Scalarization versus indicator-based selection in multi-objective CMA evolution strategies

While scalarization approaches to multi- criteria optimization become infeasible in the case of many objectives, for few objectives the benefits of population- based methods compared to a set of independent single- objective optimization trials on scalarized functions are not obvious. The multi-objective covariance matrix adaptation evolution strategy (MO-CMA-ES) is a powerful algorithm for real-valued multi-criteria optimization. This population- based approach combines mutation and strategy adaptation from the elitist CMA-ES with multi-objective selection. We empirically compare the steady-state MO-CMA-ES with different scalarization algorithms, in which the elitist CMA-ES is used as single-objective optimizer. Although only bicriteria benchmark problems are considered, the MO-CMA-ES performs best in the overall comparison. However, if the scalarized problems have a structure that can easily be exploited by the CMA-ES and that is less apparent in the vector-valued fitness function, the CMA- ES with scalarization outperforms the population-based approach.