A Correlation Analysis of Set Quality Indicator Values in Multiobjective Optimization

Arnaud Liefooghe 1, 2, * Bilel Derbel 1, 2
* Auteur correspondant
1 DOLPHIN - Parallel Cooperative Multi-criteria Optimization
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : A large spectrum of quality indicators has been proposed so far to assess the performance of discrete Pareto set approximations in multiobjective optimization. Such indicators assign, to any solution set, a real-value reflecting a given aspect of approximation quality. This is an important issue in multiobjective optimization, not only to compare the performance and assets of different approximate algorithms, but also to improve their internal selection mechanisms. In this paper, we adopt a statistical analysis to experimentally investigate by how much a selection of state-of-the-art quality indicators agree with each other for a wide range of Pareto set approximations from well-known two- and three-objective continuous benchmark functions. More particularly, we measure the correlation between the ranking of low-, medium-, and high-quality limited-size approximation sets with respect to inverted generational distance, additive epsilon, multiplicative epsilon, R2, R3, as well as hypervolume indicator values. Since no pair of indicators obtains the same ranking of approximation sets, we confirm that they emphasize different facets of approximation quality. More importantly, our statistical analysis allows the degree of compliance between these indicators to be quantified.
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Communication dans un congrès
Genetic and Evolutionary Computation Conference (GECCO 2016), Jul 2016, Denver, United States. Genetic and Evolutionary Computation Conference (GECCO 2016), 2016
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Arnaud Liefooghe, Bilel Derbel. A Correlation Analysis of Set Quality Indicator Values in Multiobjective Optimization. Genetic and Evolutionary Computation Conference (GECCO 2016), Jul 2016, Denver, United States. Genetic and Evolutionary Computation Conference (GECCO 2016), 2016. 〈hal-01159961v2〉

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