R2 Indicator Based Multiobjective Search

Dimo Brockhoff 1 Tobias Wagner 2 Heike Trautmann 3
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 : 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 extended version of our previous conference 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. Furthermore, the R2 indicator is integrated into an indicator-based steady-state evolutionary multiobjective optimization algorithm (EMOA). It is shown that the so-called R2-EMOA can accurately approximate the optimal distribution of µ solutions regarding R2.
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Evolutionary Computation, Massachusetts Institute of Technology Press (MIT Press), 2015, 23 (3), pp.369-395. 〈http://www.mitpressjournals.org/doi/10.1162/EVCO_a_00135〉. 〈10.1162/EVCO_a_00135〉
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Dimo Brockhoff, Tobias Wagner, Heike Trautmann. R2 Indicator Based Multiobjective Search. Evolutionary Computation, Massachusetts Institute of Technology Press (MIT Press), 2015, 23 (3), pp.369-395. 〈http://www.mitpressjournals.org/doi/10.1162/EVCO_a_00135〉. 〈10.1162/EVCO_a_00135〉. 〈hal-01329559〉

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