**6. Conclusions**

This paper proposes a methodology for reassigning available ATCs to air sectors after the occurrence of an incident, such as one or more ATCs having to be relieved and/or a change in sectorization due to an increase in air traffic.

The methodology has been applied to a set of seven representative instances corresponding to three different control centers in Spain, provided by CRIDA experts. Although solutions including the available number of ATCs are achieved for all the instances using the SA and VNS metaheuristics, the solutions derived by SA are feasible in three out of the seven instances, whereas no feasible solutions are reached by VNS in any of the seven instances under consideration.

The SA-derived solutions outperform VNS solutions in terms of both the number of violated constraints in all seven instances and solution compactability in six out the seven instances, and both are very similar with regard to the number of control center changes at the time of the incident. VNS computation times are clearly better than for SA. However, CRIDA experts were also satisfied with SA computation times. Thus, SA solutions are preferred.

The proposed methodology constitutes an improvement on the current approach adopted by the network managers, who in an attempt to find a solution as quickly as possible, forsake optimization, often leading to systematic violation of ATC labor conditions. Using the proposed methodology, an optimization process outputs a solution, aimed at meeting as many labor conditions as possible and taking into account the relative importance of the violation of each constraint, in a relatively short time (and the stopping criterion could be modified to output the best solution found in a specified time).

The next step before the methodology can be applied is its integration into the information systems at the network manager operations centers to analyze other types of incidents and compare, in batch mode, the quality of the real solutions applied by the network managers against solutions provided by the proposed methodology.

Besides, network managers will be asked to evaluate the solutions derived by the proposed methodology, and their opinions will be useful for tuning some parameters of the methodology like the relative importance of objectives or how they are measured.

**Author Contributions:** Conceptualization, A.J.-M., F.T., and A.M.; methodology, F.T.; software, F.T.; validation, F.T., A.J.-M. and A.M.; formal analysis, A.J., F.T. and A.M.; investigation, A.J.-M., F.T. and A.M.; writing—original draft preparation, A.J.-M. and A.M.; writing—review and editing, A.J.-M. and A.M.; visualization, F.T., A.J.-M. and A.M.; supervision, A.J.-M. and A.M.; project administration, A.J.-M. and A.M.; funding acquisition, A.J.-M. and A.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Spanish Ministry of Economy and Competitiveness project gran<sup>t</sup> number MTM2017-86875-C3-3-R. The authors are also grateful to Sergio Flórez, who implemented the VNS algorithm and applied simulation techniques for his M.S. final project, and José Miguel de Pablo, Andrés Perillo and Álvaro Rodríguez, from the Reference Center for Research, Development and Innovation in ATM, whose expertise enhanced the reported research.

**Conflicts of Interest:** The authors declare no conflict of interest.
