Solving a new mathematical model for the integrated cockpit crew pairing and rostering problem by meta-heuristic algorithms under the COVID-19 pandemic

This study examines the problem of crew pairing and rostering under COVID-19 conditions. To keep the cockpit crew members safe against COVID-19, the problem is investigated in such a way that each cockpit crew member spends less daily sit time period in the airports and returns to his/her home base at the end of the day to take a rest. This study aims to introduce a Mixed-Integer Linear Programming (MILP) formulation for the problem. In order to solve the problem, three meta-heuristic algorithms including Genetic Algorithm (GA), Firefly Algorithm (FA), and Particle Swarm Optimization (PSO) are applied based on a new chromosome representation. The proposed algorithms could obtain solutions with the least possible number of cockpit crew members to cover the existing flights by considering some rules and regulation related to employing cockpits. Moreover, the findings indicate that the algorithms can provide solutions near the optimal solutions (1.94%, 2.49%, and 2.43% gaps for the GA, FA, and PSO on average, respectively) for the small-scale instances extracted from the data sets. Additionally, the proposed GA can find lower-cost solutions in comparison to the FA and PSO in approximately similar CPU time for problem instances with different sizes.