**A Comparative Analysis of Simulated Annealing and Variable Neighborhood Search in the ATCo Work-Shift Scheduling Problem**

### **Faustino Tello \*, Antonio Jiménez-Martín \*, Alfonso Mateos \* and Pablo Lozano \***

Departamento de Inteligencia Artificial, E.T.S.I. Informáticos, Universidad Politécnica de Madrid, Campus de Montegancedo S/N, 28660 Boadilla del Monte, Spain

**\*** Correspondence: faustino.tello@upm.es (F.T.); antonio.jimenez-martin@upm.es (A.J.-M.); alfonso.mateos@upm.es (A.M.); plozano94@gmail.com (P.L.)

Received: 25 June 2019; Accepted: 16 July 2019; Published: 17 July 2019

**Abstract:** This paper deals with the air traffic controller (ATCo) work shift scheduling problem. This is a multi-objective optimization problem, as it involves identifying the best possible distribution of ATCo work and rest periods and positions, ATCo workload and control center changes in order to cover an airspace sector configuration, while, at the same time, complying with ATCo working conditions. We propose a three-phase problem-solving methodology based on the variable neighborhood search (VNS) to tackle this problem. The solution structure should resemble the previous template-based solution. Initial infeasible solutions are built using a template-based heuristic in Phase 1. Then, VNS is conducted in Phase 2 in order to arrive at a feasible solution. This constitutes the starting point of a new search process carried out in Phase 3 to derive an optimal solution based on a weighted sum fitness function. We analyzed the performance in the proposed methodology of VNS against simulated annealing, as well as the use of regular expressions compared with the implementation in the code to verify the feasibility of the analyzed solutions, taking into account four representative and complex instances of the problem corresponding to different airspace sectorings.

**Keywords:** air traffic management; work-shift scheduling problem; variable neighborhood search; performance analysis
