Very Fast Non-dominated Sorting

New and very ecient parallel algorithm for the Fast Non-dominated Sorting of Pareto fronts is proposed. By decreasing its computational complexity, the application of the proposed method allows us to increase the speedup of the best up to now Fast and Elitist Multi-objective Genetic Algorithm (NSGA-II) more than two orders of magnitudes. Formal proofs of time complexities of basic as well as improved versions of the procedure are presented. Provided experimental results fully conrm theoretical ndings