks with multiple discriminators (2019, methodology): “Previous literature has discussed in depth the effects of the selection of η in the case of population-based methods (Auger et al., 2009; 2012).”
- A tutorial on multiobjective optimization: fundamentals and evolutionary methods (2018, background): “For biobjective problems, it is highest at points where the slope is equal to (cid:11) 45 (cid:15) (Auger et al. 2009).”
- Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization (2020, background): “1 Reference point specification There is a large body of literature on the effects of reference point specification [4, 33, 34].”
- Performance indicators in multiobjective optimization (2018, background): “This measure enables to better estimate the distribution of the points along the Pareto front (in fact, it can be shown that for a linear Pareto front, an uniform distribution of points maximizes the hyper-volume indicator: see [64, 65] for more details about the properties of the hyper-volume indic”
- A New Dominance Relation-Based Evolutionary Algorithm for Many-Objective Optimization (2016, background): “It has been found that choosing ri that is slightly larger than znad i is suitable since the balance between convergence and diversity of the solution set is well emphasized [76], [77].”
- Multicriteria Optimization and Decision Making: Principles, Algorithms and Case Studies (2024, neutral): “Moreover, in 2-D, when μ → ∞, the set of points maximizing the hypervolume indicator will form a dense subset on the Pareto front [2].”