Section: New Results

Indicator-Based Multiobjective Optimization

Participant: Dimo Brockhoff

External Participants: Johannes Bader (formerly at ETH Zurich, Switzerland), Youssef Hamadi (Microsoft Research, Cambridge, UK), Souhila Kaci (Université Montpellier 2, France), Lothar Thiele (ETH Zurich, Switzerland), Heike Trautmann (University of Munster, Germany) Tobias Wagner (TU Dortmund, Germany), and Eckart Zitzler (PH Bern, Switzerland)

Indicator-based (evolutionary) multiobjective optimization algorithms have been first introduced in 2004 and typically use a quality indicator, assigning a solution set a real value, as a direct, internal performance criterion. Given that the indicator and the number $\mu$ of desired points is fixed, the optimization goal, also denoted by the term optimal $\mu$-distribution, is then defined as the solution set(s) of size $\mu$ which maximizes the indicator value.

In 2013, we continued to investigate, theoretically and numerically, the optimal $\mu$-distributions for the R2 indicator, an often recommended indicator based on scalarization functions [73] . We also proposed a new multiobjective optimizer with an R2-indicator-based selection [70] . With respect to the even more common hypervolume indicator, we combined the idea of the weighted hypervolume indicator with the idea of interactive algorithms and proposed a new algorithm that adapts the weighted hypervolume's weight function according to the user's preferences during the search. Last, we summarized our knowledge on the weighted hypervolume indicator and proposed a general framework of how to employ it within the hypervolume-based W-HypE algorithm [18] .