Abstract
This paper generalizes the Improved Run-Time Complexity Algorithm for Non-Dominated Sorting by Jensen, removing its limitation that no two solutions can share identical values for any of the problem's objectives. This constraint is especially limiting for discrete combinatorial problems, but can also lead the Jensen algorithm to produce incorrect results even for problems that appear to have a continuous nature, but for which identical objective values are nevertheless possible. Moreover, even when values are not meant to be identical, the limited precision of floating point numbers can sometimes make them equal anyway. Thus a fast and correct algorithm is needed for the general case. The paper shows that generalizing the Jensen algorithm can be achieved without affecting its time complexity, and experimental results are provided to demonstrate speedups of up to two orders of magnitude for common problem sizes, when compared with the correct baseline algorithm from Deb.
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