Hybridizing non-dominated sorting algorithms: divide-and-conquer meets best order sort

Margarita Markina, Maxim Buzdalov

Research output: Chapter in Book/Report/Conference proceedingConference Proceeding (Non-Journal item)


Many production-grade algorithms benefit from combining an asymptotically efficient algorithm for solving big problem instances, by splitting them into smaller ones, and an asymptotically inefficient algorithm with a very small implementation constant for solving small subproblems. A well-known example is stable sorting, where mergesort is often combined with insertion sort to achieve a constant but noticeable speed-up.

We apply this idea to non-dominated sorting. Namely, we combine the divide-and-conquer algorithm, which has the currently best known asymptotic runtime of O(N(log N)^M−1), with the Best Order Sort algorithm, which has the runtime of O(N^2M) but demonstrates the best practical performance out of quadratic algorithms.

Empirical evaluation shows that the hybrid's running time is typically not worse than of both original algorithms, while for large numbers of points it outperforms them by at least 20%. For smaller numbers of objectives, the speedup can be as large as four times.
Original languageEnglish
Title of host publicationGECCO '17
Subtitle of host publicationProceedings of the Genetic and Evolutionary Computation Conference Companion
PublisherAssociation for Computing Machinery
Number of pages2
ISBN (Print)978-1-4503-4939-0
Publication statusPublished - 15 Jul 2017
Externally publishedYes
EventGECCO 2017: The Genetic and Evolutionary Computation Conference -
Duration: 15 Jul 201719 Jul 2017


ConferenceGECCO 2017
Period15 Jul 201719 Jul 2017


  • best order sort
  • divide-and-conquer
  • hybrid algorithms
  • non-dominated sorting


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