Year: 2024
Author: Sihong Shao, Dong Zhang, Weixi Zhang
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 5 : pp. 1277–1304
Abstract
We propose a simple iterative (SI) algorithm for the maxcut problem through fully using an equivalent continuous formulation. It does not need rounding at all and has advantages that all subproblems have explicit analytic solutions, the cut values are monotonically updated and the iteration points converge to a local optima in finite steps via an appropriate subgradient selection. Numerical experiments on G-set demonstrate the performance. In particular, the ratios between the best cut values achieved by SI and those by some advanced combinatorial algorithms in [Ann. Oper. Res., 248 (2017), 365–403] are at least 0.986 and can be further improved to at least 0.997 by a preliminary attempt to break out of local optima.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2303-m2021-0309
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 5 : pp. 1277–1304
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 28
Keywords: Maxcut Iterative algorithm Exact solution Subgradient selection Fractional programming.