On metrics for comparing nondominated sets

By Joshua D. Knowles, David Wolfe Corne. Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600), 2002

580 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/b585ea2a144c3ad922735b7ad38a68743a947b7b

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Citations in the corpus

Benchmark Problems and Performance Indicators for Search of Knee Points in Multiobjective Optimization (2020, background): “Popular performance indicators include generational distance (GD) [56], inverted GD (IGD) [57], and S-metric [58], [59], also known as hypervolume.”
Evolutionary algorithms and other metaheuristics in water resources: Current status, research challenges and future directions (2014, methodology): “(Knowles and Corne, 2002); (iii) the runtime ε-performance metric (Kollat et al.”
ParEGO: a hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems (2006, result): “some recent works [ 38 ], [39], [61] that several of these are not consistent with the partial ordering of approximation sets that follows logically from the basic principles of Pareto optimization.”
Evolutionary many-objective optimization: A short review (2008, background): “A number of performance indicators have been proposed to measure the quality of non-dominated solution sets [38]-[40].”
Multi-objective optimization using evolutionary algorithms (2001, background): “A detailed study [31] comparing most existing performance metrics based on out-performance relations has concluded that R-metrics suggested by [32] are the best.”
Using the Averaged Hausdorff Distance as a Performance Measure in Evolutionary Multiobjective Optimization (2012, background): “A discussion of these and further indicators can be found in [25] and [54].”
Quality Assessment of Pareto Set Approximations (2008, background): “Further examples can be found in (Knowles, 2002; Knowles and Corne, 2002).”
Battling Arrow’s Paradox to Discover Robust Water Management Alternatives (2016, background): “Because the metric comprehensively determines how much space is filled from every point in the set, it is the most difficult metric to meet (Knowles and Corne 2002)”
Covariance Matrix Adaptation for Multi-objective Optimization (2007, methodology): “We concisely define the performance measures used, for a detailed description of the methods we refer to the literature (Knowles and Corne, 2002; Zitzler et al., 2003; Knowles et al., 2005).”
HypE: An Algorithm for Fast Hypervolume-Based Many-Objective Optimization (2011, background): “However, this changed with the advent of theoretical studies that provided evidence for a unique property of this indicator [24], [47], [18]: it is the only indicator known to be strictly monotonic with respect to Pareto dominance and thereby guaranteeing that the Paretooptimal front achieves the ma”
An EMO Algorithm Using the Hypervolume Measure as Selection Criterion (2005, background): “In [5, 7] Knowles and Corne gave an example with two Pareto fronts, A and B, in the two dimensional case.”
On the Evolutionary Optimization of Many Conflicting Objectives (2007, background): “Many performance indicators have been proposed for EMO and a discussion of these can be found in [10] and [30].”
Borg: An Auto-Adaptive Many-Objective Evolutionary Computing Framework (2013, background): “Knowles and Corne (2002) provide a detailed discussion of the methods and issues for comparing nondominated sets.”