Section: New Results

Investigating the Optimization Goal of Indicator-Based Multiobjective Search

Participant from DOLPHIN: Dimo Brockhoff; External Participants: Heike Trautmann and Tobias Wagner (TU Dortmund University, Germany)

Using a quality indicator in the environmental selection step of evolutionary multiobjective optimization (EMO) algorithms to indicate which solutions shall be kept in the algorithms' population and which should be deleted, introduces a certain search bias. Instead of an “arbitrary” subset of the Pareto front, such (quality) indicator based search algorithms aim at approximating the set of $\mu$ solutions that optimizes a given indicator, for which the term optimal $\mu$-distribution has been introduced [63] . Also for performance assessment with respect to a given indicator, knowledge about the optimal $\mu$-distributions is helpful as interpreting the achieved indicator values with respect to the best achievable value becomes possible. For the hypervolume indicator, several results on these optimal $\mu$-distributions are known [63] , [62] , [75] , [69] , [70] , [61] [64] , but the understanding of the optimization goal for other indicators is less developed. Recently, we started to investigate the optimal $\mu$-distributions, both theoretically and numerically, for the so-called $R2$ indicator [79] —another often recommended quality indicator [90] . Instead of the binary version of [79] that takes two solution sets and assigns them a certain quality, we thereby investigated an equivalent unary indicator where one (reference) set is always fixed.

First experiments for problems with two objectives and connected Pareto fronts have been presented in [37] which won the best paper award within the EMO track at GECCO'2013 (See http://www.sigevo.org/gecco-2012/papers.html .). Further investigations on problems with disconnected Pareto fronts have been submitted to the Evolutionary Computation journal [72] . We also studied in more detail how the parameters of the $R2$ indicator such as the ideal point or the distribution of weight vectors can be used to change the optimization goal [86] and correspondingly proposed the algorithm $R2$-EMOA which is able to steer the search towards preferred regions of the Pareto front by optimizing the $R2$ indicator directly in its environmental selection [85] , [72] .