Many-to-Few Decomposition: Linking R2-Based and Decomposition-Based Multiobjective Efficient Global Optimization Algorithms

In multiobjective optimization, the R2 indicator is widely used for designing indicator-based algorithms, and the Tchebycheff approach is commonly employed in decomposition-based algorithms. Despite their wide use, the connection between these two different paradigms is still not well understood, particularly in the field of multiobjective efficient global optimization (MOEGO). Considering that expected improvement (EI) is a cornerstone in efficient global optimization, this paper first studies the relationship between R2-based EI and Tchebycheff-based EI. Then, we introduce a Many-to-Few (M2F) decomposition framework, offering a new perspective for linking the R2-based method and the Tchebycheff decomposition approach. By incorporating M2F decomposition into MOEGO, a new algorithm called R2/D-EGO is proposed. At each iteration, R2/D-EGO utilizes the Tchebycheff decomposition paradigm to generate a set of candidate solutions, each one corresponding to a different weight vector. Subsequently, a subset of query points is selected from the candidates based on the lower bound of R2-based EI. Empirical results indicate that the proposed R2/D-EGO is highly competitive in comparison with both R2-based and decomposition-based MOEGO algorithms in the parallel (or batch) setting.