Empirical analysis of a tree-based efficient non-dominated sorting approach for many-objective optimization

Non-dominated sorting has been widely adopted in evolutionary multi-objective optimization. Many approaches to non-dominated sorting have been proposed to improve its computational efficiency, but unfortunately, most of them still suffer from high computational cost, especially when the number of objectives becomes large. A tree-based efficient non-dominated sorting approach, termed T-ENS, has been recently developed by us for many-objective optimization, where a tree structure is adopted to represent solutions, such that the non-dominance relationship between solutions can be easily inferred from the position of the solutions in the tree, thereby considerably reducing the number of comparisons between solutions belonging to the same non-dominated front. To validate the computational efficiency of T-ENS, this paper provides a detailed empirical analysis by comparing T-ENS with the state-of-the-art approaches, in particular when the number of objectives is larger than three and the population size becomes large. Empirical results indicate that the T-ENS is well suited for evolutionary many-objective optimization and large-scale multi-objective optimization, where either the number of objectives or the population size is large.