## 1 Introduction
If the product option selection can be described by a mathematical model, and the expected cost and performance of the configuration under the existing maintenance capacity can be evaluated so that the performance degradation and cost can always be kept within a controllable range, the selection can be truly carried out under the guidance of customized demand. Based on this, a mathematical product option selection optimization model is proposed to provide support for customization option selection, and there is some research on that. Using different multi-objective approaches to optimize the configuration scheme is very common in other areas, such as building envelope retrofitting considering economic and energy sustainability [19], combined with NSGAII [20] or an audited \(\varepsilon\)-constraint approach [21] on parallel machine scheduling problems and spillway structure design combining the whale optimization algorithm and an artificial neural network [22]. In aviation, multi-objective particle swarm optimization is used to establish an optimal design model of an electrostatic actuator with multiple objectives, stiffness, weight and power consumption [23]. The NSGA-III algorithm proposed in this paper [24] introduces arithmetic crossover and an adaptive mutation operator to change the crossover and mutation operators, which improves the optimization performance of the algorithm. The hybrid conjugate mean value (HCMV) method is proposed using sufficient conditions for the enhancement of the efficiency and robustness of RBDO in paper [25]. Moreover, paper [12] carried out framed structures optimization in the two life cycles of production and construction under the boundary conditions of material, transportation and installation. For an aircraft aero engine health parameter estimation problem, the papers [26; 27] optimized sensor selection to improve the controllability and observability of the dynamic system. Some research has taken aircraft range as a fitness function, with a genetic al gorithm or multidisciplinary criteria being used to optimize the aircraft wing, tail and fuselage geometry, thrust requirements, and operation parameters so as to realize aircraft type selection design [28; 29; 30]. The multistage reliability-based design optimization approach accounts for such follow-on corrective decisions based on the partial realizations of random parameters at selected stages along the engineering design process, thereby further enhancing the practicality of reliability-based design optimization [31]. The results show that the integrated design process can achieve a more comprehensive performance than can sequential design. However, there are still some shortcomings in these mathematical models. No model can completely describe the customized selection needs, and most of the parameters of the model describe some structural parameters. In a real operation environment, the replacement of the product is key to maintaining a task. In addition, the impact of economic cost is rarely considered in the model, but economic cost is the most concerning factor for airlines. Finally, most of the models focus on some structures or products and do not solve the model for the whole system, so it is impossible to improve the overall situation. The purpose of this paper was to establish a mathematical optimization model based on availability and fleet maintenance cost as the objective function and reliability index as the constraint condition to serve the option selection of aircraft products. For operators, it is the fastest way to improve the overall quality of aircraft. Combined with the operation data and maintenance records of civil aircraft, on the one hand, it is used to establish the objective function related to cost; on the other hand, it is used as a basis to compare whether mathematical optimization can reduce cost and improve performance.