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On the Properties of the R2 Indicator

Dimo Brockhoff 1, * Tobias Wagner 2 Heike Trautmann 3
* Corresponding author
1 DOLPHIN - Parallel Cooperative Multi-criteria Optimization
LIFL - Laboratoire d'Informatique Fondamentale de Lille, Inria Lille - Nord Europe
2 Institute of Machining Technology
TU - Technische Universität Dortmund [Dortmund]
3 Statistics Department
TU - Technische Universität Dortmund [Dortmund]
Abstract : In multiobjective optimization, set-based performance indicators are commonly used to assess the quality of a Pareto front approximation. Based on the scalarization obtained by these indicators, a performance comparison of multiobjective optimization algorithms becomes possible. The R2 and the Hypervolume (HV) indicator represent two recommended approaches which have shown a correlated behavior in recent empirical studies. Whereas the HV indicator has been comprehensively analyzed in the last years, almost no studies on the R2 indicator exist. In this paper, we thus perform a comprehensive investigation of the properties of the R2 indicator in a theoretical and empirical way. The influence of the number and distribution of the weight vectors on the optimal distribution of μ solutions is analyzed. Based on a comparative analysis, specific characteristics and differences of the R2 and HV indicator are presented.
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https://hal.inria.fr/hal-00722060
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Submitted on : Tuesday, July 31, 2012 - 4:01:11 PM
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Dimo Brockhoff, Tobias Wagner, Heike Trautmann. On the Properties of the R2 Indicator. GECCO'2012, Jul 2012, Philadelphia, United States. pp.465-472, ⟨10.1145/2330163.2330230⟩. ⟨hal-00722060⟩

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