Mathematical Problems in Engineering

Volume 2018 (2018), Article ID 4719178, 15 pages

https://doi.org/10.1155/2018/4719178

## The Air Traffic Controller Work-Shift Scheduling Problem in Spain from a Multiobjective Perspective: A Metaheuristic and Regular Expression-Based Approach

Decision Analysis and Statistics Group, Departamento de Inteligencia Artificial, Universidad Politécnica de Madrid, Madrid, Spain

Correspondence should be addressed to Antonio Jiménez-Martín

Received 23 June 2017; Revised 15 December 2017; Accepted 8 January 2018; Published 11 February 2018

Academic Editor: Danielle Morais

Copyright © 2018 Faustino Tello et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

We address an air traffic control operator (ATCo) work-shift scheduling problem. We consider a multiple objective perspective where the number of ATCos is fixed in advance and a set of ATCo labor conditions have to be satisfied. The objectives deal with the ATCo work and rest periods and positions, the structure of the solution, the number of control center changes, or the distribution of the ATCo workloads. We propose a three-phase problem-solving methodology. In the first phase, a heuristic is used to derive infeasible initial solutions on the basis of templates. Then, a multiple independent run of the simulated annealing metaheuristic is conducted aimed at reaching feasible solutions in the second phase. Finally, a multiple independent simulated annealing run is again conducted from the initial feasible solutions to optimize the objective functions. To do this, we transform the multiple to single optimization problem by using the rank-order centroid function. In the search processes in phases 2 and 3, we use regular expressions to check the ATCo labor conditions in the visited solutions. This provides high testing speed. The proposed approach is illustrated using a real example, and the optimal solution which is reached outperforms an existing template-based reference solution.

#### 1. Introduction

The core of air traffic control operator (ATCo) activity is to facilitate airspace and airport surface traffic flow, while avoiding collisions between aircraft. To satisfy this essential safety constraint, they must detect and solve possible conflicts between trajectories.

As a human ATCo can only handle a limited amount of traffic, the airspace is divided into a number of sectors. These sectors are operated by two ATCo working positions (executive and planner). All the sectors open at any one time are referred to as* sectorization*. The sectorization changes throughout the day depending on the air traffic.

The sectorization required to handle the estimated traffic for a time period can be designed beforehand. Therefore, a very important problem in air traffic control is to determine the minimum number of ATCos necessary to cover a sectorization structure for a given time period, denoted as* airspace sector configuration*, while satisfying certain ATCo labor conditions, including, for instance, resting and working time distributions. Alternatively, the number of ATCos could be fixed. The aim then would be to distribute ATCos to cover the corresponding* airspace sector configuration*.

These optimization problems belong to the class of* timetabling and scheduling problems*. The size and complexity of these combinatorial problems make them hard or even impossible to solve with exact methods.

Different problem-solving approaches have been proposed in the literature to deal with timetabling problems [1]. The Third International Timetabling Competition (ITC2011) [2] motivated the development of several approaches for the extended* markup language for high school timetabling* (XHSTT) problem [3]. The four finalists employed metaheuristics as part of or as the main problem solver [4–7].

Recent problem-solving approaches for the XHSTT problem are based on variable neighborhood search (VNS) [8], simulated annealing (SA) [9], or* matheuristics* (the integration of metaheuristics and mathematical programming) [10, 11].

Different approaches can also be found in the literature concerning other timetabling problems, including operational research, metaheuristics, or novel intelligent methods, such as university course timetabling problems [12], job shop scheduling problems [13–15], and sports scheduling problems [16].

Regarding work-shift scheduling problems in the context of air traffic management (ATM), shiftwork management is addressed in [17], which contains a literature review about the impact of shiftwork, its consequences for health, safety, productivity, and efficiency, as well as social implications. It also refers to the EC Directive 93/104 that establishes the European regulation for working time design in ATM.

A study on shiftwork practices in both ATM and other industries, such as medical, police, and airline industries, is presented in [18]. It concludes that although there are a range of software tools, in many cases involving ATM, they are costly and not completely suited to the needs. The strengths and weaknesses of automated scheduling tools have already been outlined [19].

More recently, Stojadinovic [20] gives an in-depth description of three problem encodings capable of formulating a very broad set of different scheduling requirements considering a time period of a month or a year. The problem was solved using propositional satisfiability (SAT, [21]), MaxSAT, the pseudo-Boolean, satisfiability modulo theory, constraint satisfaction, and integer linear problem solvers. In combination with these solvers, three different optimization techniques were presented. Results suggest that SAT-related approaches outperform other problem-solving methods.

Later, Stojadinovic [22] presents a combination of the SAT problem-solving and the hill climbing method. First, the SAT solver is used to generate a feasible solution. Then, hill climbing is used to improve this solution in terms of the number of satisfied ATCo demands. Finally, SAT problem-solving is used to further improve the identified solution by fixing some parts of the solution. The process is repeated until an optimal solution is found.

A simplified version of the ATCo work-shift scheduling problem considered in this paper was previously solved. This solution considered a single core, accounting for only one type of sector. Consequently, all available ATCos were able to operate in all sectors. Another aim was to minimize the number of ATCos required to cover a given airspace sector configuration, while satisfying a set of ATCo working conditions. Additionally, the different shifts per day were simultaneously optimized.

In this paper, however, we consider the possibility there being more than one core with common sectors, taking into account the en route and approach sectors and ATCos with different operating credentials. The number of available ATCos to cover a given airspace sector configuration is now known in advance, and only one shift is optimized. Besides, we consider a multiobjective perspective, accounting for issues such as some conditions with respect to ATCo work and rest periods and positions, the structure of the solution, the number of control center changes, or the distribution of the ATCo workloads.

The problem-solving methodology used in both papers is similar in the sense that a heuristic is first proposed to build different initial solutions based on the use of an optimized template and the modification of rest period lengths and then, multiple independent runs of the simulated annealing (SA) metaheuristic are used to reach the optimal solution.

However, the heuristic in the simplified version derives different feasible solutions, whereas the new heuristic presented in this paper accounts for the sector types and ATCo credentials and derives infeasible initial solutions (more than the number of available ATCos may be used and some working conditions are violated). Hence, simulated annealing is conducted based on a multiple independent run algorithm aimed at reaching feasible solutions from the infeasible solutions derived by the heuristic. Then, a second multiple independent run of SA is conducted to reach the optimal solutions accounting for the different objectives functions mentioned above.

Note that regular expressions (Regex) [23] are used in both search processes. A Regex is a sequence of characters that define a search pattern that is matched to the string representation of every solution. In our context, the patterns represent the violation of ATCo working conditions. The benefits of using Regex are high testing speed and modularity for a clear and maintainable implementation of the optimization model.

The paper is structured as follows. Section 2 describes the ATCo work-shift scheduling problem, together with the constraints accounting for ATCo working conditions and the objective functions under consideration. The proposed problem-solving methodology together with regular expressions and their application for checking working conditions are described in Section 3. An example is used to illustrate the proposed methodology in Section 4. Finally, some conclusions are outlined in Section 5.

#### 2. Problem Description

One of the core tasks of ATCos is to avoid collisions between aircraft. To do this, the ATCo must assure that the aircraft are always separated by a minimum safety distance, denoted as* separation standards*.

The airspace is composed of volumes (elementary unit of airspace). As a human ATCo can only handle a limited amount of traffic, the airspace is divided into a number of sectors. These sectors may include one or more volumes. All the sectors open at any one time must cover all the volumes of the corresponding airspace. This is referred to as* airspace sector configuration*.

Additionally, a* core* consists of a set of sectors, and a sector may belong to several cores. A control center may be responsible for managing one or more cores, depending on the control center under consideration. If more than one core have sectors in common, then the ATCo assignment process for the respective cores should be simultaneous. Otherwise, each core should be solved separately.

Two sectors are called* related sectors* if they share a volume. As explained later, the existence of related sectors plays an important role in some working conditions and an affinity matrix specifying which sectors are related to each other will be an optimization problem input. Moreover, sectors can be categorized as* approach* and* en route* sectors. Approach sectors are generally 5 to 10 nautical miles (9 to 18 km) from the airport depending on the airport procedures, whereas* en route* sectors are further away.

Each sector is operated by two ATCos, the executive and the planner ATCos. The executive ATCo talks to the aircraft and gives instructions to the pilots to avoid conflict situations between aircraft, whereas the planner ATCo is responsible for anticipating possible conflicts between aircraft and communicating with the executive ATCo the problem before it materializes. ATCos are qualified to operate on a particular core and can be categorized as PTD or CON ATCo depending on the type of sector for which they are accredited. A PTD ATCo can operate en route and approach sectors, whereas a CON ATCo can only operate en route sectors.

The sector configuration changes throughout the day depending on the air traffic. A higher volume of air traffic means more sectors with smaller dimensions will be opened, thus requiring more ATCos. As a result, sectors are dynamically divided and merged over time depending on the air traffic, and the number of ATCos necessary to cover the open sectors varies accordingly.

The sector configurations needed to handle the estimated traffic for a time period (usually a day) can be designed beforehand. This is denoted as* airspace sector configuration*.

Therefore, a very important problem in air traffic control could be to determine the minimum number of ATCos necessary to cover an airspace sector configuration for a given time period, while satisfying certain strong constraints accounting for ATCo working conditions, including, for instance, resting and working time distributions.

In this paper, however, we consider that the number of available ATCos is fixed in advance and the problem is to cover the given airspace sector configuration taking into account working conditions but accounting for the optimization of the ATCo work and rest periods and positions, the structure of the solution, the number of control center changes, or the distribution of the ATCo workloads.

Besides, ATCos can work different shifts. Shift lengths may vary at different control centers, and some may not even be considered. Figure 1 shows the five ATCo shifts used at Canary Islands: long morning (LMS) (6:30–15:00 h.), morning (MS) (7:30–15:00), afternoon (AS) (15:00–22:00), long afternoon (LAS) (15:00–23:00), and night (NS) (22:00–7:30).