An Improved Dimension-Sweep Algorithm for the Hypervolume Indicator

By Carlos M. Fonseca, Luís Paquete, Manuel López-Ibáñez. International Conference on Evolutionary Computation, 2006

567 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Computer Networks and Communications, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/d3f6adedc2bdf9547cdfa4a858920d262af4dac4

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Citations in the corpus

Multiobjective Optimization on a Limited Budget of Evaluations Using Model-Assisted -Metric Selection (2008, unknown): “[27].”
Preference-Inspired Coevolutionary Algorithms for Many-Objective Optimization (2013, unknown): “calculated using conventional methods [22], [47].”
Automatically improving the anytime behaviour of optimisation algorithms (2014, methodology): “We use a publicly available implementation of the hypervolume measure [26], and the MMAS implementation is based on”
An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints (2014, background): “For example, computing hyper-volume metric requires exponentially more computations with the number of objectives [18], [19].”
Quality Assessment of Pareto Set Approximations (2008, background): “This comes at the cost of high computational cost: the best known algorithms for computing the hypervolume have running times which are exponential in the number of objectives (see While, 2005; While et al., 2005, 2006; Fonseca et al., 2006; Beume and Rudolph, 2006).”
A Fast Way of Calculating Exact Hypervolumes (2012, background): “We can see how crucial this step is to the efficiency of these calculations by plotting the percentage of dominated points in S′ for various types of data.”
The Hypervolume Indicator Revisited: On the Design of Pareto-compliant Indicators Via Weighted Integration (2007, background): “On the other hand, there are some studies that discuss the usage of this measure for multiobjective search [10, 20, 4] and in particular the issue of fast hypervolume calculation has been a focus of research recently [16, 17, 6, 1].”
HypE: An Algorithm for Fast Hypervolume-Based Many-Objective Optimization (2011, unknown): “Recently, advanced algorithms for hypervolume calculation have been proposed, a dimension-sweep method (Fonseca et al., 2006) with a worst-case runtime complexity of O(Nn-2 log N ), and a specialized algorithm related to”