A personnel and equipment scheduling method based on a multi-machine support operation scheduling model

Abstract

The present application relates to the field of aircraft support technology, in particular to a personnel and equipment scheduling method based on multi-machine support operation scheduling model. The method comprises the following steps: in the first step, multiple optimization objectives and constraint conditions of the algorithm are determined, and a mathematical model is constructed; in the second step, considering the actual support process, a personnel and equipment algorithm integrating global-local optimization and multi-criteria decision is designed; in the third step, the designed algorithm is used for real-time scheduling. Through the integration of global-local optimization strategy, multi-criteria decision and non-dominated sorting genetic algorithm (NSGA-II) algorithm, the present application can realize the double-objective optimization of minimizing the maximum completion time and balancing the equipment load in multi-machine scheduling support tasks.

Description

Technical Field

[0001] This invention relates to the field of aircraft support technology, specifically to a personnel and equipment scheduling method based on a multi-aircraft support operation scheduling model. Background Technology

[0002] Aircraft sortie capability is a key measure of an air force's combat capability, and ensuring the ability to efficiently, quickly, and in large numbers deploy aircraft to perform missions is of paramount importance. Aircraft sortie capability primarily depends on the ability to efficiently and safely complete support operations such as maintenance, refueling, arming, and takeoff. For support missions, ensuring the rational allocation of aircraft support resources, such as personnel and equipment, is crucial to improving aircraft support efficiency.

[0003] Studies have shown that the allocation, command, and control of aircraft support resources is essentially a complex combinatorial optimization problem, characterized by high complexity, strong timeliness, high decision-making difficulty, and many uncertainties. Its allocation and combination are considered to be NP-hard problems. According to the research by Bazargan et al. (2010) in the Journal of Air Transport Management [BAZARGAN M, FLEMING K, SUBRAMANIA NP. A simulation study to investigate runway capacity using TAAM[J]. Journal of Air Transport Management, 2010, 16(6):324-329. DOI:10.1016 / j.jairtraman.2010.04.001.], delays in airport ground support scheduling can lead to cascading flight delays, with approximately 40% of flight delays stemming from inefficiencies in ground support. Dorndorf et al. (2007) proved in Computers & Operations Research [DORNDORFU, JAEHNF, PESCHE. Modelling flightgatescheduling as a constraint satisfaction problem[J]. Computers & Operations Research, 2007, 34(5):1382-1396.DOI:10.1016 / j.cor.2005.05.018.] that the problem can be modeled as a mixed integer programming (MIP) or constraint satisfaction problem (CSP), but exact algorithms face the challenge of high computational complexity in real-time scheduling.

[0004] In recent years, metaheuristic algorithms (such as genetic algorithms and ant colony optimization) and reinforcement learning methods have been introduced to improve solution efficiency. For example, Chen et al. (2021) proposed a dynamic scheduling framework based on deep Q-networks in Transportation Research Part C [CHENJ, MAOJ, LIUY, et al. Dynamic scheduling of airport ground handling vehicles using deep reinforcement learning[J]. Transportation Research Part C: Emerging Technologies, 2021, 132:103400.DOI:10.1016 / j.trc.2021.103400.], which reduced the idle time of support vehicles by 15% in the simulation environment. However, existing research still faces challenges such as insufficient actual operational data and difficulties in multi-agent collaborative optimization [ZHANGY, TANGJ, WANGH. A hybrid optimization approach for airport ground handling scheduling under uncertainty[J]. IEEE Transactions on Intelligent Transportation Systems, 2019, 20(10):3765-3776. DOI:10.1109 / TITS.2019.2915518.], and there is an urgent need to further explore intelligent optimization methods driven by data-model hybrid approaches.

[0005] Because of the random nature of operational scheduling, unexpected tasks and equipment failures can easily occur, causing aircraft takeoff and landing support operations to deviate from the pre-planned schedule. In such cases, it is necessary to dynamically adjust and replan the current scheduling scheme. After an emergency occurs, general static scheduling strategies are ineffective, and effective dynamic scheduling strategies must be used to quickly develop new aircraft support operation plans to ensure that aircraft can still complete support operations efficiently and safely.

[0006] In summary, based on the actual needs of formulating aircraft support operation scheduling schemes, and starting from the dynamic scheduling strategy for aircraft support operations, this paper studies a multi-aircraft support operation scheduling algorithm based on the NSGA-II algorithm (fast non-dominated sorting genetic algorithm) in light of the multi-constraint and multi-objective characteristics of dynamic scheduling problems. This is of great significance for ensuring that aircraft can carry out support operations quickly, efficiently, and safely, and for improving aircraft sortie capabilities and the comprehensive combat capabilities of the Air Force. Summary of the Invention

[0007] To address the aforementioned problems, this application provides a personnel and equipment scheduling method based on a multi-machine support operation scheduling model, characterized by comprising:

[0008] S1: Using the set of aircraft P, the set of processes J, the process priority O, the set of personnel C, the type of personnel K, the set of equipment D, and the type of equipment M as input data, define process constraints, personnel constraints, and equipment constraints, and construct a multi-objective optimization model with minimizing the maximum completion time and minimizing the equipment load variance as dual optimization objectives;

[0009] S2: Based on the multi-objective optimization model constructed in S1, an improved non-dominated sorting genetic algorithm that integrates variable neighborhood search is used to solve the problem, generating a Pareto solution set, and selecting the optimal scheduling scheme from the Pareto solution set.

[0010] S3: Based on the optimal scheduling scheme selected by S2, execute real-time scheduling and output the start time, end time, assigned personnel number and equipment number for each process of each aircraft.

[0011] 2. The personnel and equipment scheduling method based on a multi-machine support operation scheduling model as described in claim 1, characterized in that the process constraint expression is:

[0012] ;

[0013] ;

[0014] This represents the start time of the nth process for the p-th aircraft. This represents the end time of the nth process for the p-th aircraft. This represents the support time for the nth process of the p-th aircraft; This represents the support time for the h-th process of the p-th aircraft. This represents the start time of the h-th process for the p-th aircraft; where... , P represents the set of aircraft. The set of processes representing the p-th aircraft;

[0015] The personnel constraint expression is:

[0016] During aircraft support operations, for any personnel c and time point t, personnel c can support at most one aircraft; the expression for this constraint is:

[0017] ;

[0018] in This represents an indicator function (1 if the condition is true, 0 otherwise); Whether representative C has been assigned to process n of aircraft p; if so, then... =1 if it is 1, otherwise 0; C represents a group of people;

[0019] For any given process, the number of certain personnel assigned to it must be less than or equal to the maximum number of such personnel. The expression for this constraint is:

[0020] ;

[0021] Let n represent the total number of personnel of type k required for process n of aircraft p. The number of people of type k;

[0022] The device constraint expression is:

[0023] During aircraft support operations, for any device d and time point t, device d can support at most one aircraft; the expression for this constraint is:

[0024]

[0025] Where P represents the set of aircraft. The set of processes representing the p-th aircraft. This represents an indicator function (1 if the condition is true, 0 otherwise); This indicates whether equipment d has been assigned to process n of aircraft p. If it has been assigned, then... The value is 1 if it is not 0 otherwise; D represents the set of devices.

[0026] For any given process, the number of a certain type of equipment allocated to it must be less than or equal to the maximum number of such equipment. This constraint is expressed as:

[0027] ;

[0028] Let n represent the total number of equipment of type m required for process n of aircraft p. This represents the number of devices of type m.

[0029] 3. The personnel and equipment scheduling method based on the multi-aircraft support operation scheduling model as described in claim 1, characterized in that the maximum completion time is the time taken to complete all aircraft support processes, and the expression for this optimization objective is:

[0030] ;

[0031] in That is, the maximum completion time. This represents the time when the last completed process was finished.

[0032] 4. The personnel and equipment scheduling method based on a multi-machine support operation scheduling model as described in claim 1, characterized in that the equipment load variance is the variance of the working time of each device; the smaller this value, the higher the average utilization rate of the equipment. The expression for this optimization objective is:

[0033] ;

[0034] in for:

[0035] ;

[0036] in This represents the load of device d upon completion. This represents the average load across all devices.

[0037] 5. The personnel and equipment scheduling method based on a multi-machine support operation scheduling model as described in claim 1, wherein step S2 includes:

[0038] S21: Based on the S1 multi-objective optimization model, the task sequence is exchanged through genetic mutation operation to maintain population diversity, and a greedy algorithm is used to allocate personnel and equipment resources to the processes in the task sequence.

[0039] S22: For all solutions after resource allocation in S21, divide the Pareto front by non-dominated sorting, and introduce variable neighborhood search to refine the Pareto front solutions;

[0040] S23: Based on the Pareto solution set adjusted in S22, the optimal scheduling scheme is selected by combining the entropy weight method and the sorting method for approximating the ideal solution.

[0041] 6. The personnel and equipment scheduling method based on a multi-machine support operation scheduling model as described in claim 5, characterized in that the specific method for exchanging task sequences through genetic mutation in step S21 is as follows:

[0042] The parent population of size R is randomly divided into two subpopulations. Two intersection points a and b are randomly selected, and the process sequences of all individuals in the two subpopulations within the interval [a, b] are exchanged. After merging, the offspring population is obtained. Individuals in the offspring population are repaired by replacing redundant processes with missing processes, and the positions of processes in the individuals are exchanged according to a preset mutation rate.

[0043] 7. The personnel and equipment scheduling method based on a multi-machine support operation scheduling model as described in claim 1, characterized in that the specific method for allocating resources using the greedy algorithm in step S21 is as follows:

[0044] Calculate the idle time of person C:

[0045] ;

[0046] and the idle time of device d:

[0047] ;

[0048] where and respectively represent the time when the person and the device were last used;

[0049] Taking the maximization of the minimum idle time as the goal, the person and device with the longest idle time are preferentially allocated to the process, and the objective expression is:

[0050] ;

[0051] represents the set of persons assigned to the task, represents the set of devices assigned to the task.

[0052] 8. The personnel and device scheduling method based on the multi-machine support operation scheduling model according to claim 1, characterized in that the specific method of variable neighborhood search in S22 is:

[0053] For the solution x on the first Pareto front F1, a neighborhood is defined:

[0054] ;

[0055] where represents the solution set of the second front, represents the rank in ; is the rank threshold; when the solution y satisfies rank(y)≤τ, it is judged whether to replace x with y according to a preset acceptance probability p, wherein the replacement is performed when rand()<p.

[0056] 9. The personnel and device scheduling method based on the multi-machine support operation scheduling model according to claim 1, characterized in that,

[0057] normalizing the j-th optimization objective value of the i-th solution in the Pareto solution set output by S22 to obtain:

[0058] ;

[0059] calculating the specific gravity , where m is the total number of solutions, ;

[0060] calculating the information entropy , and calculating the weight , where n is the total number of optimization objectives;

[0061] Calculate the weighted normalized decision elements .

[0062] 10. The personnel and equipment scheduling method based on a multi-machine support operation scheduling model as described in claim 9, characterized in that the specific steps of the TOPSIS method in S23 are as follows:

[0063] Weighted normalized decision elements obtained from the entropy weight method in S23 Determine the ideal solution max(v) ij and the negative ideal solution min(v) ij );

[0064] Calculate the distance from each solution i to the ideal solution. ;

[0065] and distance to the negative ideal solution ;

[0066] Calculate relative proximity ;

[0067] choose The largest solution is taken as the optimal scheduling scheme.

[0068] The features and beneficial effects of this invention are:

[0069] (1) This invention addresses the maximum completion time and equipment load variance Simultaneously optimizing two conflicting objectives can generate a set of high-quality, diverse scheduling schemes for decision-makers to choose from based on actual needs. Compared to single-objective optimization algorithms, this approach better balances efficiency, resource utilization, and fairness, and is more adaptable to the requirements of multi-machine assurance.

[0070] (2) This invention innovatively considers that when selecting the optimal solution in each iteration, a variable neighborhood search (VNS) is performed to adjust the Pareto front for solutions with high potential Pareto fronts, thereby enhancing the local development capability of the algorithm. At the same time, in order to prevent the generation of invalid solutions, a constraint repair mechanism is used to ensure that the generated neighborhood solutions always meet hard constraints such as personnel skill matching and equipment capacity limitations.

[0071] (3) This invention innovatively proposes a method for providing scientific decision support using the entropy weight method and the TOPSIS method. For the final set of optimal solutions, the algorithm can objectively calculate the weights between each objective and select the scheduling scheme with the best overall performance from the data level. The entropy weight method can eliminate subjective errors and automatically allocate weights between different optimization objectives, making it suitable for situations where the importance of different objectives is unknown. If the decision-maker wants to adjust the objective weights with preference when selecting a solution, TOPSIS can adapt flexibly.

[0072] (4) This invention uses a hybrid global (NSGA-II) and local (VNS) search algorithm to enable the system to adapt to highly complex scheduling environments of different scales. It can still generate feasible solutions quickly under strict constraints. The algorithm is robust and can efficiently complete scheduling tasks in various real-world scenarios. Attached Figure Description

[0073] Figure 1 This is a flowchart of the overall technical solution of the present invention.

[0074] Figure 2 This is a flowchart of the improved selection of the optimal solution according to the present invention.

[0075] Figure 3 This is the overall technical solution of the present invention.

[0076] Figure 4 This is a schematic diagram of the Pareto front and variable neighborhood search principle in this invention, wherein... Figure 4 (a) shows the distribution of the two Pareto fronts. Figure 4 (b) A variable neighborhood search mechanism is demonstrated that refines the first front solution based on the second front solution.

[0077] Figure 5 This is a Gantt chart showing the scheduling results of the multi-machine support operation of this invention, which displays the time arrangement and personnel and equipment allocation details for each process. Detailed Implementation

[0078] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below with reference to the accompanying drawings. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are only some, not all, of the embodiments of this application. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application. The embodiments of this application will be described in detail below with reference to the accompanying drawings.

[0079] This invention aims to propose a multi-level guarantee scheduling optimization method based on an improved NSGA-II algorithm. Specifically, for multi-machine collaborative operation and multi-task hierarchical guarantee scenarios, this invention first considers task priority, dynamic resource allocation, and personnel-equipment matching constraints to determine multiple optimization objectives, including task completion time, resource utilization, and load balancing, establishing a multi-objective optimization model. Second, addressing the convergence problem of traditional scheduling algorithms under large-scale, multi-constraint conditions, a hybrid global-local optimization NSGA-II improved framework is proposed, using Variable Neighborhood Search (VNS) as a local optimization module to enhance the algorithm's fine-grained search capability at the Pareto front. Finally, combining the entropy weight method-TOPSIS multi-criteria decision-making method, the scheduling scheme that best meets the actual needs is selected from the Pareto optimal solution set, and the feasibility and superiority of the algorithm are verified through simulation and real-world testing. The overall technical solution process is as follows: Figure 1 As shown.

[0080] The personnel and equipment scheduling algorithm based on the multi-machine support operation scheduling model includes the following steps:

[0081] S1: Define the various optimization objectives and constraints of the algorithm, determine the input data such as aircraft set, process flow, personnel type, and equipment type, and establish mathematical expressions for process sequence constraints, resource uniqueness constraints, and resource demand matching constraints. With minimizing the maximum completion time and equipment load variance as the dual optimization objectives, construct a complete multi-objective optimization model.

[0082] S2: To address the shortcomings of traditional algorithms in complex scheduling problems, an improved NSGA-II algorithm that integrates variable neighborhood search is proposed.

[0083] Population diversity is maintained through genetic mutation and task sequence exchange, and resource allocation is implemented using a greedy algorithm. A Pareto front is introduced through non-dominated sorting, and variable neighborhood search is used to refine the Pareto front solution. Finally, the optimal scheduling scheme is selected from the Pareto solution set by combining the entropy weight method and the TOPSIS method.

[0084] S3: Real-time scheduling is performed using an improved algorithm.

[0085] S1 includes the following steps:

[0086] S11: Define the constraints, including process constraints, personnel constraints, and equipment constraints;

[0087] S12: Define the optimization objectives, including minimizing the maximum completion time and minimizing the equipment load variance;

[0088] S13: Define the system input data, including aircraft sets, process flows, personnel sets, and equipment sets.

[0089] Based on the above elements, a complete multi-objective optimization model can be constructed.

[0090] The process constraints, personnel constraints, and equipment constraints in S11 are as follows:

[0091] Process constraints:

[0092] During aircraft support operations, the processing sequence must strictly adhere to the processing procedures. The target process can only proceed after the preceding process is completed. The difference between the end time and start time of each process is the support time for that process. The expression for this constraint is:

[0093] , (1)

[0094] This represents the start time of the nth process for the p-th aircraft. This represents the support time for the h-th process of the p-th aircraft. This represents the start time of the h-th process for the p-th aircraft. This represents the end time of the nth process for the p-th aircraft. , ;

[0095] Personnel constraints:

[0096] During aircraft support operations, for any personnel c and time point t, personnel c can support at most one aircraft. The expression for this constraint is:

[0097] (2)

[0098] Where P represents the set of aircraft. The set of processes representing the p-th aircraft. This represents an indicator function (1 if the condition is true, 0 otherwise). Is representative C assigned to process n of aircraft p? If so, then... The value is 1 if the condition is met, otherwise it is 0. C represents the set of people.

[0099] For any given process, the number of certain personnel assigned to it must be less than or equal to the maximum number of such personnel. The expression for this constraint is:

[0100] (3)

[0101] Let n represent the total number of personnel of type k required for process n of aircraft p. This represents the number of people of type k.

[0102] Equipment constraints:

[0103] During aircraft support operations, for any device d and time point t, device d can support at most one aircraft. The expression for this constraint is:

[0104] (4)

[0105] Where P represents the set of aircraft. The set of processes representing the p-th aircraft. This represents an indicator function (1 if the condition is true, 0 otherwise). This indicates whether equipment d is assigned to process n of aircraft p. If so, then... The value is 1 if the condition is met, otherwise it is 0. D represents the set of devices.

[0106] For any given process, the number of a certain type of equipment allocated to it must be less than or equal to the maximum number of such equipment. This constraint is expressed as:

[0107] (5)

[0108] Let n represent the total number of equipment of type m required for process n of aircraft p. This represents the number of devices of type m.

[0109] The maximum completion time in S12 and the equipment load variance are as follows:

[0110] Maximum completion time:

[0111] The maximum completion time is the time required to complete all aircraft support procedures. The shorter this time, the more frequently aircraft can be deployed. The expression for this optimization objective is:

[0112] (6)

[0113] in That is, the maximum completion time. This represents the time when the last completed process was finished.

[0114] Equipment load variance:

[0115] Equipment load variance is the variance of the operating time of each piece of equipment. A smaller value indicates higher average equipment utilization, which reduces maintenance costs. The expression for this optimization objective is:

[0116] (7)

[0117] in for:

[0118] (8)

[0119] in This represents the load of device d upon completion. This represents the average load across all devices.

[0120] The aircraft assembly, process flow, personnel assembly, and equipment assembly in S13 are as follows:

[0121] P, J, O, C, K, D, M represent the set of aircraft, the set of processes, the priority of processes, the set of personnel, the type of personnel, the set of equipment, and the type of equipment, respectively.

[0122] in Let n represent the priority of the nth operation of aircraft p. During the support process, operations with the same priority can be executed in any order, while operations with higher priority can only be executed after all operations with lower priority have been completed.

[0123] This represents the nth process of the p-th aircraft.

[0124] S2 includes the following steps:

[0125] S21: Maintain population diversity by exchanging task sequences through genetic mutations and implement resource allocation using a greedy algorithm;

[0126] S22: Pareto front is introduced through non-dominated sorting, and variable neighborhood search is introduced to refine the Pareto front solution;

[0127] S23: Finally, the optimal scheduling scheme is selected from the Pareto solution set by combining the entropy weight method and the TOPSIS method.

[0128] In S21, population diversity is maintained through genetic mutation task sequences, and resource allocation is performed using a greedy algorithm as follows:

[0129] Genetic variation crossover sequence maintains population diversity:

[0130] Let the population size be R, where each solution is a global sequence with the following format: ,in (Total number of all processes), each element = = This represents the nth process of aircraft p.

[0131] The parent population of size R is randomly divided into two populations of size R / 2, denoted as R / 2. and Randomly select starting points a and b, where 1 ≤ a ≤ b ≤ N, and then swap them. and The sequence of all individuals in a population between [a, b] forms the population. and ,(like Figure 2 As shown, the genes on each chromosome of each population represent aircraft numbers and procedures. After the exchange is completed, and Combine to form a offspring population S. Then, perform further repairs on the individuals in this offspring population S (replacing redundant steps with missing steps). For each individual in the offspring population, swap the positions of steps in the list according to the mutation rate (e.g., ...). Figure 3 (As shown).

[0132] Greedy algorithms implement resource allocation:

[0133] When allocating personnel and equipment resources, priority should be given to personnel and equipment that have been idle for the longest time.

[0134] The idle time of personnel is:

[0135] (9)

[0136] The equipment's idle time is:

[0137] (10)

[0138] in , These represent the last time the personnel and equipment were used, respectively.

[0139] When allocating resources, the optimization objective is to maximize the minimum idle time (ensuring that the least used resources are prioritized), as shown in the following expression:

[0140] (11)

[0141] The group of people who are responsible for task assignment. A collection of devices that represent task assignments.

[0142] In S22, a Pareto front is introduced through non-dominated sorting, and a variable neighborhood search is used to refine the Pareto front solution as follows:

[0143] Introducing the Pareto front through non-dominated sorting:

[0144] For all process solutions in S21 that have had their resources allocated, calculate their maximum completion time. and equipment load variance The Pareto front is defined based on these two optimization objectives. For example... Figure 4 As shown in (a), and For two Pareto fronts.

[0145] Solution a dominates solution b if and only if:

[0146] (12)

[0147] Crowded distance calculation:

[0148] For each solution x, let =0;

[0149] The crowding distance for the boundary solutions (minimum and maximum values) is set to infinity:

[0150] (13)

[0151] For non-boundary solutions The expression for its crowding distance is:

[0152] (14)

[0153] in It is the objective function ( ), and The maximum and minimum values ​​of objective j in the current Pareto front.

[0154] Introducing a variable neighborhood search to finely adjust the Pareto front solution:

[0155] First, the neighborhood is defined based on the frontier hierarchy, for the Pareto front. Let the neighborhood N(x) of the solution x on the solution be:

[0156] (15)

[0157] in The solution set representing the second frontier. represent exist the ranking in. is the ranking threshold.

[0158] For the solutions that meet the threshold condition , the condition for replacing x is rand()<p, where p is a preset acceptance probability.

[0159] Taking Figure 4 (b) as an example, in the provided solution set, use on to replace on .

[0160] In S23, the final step of selecting the optimal scheduling scheme from the Pareto solution set by combining the entropy weight method and the TOPSIS method is as follows:

[0161] Scheduling decision by the entropy weight method:

[0162] The entropy weight method objectively determines the weight of each optimization objective by calculating the information entropy of each objective value (the smaller the entropy, the greater the difference between the objective values, and the higher the weight).

[0163] (16)

[0164] is the j-th optimization objective value of the i-th solution, is the normalization result of. If there are a total of m solutions in the final solution set, the specific gravity has the formula:

[0165] (17)

[0166] The formula for information entropy is:

[0167] (18)

[0168] The formula for weight is:

[0169] (19)

[0170] (20)

[0171] is a decision element, representing the weighted normalization result of the j-th objective value of the i-th solution. A larger value thereof indicates that is better on the optimization objective j.

[0172] Scheduling decision by the TOPSIS method:

[0173] The TOPSIS method selects the solution closest to the ideal solution (optimal for all objectives) and furthest from the negative ideal solution (worst for all objectives). This method is particularly suitable for scheduling decisions when the weights (user IDs) are known. For each solution i, calculate its distances to the ideal and negative ideal solutions:

[0174] (twenty one)

[0175] (twenty two)

[0176] Calculate relative proximity

[0177] (twenty three)

[0178] When choosing a solution, prioritize selecting The largest solution.

[0179] S3: Real-time scheduling is performed using an improved algorithm.

[0180] The final solution includes the following information: the start and end times of each process for each aircraft, and the personnel and equipment numbers assigned to each process. Experiments have shown that this invention can efficiently allocate personnel and equipment in multi-aircraft support operations within a short time. The results can be visualized using a Gantt chart, as shown below. Figure 5 As shown in the image, each process is labeled from top to bottom with the following information: process number, machine type, list of machine numbers, personnel type, list of personnel numbers, process start time, and process duration.

[0181] The above description is merely a preferred embodiment of the present invention. It should be understood that the multi-machine guaranteed scheduling algorithm based on NSGA-II provided by the present invention significantly improves the global optimization capability and practical operability of the scheduling scheme by integrating variable neighborhood search (VNS) and multi-criteria decision-making methods. For those skilled in the art, adaptive adjustments or extensions can be made to the algorithm parameters, neighborhood operation design, objective function weight allocation, etc., without departing from the core idea of ​​the present invention. These obvious modifications and variations should all be included within the protection scope of the present invention.

[0182] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A personnel and equipment scheduling method based on a multi-machine support operation scheduling model, characterized in that, include: S1: Using the set of aircraft P, the set of processes J, the process priority O, the set of personnel C, the type of personnel K, the set of equipment D, and the type of equipment M as input data, define process constraints, personnel constraints, and equipment constraints, and construct a multi-objective optimization model with minimizing the maximum completion time and minimizing the equipment load variance as dual optimization objectives; S2: Based on the multi-objective optimization model constructed in S1, an improved non-dominated sorting genetic algorithm that integrates variable neighborhood search is used to solve the problem, generating a Pareto solution set, and selecting the optimal scheduling scheme from the Pareto solution set. S3: Based on the optimal scheduling scheme selected by S2, execute real-time scheduling and output the start time, end time, assigned personnel number and equipment number for each process of each aircraft.

2. The personnel and equipment scheduling method based on a multi-machine support operation scheduling model as described in claim 1, characterized in that, The process constraint expression is: ； ； This represents the start time of the nth process for the p-th aircraft. This represents the end time of the nth process for the p-th aircraft. This represents the support time for the nth process of the p-th aircraft; This represents the support time for the h-th process of the p-th aircraft. This represents the start time of the h-th process for the p-th aircraft; where... , P represents the set of aircraft. The set of processes representing the p-th aircraft; The personnel constraint expression is: During aircraft support operations, for any personnel c and time point t, personnel c can support at most one aircraft; the expression for this constraint is: ； in This represents an indicator function (1 if the condition is true, 0 otherwise); Whether representative C has been assigned to process n of aircraft p; if so, then... =1 if it is 1, otherwise 0; C represents a group of people; For any given process, the number of certain personnel assigned to it must be less than or equal to the maximum number of such personnel. The expression for this constraint is: ； Let n represent the total number of personnel of type k required for process n of aircraft p. The number of people of type k; The device constraint expression is: During aircraft support operations, for any device d and time point t, device d can support at most one aircraft; the expression for this constraint is: Where P represents the set of aircraft. The set of processes representing the p-th aircraft. This represents an indicator function (1 if the condition is true, 0 otherwise); This indicates whether equipment d has been assigned to process n of aircraft p. If it has been assigned, then... The value is 1 if it is not 0 otherwise; D represents the set of devices. For any given process, the number of a certain type of equipment allocated to it must be less than or equal to the maximum number of such equipment. This constraint is expressed as: ； Let n represent the total number of equipment of type m required for process n of aircraft p. This represents the number of devices of type m.

3. The personnel and equipment scheduling method based on a multi-machine support operation scheduling model as described in claim 1, characterized in that, The maximum completion time is the time required to complete all aircraft support procedures. The expression for this optimization objective is: ； in That is, the maximum completion time. This represents the time when the last completed process was finished.

4. The personnel and equipment scheduling method based on a multi-machine support operation scheduling model as described in claim 1, characterized in that, Equipment load variance is the variance of the operating time of each piece of equipment. The smaller this value, the higher the average utilization rate of the equipment. The expression for this optimization objective is: ； in for: ； in This represents the load of device d upon completion. This represents the average load across all devices.

5. The personnel and equipment scheduling method based on a multi-machine support operation scheduling model as described in claim 1, characterized in that, S2 includes: S21: Based on the S1 multi-objective optimization model, the task sequence is exchanged through genetic mutation operation to maintain population diversity, and a greedy algorithm is used to allocate personnel and equipment resources to the processes in the task sequence. S22: For all solutions after resource allocation in S21, divide the Pareto front by non-dominated sorting, and introduce variable neighborhood search to refine the Pareto front solutions; S23: Based on the Pareto solution set adjusted in S22, the optimal scheduling scheme is selected by combining the entropy weight method and the sorting method for approximating the ideal solution.

6. The personnel and equipment scheduling method based on a multi-machine support operation scheduling model as described in claim 5, characterized in that, The specific method for exchanging task sequences through genetic variation in S21 is as follows: The parent population of size R is randomly divided into two subpopulations. Two intersection points a and b are randomly selected, and the process sequences of all individuals in the two subpopulations within the interval [a, b] are exchanged. After merging, the offspring population is obtained. Individuals in the offspring population are repaired by replacing redundant processes with missing processes, and the positions of processes in the individuals are exchanged according to a preset mutation rate.

7. The personnel and equipment scheduling method based on a multi-machine support operation scheduling model as described in claim 1, characterized in that, The specific method for resource allocation using the greedy algorithm in S21 is as follows: Calculate the idle time of person C: ； And the idle time of device d: ； in and These represent the last time the personnel and equipment were used, respectively. With the goal of maximizing minimum idle time, priority is given to allocating personnel and equipment with the longest idle time to processes. The objective expression is: ； The group of people who are responsible for task assignment. A collection of devices that represent task assignments.

8. The personnel and equipment scheduling method based on a multi-machine support operation scheduling model as described in claim 1, characterized in that, The specific method for variable neighborhood search in S22 is as follows: For a solution x on the first Pareto front F1, define the neighborhood: ； where represents the solution set of the second front, represents in the rank in; is the rank threshold; when the solution y satisfies rank(y)≤τ, it is determined whether to replace x with y at a preset acceptance probability p, wherein the replacement is performed when rand()<p.

9. The personnel and equipment scheduling method based on a multi-machine support operation scheduling model as described in claim 1, characterized in that, The optimization objective value of the i-th solution in the Pareto solution set output by S22. After normalization, we get: ； Calculate the proportion , where m is the total number of solution sets. ; Calculate information entropy And calculate the weights , where n is the total number of optimization objectives; Calculate the weighted normalized decision elements .

10. The personnel and equipment scheduling method based on a multi-machine support operation scheduling model as described in claim 9, characterized in that, The specific steps of the TOPSIS method in S23 are as follows: Weighted normalized decision elements obtained from the entropy weight method in S23 Determine the ideal solution max(v) ij and the negative ideal solution min(v) ij ); Calculate the distance from each solution i to the ideal solution. ; Distance to the negative ideal solution ; Calculate relative proximity ; choose The largest solution is taken as the optimal scheduling scheme.

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