## 3 Mission and Reliability Driven Fleet Selective Maintenance Planning Two-Stage Method  
### A Two-Stage Method Considering Multiple Optimization Objectives and Maintenance Time Constraints  
The selective maintenance planning problem of fleet mentioned in this paper has the following characteristics: First, the available maintenance resources in the maintenance task are limited. Second, the repaired equipment should be able to meet the reliability requirements during the next mission. Due to the complexity of the equipment operating conditions, the initial health condition of the fleet is complex and changeable. Previously used time-based maintenance strategies did not take the dynamic perception of equipment conditions into account, so some inefficient support operations could be taken, while some key components could not properly be maintained, resulting in a waste of potential remaining useful life [27]. In this context, the main purpose of the fleet maintenance planning is to make a maintenance strategy which systematically considers the mission requirements and the limited maintenance resources within the required time and reduces the time and cost as much as possible. In addition, maintenance planning should be based on the health conditions of the fleet and the key components of each equipment, as well as the allocation of maintenance resources, such as tools and spare parts, to select the appropriate maintenance objects, maintenance methods and maintenance order. The maintenance planning problem is a multiobjective optimization problem, and there are two optimization objectives: maintenance cost and mission satisfied capability. There are two methods to solve this kind of problem: One is to convert the multiobjective problem into a single-objective problem by weighting the optimization objective, but this method misses some important search regions in the solution space. The second is to find the nondominant solution set on the Pareto frontier of the problem and select the strategy according to the given rules. Due to the complexity of the application environment, it is unacceptable to simply transform the optimization objectives into a single-optimization objective, resulting in possible omissions. At the same time, in order to enhance the rate of convergence, we can reduce the complexity of the problem by dividing the solving process into two stages. Therefore, a nondominated maintenance strategy solution set can be obtained by using a heuristic algorithm and Pareto nondominated sorting method to optimize two optimization objectives in the problem. Then, considering the different requirements on the minimum mission satisfied capability, the obtained nondominated solution set is divided into different intervals according to the task success rate, and several solutions with the highest fitness are selected as alternatives in each interval. According to the assumption, one group of maintenance equipment can only serve one equipment at the same time. Therefore, after the maintenance strategy of the fleet is determined, the planning of maintenance scheduling can be regarded as a flow shop scheduling problem with the goal of minimizing maintenance time. According to the above analysis of the problem, the problem can be divided into two stages to solve in turn, and a series of solution sets can be obtained to strike a balance between the two optimization objectives of cost and equipment group task capability, with the corresponding minimized maintenance hours and the optimal maintenance schedule. The problem can be solved as follows:  
The first stage of the problem aims to maximize the mission satisfied capability and minimize the maintenance cost, takes the total maintenance cost and the task success rate as constraints, completes the multiobjective selective maintenance decision, sorts and filters the resulting solution set and inputs the second stage of the problem. The second stage of the problem can be classified as a job-shop scheduling problem.