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. Moreover, the performance indicator can also be used as a selection criterion to directly optimize the performance of the resulting solution sets. Prominent examples of evolutionary algorithms that use an indicator-based selection are IBEA, SMS-EMOA, MO-CMA-ES, (W-)HypE, and others.

The R2-EMOA follows these successful algorithms and replaces the hypervolume-based selection of the (μ+λ)-SMS-EMOA by an R2 indicator based selection [1],[2]. This not only allows to optimize another quality indicator, but one can get around the large computation time of the hypervolume while still being able to integrate user preferences into the search [3].

Paper References

[1] H. Trautmann, T. Wagner, and D. Brockhoff. R2-EMOA: Focused Multiobjective Search Using R2-Indicator-Based Selection. Learning and Intelligent Optimization Conference (LION 2013), Springer, 2013. Short paper. Accepted for publication.

[2] D. Brockhoff, T. Wagner, and H. Trautmann. R2 Indicator Based Multiobjective Search. Evolutionary Computation, MIT Press, 2013. Submitted (shorter version published at GECCO'2012 [4]).

[3] T. Wagner and H. Trautmann and D. Brockhoff. Preference Articulation by Means of the R2 Indicator. Conference on Evolutionary Multi-Criterion Optimization (EMO 2013), Springer, 2013. Accepted for publication.

[4] D. Brockhoff, T. Wagner, and H. Trautmann. On the Properties of the R2 Indicator. In Genetic and Evolutionary Computation Conference (GECCO 2012), pages 465-472. ACM, 2012. Best Paper Award in EMO Track.

Source Code of the R2-EMOA

The following MATLAB source code is based on the SMS-EMOA implementation of Tobias Wagner and Fabian Kretzschmar and, as its base version, is again provided under the GPL (version 2) license:

Algorithm Source Code version 1.1 (March 15, 2013, 160KB)

Old versions and bugs