Preference Articulation by Means of the R2 Indicator

Tobias Wagner 1 Heike Trautmann 1 Dimo Brockhoff 2
2 DOLPHIN - Parallel Cooperative Multi-criteria Optimization
LIFL - Laboratoire d'Informatique Fondamentale de Lille, Inria Lille - Nord Europe
Abstract : 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.
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Evolutionary Multi-criterion Optimization (EMO 2013), Mar 2013, Sheffield, United Kingdom. 7811, pp.81-95, 2013, Lecture Notes in Computer Science Volume. 〈10.1007/978-3-642-37140-0_10〉
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Tobias Wagner, Heike Trautmann, Dimo Brockhoff. Preference Articulation by Means of the R2 Indicator. Evolutionary Multi-criterion Optimization (EMO 2013), Mar 2013, Sheffield, United Kingdom. 7811, pp.81-95, 2013, Lecture Notes in Computer Science Volume. 〈10.1007/978-3-642-37140-0_10〉. 〈hal-00807867〉

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