Civil aviation fleet-oriented maintenance plan and work package integrated optimization method

Abstract

The application provides a civil aviation fleet-oriented maintenance plan and work package integrated optimization method, which firstly takes the minimization of total maintenance cost as an objective function, takes maintenance item quantity constraints, maintenance item and maintenance work package corresponding relationship constraints, maintenance resource constraints, maintenance interval constraints, variable relationship constraints and variable value constraints as constraint conditions, and constructs a mathematical programming model for fleet maintenance plan and work package integrated optimization; then linearization processing is conducted on the established mathematical programming model by introducing auxiliary variables; finally, a two-stage heuristic algorithm of differential evolution-adaptive large-scale neighborhood search is used to solve the linearized mathematical programming model, that is, the two-stage interactive strategy is designed to iteratively solve the integrated optimization purpose. The application realizes the dual goals of reducing the total maintenance cost and improving the maintenance scheme making efficiency, and provides a scientific solution for complex optimization problems in civil aviation maintenance management.

Description

Technical Field

[0001] This invention relates to the field of civil aircraft maintenance technology, specifically to an integrated optimization method for maintenance plans and work packages for civil aviation fleets. Background Technology

[0002] As a driving force for internationalization, the civil aviation industry connects the world. It is not only a crucial pillar for building a strong transportation nation and improving the modern comprehensive transportation system, but also a strategic industry driving national economic growth and enhancing international competitiveness. The rapid development of the civil aviation industry has brought new development opportunities to airlines, but it also exposes them to surged competitive pressure. Unlike other industries, the cost structure of the civil aviation industry dictates that cost reduction and efficiency improvement are more effective in increasing profits than simply increasing market share, and are a vital way for airlines to enhance their core competitiveness. Aircraft maintenance costs, as a significant component of total costs, have long been a focus of attention. Developing efficient maintenance plans is one of the key measures to reduce aircraft maintenance costs.

[0003] Aircraft maintenance program development is a complex process that requires comprehensive consideration of aircraft reliability, availability, and economy. Maintenance plan development and work package generation are crucial steps in aircraft maintenance program development. In practice, airlines first need to determine the maintenance intervals for maintenance items related to aircraft components based on their remaining lifespan. Then, airlines schedule these maintenance items based on their intervals, specifying the required maintenance items and their completion dates and locations. To reduce round-trip maintenance, airlines typically group multiple maintenance items with similar start times together to form maintenance work packages, which are then deployed to maintenance facilities (hangars, etc.) to implement the maintenance schedule. The development of maintenance work packages is closely related to the maintenance times of individual maintenance items; the latest start time of a maintenance item directly affects the combination of maintenance work packages, while the combination of maintenance work packages must adapt to the time requirements of the maintenance items. A strong coupling exists between the two. How to rationally schedule the planned execution time of maintenance items and how to rationally combine maintenance items into different maintenance work packages are two inseparable parts of maintenance program development.

[0004] However, current maintenance solution development methods generally focus on optimizing a single aspect of maintenance plans or maintenance work packages, lacking a global perspective that combines both. This means that existing methods fail to fully consider the complexity and coupling of maintenance plan development and maintenance work package combination, resulting in maintenance solutions that cannot achieve global optimization. For example, the Chinese patent application CN117829817A, "An Optimization Analysis Method for Aircraft Maintenance Solutions Based on Statistical Analysis of Maintenance Data," uses a method based on statistical analysis of maintenance data. It classifies maintenance solution items, defines cumulative failure probability thresholds and sample sizes for different categories, analyzes maintenance data using data mining techniques, establishes data indexing rules and storage, and uses statistical models to fit the cumulative failure function to optimize maintenance solution intervals. However, this method still only starts from the perspective of maintenance plan development, independent of maintenance work package optimization, and does not obtain a globally optimal maintenance solution. In addition, civil aviation companies often rely on traditional manual experience to develop maintenance work packages, failing to scientifically quantify the relationship between maintenance intervals, maintenance resources, and maintenance work packages, resulting in repeated aircraft maintenance and high maintenance costs.

[0005] In fleet maintenance program optimization practices, the batch-based nature of maintenance project plans significantly impacts maintenance work package optimization. It is essential to embed the production characteristics of fleet maintenance into the maintenance work package decision model, breaking through the traditional research framework that separates maintenance plan optimization from maintenance project combination. Only by achieving integrated optimization of maintenance plans and maintenance work packages can the safety performance of aircraft be fully guaranteed, fundamentally improving the overall efficiency and effectiveness of the civil aviation maintenance industry chain. Therefore, how to rationally formulate fleet maintenance programs based on the maintenance intervals of aircraft maintenance projects and achieve integrated optimization of maintenance plans and work packages has become a pressing technical challenge. Summary of the Invention

[0006] To address the shortcomings of existing methods for optimizing civil aviation aircraft maintenance plans, this invention proposes an integrated optimization method for maintenance plans and work packages for civil aviation fleets. This method overcomes the limitations of local optimization in existing technologies by constructing an integrated optimization model for fleet maintenance plans and work packages. It proposes a two-stage heuristic optimization algorithm to achieve overall optimal maintenance solutions, thereby realizing the dual goals of reducing total maintenance costs and improving the efficiency of maintenance plan development. This provides a scientific solution to complex optimization problems in civil aviation maintenance management.

[0007] The technical solution of this invention is as follows:

[0008] A method for integrating and optimizing maintenance plans and work packages for civil aviation fleets includes the following steps:

[0009] Step 1: Using minimizing the total maintenance cost as the objective function, the total maintenance cost includes the loss cost of early maintenance, the discrete cost of the planned start time of maintenance items within the maintenance work package, and the basic cost of the maintenance work package; constructing a mathematical programming model for integrated optimization of fleet maintenance planning and work packages, with constraints on the number of maintenance items within the maintenance work package, the correspondence between maintenance items and maintenance work packages, maintenance resources, maintenance intervals, the relationship between variables, and the value constraints of variables as constraints.

[0010] Step 2: Introduce auxiliary variables to linearize the mathematical programming model established in Step 1;

[0011] Step 3: The linearized mathematical programming model is divided into two stages: the maintenance plan optimization stage and the maintenance work package optimization stage. The two-stage heuristic algorithm of differential evolution and adaptive large-scale neighborhood search is used to solve the problem. The final maintenance solution is obtained by iteratively solving the two-stage heuristic algorithm. The maintenance plan optimization stage is solved by differential evolution algorithm, and the maintenance work package optimization stage is solved by adaptive large-scale neighborhood search algorithm.

[0012] Furthermore, in step 2, the mathematical programming model is linearized, including absolute value linearization and product linearization.

[0013] Furthermore, in step 3, the interaction process of the two-stage heuristic algorithm of differential evolution and adaptive large-scale neighborhood search is as follows: First, an initial solution is randomly generated and input into the differential evolution algorithm. After mutation, crossover, and selection, and multiple iterations, the first-stage solution is generated. Then, the preliminary result of the first stage is used as the parameter and initial solution of the second stage and input into the adaptive large-scale neighborhood search algorithm. After destruction, repair, and interference, the second-stage solution is generated. Then, the second-stage solution is used as the parameter and initial solution and re-input into the differential evolution algorithm, and the previous calculation steps are repeated. Finally, the interaction is iterated repeatedly until the required number of iterations is reached, and then the final solution is output.

[0014] Furthermore, in step 3, the objective function of the maintenance plan optimization stage is to minimize the loss cost of early maintenance of maintenance items within the maintenance work package and the basic cost of the maintenance work package, and the decision variables are the planned start time of the maintenance item and whether the maintenance work package is used; the objective function of the maintenance work package optimization stage is to minimize the discrete cost of the planned start time of maintenance items within the maintenance work package, and the decision variable is whether the aircraft maintenance item is in the maintenance work package.

[0015] Furthermore, in step 3, the differential evolution algorithm uses a mixed encoding method of 0-1 binary variables and integer variables to represent individuals. The binary variables describe whether the maintenance work package is used, and the integer variables describe the planned start time of the maintenance work package.

[0016] Furthermore: In the differential evolution algorithm, the mutation operation is achieved for 0-1 binary variables through the XOR operation in Boolean logic.

[0017] First, three individual indices are randomly selected from the initial population. , , As a basis vector;

[0018] Secondly, assuming the initial individual is Mutant individuals are generated in the following way :

[0019]

[0020]

[0021] in, It is a scaling factor, and , This represents the XOR operation in Boolean logic. Based on the initial individual and randomly select three individual indexes , , The generated intermediate entity.

[0022] Furthermore, in the differential evolution algorithm, different crossover strategies are designed for 0-1 binary variables and integer variables respectively:

[0023] 0-1 binary variable crossover strategy: For 0-1 variables, two rules are designed for gene selection: one is fixed-position crossover, selecting the first position in the array to obtain genes from mutated individuals; the other is probability-based crossover, based on the crossover probability parameter. Then generate random numbers. When the random number is less than If the mutation occurs, the gene is obtained from the mutated individual; otherwise, the gene is obtained from the initial individual.

[0024] Integer variable crossover strategy: For integer variables, design orthogonal experiments for gene selection: First, generate a standard two-dimensional orthogonal array. .in The number of rows required for the orthogonal array. Each column represents the start time; secondly, when an element in the orthogonal array is 1, the start time of its corresponding crossover individual is equal to the start time of the initial individual; when an element in the orthogonal array is 2, the start time of its corresponding crossover individual is equal to the start time of the mutated individual.

[0025] Furthermore, in step 3, the adaptive large-scale neighborhood search algorithm uses the solution of the differential evolution algorithm as the initial solution. During the iterative search phase, it selects a destruction operator or a repair operator to destroy or repair the current solution based on the performance of the operators, and uses an interference operator to interfere with the search area to form a neighborhood solution. If the neighborhood solution performs better, it is set as the current optimal solution, and the acceptance criterion is used to determine whether to accept the solution. Once accepted, it is updated as the current solution, and the search continues from there. The current iteration number is updated until the termination condition is met, at which point the algorithm stops and outputs the current optimal solution.

[0026] Furthermore, in step 3, the destruction operator adopts a two-stage destruction operator. In the first stage, the destroyed maintenance work package is selected based on the destruction rate. In the second stage, given the destroyed work package, the maintenance items within the destroyed work package are selected based on the destruction rate.

[0027] Furthermore, in step 3, the repair operators include a random repair operator, a greedy repair operator, and a regret value repair operator; the random repair operator refers to randomly inserting the deleted repair item into the repair work package, while ensuring that the constraints are still met after insertion; the greedy repair operator inserts the deleted repair item into the repair work package with the smallest objective function increment, while ensuring that the constraints are still met after insertion; the regret value repair operator refers to prioritizing the insertion of the repair item with the largest regret value for the deleted repair item, and selecting its insertion position as the priority.

[0028] Beneficial effects:

[0029] The maintenance planning and work package integration optimization method for civil aviation fleets proposed in this invention has the following effects:

[0030] (1) This invention constructs a mathematical programming model for the integrated optimization of fleet maintenance plans and work packages, which effectively solves the problem of lack of global optimal perspective and quantitative analysis method in the existing technology, and realizes a comprehensive consideration of the reliability, availability and economy of civil aircraft maintenance.

[0031] (2) By introducing new auxiliary variables and constraints, this invention effectively solves the problem of difficulty in solving nonlinear mathematical expressions in the model and improves the model solving efficiency.

[0032] (3) Based on the characteristics of the optimization model, the present invention designs a two-stage interactive heuristic algorithm, which effectively improves the solution quality and speed of the integrated optimization model and realizes efficient solution of large-scale problem examples.

[0033] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0034] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0035] Figure 1 Logic for developing integrated maintenance plans and work packages;

[0036] Figure 2 : Overall design concept diagram of the two-stage heuristic algorithm;

[0037] Figure 3 Solution for increased repair work package quantity;

[0038] Figure 4 Solution for reducing the number of repair work packages;

[0039] Figure 5 The approach to handling situations where the number of repair work kits remains unchanged;

[0040] Figure 6 The rationale for adjusting aircraft service calendar dates;

[0041] Figure 7 The overall approach to initial population generation;

[0042] Figure 8 Interference operator strategy;

[0043] Figure 9 Schematic diagram of the overall framework of the differential evolution algorithm;

[0044] Figure 10 Schematic diagram of the differential variation framework;

[0045] Figure 11 Schematic diagram of differential cross-framework;

[0046] Figure 12 Schematic diagram of the overall framework of the adaptive large-scale neighborhood search algorithm;

[0047] Figure 13 : Schematic diagram of the random destruction framework of the work package;

[0048] Figure 14 : Schematic diagram of the worst-case scenario for the repair project;

[0049] Figure 15 : Schematic diagram of the regret value repair operator framework; Detailed Implementation

[0050] This invention proposes an integrated optimization method for maintenance plans and work packages of civil aviation fleets, which mainly includes optimization problem description, model construction, model linearization, and model solving using a two-stage heuristic algorithm. Each part is described in detail below.

[0051] I. Description of the problem in the integration and optimization of civil aviation fleet maintenance plans and work packages:

[0052] The most crucial task in maintenance planning is determining the planned start time of a maintenance project within the constraints of its inherent characteristics and available resources. Since the maintenance interval is a time frame, it includes two key time points: the earliest planned start time based on economic principles and the latest planned start time based on safety principles. For any given maintenance project, the planned start time should generally be within its maintenance interval, ideally no earlier than its earliest planned start time and no later than its latest planned start time. Based on this, to ensure the maintenance plan is implemented effectively, the airline's engineering department issues maintenance instructions to the maintenance site in the form of work cards. These work cards primarily include technical instructions, work standards, and precautions for the maintenance project—essentially outlining "when," "what," and "how." These work cards are then compiled, "packaging" all maintenance items required for a single maintenance operation into a maintenance work package. This work package clearly lists the work card number and specifies the maintenance information for each item (such as maintenance method, required resources, and estimated man-hours).

[0053] This invention addresses the problem of integrating and optimizing maintenance plans and work packages for civil aviation fleets. A maintenance work package refers to a combination scheme of maintenance items, with the aim of combining maintenance items with similar maintenance intervals within the fleet. A maintenance plan refers to the planned start time of a maintenance item. Considering that maintenance engineers may dynamically adjust the maintenance order of maintenance items based on actual maintenance resources during the actual execution of a work package, the specific execution time of each maintenance item within its maintenance work package is not considered. Instead, the start time of the work package to which the maintenance item belongs is used to represent the start time of the maintenance item.

[0054] refer to Figure 1 The problem of integrating and optimizing maintenance plans and work packages for civil aviation fleets can be described as follows: Within a set timeframe for developing maintenance plans, the fleet has... Each aircraft is an independent aircraft, and each aircraft has For each maintenance project type, independent maintenance projects need to be combined into work packages, and their start times must be determined. The maximum number of maintenance work packages that can be developed within the maintenance plan preparation timeframe is [number missing]. ,airplane Repair items Each maintenance item must be included in only one work package. There is a minimum total number of maintenance items within a work package; a work package can only be successfully formed when a certain number of maintenance items are included. Otherwise, these maintenance items must be merged into other work packages. All maintenance items must be placed in a specific work package to form a complete maintenance work package plan. During the maintenance plan development process, the earliest start time (economic principle), the latest start time (safety principle), and the required maintenance man-hours for each maintenance item are known, and the planned start time of any maintenance item must not be later than its latest start time.

[0055] II. Constructing an integrated optimization model for civil aviation fleet maintenance plans and work packages:

[0056] (a) Model Assumptions

[0057] To facilitate the characterization of the practical problem as a mathematical model, the following reasonable assumptions are made:

[0058] (1) The scheduling process of aircraft traveling to and from the maintenance site is not considered;

[0059] (2) When there is only a difference in the number of repairs during the preparation time of the repair plan (e.g., the first time the 21-020-00 repair project is executed and the second time the 21-020-00 repair project is executed), add an explanation of the number of executions after the project number (e.g., 21-020-00-(1) repair project and 21-020-00-(2) repair project), and regard them as different types of repair projects;

[0060] (3) There is no difference between maintenance sites, that is, each maintenance site can perform all maintenance items for any aircraft.

[0061] (4) Each aircraft is independent of the others, and there is no specific order of execution for maintenance items on different aircraft;

[0062] (5) Each maintenance item is independent of the others, that is, there is no specific order of execution between different types of maintenance items (e.g., there is no fixed order between items 21-020-00 and 21-030-01).

[0063] (6) The maintenance items in the maintenance work package are performed sequentially without considering the specific execution order of the maintenance items in the maintenance work package. The start time of the work package to which the item belongs is taken as the planned start time of the item.

[0064] (7) During the execution of the maintenance work package, the maintenance resources provided by the maintenance site will not change.

[0065] (II) Explanation of Parameter Symbols

[0066] : The fleet of aircraft assembled;

[0067] The total number of aircraft in the fleet;

[0068] Aircraft Index ;

[0069] : A collection of repair project types;

[0070] The total number of maintenance item types within the time frame for preparing the maintenance plan;

[0071] Repair Item Type Index ;

[0072] : Collection of repair work kits;

[0073] The maximum number of maintenance work packages to be developed within the timeframe for developing the maintenance plan;

[0074] Repair work package index ;

[0075] The total cost of the repair plan;

[0076] The cost of premature repairs;

[0077] Discrete cost of the planned start time of maintenance items within the maintenance work package;

[0078] The basic cost of the repair work kit;

[0079] : Penalty coefficient for early repair;

[0080] : Penalty coefficient for the discreteness of the planned start time of maintenance items within the maintenance work package;

[0081] : Basic cost coefficient of the repair work package;

[0082] :airplane Repair items Number of days required;

[0083] :airplane Repair items Required man-hours;

[0084] Minimum requirement for the number of repair items in a repair work package;

[0085] The total number of maintenance items for the entire fleet within the timeframe for preparing the maintenance plan;

[0086] The maximum total man-hours that the repair site can provide to complete all repair items in the repair work package;

[0087] [ t ik left , t ik right ] :airplane Repair items Maintenance intervals;

[0088] [ T left , T right ] Timeframe for developing the maintenance plan;

[0089] A sufficiently large number.

[0090] (III) Definition of Decision Variables

[0091] : 0-1 variable, airplane Repair items Is it in the repair work package? If so, then ;otherwise, ;

[0092] : 0-1 variable, the first If the repair kit is used, then... ;otherwise, ;

[0093] Integer variables, maintenance work packages The planned start time (calendar day).

[0094] (iv) Mathematical Model Construction

[0095] (1) Objective Function. Operations research optimization techniques are introduced to minimize the total maintenance cost, as shown in Equation (2-1). This objective mainly includes: ① Loss cost of early maintenance: represented by the difference between the planned start time of the maintenance work package and the latest start time set according to the maintenance interval, as shown in Equation (2-2); ② Discrete cost of the planned start time of maintenance items within the maintenance work package: measures the degree of difference in the latest start time of each maintenance item within a single maintenance work package, as shown in Equation (2-3); ③ Basic cost of the maintenance work package: if multiple maintenance items are combined into a maintenance work package, the maintenance work package must correspond to a basic cost. The number of maintenance work packages is related to the number of round-trip maintenance trips of the aircraft, as shown in Equation (2-4).

[0096] (2-1)

[0097] (2-2)

[0098] (2-3)

[0099] (2-4)

[0100] (2) Constraint on the number of maintenance items in a maintenance work package. This constraint means that each maintenance work package must contain a certain number of maintenance items; otherwise, a work package cannot be formed, as shown in equation (2-5).

[0101] , (2-5)

[0102] (3) Constraints on the correspondence between maintenance items and maintenance work packages. This mainly includes two aspects of constraints: ① One-to-one constraint, that is, any maintenance item can only exist in one maintenance work package, as shown in equation (2-6); ② Many-to-many constraint, that is, the sum of maintenance items in all maintenance work packages should be equal to the total number of maintenance items in the entire fleet, as shown in equation (2-7).

[0103] , (2-6)

[0104] , (2-7)

[0105] (4) Maintenance resource constraints. This constraint means that the carrying capacity of the maintenance work package is limited by the man-hours required for the maintenance items. That is, the total man-hours required to perform all maintenance items in the maintenance work package shall not exceed the maximum total man-hours that the maintenance site can provide to complete all maintenance items in the maintenance work package, as shown in equation (2-8).

[0106] , (2-8)

[0107] (5) Maintenance Interval Constraint. Given the maintenance interval (earliest start time and latest start time) of a maintenance item, if the maintenance item is grouped into a work package ( If the planned start time of the maintenance work package is not greater than its latest start time, then the plan start time of the maintenance work package shall not exceed its latest start time, as shown in equation (2-9).

[0108] , (2-9)

[0109] (6) Constraints between variables. A series of empty maintenance work packages are preset. A maintenance work package is only used if it contains maintenance items. Equation (2-10).

[0110] , (2-10)

[0111] (7) Variable value constraints. Equation (2-11) represents the time range for compiling the maintenance plan and the maintenance work package. Plan start time Within this time frame, equations (2-12) and (2-13) define the range of values ​​for the variables.

[0112] , (2-11)

[0113] , (2-12)

[0114] , (2-13)

[0115] In summary, the mathematical programming model for the problem is as follows:

[0116]

[0117] st formula (2-5)-formula (2-13).

[0118] 3. Linearize the constructed integrated optimization model of civil aviation fleet maintenance plans and work packages:

[0119] By introducing new variables and constraints, equations (2-2) and (2-3) are linearized to improve the solution efficiency of the model.

[0120] (a) Absolute value linearization

[0121] First, the absolute value part in equation (2-3) is linearized.

[0122] (1) Explanation of new symbols

[0123] Continuous variables ;

[0124] Continuous variables .

[0125] (2) Model linearization

[0126] Depend on and The definition leads to:

[0127] , (3-1)

[0128] , (3-2)

[0129] Therefore, after linearization, equation (2-3) is equivalent to:

[0130] (3-3)

[0131] Therefore, the absolute value part in equation (2-3) has been linearized.

[0132] (ii) Product linearization

[0133] Next, the product forms in equations (2-2) and (3-3) are linearized.

[0134] (1) Explanation of new symbols

[0135] Integer variables, auxiliary decision variables ;

[0136] Real variables, auxiliary decision variables ;

[0137] A sufficiently large number.

[0138] (2) Model linearization

[0139] First, linearize equation (2-2). This is because the equation contains products. ,in For 0-1 variables, Let be an integer variable, and from equation (2-11) we can obtain... t j ∈ [ T left , T right ] Furthermore, multiplying a 0-1 variable by an integer variable can be viewed as a special form of multiplying a 0-1 variable by a continuous variable. Therefore, constraints (3-4)-(3-6) are added to linearize the product part in equation (2-2):

[0140] , (3-4)

[0141] , (3-5)

[0142] , (3-6)

[0143] when At that time, according to equation (3-5), we get ;when At that time, according to equation (3-4), we get According to equation (3-6), we get Thus we obtain Therefore, auxiliary decision variables Able to accurately represent products .

[0144] In summary, the nonlinear formula (2-2) can be transformed into the linear formula (3-7):

[0145] (3-7)

[0146] Next, equation (3-3) is linearized. This equation contains a product. Since it is difficult to determine its actual maximum value, a sufficiently large number is introduced. As To maximize the product, we add constraints (3-8)-(3-10) to linearize the product part in equation (3-3):

[0147] , (3-8)

[0148] , (3-9)

[0149] , (3-10)

[0150] Similarly, when At that time, according to equation (3-9), we get ;when At that time, according to equation (3-8), we get According to equation (3-10), we get Thus we obtain Therefore, auxiliary variables Able to accurately represent products .

[0151] In summary, the nonlinear formula (3-3) can be transformed into the linear formula (3-11):

[0152] (3-11)

[0153] IV. Design a two-stage algorithm to solve the linearized model:

[0154] (I) Two-phase algorithm flow

[0155] Given that the model simultaneously embodies the problem characteristics and constraints of both maintenance plans and work packages, this invention decomposes the integrated optimization model into two parts: a maintenance plan optimization stage and a maintenance work package optimization stage. A two-stage heuristic algorithm (DE-ALNS algorithm) based on differential evolution and adaptive large-scale neighborhood search is designed to solve this problem, achieving the technical goal of efficiently solving the model. The overall algorithm flow is as follows:

[0156] First, the first stage is the maintenance plan optimization stage. The decision variables in this stage are: and ,in Since the variables are integers and their units are calendar days, they can be approximated as the floor function of continuous variables during the solution process. Therefore, the Differential Evolution (DE) algorithm is considered to solve this stage model. The objective function of this stage is to minimize the loss cost of early repair of maintenance items within the maintenance work package and the basic cost of the maintenance work package. The main decisions are the planned start time of the maintenance project and whether the maintenance work package is used. The mathematical model of this stage involves equations (2-2) and (2-4), and constraints (2-9) and (2-11).

[0157] The second phase is the maintenance work package optimization phase, with the decision variables being: , Since the variables are 0-1, the Adaptive Large-Scale Neighborhood Search (ALNS) algorithm is considered to solve the model for this stage. The objective function of this stage is to minimize the discrete cost of the planned start time of maintenance items within the maintenance work package, mainly solving the matching problem between maintenance items and maintenance work packages. The mathematical model for this stage includes equation (2-3), and constraints (2-5)-(2-8) and (2-10).

[0158] Finally, the two stages iterate continuously to obtain a satisfactory solution to the problem. The specific interaction strategy is as follows: First, an initial solution is randomly generated and input into the DE algorithm. After mutation, crossover, and selection, and multiple iterations, the first-stage solution is generated. Then, the preliminary result of the first stage is used as the parameter and initial solution of the second stage and input into the ALNS algorithm. After destruction, repair, and interference, the second-stage solution is generated. Then, the second-stage solution is used as the parameter and initial solution and re-input into the DE algorithm, and the previous calculation steps are repeated. Finally, the interaction is iterated repeatedly until the required number of iterations is reached, and then the final solution is output.

[0159] Please refer to the overall design concept. Figure 2 The algorithm design for the two stages will be described in detail below.

[0160] (ii) Differential Evolution Algorithm

[0161] The DE algorithm for solving the maintenance plan optimization phase is described as follows: First, an initial feasible solution is randomly generated as the algorithm input. During this process, since maintenance items are included in maintenance work packages, in order to meet the constraints and comply with the requirements of the two-phase interaction, as the usage of maintenance work packages is continuously adjusted, the maintenance items within them need to be adjusted accordingly. Specifically, this includes increasing the number of maintenance work packages (see reference). Figure 3 ), reduce (reference) Figure 4 ) and unchanged (reference) Figure 5 There are three scenarios. The parameters involved in the initialization algorithm include: population size, number of iterations, scaling factor, crossover probability, etc., recording the current solution and the current optimal solution; initializing the population, and simultaneously initializing the chaotic sequence and orthogonal experimental table. In the iterative search phase, each iteration requires randomly selecting three individual indices. , , Differential mutation is performed using logical XOR operations (as shown in Algorithm 4.2). Based on the mutation results, a chaotic perturbation is applied to update the current solution. Then, orthogonal experiments are used to perform crossover operations on the current solution, and the current solution is updated again (as shown in Algorithm 4.3). If the fitness of a solution is less than the current optimal solution, it is recorded as the current optimal solution. Chaotic search is used to generate chaotic solutions; if the fitness of a chaotic solution is less than the current optimal solution, it is recorded as the current optimal solution. Finally, the current iteration count is updated, and iteration continues until the maximum iteration count is reached, at which point the iteration ends, and the current optimal solution is output. The overall framework of the differential evolution algorithm is as follows: Figure 9 As shown:

[0162] The DE algorithm is described in detail below:

[0163] (1) Encoding method:

[0164] This phase includes repair work packages. Whether to use and repair work kit The solution for the two variables, planned start time and unused package, uses a mixed encoding method of 0-1 binary variables and integer variables to represent individuals. The binary variable describes whether the maintenance work package is used, and the integer variable describes the planned start time of the maintenance work package. As shown in Table 1, isUsedPackage represents the maintenance work package. Whether a binary variable is used, pack_start_time indicates the maintenance work package. An integer variable indicating the planned start time.

[0165] Because the maintenance work package contains maintenance items, and the maintenance items and the maintenance work package influence each other and are coupled, a section is added to... and The encoding for the two-dimensional index, as shown in Table 2, is used to store information about maintenance items within the maintenance work package, namely eventsInfo.

[0166] The specific encoding methods of the DE algorithm are shown in Table 1 and Table 2.

[0167] Table 1. Encoding methods of the DE algorithm

[0168]

[0169] In Table 1 For example, the eventsInfo vector is explained in Table 2.

[0170] Table 2. Vector Encoding Method for eventsInfo

[0171]

[0172] The three-dimensional arrays in Table 2 represent the earliest start time, latest start time, and required maintenance man-hours for each maintenance item, respectively. , For example, the earliest start time for this maintenance project is the 16th calendar day, and the latest start time is the 60th calendar day. The project requires 15 man-hours to execute.

[0173] (2) Population initialization:

[0174] Since maintenance items are included in the maintenance work package, in order to meet the constraints and comply with the two-phase interaction requirements, the maintenance items within the maintenance work package need to be adjusted as the usage of the maintenance work package changes (Case 1-Case 3). Based on this, an initial population strategy is designed, and the overall idea for generating the initial population is as follows: Figure 7 As shown: including:

[0175] Parameter input: Pass in a set of pre-defined original work packages and the items within each work package as input data;

[0176] Random generation: Based on the input parameters, a certain number of work packages are randomly generated;

[0177] Processing maintenance projects: Compare the original work package quantity with the randomly generated work package quantity;

[0178] Generation start time: The start time for randomly generating work packages according to constraints;

[0179] Update Individual: Update information within an individual ( and ), and sort the work packages according to their start time;

[0180] Calculate fitness: Calculate the fitness value of an individual. Here, fitness is calculated using the conventional fitness calculation method in differential evolution algorithms to obtain the initial individual. ;

[0181] Check population size: Determine if the number of individuals generated so far has reached the preset population size; if not, return to the "Random Generation" step to continue generating the next individual; if the population size has been reached, proceed to the next step.

[0182] Determine the initial population: This ultimately forms a complete initial population.

[0183] The initial parameters for the first iteration are randomly generated, while the initial parameters for subsequent iterations are provided by the second-stage ALNS algorithm.

[0184] In the initial population generation process of the algorithm, the "handling maintenance projects" step includes three cases:

[0185] Case 1: The original number of work packages is less than the number of randomly generated work packages, meaning the number of maintenance work packages increases ( Figure 3 ).

[0186] like Figure 3 As shown, when the number of maintenance work packages increases, maintenance items need to be inserted into the newly generated work packages. One maintenance item from an existing maintenance work package is retained (randomly selected), and the other maintenance items are used as backups. When a new work package is added, one item is randomly selected from the backups and inserted, then deleted from the existing work package. The remaining maintenance items retain their original state.

[0187] Case 2: The original number of work packages is greater than the number of randomly generated work packages, meaning the number of maintenance work packages is reduced. Figure 4 ).

[0188] like Figure 4As shown, when the number of maintenance work packages decreases, all maintenance items within the work package to be deleted need to be removed. Selecting to delete a maintenance work package from the end will first insert all maintenance items within that work package into the work package whose start time is closest to that of the maintenance item, and then delete the empty work package.

[0189] Case 3: The original number of work packages is equal to the number of randomly generated work packages, meaning the number of maintenance work packages remains unchanged. Figure 5 ).

[0190] like Figure 5 As shown, when the number of maintenance work packages remains unchanged, the original work package and its internal maintenance items are retained, and the entire package is transferred to the work package with isUsedPackage=1.

[0191] Because maintenance items and maintenance work packages are highly correlated, at each stage of this algorithm, when the number of maintenance work packages changes, the maintenance items need to be adjusted according to the above strategy. Subsequent steps will not be elaborated further. It is important to note that the maintenance item adjustment at this stage is to retain all items and ensure... The work package contains maintenance items, and the specific maintenance item allocation scheme is solved in the second stage.

[0192] (3) Mutation operation:

[0193] Since the problem solved by the first-stage DE algorithm includes integer variables and 0-1 binary variables, where integer variables can be converted from the result of continuous variables by rounding down, the continuous variable mutation operation of the classic differential evolution algorithm is adopted; however, it is difficult to use the same mutation strategy for 0-1 binary variables and continuous variables. Therefore, this invention introduces the XOR operation in Boolean logic to perform special differential mutation.

[0194] First, three individual indices are randomly selected from the initial population. , , As a basis vector;

[0195] Secondly, assuming the initial individual is Mutant individuals are generated in the following way :

[0196]

[0197]

[0198] in, It is a scaling factor, and In this embodiment, the scaling factor is set to 0.6; This represents the XOR operation in Boolean logic. Based on the initial individual and randomly select three individual indexes , , The generated intermediate individuals;

[0199] Subsequently, because this differential mutation strategy is prone to getting trapped in local optima, a chaotic search strategy was incorporated into the process. Specifically, a chaotic sequence was generated using a Logistic mapping and applied as a perturbation factor in the generation of experimental individuals.

[0200] Finally, boundary checks and corrections are performed on the continuous variable components to ensure they fall within the search space. [ lb , ub ] Inside, among them, Indicates the lower bound of the search space. The lower bound of the search space is represented as:

[0201]

[0202] Differential variation framework such as Figure 10 As shown, the final output is the mutated individual.

[0203] (4) Cross operation:

[0204] This invention designs different crossover strategies for 0-1 binary variables and integer variables, as detailed below:

[0205] 0-1 Binary Variable Crossover Strategy: For 0-1 binary variables, two rules are designed for gene selection. One is fixed-position crossover, selecting the first position in the array (index 0) from the mutated individual. The first method involves obtaining genes; the second method involves crossover based on probability, with the crossover probability as the input parameter. Use a generator to generate random numbers. When the random number is less than... At that time, from the mutated individual Genes are obtained from the initial individual; otherwise, they are obtained from the initial individual. Genes are obtained from [the source].

[0206] Integer Variable Crossover Strategy: For integer variables, orthogonal experiments are designed for gene selection. First, a standard two-dimensional orthogonal array is generated. .in The number of rows required for the orthogonal array. Each column represents the start time. Secondly, when an element in the orthogonal array is 1, the start time of its corresponding crossover individual is equal to that of the initial individual. The start time of the crossover individual; when an element in the orthogonal array is 2, the start time of its corresponding crossover individual is equal to the start time of the mutated individual. The start time; ultimately generating crossover individuals. Cross-frames, such as Figure 11 As shown.

[0207] (5) Chaotic search strategy:

[0208] Chaotic search is mainly applied to mutation and selection operations in the DE algorithm design of this invention. The specific application strategy is described below:

[0209] Mutation operation: Use a chaotic search function to perturb the continuous variable and the 0-1 variable respectively.

[0210] For continuous decision variables, add the following perturbation strategy:

[0211]

[0212] in, It is a perturbation factor obtained from a chaotic sequence. This represents the disturbance range, which is set to 0.1 in this embodiment. For continuous variables, This is the lower bound for continuous variables.

[0213] For 0-1 decision variables, a perturbation factor is randomly generated, and a chaos threshold is set to 0. When the perturbation factor is greater than the chaos threshold, the opposite value of the experimental vector is taken; otherwise, the original value is retained.

[0214] Selection operation: Chaotic individuals are generated using chaotic sequences and participate in the selection operation.

[0215] (6) Select operation:

[0216] The selection operation of the DE algorithm in this invention mainly consists of two stages: The first stage compares mutated individuals with crossover individuals, retaining those with better fitness performance. The second stage generates chaotic individuals using a chaotic sequence, calculates their fitness, and compares them with the individuals retained in the first stage, retaining those with better fitness performance.

[0217] (III) Adaptive Large-Scale Neighborhood Search Algorithm

[0218] The ALNS algorithm is designed to solve the model in the optimization stage of the maintenance work package. This invention combines the characteristics of the problem to design a two-stage destruction operator, three repair operators and interference operators to effectively search the solution space.

[0219] The overall flow of the ALNS algorithm in the optimization phase of solving the maintenance work package is described as follows: The solution from the DE algorithm is input into the ALNS algorithm as the initial solution. In the iterative search phase, operator performance is obtained through an adaptive mechanism. Based on the operator performance, a destruction operator or a repair operator is selected to destroy or repair the current solution. An interference operator is used to disturb the search region, thereby forming neighborhood solutions. If the neighborhood solution performs better, it is set as the current optimal solution. The simulated annealing acceptance criterion is used to determine whether to accept the solution. Once accepted, it is updated as the current solution, and the search continues from there. Operator weights are updated based on the quality of neighborhood solutions, the probability of operator selection is adjusted, and the simulated annealing temperature is updated. Finally, the current iteration count is updated until the termination condition is met, at which point the algorithm stops and the current optimal solution is output. The algorithm framework is as follows: Figure 12 As shown.

[0220] The ALNS algorithm is described in detail below:

[0221] (1) Encoding method:

[0222] This stage solves for the aircraft. Repair items Is it in the repair work package? In the middle, the numbers of the maintenance work packages are stored in the form of multidimensional arrays. The ALNS algorithm includes the planned start time (pack_start_time) and internally stored maintenance project information (events). This maintenance project information mainly includes the aircraft ID (airplane_id), project ID (repair_type_id), earliest start time (earliest_start_time), latest start time (latest_start_time), and required maintenance man-hours (main_laborhours). Therefore, the specific encoding of the ALNS algorithm is shown in Tables 3 and 4.

[0223] Table 3 ALNS Encoding Method

[0224]

[0225] Taking package=1 in Table 3 as an example, the events vector is explained in Table 4.

[0226] Table 4 Events Vector Encoding Methods

[0227]

[0228] The two-stage algorithms have largely the same encoding methods and contain essentially the same content. Only simple adjustments are needed when they interact.

[0229] (2) Initial solution generation:

[0230] Since this invention designs a two-stage solution algorithm for ensemble optimization problems, this indicates that the ALNS algorithm and the DE algorithm need to interact. The key to this interaction is the generation of the initial solution, and the approach to generating the initial solution differs from that of using the algorithm alone. As mentioned earlier, except for the initial random generation of the initial solution, the initial solution of the DE algorithm is the iterative output solution of the ALNS algorithm, and similarly, the initial solution of the ALNS algorithm is also the output solution of the DE algorithm. Since the overall algorithmic approach originates from the DE algorithm, the initial solutions throughout the entire iterative process of the ALNS algorithm can be derived from the DE input of the previous stage.

[0231] (3) Design of the destruction operator:

[0232] After generating the initial solution, the current solution is broken using a destruction operator. The key parameter of the destruction operator is the destruction rate. The calculation method is as follows:

[0233]

[0234] in This refers to the number of repair work packages or repair items deleted in the current solution. This refers to the total number of maintenance work packages or maintenance items in the current solution.

[0235] Since this involves a maintenance work package and its internal maintenance items, a two-stage failure operator is designed, with the failure rate set to 0.2 in both stages. The failure operator is designed as follows:

[0236] Phase 1: Selecting the damaged repair kit:

[0237] Package Random Removal (PRR): Randomly selects 20% of the packages to be removed and returns the index of the package.

[0238] Package Worst Removal (PWR): Selects the 20% of packages that contribute the most to the objective function and removes them, returning the index of the package.

[0239] Phase Two: Given the known damage to the repair work package, select the repair items within the damaged work package:

[0240] Events Random Removal (ERR): 20% of the maintenance items in each selected work package are randomly selected for removal (rounded down). If the number of maintenance items removed is less than the minimum number of maintenance items in the package, the minimum number of maintenance items is retained.

[0241] Events Worst Removal (EWR): Within each work package, select the 20% of maintenance events that contribute the most to the objective function and destroy them (rounded down), while retaining the minimum number of maintenance events. Figure 13 and Figure 14 These represent the frames for PRR and EWR, respectively. For example... Figure 13 As shown, PRR sets up an array of variables to store the work package index. This is input into the second-stage repair project damage; PWR is similar, outputting an array of variables. ,and Together .like Figure 14 As shown, EWR sets up a set of variables to store maintenance items. This is input into the repair phase; ERR is similar, outputting a set of variables. Together they form .

[0242] (4) Design of the repair operator:

[0243] Repair operators are used to insert removed repair items into corrupted solutions. Three repair operators are designed: random repair operator, greedy repair operator, and regret value repair operator.

[0244] a. Random Repair Operator

[0245] The basic idea of ​​the random repair operator is to randomly insert the repair items to be deleted into the repair work package, but it is necessary to ensure that the constraints are still met after the insertion.

[0246] The specific operation process is as follows: Remove items from the collection. Randomly select an item Randomly insert a position into the current solution and check if the man-hour limit for this work package has been exceeded. If it has, select a new position. Set a limit on the number of insertions; if the limit is exceeded, repair operations cannot be performed, and the process returns to the initial state and starts again.

[0247] b. Greedy Repair Operator

[0248] The basic idea of ​​the greedy repair operator is to insert the repair item to be deleted into the repair work package with the smallest increment of the objective function, but it is necessary to ensure that the constraint conditions are still met after the insertion.

[0249] The specific operation process is as follows: Remove items from the collection. Select items in sequence Iterate through the current solutions and find the positions in the current solutions where the objective function increment corresponding to the maintenance project is minimized. and the project Insert at position and remove it from the set Deleted until the set is empty. Empty.

[0250] c. Regret value repair operator

[0251] The basic idea of ​​the regret value repair operator is that, unlike the two mentioned above, the regret value repair operator is based on a predictive mechanism. For the deleted repair item, the repair item with the largest regret value is inserted first, and the insertion position is selected for it.

[0252] The specific operation process is as follows: Remove items from the collection. Select items in sequence Iterate through the current solutions and calculate the minimum value of the objective function corresponding to the maintenance project. and its location And the second smallest value of the objective function corresponding to this maintenance project. and its location and calculate the project Regret value As shown in the following formula:

[0253]

[0254] Compare the regret values ​​of each repair item, prioritize inserting the repair item with the highest regret value, and prioritize selecting the position with the minimum objective function value. The specific framework is as follows: Figure 15 As shown.

[0255] (5) Design of interference operator:

[0256] To help the ALNS algorithm escape local optima, a disturbance operator is used to perturb the search region. The disturbance operator is designed as follows: two maintenance work packages are randomly selected, and two maintenance items within them are randomly swapped. This swap causes small changes, which helps to break the stability of the current solution, allowing the algorithm to explore previously unvisited areas and increasing the likelihood of finding the global optimum. Figure 8 As shown in the figure, work package 3 and work package 5 are randomly selected as exchange work packages. Repair item 3 is selected from work package 3, and repair item b is selected from work package 5 for exchange.

[0257] (6) Design of the adaptive mechanism:

[0258] The adaptive mechanism refers to ALNS calculating operator weights in each iteration based on the operator's past performance; that is, the better an operator performs, the more frequently it should be selected. Here, a roulette wheel is used to select destructive and repairing operators. During the iteration process, the quality of the solutions generated by each set of operators is scored according to the following rules:

[0259] a. Global Optimal Reward: If the generated solution is the global optimal solution, it will be assigned a high score.

[0260] b. Improved solution scoring: If the generated solution is better than the current solution but worse than the global optimal solution, it is given a higher score.

[0261] c. Simulated annealing criterion scoring: If the generated solution is inferior to the current solution, it is assigned a lower score according to the acceptance criterion of simulated annealing.

[0262] After a certain number of iterations, the weights of each operator are updated using a formula, as follows:

[0263]

[0264] in Represents an operator, Indicates the stage, Operator Total score, Operator The number of times selected, This represents the probability of operator weight updates. In this embodiment, the operator weight update probability is set. .

[0265] (7) Acceptance criteria:

[0266] This invention employs simulated annealing as the acceptance criterion, that is, during the ALNS iterative search process, based on the current solution... Constructed neighborhood solution The probability of it being accepted is

[0267]

[0268] in, A constant greater than 0, representing the temperature of the simulated annealing. Each iteration reduces the value by a fixed value or percentage. ,in For cooling rate, and This invention accepts the neighborhood solution with a probability of 0.5, and then takes... This is to prevent the temperature from dropping too quickly.

[0269] In summary, even if the constructed neighborhood solution is worse than the objective function value of the current solution, it still has a certain probability of being accepted. However, as the gap gradually increases, the probability of acceptance gradually decreases.

[0270] Above, we presented a complete method for integrating and optimizing maintenance plans and work packages for civil aviation fleets. To better understand the above technical solutions, we will now provide a detailed description of them in conjunction with the accompanying drawings and specific implementation methods. The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the invention.

[0271] This embodiment considers a fleet of 61 aircraft. The fleet requires the development of maintenance plans and work packages for 11 maintenance items, including operational checks. Aircraft service status data (as shown in Table 5) is input into the model. For adjustments to the approach, please refer to... Figure 6 Maintenance man-hours and days data (as shown in Table 6), maintenance interval data (as shown in Table 7).

[0272] Table 5. Example of adjusted service calendar dates for the case aircraft.

[0273]

[0274] Table 6. Examples of maintenance man-hours and days for the project.

[0275]

[0276] Table 7. Example of maintenance interval data for case study projects

[0277]

[0278] The final maintenance plan and work package scheme were obtained. The total maintenance cost of the scheme was RMB 18,423.362, which included 37 maintenance work packages, as shown in Table 8. Taking [4, 8] as an example, it represents the 8th maintenance item for the 4th aircraft.

[0279] Table 8. Examples of Maintenance Plans and Work Packages (Partial)

[0280]

[0281] The current maintenance plans for these 11 maintenance projects were quantified using an integer linear model, and the total estimated cost of the existing plans was approximately RMB 20,705.118. This was compared with the method proposed in this invention. In the short term, the new plan is significantly cheaper than the existing plan in terms of cost reduction (approximately 11.02%) for single maintenance plans and work packages, representing a substantial improvement. In the long term, the new plan is more flexible and can be dynamically adjusted according to actual conditions.

[0282] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A method for integrated optimization of maintenance plans and work packages for civil aviation fleets, characterized in that: Includes the following steps: Step 1: Using minimizing the total maintenance cost as the objective function, the total maintenance cost includes the loss cost of early maintenance, the discrete cost of the planned start time of maintenance items within the maintenance work package, and the basic cost of the maintenance work package; constructing a mathematical programming model for integrated optimization of fleet maintenance planning and work packages, with constraints on the number of maintenance items within the maintenance work package, the correspondence between maintenance items and maintenance work packages, maintenance resources, maintenance intervals, the relationship between variables, and the value constraints of variables as constraints. Step 2: Introduce auxiliary variables to linearize the mathematical programming model established in Step 1; Step 3: The linearized mathematical programming model is divided into two stages: the maintenance plan optimization stage and the maintenance work package optimization stage. The two-stage heuristic algorithm of differential evolution and adaptive large-scale neighborhood search is used to solve the problem. The final maintenance solution is obtained by iteratively solving the two-stage heuristic algorithm. The maintenance plan optimization stage is solved by differential evolution algorithm, and the maintenance work package optimization stage is solved by adaptive large-scale neighborhood search algorithm.

2. The method for integrated optimization of maintenance plans and work packages for civil aviation fleets according to claim 1, characterized in that: Step 2 involves linearizing the mathematical programming model, including absolute value linearization and product linearization.

3. The method for integrated optimization of maintenance plans and work packages for civil aviation fleets according to claim 1, characterized in that: In step 3, the interaction process of the two-stage heuristic algorithm of differential evolution and adaptive large-scale neighborhood search is as follows: First, an initial solution is randomly generated and input into the differential evolution algorithm. After mutation, crossover, selection, and multiple iterations, the first-stage solution is generated. Then, the preliminary results of the first stage are used as the parameters and initial solution of the second stage and input into the adaptive large-scale neighborhood search algorithm. After destruction, repair, and interference, the second-stage solution is generated. Then, the solution from the second stage is used as parameters and the initial solution to be re-input into the differential evolution algorithm, and the previous calculation steps are repeated; finally, the interaction is repeated repeatedly until the required number of iterations is reached, and then the final solution is output.

4. The method for integrated optimization of maintenance plans and work packages for civil aviation fleets according to claim 1, characterized in that: In step 3, the objective function of the maintenance plan optimization stage is to minimize the loss cost of early maintenance of maintenance items within the maintenance work package and the base cost of the maintenance work package, and the decision variables are the planned start time of the maintenance item and whether the maintenance work package is used; the objective function of the maintenance work package optimization stage is to minimize the discrete cost of the planned start time of maintenance items within the maintenance work package, and the decision variable is whether the aircraft maintenance item is in the maintenance work package.

5. The method for integrated optimization of maintenance plans and work packages for civil aviation fleets according to claim 2, characterized in that: In step 3, the differential evolution algorithm uses a mixed encoding method of 0-1 binary variables and integer variables to represent individuals. The binary variables describe whether the maintenance work package is used, and the integer variables describe the planned start time of the maintenance work package.

6. The method for integrated optimization of maintenance plans and work packages for civil aviation fleets according to claim 5, characterized in that: In the differential evolution algorithm, the mutation operation is achieved for 0-1 binary variables through the XOR operation in Boolean logic: First, three individual indices are randomly selected from the initial population. , , As a basis vector; Secondly, assuming the initial individual is Mutant individuals are generated in the following way : in, It is a scaling factor, and , This represents the XOR operation in Boolean logic. Based on the initial individual and randomly select three individual indexes , , The generated intermediate entity.

7. The method for integrated optimization of maintenance plans and work packages for civil aviation fleets according to claim 6, characterized in that: In the differential evolution algorithm, different crossover strategies are designed for binary variables (0-1) and integer variables respectively: 0-1 binary variable crossover strategy: For 0-1 variables, two rules are designed for gene selection: one is fixed-position crossover, selecting the first position in the array to obtain genes from mutated individuals; the other is probability-based crossover, based on the crossover probability parameter. Then generate random numbers. When the random number is less than If the mutation occurs, the gene is obtained from the mutated individual; otherwise, the gene is obtained from the initial individual. Integer variable crossover strategy: For integer variables, design orthogonal experiments for gene selection: First, generate a standard two-dimensional orthogonal array. ,in The number of rows required for the orthogonal array. Each column represents the start time; Secondly, when an element in the orthogonal array is 1, the start time of its corresponding crossover individual is equal to the start time of the initial individual; when an element in the orthogonal array is 2, the start time of its corresponding crossover individual is equal to the start time of the mutated individual.

8. The method for integrated optimization of maintenance plans and work packages for civil aviation fleets according to claim 1, characterized in that: In step 3, the adaptive large-scale neighborhood search algorithm uses the solution of the differential evolution algorithm as the initial solution. During the iterative search phase, it selects a destruction operator or a repair operator to destroy or repair the current solution based on the performance of the operators, and uses a disturbance operator to disturb the search area to form a neighborhood solution. If the neighborhood solution performs better, it is set as the current optimal solution. The algorithm then judges whether to accept the solution based on the acceptance criterion. Once accepted, it is updated as the current solution, and the search continues from there. The current iteration number is updated until the termination condition is met, at which point the algorithm stops and outputs the current optimal solution.

9. The method for integrated optimization of maintenance plans and work packages for civil aviation fleets according to claim 8, characterized in that: In step 3, the destruction operator adopts a two-stage destruction operator. In the first stage, the destroyed maintenance work package is selected based on the destruction rate. In the second stage, given the destroyed work package, the maintenance items within the destroyed work package are selected based on the destruction rate.

10. The method for integrated optimization of maintenance plans and work packages for civil aviation fleets according to claim 8, characterized in that: In step 3, the repair operators include a random repair operator, a greedy repair operator, and a regret value repair operator. The random repair operator randomly inserts the deleted repair item into the repair work package, ensuring that the constraints are still met after insertion. The greedy repair operator inserts the deleted repair item into the repair work package with the smallest objective function increment, ensuring that the constraints are still met after insertion. The regret value repair operator prioritizes inserting the repair item with the largest regret value among the deleted repair items and selects its insertion position.

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