Various algorithms have been devised to perform non-dominated sorting. The first algorithm for non-dominated sorting was introduced in 1995 N. Srinivas and K. Deb in a paper presenting the NSGA optimization algorithm <ref name="NSGA">{{cite journal |last1=Srinivas |first1=N. |last2=Deb |first2=Kalyanmoy |title=Multiobjective optimization using non- dominated sorting in genetic algorithms |journal=Evolutionary Computation |date=1994 |volume=2 |issue=3 |pages=221–248 |url=https://ieeexplore.ieee.org/document/6791727}}</ref>. It hadhas a complexity of {{math|''O''(''MN'' <sup>3</sup>)}} where {{mvar|M}} is the number of objectives and {{mvar|N}} is the populationsize size of the set of elements. More recent algorithms have been developed with improved time complexity such as '''Fast Non-Dominated Sorting (FNS)''' ({{math|''O''(''MN'' <sup>2</sup>)}})<ref name="FNS">{{cite journal |last1=Deb |first1=Kalyanmoy |last2=Pratap |first2=Amrit |last3=Agarwal |first3=Sameer |last4=Meyarivan |first4=TAMT |title=A fast and elitist multi-objective genetic algorithm: NSGA-II |journal=IEEE transactions on evolutionary computation |date=2002 |volume=6 |issue=2 |pages=182-197 |url=https://ieeexplore.ieee.org/abstract/document/996017}}</ref>, '''Jensen’s algorithm''' ({{math|''O''(''N'' log<sup> ''M''−1</sup> ''N'')}}) <ref name="Jensen">{{cite journal |last1=Jensen |first1=Mikkel T |title=Reducing the run-time complexity of multiobjective EAs: The NSGA-II and other algorithms |journal=IEEE Transactions on Evolutionary Computation |date=2003 |volume=7 |issue=5 |pages=503-515 |url=https://ieeexplore.ieee.org/abstract/document/1237166}}</ref>, or the '''Efficient Non-Dominated Sorting (ENS)''' (from {{math|''O''(''MN'' log ''N'')}} to {{math|''O''(''MN'' <sup>2</sup>)}}) <ref name="ENS">{{cite journal |last1=Zhang |first1=Xingyi |last2=Tian |first2=Ye |last3=Cheng |first3=Ran |last4=Jin |first4=Yaochu |title=An efficient approach to nondominated sorting for evolutionary multiobjective optimization |journal=IEEE Transactions on Evolutionary Computation |date=2014 |volume=19 |issue=2 |url=https://ieeexplore.ieee.org/abstract/document/6766752}}</ref>.
The non-dominated sorting algorithm used in <ref name="NSGA" /> can be described simply as follows:
