An EMO Algorithm Using the Hypervolume Measure as Selection Criterion

By Michael T. M. Emmerich, Nicola Beume, Boris Naujoks. International Conference on Evolutionary Multi-Criterion Optimization, 2005

670 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/a84d0dfe75bb1c7f41cc4545ad790b56b420a72a

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In Artificial Intelligence

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Citations in the corpus

Theory of the hypervolume indicator: optimal μ-distributions and the choice of the reference point (2009, background): “In recent years, search algorithms based on the hypervolume indicator [27], a set measure reﬂecting the volume enclosed by a Pareto front approximation and a reference set, have become increasingly popular, e.g., [16, 9, 14].”
The Hypervolume Indicator Revisited: On the Design of Pareto-compliant Indicators Via Weighted Integration (2007, methodology): “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].”
Multiobjective Optimization on a Limited Budget of Evaluations Using Model-Assisted -Metric Selection (2008, neutral): “[22].”
Preference-Inspired Coevolutionary Algorithms for Many-Objective Optimization (2013, methodology): “The hypervolume indicator [22], which is the only unary quality measure that is strictly monotonic with regard to Pareto dominance, is often used as an indicator [23], [24].”
Covariance Matrix Adaptation for Multi-objective Optimization (2007, methodology): “, 2002) or a new modification thereof based on the contributing hypervolume of individuals (Emmerich et al., 2005).”
A survey on multi-objective evolutionary algorithms for many-objective problems (2014, methodology): “The Pareto-based MOEAs selected for comparison were NSGA-II [24], SPEA2 [110], and -MOEA [67]; aggregation approaches were the MSOPS and the Repeated Single Objective (RSO) [41]; while indicator-based methods were two variants of the Indicator-based Evolutionary Algorithms (IBEA) [106] and the SMS-E”
SMS-EMOA: Multiobjective selection based on dominated hypervolume (2007, methodology): “In each generation, the metamodel-assisted SMS-EMOA [7] generates a surplus of individuals by mutations of one chosen individual.”
Handling Constrained Multiobjective Optimization Problems With Constraints in Both the Decision and Objective Spaces (2019, background): “Then, HV measures the volume enclosed by P and a speciﬁed reference point in the objective space [52].”
Multicriteria Optimization and Decision Making: Principles, Algorithms and Case Studies (2024, positive): “The SMS-EMOA [29] and HypE [4] can be seen as instantiations of indicatorbased methods, the design of which is directly governed by a performance indica-”
Many-Objective Evolutionary Algorithms (2015, methodology): “…is a function I: The hypervolume indicator ( I HV , aka S metric) was described as the Lebesgue measure L of the union of the hypercubes c i corresponding to each solution a i ∈ A [Zitzler and Thiele 1998; Emmerich et al. 2005]: (cid:2) (cid:2) , where z † is the worst point in the objective space.”
A Fast Way of Calculating Exact Hypervolumes (2012, background): “Hypervolume is also increasingly used in-line in multiobjective evolutionary algorithms, either to promote diversity [6], or as part of an archiving mechanism [7], [8], or as part of the selection process [9], [10].”
HypE: An Algorithm for Fast Hypervolume-Based Many-Objective Optimization (2011, positive): “Most hypervolume-based algorithms ﬁrst perform a nondominated sorting and then rank solutions within a particular front according to the hypervolume loss that results from the removal of a speciﬁc solution (Knowles and Corne, 2003; Emmerich et al., 2005; Igel et al., 2007; Bader et al., 2008).”
IGD Indicator-Based Evolutionary Algorithm for Many-Objective Optimization Problems (2018, background): “For instance, several MOEAs based on the hypervolume (HV) were proposed in [31]–[33]; however, their major disadvantages were the costly overhead in calculating the HV values especially in solving MaOPs.”
Evolutionary many-objective optimization: A short review (2008, background): “Several variants of IBEAs have been proposed in the literature [44]-[46].”
A tutorial on multiobjective optimization: fundamentals and evolutionary methods (2018, methodology): “NSGA-II served as a representative of Pareto based approaches, SMS-EMOA as an example of Indicator-based approaches, and MOEA/D as an example of decomposition based approaches.”
A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition (2017, methodology): “based on indicator based framework are SMS-EMOA [7], SIBEA [8], etc.”
ParEGO: a hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems (2006, methodology): “Most recently, three papers [20], [22], and [23] have appeared that use a Kriging approach based on the DACE model [52] within an MOEA.”