Joint optimization method for multi-phase task equipment selective maintenance decision and task allocation

Abstract

The present application relates to the field of equipment maintenance support, and particularly discloses a multi-stage task equipment selective maintenance decision and task allocation joint optimization method. Step S1: statistics of task type, statistics of the number of each unit continuous execution tasks under the task type and the interval period between tasks; Step S2: providing maintenance measures within the interval period, statistics of the maintenance measures and the corresponding maintenance effect, and calculation of the state probability distribution after executing the maintenance measures; Step S3: calculation of the total maintenance cost within the interval period of all tasks; Step S4: since each stage task contains multiple subtasks, the total task demand of each type unit needs to be calculated according to the state and maintenance of each unit before the task starts; Step S5: allocation of tasks and meeting the demand of each stage task; Step S6: calculation of the task completion probability according to the task demand of each stage. The present application aims to solve the problem of independent optimization of equipment selective maintenance decision and task allocation under the previous multi-stage task.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of combat equipment maintenance, and discloses a multi-stage task equipment selection maintenance decision and task allocation joint optimization method. BACKGROUND

[0002] Modern war, which is mainly marked by the technical level of weapon equipment, is carried out under the conditions of modern politics, economy, military, science and technology, and geography. With the progress of science and technology and the development of weapon equipment, the content of modernization is increasingly rich, the standard of modernization is gradually improved, and modern war is continuously developed. After the emergence of electricity, many countries rely on developed economy and advanced technology to modernize the army, not only investing in new military branches, such as air force and airborne troops, and modernized army and navy, but also using a large number of advanced aircraft, tanks, artillery, automatic weapons for infantry, warships and other technical equipment.

[0003] In modern war, these equipments often require continuous execution of a series of tasks, how to reasonably allocate limited maintenance resources to multiple task intervals, and reasonably allocate combat equipment to different tasks according to the requirements of combat tasks is an important problem to be solved, therefore, the inventor provides a multi-stage task equipment selection maintenance decision and task allocation joint optimization method in order to solve the above-mentioned problems. SUMMARY

[0004] The purpose of the present application is to solve the problem of unreasonable resource allocation during equipment maintenance in the use of traditional modern war.

[0005] In order to achieve the above-mentioned purpose, the basic scheme of the present application provides a multi-stage task equipment selection maintenance decision and task allocation joint optimization method, comprising the following steps:

[0006] Step S1: statistics of task types, statistics of the number of units continuously executing tasks under each task type and the interval between tasks;

[0007] Step S2: providing maintenance measures in the interval, statistics of the maintenance measures and the corresponding maintenance effect, and calculating the state probability distribution after executing the maintenance measures;

[0008] Step S3: calculating the total maintenance cost in all task intervals;

[0009] Step S4: since each stage task contains multiple subtasks, the total task demand of each type of unit needs to be calculated according to the state and maintenance of each unit before the task starts;

[0010] Step S5: allocating tasks and meeting the demand of each stage task;

[0011] Step S6: Calculate the probability of completing the task according to the task requirements of each stage.

[0012] Further, in step S2, the state probability distribution calculation formula is:

[0013]

[0014] wherein, l represents a task unit; v represents the number of executable maintenance measures; A v represents the maintenance effect of maintenance measure v; k represents the task stage; represents the initial state distribution of unit l at the beginning of the kth task interval period.

[0015] Further, in step S3, the maintenance cost calculation formula is:

[0016]

[0017] wherein, N represents the total number of units; D represents the number of tasks; c c represents the cost of executing maintenance measure v; represents whether the decision maker takes maintenance measure v for unit l in the kth task interval period, represents that maintenance measure v is taken, otherwise

[0018] Further, any unit can only take one maintenance measure in a task interval period, so there is the following constraint:

[0019]

[0020] Further, in step S4, the total number requirement is

[0021]

[0022] wherein, M k represents the number of subtasks in the kth task.

[0023] Further, let the decision variable represent whether unit l is assigned to subtask m in the kth task; represents that unit l is assigned to subtask m in the kth task, otherwise The final task allocation result must meet the requirements of each stage task, that is:

[0024]

[0025] wherein J j is the set of the jth type of unit.

[0026] Furthermore, because the working environments of different phases of tasks and different subtasks within the same phase of a task are different, the degradation patterns of the same unit differ when performing different tasks; therefore, an environment coefficient is used. To characterize the impact of the task's working environment on the unit's state degradation, the state transition strength matrix of unit l when executing the m-th subtask in the k-th task is... for:

[0027] Among them, Λ l This represents the basic state transition strength matrix of element l. Let m be the environmental coefficient of the m-th subtask m in the k-th task, and The effect of the working environment of this task on the accelerated degradation of unit l was characterized.

[0028] Furthermore, unit l is assigned to subtask m in the k-th task, and the state transition intensity matrix of unit l is... Attached Solving the Kolmogorov differential equations yields the state probability distribution of unit l after completing its task, which is the state probability distribution of unit l at the beginning of the k-th task interval. So, what is the probability that unit l completes the k-th task? for

[0029]

[0030] Furthermore, based on the requirements of the m-th subtask of the k-th task, i.e. At least one in each unit Each unit completes a task, and the probability of task completion for subtask m can be evaluated. The probability of completing the k-th task is:

[0031]

[0032] Furthermore, the joint optimization model for selective maintenance decision-making and task allocation under multi-stage tasks, based on the task completion probability, is as follows:

[0033] A, max min{R 1 ,R 2 ,…,R D};

[0034] B

[0035] C

[0036] D、

[0037] E,

[0038] F、

[0039] G、

[0040] Wherein: A is a target function, indicating the maximum minimum stage task completion probability; B indicates that the maintenance cost cannot exceed the maintenance budget C0; C indicates that any unit can only take one maintenance measure in a task interval period; D indicates that any unit can only be assigned to one of the subtasks in a task; E indicates that the task allocation scheme must meet the quantity demand of each task for each type of unit; F and G are multi-stage task equipment selection maintenance decision and task allocation joint optimization methods.

[0041] The principle and effect of the basic scheme are that:

[0042] The present application aims at the case that the combat units need to continuously perform multiple stage tasks, and constructs a selective maintenance decision and task allocation joint optimization model under multi-stage tasks. The limited maintenance budget is reasonably allocated to each task interval period, the optimal maintenance strategy is formulated for each unit, and each unit is allocated to different subtasks to complete each stage task. Different subtasks in each stage task are represented by defining an environmental coefficient to represent the influence of the working environment on the unit state degradation, and the task completion probability of the unit is obtained by solving the Markov model, and then the completion probability of the stage task is obtained. Finally, a multi-stage task selective maintenance decision and task allocation joint optimization model based on the maximum-minimum stage task completion probability is constructed, and a co-evolution mechanism is used to decompose it into multiple sub-problems for solving. Finally, the correctness and effectiveness of the proposed model and algorithm are verified through two examples. The results show that under multi-stage tasks, the selective maintenance strategy considering the effect of imperfect maintenance and the equipment task allocation can obtain better results, and the designed co-evolution strategy can effectively solve the problem of selective maintenance decision and task allocation joint optimization under multi-stage tasks by decomposing the complex problem into multiple sub-problems, and good optimization effect is obtained. BRIEF DESCRIPTION OF DRAWINGS

[0043] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0044] Figure 1 The co-evolution genetic algorithm flowchart of the multi-stage task equipment selective maintenance decision and task allocation joint optimization method proposed in the embodiments of the present application is shown;

[0045] Figure 2 A task timing diagram of the multi-stage task equipment selection and maintenance decision and task allocation joint optimization method proposed in the embodiments of the present application is shown.

[0046] Figure 3 The maximum-minimum task completion probability and maintenance budget relationship of the multi-stage task equipment selection and maintenance decision and task allocation joint optimization method proposed in the embodiments of the present application is shown. DETAILED DESCRIPTION

[0047] In order to further illustrate the technical means and effects adopted by the present application to achieve the predetermined application purposes, the specific embodiments, structures, features and effects according to the present application are described in detail as follows in combination with the drawings and preferred embodiments.

[0048] As shown in Figure 1 , in the multi-stage task equipment selection and maintenance decision and task allocation joint optimization method, the following situations occur:

[0049] Assumption 1: J types of N combat units need to continuously perform D tasks, and the task timing diagram is as shown in Figure 1 . Among them, task k contains M k independent sub-tasks, the number of units required for each sub-task is known, and the requirements of each sub-task must be met to normally execute the task.

[0050] Assumption 2: The sub-task structure function φ(·) is known, which is a K of N system, that is, at least K units survive during the task execution period, and the task can be successfully executed. The task completion probability is the product of the completion probabilities of each sub-task.

[0051] Assumption 3: All units are multi-state units, and the degradation process obeys a homogeneous Markov process.

[0052] Assumption 4: Maintenance activities can only be carried out in the interval period before task execution, no maintenance measures are taken during task execution, and each unit only undergoes state degradation during the task execution period.

[0053] Assumption 5: The initial state of each unit at the beginning of the first task interval period cannot be accurately obtained, and only the state probability distribution thereof can be inferred. The state probability distribution of the unit at the end of each stage task can be derived through multi-state reliability theory.

[0054] Assumption 6: The duration of each stage task is determined, and is known at the beginning of the first task interval period.

[0055] Assumption 7: In each maintenance period, each unit has multiple maintenance options, including: no maintenance, imperfect maintenance and perfect maintenance. The maintenance effect is related to the maintenance resource (maintenance cost) put into the unit.

[0056] Therefore, in order to solve the above assumptions, it is necessary to carry out joint optimization of the model, specifically:

[0057] Under the multi-stage task, each unit needs to continuously perform D tasks, and the maintenance strategy of each unit needs to be determined in the task interval period, and each unit is allocated to different sub-tasks to jointly perform the task at the beginning of the stage task. In the task interval period, each unit has multiple maintenance options, V represents the number of executable maintenance options, A v represents the maintenance effect of maintenance option v, defined as formula:

[0058]

[0059] Let be the initial state distribution of unit l at the beginning of the kth task interval period, then the state probability distribution of unit l after performing maintenance option v is:

[0060]

[0061] Let decision variable represent whether maintenance option v is taken for unit l in the kth task interval period. represent that maintenance option v is taken, otherwise The total maintenance cost in all task interval periods is:

[0062]

[0063] Where N is the total number of units, c v represents the cost of performing maintenance option v.

[0064] However, any unit can only take one maintenance option in a task interval period, so there is the following constraint:

[0065]

[0066] Since each stage task includes multiple sub-tasks, the decision maker needs to allocate each type of unit to different sub-tasks according to the state and maintenance of each unit before the task starts to meet the task demand. Let M k represent the number of sub-tasks in the kth task, represent the number of j-type units required by the mth sub-task in the kth task, then the total number of units required by the mth sub-task in the kth task is

[0067]

[0068] decision variable denotes whether unit l is assigned to subtask m in the kth task. denotes that unit l is assigned to subtask m in the kth task, otherwise

[0069] The final task assignment result must meet the requirements of each stage task, i.e.

[0070]

[0071] where J j is the set of the jth type of units.

[0072] However, any unit can only be assigned to one subtask in the same stage task, so there is the following constraint:

[0073]

[0074] In addition, because the working environment of different stage tasks and different subtasks in the same stage task is different, the degradation law of the same unit when executing different tasks is different. Therefore, an environment coefficient is used to represent the influence of the task working environment on the unit state degradation, then the state transition intensity matrix of unit l when executing the mth subtask of the kth task is

[0075]

[0076] where Λ l denotes the basic state transition intensity matrix of unit l, is the environment coefficient of the mth subtask m in the kth task, and characterizes the accelerated degradation effect of the task working environment on unit l.

[0077] Assuming that unit l is assigned to subtask m in the kth task, the state transition intensity matrix of unit l is substituted into equation Solving the Kolmogorov differential equation set can obtain the state probability distribution of unit l after executing the task, i.e. the state probability distribution of unit l at the beginning of the kth task interval Then, the probability of unit l completing the kth task is

[0078]

[0079] Further, according to the requirements of the mth subtask of the kth task, i.e.​​ At least one of the units The task completion probability of the mth subtask can be evaluated The completion probability of the kth task is:

[0080]

[0081] Based on the above description of the selective maintenance decision and equipment task allocation problem under multi-stage tasks, the joint optimization model of selective maintenance decision and task allocation under multi-stage tasks based on the maximum-minimum stage task completion probability is as follows:

[0082] A, max min{R 1 ,R 2 ,…,R D};

[0083] B,

[0084] C,

[0085] D,

[0086] E,

[0087] F,

[0088] G,

[0089] Wherein: A is the objective function, indicating the maximum minimum stage task completion probability; B indicates that the maintenance cost cannot exceed the maintenance budget C0; C indicates that any unit can only take one maintenance measure in a task interval period; D indicates that any unit can only be assigned to one of the subtasks in a task; E indicates that the task allocation scheme must meet the number requirements of each task for each type of unit; F and G are the joint optimization method of multi-stage task equipment selective maintenance decision and task allocation.

[0090] In actual situations, the joint optimization model of selective maintenance decision and task allocation under multi-stage tasks established is a nonlinear programming problem containing discrete decision variables, and this problem will become more complex with the increase of the number of task stages and units. Cooperative co-evolutionary genetic algorithm (CCGA) is a meta-heuristic algorithm based on the idea of cooperative evolution, which can handle this kind of complex optimization problem by decomposing the complex original problem into multiple sub-problems and optimizing them separately.

[0091] Co-evolutionary genetic algorithm was first proposed by Potter and Jong in 1994, which is a meta-heuristic algorithm based on the co-evolutionary idea. Co-evolutionary genetic algorithm first decomposes the original problem into multiple lower-dimensional sub-problems, and then puts them into multiple independent evolutionary sub-populations for iterative optimization. When evaluating individuals, multiple sub-populations are evaluated jointly, and finally the representative individuals in each sub-population are combined to form a complete solution, thus realizing co-evolution. Compared with traditional genetic algorithm, the advantages of co-evolutionary genetic algorithm are: ① multiple sub-problems are solved in parallel to improve the optimization rate; ② each problem is optimized independently to ensure diversity; ③ modular solution enhances the robustness of the solution; ④ the original complex problem is decomposed, which can appropriately reduce the dimension explosion problem caused by the increase of problem size.

[0092] As shown in Figure 1 , for the selective maintenance decision and task allocation joint optimization model under multi-stage task proposed in the invention, the original problem is first decomposed into a corresponding number of sub-problems according to the number of multi-stage tasks, i.e. each sub-problem corresponds to the maintenance decision and task allocation joint optimization problem of each stage task.

[0093] The optimization step is:

[0094] In this problem, there are two sub-problems: maintenance decision and task allocation. For a problem with N units, the traditional chromosome coding method needs to code the two sub-problems respectively. This coding method requires a coding length of 2N, which is low in coding efficiency and thus affects the performance of the algorithm. Therefore, the invention adopts a random key coding method, in which the value of each gene bit is randomly generated between [0, 1], and the maintenance strategy and task allocation strategy are encoded at the same time. Then the corresponding maintenance strategy and task allocation strategy are parsed through a special decoding method. Through this coding and decoding method, the chromosome coding length is reduced to N, improving the coding efficiency.

[0095] The random key coding generates a random key r l between [0, 1] for each unit

[0096] Step 1: divide the interval [0, 1] into V equal intervals, where V represents the number of maintenance measures that each unit can take. Therefore, different intervals represent different maintenance measures. If the value of r l is in the vth interval, it means that maintenance measure v is taken for unit l, and so on. In this way, the maintenance strategy for all units can be obtained.

[0097] Step 2: after parsing the unit maintenance strategy, normalize the key r l according to the interval where its value is located to obtain the normalized key r' l , i.e.

[0098]

[0099] Step 3: The normalized keys are sorted in order, and then each subtask is assigned according to the sorted results of the units. For example, if subtask 1 and subtask 2 require 2 and 3 type 1 units to participate in the task, respectively, the first 2 units in the type 1 units are assigned to subtask 1, and the next 3 units are assigned to subtask 2, and so on, so that the task allocation strategy can be obtained.

[0100] (2) Fitness function

[0101] The fitness value is a standard for evaluating the performance of individuals in the population. In this problem, the optimization goal is to maximize the task completion probability under the limited maintenance budget. In order to comprehensively evaluate the performance of individuals under the constraint of maintenance budget, a penalty function is introduced to punish individuals that violate the constraint, and the fitness value of individuals that violate the constraint is reduced when evaluating the fitness value, so as to improve the ability of the algorithm to eliminate inferior solutions. The penalty function is set as follows:

[0102]

[0103] where p s is the penalty value of individual s; G is a penalty factor, which is a large positive real number; C0is the maintenance budget; C s is the maintenance cost required by the individual s to represent the scheme. Then the fitness function is:

[0104] f s = R s -p s ,

[0105] where f s is the fitness value of individual s; R s is the task completion probability corresponding to individual s.

[0106] (3) Selection operation

[0107] Selection is to make the excellent genes in the iteration process of the population be saved, and to select the excellent individuals in the current population to participate in the subsequent crossover and mutation operations. The tournament method is used for individual selection in this algorithm, that is, a certain number of individuals are selected from the current population, and the fitness values of the individuals are compared, and the best individual is selected to be saved. Repeat the operation until the parent population of the required size is generated.

[0108] (4) Crossover operation and mutation operation

[0109] The purpose of the crossover operation is to generate a new population by randomly combining the parent population, which is the main step of the genetic algorithm. The single-point crossover method is used in this algorithm, that is, the starting point of the gene segment to be crossed is randomly determined, and then the parts of the two parent chromosomes from the position to the end of the chromosome are exchanged to obtain the child chromosomes. Mutation operation is to increase the diversity of the population. The process of randomly disturbing the child population generated in each iteration to produce new individuals can effectively enhance the local search ability of the algorithm. In this problem, the mutation operation of the child population is completed by mutating each gene site to a random value in the feasible region with a certain probability.

[0110] (5) Elite preservation strategy

[0111] To prevent the loss of good individuals in the iteration process of the algorithm, the elite preservation strategy is introduced, that is, in each population evolution to generate a child population, the k individuals with the highest fitness value in the parent population are selected and reserved in the child population to participate in the next iteration, which fully guarantees the high quality of the population in the iteration process and prevents the loss of good genes in the crossover and mutation process.

[0112] Implementation steps:

[0113] Algorithm 1 of joint optimization method of maintenance decision and task allocation based on multi-stage task equipment selection

[0114] The two types of 6 units need to continuously perform two tasks, and the duration of each stage task is 10 hours. Each stage task contains two subtasks, and the task parameters are shown in Table 3-1. Among them, α m is the working environment coefficient of each subtask, N m,1 and N m,2 are the number requirements of each subtask for the two types of units, N m is the total number requirement of each subtask, and K m is the minimum number of units required to survive in the subtask.

[0115] Table 1-1 Task-related parameters

[0116]

[0117]

[0118] Each unit is a 4-state unit, and state 4 is the perfect state and state 1 is the failure state. The type of each unit and the state probability distribution at the beginning of the first task interval are shown in Table 1-1-1.

[0119] Table 1-1-1 Unit parameters

[0120]

[0121] For this small-scale example, the genetic algorithm in Section 3.3 is used to solve. The algorithm parameters are set as follows: population size is 100, maximum iteration number is 100, crossover probability and mutation probability are 0.9 and 0.1 respectively, and the number of elite strategy reserved is 10. Under the condition of maintenance budget C0= 300,000 yuan, four kinds of models are solved respectively. Model I is the joint optimization model of selective maintenance and task allocation considering the effect of imperfect maintenance under multi-stage task proposed in this chapter, model II is the joint optimization model of selective maintenance and task allocation without considering the effect of imperfect maintenance under multi-stage task, model III is the selective maintenance decision model considering the effect of imperfect maintenance under multi-stage task, and model IV is the selective maintenance decision model without considering the effect of imperfect maintenance under multi-stage task. The optimal selective maintenance strategy and task allocation strategy of each model are shown in Tables 1-2 to 1-4. Among them, C k is the maintenance cost allocated to the kth task interval, is the completion probability of the mth subtask of the kth stage task, R k is the completion probability of the kth stage task.

[0122] Table 1-2 Optimal selective maintenance strategy and task allocation strategy of model I

[0123]

[0124] * is the maximum-minimum task completion probability

[0125] Table 1-3 Optimal selective maintenance strategy and task allocation strategy of model II

[0126]

[0127] * is the maximum-minimum task completion probability

[0128] From Table 1-2, the maintenance costs allocated to the first and second task interval periods are 180,000 yuan and 120,000 yuan, respectively, 7 maintenances are performed on the units collectively in the two task interval periods, and each unit is maintained at least once in the two task interval periods, and the final task completion probabilities are 0.8956 and 0.8945. It is shown that by jointly optimizing the maintenance strategy and the task allocation strategy of the multi-stage task, the needs of different stages of tasks and different sub-tasks can be effectively responded to, and the balance between the completion probabilities of the tasks of different stages is finally achieved, and a more optimal strategy is obtained. Compared with the results in Table 1-3, in model II, the imperfect maintenance effect is not considered, and only 5 units can be maintained, unit 3 is not maintained in the two task interval periods, and the final task completion probabilities are 0.8871 and 0.8950, and the minimum stage task success probability and the maximum stage task success probability are less than those of model I, which shows that considering the imperfect maintenance effect can more reasonably allocate the maintenance budget.

[0129] Table 1-4 lists the optimal selective maintenance strategies of model III and model IV. By comparing model I with model III and model II with model IV, it can be seen that considering the task allocation of the unit in the selective maintenance decision under the multi-stage task can better adapt to the needs of the multi-task operational environment, obtain a more optimal operational strategy, and improve the task completion probability.

[0130] Table 1-4 Optimal selective maintenance strategies of model III and model IV

[0131]

[0132] * The maximum-minimum task completion probability is represented

[0133] Figure 2 The relationship between the maximum-minimum task completion probability and the maintenance budget of the four models is shown. It can be seen that under different maintenance budgets, the joint optimization of selective maintenance and task allocation considering the effect of imperfect maintenance all obtains the best optimization effect. When the maintenance budget is 0, i.e., no maintenance measures can be taken, model I and model II can improve the task completion probability by changing the task allocation strategy.

[0134] Table 1-5 lists the optimization strategies under different task durations, where T 1 and T 2The durations of task 1 and task 2, respectively. It can be seen that the maximum-minimum task completion probabilities are different for different task durations. As the relative sizes of the two task durations change, the total maintenance cost allocated to the two task intervals also changes, indicating that joint optimization of maintenance decisions and task allocation within the two task intervals can result in a better strategy. When the task durations are {12, 10}, {10, 8}, and {10, 12}, the maximum-minimum task completion probabilities are the first task completion probabilities.

[0135] Table 1-5 Optimal strategies for different task durations

[0136]

[0137] * The maximum-minimum task completion probability

[0138] Algorithm 2: Joint optimization of maintenance decision and task allocation based on multi-phase task equipment selection

[0139] The 3 types of 16 combat units need to perform 3 tasks in succession, and the durations of the 3 tasks are 10 hours, 12 hours, and 10 hours, respectively. Each task includes 3 subtasks, and the relevant parameters of the tasks are shown in Table 1-6. Among them, is the work environment coefficient of each subtask under each task, and are the number requirements of 3 types of units for different subtasks of each phase task, is the total number requirement of units for each subtask, is the minimum number of units required to survive in each subtask.

[0140] Each unit has 4 maintenance measures to choose from, and maintenance measure 1 and maintenance measure 4 are no maintenance and perfect maintenance, respectively, and maintenance measure 2 and maintenance measure 3 are two degrees of imperfect maintenance. The maintenance costs of the 4 maintenance measures are 0, 2, 4, and 6 million yuan, respectively

[0141] Table 1-6 Task parameters

[0142]

[0143] In the case of maintenance budget C0= 150 million, the algorithm parameters are set as follows: population size is 100, maximum iteration number is 200, crossover probability and mutation probability are 0.9 and 0.1 respectively, and the number of elite strategy reserved is 10. After running 20 times continuously, the running results are shown in Tables 1-7. As can be seen from Tables 1-7, the minimum stage task completion probability corresponding to the optimal solution searched by CCGA is 0.8796, which is better than 0.8599 corresponding to the optimal solution of GA. At the same time, the higher average value shows that the overall performance of CCGA is significantly better than that of GA, and even the average value 0.8687 obtained by CCGA is also better than the optimal value obtained by GA. The smaller standard deviation shows that CCGA has better robustness, which indicates the superiority of the idea of decomposing complex problems into multiple sub-problems for solving by CCGA.

[0144] Table 1-7 Comparison of optimization results

[0145]

[0146] The optimal selective maintenance strategy and task allocation strategy are shown in Table 1-8. As can be seen, by jointly optimizing the maintenance strategy and task allocation strategy of each stage, the multi-stage task demand can be effectively responded to, and the maintenance resources are more balancedly allocated to each stage task. At the same time, the optimized tasks of each stage have similar completion probabilities, i.e. by maximizing the minimum stage task completion probability, the maintenance resources can be reasonably allocated according to the demand of each stage task, so that the completion probability of each stage task remains at a high level.

[0147] Table 1-8 Optimal selective maintenance strategy and task allocation strategy

[0148]

[0149] * Indicates the maximum-minimum task completion probability

[0150] Table 1-9 gives the optimal selective maintenance strategy and task allocation strategy without considering the non-perfect maintenance effect model. As can be seen from the comparison with Table 1-8, under the non-perfect maintenance effect model, on average, only 8 units can be maintained in each stage, and among them, 5 units only perform maintenance once in 3 task interval periods; while under the proposed model, except for units 2 and 14, all other units can perform maintenance at least twice, which shows that considering the non-perfect maintenance effect can more reasonably allocate the maintenance budget to each unit, thereby improving the stage task completion probability.

[0151] Table 1-9 Optimal selective maintenance strategy and task allocation strategy without considering non-perfect maintenance effect

[0152]

[0153] * Represents the maximum-minimum task completion probability

[0154] To demonstrate the effectiveness of jointly optimizing selective maintenance decisions and task allocation in multi-stage tasks, the joint optimization method is compared with the two-stage optimization method, and the results are shown in Table 1-10. The two-stage optimization method optimizes selective maintenance decisions and task allocation independently; that is, it optimizes the maintenance strategies for all stages in the first stage, and then optimizes the task allocation strategy for each unit based on the optimized maintenance strategies in the second stage. As shown in Table 1-10, compared with the two-stage optimization method optimizing the two problems independently, the joint optimization achieves better results, with an increased probability of completion for each sub-task. It is worth noting that in the two-stage optimization method, the task allocation strategy is the initial task allocation strategy, meaning that the optimization in the second stage does not bring any actual improvement. This indicates that optimizing selective maintenance decisions and task allocation independently exhibits significant locality, getting trapped in a local optimum in the first stage.

[0155] Table 1-10 Optimal Selective Maintenance Strategy and Task Allocation Strategy in Two-Stage Optimization

[0156]

[0157] * Represents the maximum-minimum task completion probability

[0158] like Figure 3 As shown, four models—the joint optimization model of selective maintenance and task allocation considering the effects of non-intact maintenance, the joint optimization model of selective maintenance and task allocation not considering the effects of non-intact maintenance, the selective maintenance decision model considering the effects of non-intact maintenance, and the selective maintenance decision model not considering the effects of non-intact maintenance—are further compared under different maintenance budgets. The results are as follows: Figures 1-3 As shown in the figure, it can be seen that, under different maintenance budgets, the joint optimization of selective maintenance and task allocation, which considers the effects of non-perfect maintenance, achieves the best optimization results.

[0159] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A joint optimization method for selective maintenance decision-making and task allocation for multi-stage mission equipment, characterized by: The method comprises the following steps: Step S1: counting the task type, counting the number of continuous execution tasks of each unit under the task type and the interval period between tasks; Step S2: providing maintenance measures within the interval period, counting the maintenance measures and the corresponding maintenance effect, and calculating the state probability distribution after the maintenance measures are executed; Step S3: calculating the total maintenance cost within the interval period of all tasks; Step S4: since each stage task contains multiple subtasks, the total task demand of each type of unit needs to be calculated according to the state and maintenance of each unit before the task starts; Step S5: allocating tasks and meeting the demand of each stage task; Step S6: calculating the task completion probability according to the task demand of each stage; In step S2, the state probability distribution calculation formula is: ， wherein represents a task unit; represents the number of executable repair measures; represents a repair measure a repair effect of; represents a task phase; represents a unit an initial state distribution at the beginning of the first task interval period; Because of the different working environments of different stage tasks and different subtasks in the same stage task, the degradation rules of the same unit are different when it executes different tasks. Therefore, using an environment coefficient to represent the influence of the working environment of the task on the unit state degradation, the state transition intensity matrix of the unit when it executes the i-th subtask in the j-th task is: ;​​​ wherein, representing unit the basic state transition intensity matrix, is the first task in the first subtask environment coefficient, and , characterized by the task of the working environment on the unit accelerated degradation effect; The unit is assigned to the subtasks in the first task, the state transition intensity matrix of the unit is brought into the formula to solve the Kolmogorov differential equation set, the state probability distribution of the unit after executing the task, that is, the state probability distribution of the unit at the beginning of the first task interval period ; then, the probability of the unit to complete the first task is ， According to the The first task The requirements of each sub-task, namely At least one in each unit Each unit completes the task, and sub-tasks can be evaluated. Task completion probability Then the first The probability of completing each task is: ， The joint optimization model of selective maintenance decision and task allocation under multi-stage tasks established based on the task completion probability is as follows: A、 ； B、 ； C、 ； D、 ； E、 ； F、 ； G、 ； Wherein: A is the objective function, indicating the maximum minimum phase task completion probability; B indicates that the repair cost cannot exceed the repair budget ; C indicates that any unit can only take one maintenance measure in a task interval period; D indicates that any unit can only be assigned to one of the sub-tasks in a task; E indicates that the task allocation scheme must meet the quantity demand of each task for each type of unit; F and G are multi-stage task selective maintenance decision and task allocation joint optimization methods.

2. The multi-phase mission equipment selective maintenance decision and mission assignment joint optimization method of claim 1, wherein, In step S3, the maintenance cost calculation formula is: ， wherein, denotes the total number of units; denotes the number of tasks; denotes the cost of performing a maintenance measure ; denotes whether the decision maker has taken a maintenance measure on the unit in the i-th task interval period, denotes that a maintenance measure has been taken, otherwise .​ 3. The multi-phase mission equipment selective maintenance decision and mission assignment joint optimization method of claim 2, wherein, Any unit can only take one maintenance measure within an interval period of a task, so there are the following constraints: 。 4. The multi-phase mission equipment selective maintenance decision and mission assignment joint optimization method of claim 1, wherein, In step S4, the total quantity demand is ， wherein, represents the number of subtasks in the th task.

5. The multi-phase mission equipment selective maintenance decision and mission assignment joint optimization method of claim 4, wherein, Let decision variable denote whether a unit is assigned to a subtask in the i-th task ; denote whether a unit is assigned to a subtask in the i-th task , otherwise ; the final task assignment must satisfy the requirements of the tasks in each stage, i.e.:​​​​ ， wherein is a first set of class units.

Images