Rank-based Non-dominated Sorting

Non-dominated sorting is a computational bottleneck in Pareto-based multi-objective evolutionary algorithms (MOEAs) due to the runtime-intensive comparison operations involved in establishing dominance relationships between solution candidates. In this paper we introduce Rank Sort, a non-dominated sorting approach exploiting sorting stability and ordinal information to avoid expensive dominance comparisons in the rank assignment phase. Two algorithmic variants are proposed: the first one, RankOrdinal (RO), uses ordinal rank comparisons in order to determine dominance and requires O(N) space; the second one, RankIntersect (RS), uses set intersections and bit-level parallelism and requires O(N^2) space. We demonstrate the efficiency of the proposed methods in comparison with other state of the art algorithms in empirical simulations using the NSGA2 algorithm as well as synthetic benchmarks. The RankIntersect algorithm is able to significantly outperform the current state of the art offering up to 30% speed-up for many objectives. C++ implementations are provided for all algorithms.