Sumit Mishra
Maxim Buzdalov
ABSTRACT
Non-dominated sorting is a procedure which is heavily used by many evolutionary multiobjective algorithms. Despite it can be done in polynomial time, it remains an asymptotical bottleneck in many of these algorithms. What is more, some algorithms for non-dominated sorting, which are fast on average, are ridiculously slow in the worst case. Here we prove that a recent algorithm, the dominance degree approach from the paper "Ranking Vectors by Means of the Dominance Degree Matrix" by Zhou et al., has the worst-case time complexity of Θ(M N2 + N3). The Θ(N3) term, which is unusually high for this problem, indicates that this particular algorithm can not be recommended for performance-critical applications.
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Digital Library
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- Yuren Zhou, Zefeng Chen, and Jun Zhang. 2017. Ranking Vectors by Means of the Dominance Degree Matrix. IEEE Transactions on Evolutionary Computation 21, 1 (2017), 34--51.Google ScholarDigital Library
Index Terms
- Time complexity analysis of the dominance degree approach for non-dominated sorting
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