Correction to: Scientific Reports https://doi.org/10.1038/s41598-022-26264-1, published online 27 December 2022
This Article contained errors in the algorithm in the Results section, under the subheading ‘Algorithm: Pseudocode’.
In “Input”, that the initial level value needs to be an overestimate of the optimal dual values was omitted. In addition, \(q^{max}\) has been initialized as a small value.
In line 1, the \(y^{feas}\) was omitted.
In line 5, the equation number was incorrectly given as ‘(20)’.
In line 7, the subscript "0" for \(q^{max}\) has been removed.
In line 13, the subscript "j" for \(q^{max}\) has been removed, and \(q^{max}\) has been set as a small value.
In line 15, the \(y^{feas}\) was omitted, and what f is has been clarified.
The original algorithm appears below.

The original Article has been corrected.
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Bragin, M.A., Tucker, E.L. Author Correction: Surrogate “Level-Based” Lagrangian Relaxation for mixed-integer linear programming. Sci Rep 13, 3474 (2023). https://doi.org/10.1038/s41598-023-30358-9
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DOI: https://doi.org/10.1038/s41598-023-30358-9