Preference Articulation by Means of the R2 Indicator

Wagner, T.1, a; Trautmann, H.2, b; Brockhoff, D.3, c

Institut für Spanende Fertigung, Technische Universität Dortmund, Baroper Str. 303, 44227 Dortmund
Lehrstuhl Computergestützte Statistik, Technische Universität Dortmund, 44227 Dortmund
INRIA Lille - Nord Europe, Parc scientifique de la Haute Borne 40, avenue Halley - Bât A - Park Plaza, 59650 Villeneuve d'Ascq, Frankreich

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In multi-objective optimization, set-based performance indicators have become the state of the art for assessing the quality of Pareto front approximations. As a consequence, they are also more and more used within the design of multi-objective optimization algorithms. The R2 and the Hypervolume (HV) indicator represent two popular examples. In order to understand the behavior and the approximations preferred by these indicators and algorithms, a comprehensive knowledge of the indicator’s properties is required. Whereas this knowledge is available for the HV, we presented a first approach in this direction for the R2 indicator just recently. In this paper, we build upon this knowledge and enhance the considerations with respect to the integration of preferences into the R2 indicator. More specifically, we analyze the effect of the reference point, the domain of the weights, and the distribution of weight vectors on the optimization of μ solutions with respect to the R2 indicator. By means of theoretical findings and empirical evidence, we show the potentials of these three possibilities using the optimal distribution of μ solutions for exemplary setups.


Hypervolume Indicator, Multi-Objective Optimization, Performance Assessment, R2 Indicator


In: Proceedings of the 7th International Conference Evolutionary Multi-Criterion Optimization (EMO 2013), 19.3.-22.3. 2013, Sheffield, UK, Pursehouse, R.; Fleming, P. J.; Fonseca, C. M.; Greco, S.; Shaw, J. (Hrsg.), ISBN 978-3-642-37139-4, S. 81-95, doi: 10.1007/978-3-642-37140-0_10