The airline crew scheduling problem is considered. A multistage approach for constructing crew and aircraft schedules is described, as well as a two-stage approach for solving Airline Crew Pairing Problem. A mathematical model of the second sub-stage, the problem of efficient selection of pairings from the generated set, is constructed. The main constraints and the optimality criterion of the problem are formulated. The representation of the problem through the set covering problem is illustrated. The use of the genetic algorithm for constructing an efficient schedule is proposed. Also, a solution to the problem of schedule correctness using a minimal set of mappings is proposed. Different ways of using the minimum set were analyzed. An approach that adds correctness control at all stages of the genetic algorithm was chosen. The individual model, generation, and crossing algorithms considering correctness control are described. The results of the algorithm on data from five thousand flights are presented.