A joint optimization method for equipment selective maintenance decision-making and task allocation

Abstract

The present invention relates to the field of equipment maintenance and support, and specifically discloses a joint optimization method for equipment selective maintenance decision-making and task allocation. Under the constraint of limited maintenance costs, an optimal maintenance strategy is formulated for each unit, and each unit is allocated to different subtasks to collaboratively perform the next phase of combat tasks. A task allocation objective function is established with the goal of maximizing the probability of task completion. Finally, a joint optimization model for selective maintenance decision-making and task allocation is established with the goal of maximizing the completion probability of the entire task. A random key-based genetic algorithm is used to solve the joint optimization model for selective maintenance decision-making and task allocation, and the optimized selective maintenance strategy and task allocation strategy for each unit are determined. This solves the problem in traditional equipment maintenance and support that equipment selective maintenance decision-making and task allocation are optimized separately, resulting in unscientific decision-making.

Description

Technical Field

[0001] The present application relates to the technical field of combat equipment maintenance, and specifically discloses a joint optimization method for equipment selective maintenance decision-making and task allocation. Background Art

[0002] Following the advent of electricity, the economy rapidly developed. The second technological revolution, marked by its widespread use, promoted industrial electrification, significantly increased productivity, and revitalized the economy. Military equipment modernization not only introduced new branches and arms, such as the Air Force and Airborne Force, as well as a modernized Army and Navy, but also employed a large number of advanced aircraft, tanks, artillery, infantry automatic weapons, ships, and other technical equipment.

[0003] With the continuous improvement of equipment technology and the comprehensive development of equipment level, the maintenance technology of equipment is also constantly improving in the process of use. Most of the current research on equipment maintenance regards equipment selective maintenance decision and task allocation as two independent issues. However, in actual combat needs, decision makers not only need to formulate maintenance strategies based on limited maintenance resources, but also need to allocate unit combat tasks based on mission requirements and unit maintenance status. The combination of the two can better ensure the completion of the mission.

[0004] Therefore, in view of this, the inventor provides a joint optimization method for equipment selective maintenance decision-making and task allocation to solve the above problems. Summary of the Invention

[0005] The purpose of the present invention is to solve the problem in traditional equipment maintenance planning that equipment selective maintenance decision and task allocation are independent, resulting in inconsistent final decisions.

[0006] To achieve the above objectives, the basic solution of the present invention provides a joint optimization method for equipment selective maintenance decision-making and task allocation, comprising the following steps:

[0007] Step S001: Assume that each unit has S states, where state 1 is a completely failed state, state S is a fully working state, and the remaining states are intermediate states. The state degradation process of each unit is described using a homogeneous Markov model, a unit state transition intensity matrix is ​​established, and the state distribution probability of the unit is obtained by solving the Kolmogorov differential equation;

[0008] Step S002: Classify maintenance measures into three categories according to maintenance effects: no maintenance, complete maintenance, and incomplete maintenance, and define a maintenance matrix based on the maintenance effects;

[0009] Step S003: Based on the state transition intensity matrix and the maintenance matrix, the optimal maintenance strategy and equipment task allocation strategy are formulated for each unit in combination with the maintenance cost and the working environment. Each unit is then assigned to different subtasks to collaboratively execute the next phase of combat missions, maximizing the probability of mission completion.

[0010] Step S004: combining the maintenance strategy and the equipment task allocation strategy to establish a joint optimization model of selective maintenance decision and task allocation;

[0011] Step S005: A random key-based genetic algorithm is used to solve the joint optimization model of selective maintenance decision and task allocation to obtain the optimal maintenance decision and task allocation method.

[0012] Furthermore, in step S001, the entire state transition process of a single unit l can be represented by the state transition intensity matrix Λ l express: is the transition strength of unit l from state i to state j, and

[0013] Furthermore, in step S002, the maintenance effect matrix A is defined. v as follows: in, A represents the probability that the unit will recover to state j after taking maintenance measure v if it is in state i. v Describes the maintenance effect of maintenance measure v, that is, the state transition of the unit after maintenance.

[0014] Furthermore, when the selected unit does not take maintenance, the maintenance effect matrix A v is the identity matrix.

[0015] Furthermore, when the selected unit is fully repaired, the maintenance effect matrix A v for

[0016]

[0017] Furthermore, when the selected unit is not repaired properly, there is and restrictions.

[0018] Furthermore, in step S005, the basic process of the genetic algorithm includes the following steps:

[0019] Step A001: population initialization;

[0020] Step A002: Generate a random key and decode it;

[0021] Step A003: Perform fitness evaluation;

[0022] Step A004: Perform selection, crossover, and mutation to produce offspring populations;

[0023] Step A005: retain elite individuals;

[0024] Step A006: Determine whether the maximum number of iterations has been reached. If so, end the process. If not, return to step A002 and repeat the process.

[0025] Furthermore, in step A002, the random key encoding generates a random key r between [0,1] for each unit. l , the key decoding mainly includes the following steps:

[0026] Step B001: Divide the interval [0,1] into V intervals of equal length, where V represents the number of maintenance measures that can be taken for each unit, and different intervals represent different maintenance measures;

[0027] Step B002: Analyze the unit maintenance strategy, and after the analysis is completed, the key r l Normalize according to the interval where its value is located to obtain the normalized key r l ';

[0028] Step B003: Sort the units in order using the normalized key, and then assign each subtask according to the unit sorting result.

[0029] Furthermore, in step A004, a tournament method is used to perform individual selection.

[0030] Furthermore, in step A004, a single-point crossover method is used to perform a crossover operation.

[0031] The principles and effects of this basic solution are:

[0032] 1. In the case where combat units need to jointly perform multiple parallel subtasks, the present invention constructs a joint optimization model of selective maintenance decision-making and task allocation considering non-intact maintenance.

[0033] 2. Under the constraint of limited maintenance costs, the present invention formulates an optimal maintenance strategy for each unit and assigns each unit to different subtasks to complete the combat mission. Each unit is modeled as a multi-state unit, and an environmental coefficient is defined to characterize the impact of the working environment of different subtasks on the degradation of the unit state. By solving the Markov model, the unit's task completion probability is obtained, and then the completion probability of the subtask and the entire task is obtained.

[0034] 3. The present invention combines the Markov model to ultimately construct a joint optimization model for selective maintenance decision-making and task allocation with the goal of maximizing the probability of task completion. A genetic algorithm based on random key encoding is designed to solve the problem. Considering equipment task allocation in selective maintenance decisions can produce better results, and the optimization strategy that considers non-intact maintenance is better than the optimization strategy that does not consider non-intact maintenance. This solves the problem of traditional equipment maintenance plans where equipment selective maintenance decisions and task allocation are independent, resulting in inconsistent final decisions.

[0035] 4. This invention divides the interval [0,1] into V intervals of equal length. Different intervals represent different maintenance measures. When r l If the value of is in the vth interval, it means that maintenance measure v is taken for unit l. Similarly, the maintenance strategy for all units can be obtained.

[0036] 5. This invention uses a selection operation to preserve high-quality genes during the population iteration process and screen high-quality individuals in the current population for subsequent crossover and mutation operations. This invention uses a tournament method for individual selection, which selects a certain number of individuals from the current population, compares their fitness values, and selects the most outstanding individuals to be retained. This operation is repeated until a parent population that meets the required size for iteration is generated.

[0037] 6. The purpose of the crossover operation in the present invention is to generate a new population by randomly combining parent populations. It is the main link of the genetic algorithm. The present invention adopts a single-point crossover method, that is, first randomly determine the starting point of the gene segment to be crossed, and then exchange the two parent chromosomes from this position to the end of the chromosome to obtain the daughter chromosome.

[0038] 7. The present invention adopts mutation operation to increase the diversity of the population. The process of randomly perturbing the offspring population generated in each iteration to generate new individuals can effectively enhance the local search capability of the genetic algorithm. In this problem, the mutation operation of the offspring population is completed by mutating each gene position to a random value in the feasible domain with a certain probability.

[0039] 8. In order to prevent the loss of high-quality individuals during the iterative process of the genetic algorithm, the present invention introduces an elite retention strategy. That is, each time a population evolves to generate a sub-population, the k individuals with the highest fitness values ​​in the parent population are selected and retained in the sub-population to participate in the next iteration, fully ensuring the high quality of the population during the iteration process and preventing the loss of high-quality genes during the crossover mutation process. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For those skilled in the art, other drawings can be obtained based on these drawings without creative work.

[0041] Figure 1 A flowchart of a genetic algorithm for a joint optimization method of equipment selective maintenance decision-making and task allocation proposed in an embodiment of the present application is shown;

[0042] Figure 2 A homogeneous Markov model of multiple state units of a joint optimization method for equipment selective maintenance decision-making and task allocation proposed in an embodiment of the present application is shown;

[0043] Figure 3 A schematic diagram of problem coding for a joint optimization method for equipment selective maintenance decision-making and task allocation proposed in an embodiment of the present application is shown;

[0044] Figure 4 A schematic diagram of random key decoding of a joint optimization method for equipment selective maintenance decision-making and task allocation proposed in an embodiment of the present application is shown;

[0045] Figure 5 The relationship between the task completion probability and the maintenance budget of a joint optimization method for equipment selective maintenance decision-making and task allocation proposed in an embodiment of the present application is shown;

[0046] Figure 6 The embodiment of the present invention shows a method for joint optimization of equipment selective maintenance decision and task allocation. Figure 1-5 The relationship between task completion probability and maintenance budget. DETAILED DESCRIPTION

[0047] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0048] The following is a further detailed description through specific implementation methods:

[0049] A joint optimization method for equipment selective maintenance decision-making and task allocation is proposed. First, this method is proposed based on the following six conditions:

[0050] Condition 1: A mission requires N combat units of J types to execute together, all units are multi-state units, and the degradation process obeys a homogeneous Markov process.

[0051] Condition 2: A task contains multiple independent subtasks. The number of units of each type required by each subtask is known, and the requirements of each subtask must be met for the task to be executed normally.

[0052] Condition 3: The structure functions φ(·) of each subtask are known and are all KofN systems. This means that a task can only be successfully executed if at least K units survive during the entire task execution period. The total task completion probability is the product of the completion probabilities of each subtask.

[0053] Condition 4: Maintenance activities can only be carried out during the interval before the task is executed, and no maintenance measures will be taken during the task execution.

[0054] Condition 5: The initial state of each unit cannot be accurately obtained, and only the state probability distribution can be inferred.

[0055] Condition 6: During the maintenance period, each unit has multiple maintenance options available, including no maintenance, partial maintenance, and complete maintenance. The maintenance effect is related to the maintenance resources (maintenance costs) invested by the unit.

[0056] The above six conditions are based on reality and are feasible.

[0057] The present invention provides a joint optimization method for equipment selective maintenance decision-making and task allocation. Based on the above six conditions, the basic steps include:

[0058] Step S001: Assume that each unit has S states, where state 1 is a completely failed state, state S is a fully working state, and the remaining states are intermediate states. The state degradation process of each unit is described using a homogeneous Markov model, a unit state transition intensity matrix is ​​established, and the state distribution probability of the unit is obtained by solving the Kolmogorov differential equation;

[0059] Step S002: Classify maintenance measures into three categories according to maintenance effects: no maintenance, complete maintenance, and incomplete maintenance, and define a maintenance matrix based on the maintenance effects;

[0060] Step S003: Based on the state transition intensity matrix and the maintenance matrix, the optimal maintenance strategy and equipment task allocation strategy are formulated for each unit in combination with the maintenance cost and the working environment. Each unit is then assigned to different subtasks to collaboratively execute the next phase of combat missions, maximizing the probability of mission completion.

[0061] Step S004: combining the maintenance strategy and the equipment task allocation strategy to establish a joint optimization model of selective maintenance decision and task allocation;

[0062] Step S005: A random key-based genetic algorithm is used to solve the joint optimization model of selective maintenance decision and task allocation to obtain the optimal maintenance decision and task allocation method.

[0063] The following is the specific implementation process of each step:

[0064] Based on the above 6 assumptions, it can be seen that each combat unit is a multi-state unit. Assuming that each unit has S states, state 1 is a completely failed state, state S is a good working state, and the remaining S-2 states are intermediate states. The state degradation process of each unit is described by the homogeneous Markov model, as shown in the following figure: Figure 2 As shown, state S and state 1 are respectively a good working state and a completely failed state. is the transition strength of unit l from state i to state j.

[0065] Then the entire state transfer process of unit l can be described by the state transfer intensity matrix Λ l express:

[0066]

[0067] in, Then at any time t, the probability distribution of unit l in each state can be obtained by solving the Kolmogorov differential equations:

[0068]

[0069] in, represents the state probability distribution of unit l at time t, is the probability that unit l is in state i at time t;

[0070] In order to better control the maintenance status of each unit after implementing maintenance measures and enable each unit to be allocated corresponding maintenance support, maintenance measures can be divided into the following three categories according to the effect after maintenance:

[0071] (1) No maintenance: No maintenance measures are taken on the unit. In this case, the state probability distribution of the unit before and after the task interval remains unchanged, and no maintenance resources are consumed.

[0072] (2) Complete repair: After a complete repair, the unit is restored to a complete working condition, that is, "repaired as new". Complete repair consumes the most maintenance resources.

[0073] (3) Non-perfect repair: After repair, the unit's status is restored to a certain extent, and the more repair resources invested, the greater the degree of recovery.

[0074] The present invention defines the maintenance matrix A according to the effect of the maintenance measures v as follows:

[0075]

[0076] in, A represents the probability that the unit will recover to state j after taking maintenance measure v if it is in state i. v Describes the maintenance effect of maintenance measure v, that is, the state transition of the unit after maintenance. If no maintenance is taken on the unit, this matrix is ​​the unit matrix. For intact maintenance, the maintenance effect matrix A v for:

[0077]

[0078] That is, no matter what state the unit is in, it will be in the best state after repair. In addition, for non-intact repairs, there is and At the same time, the more maintenance resources invested in non-perfect repairs, the greater the probability that the unit will be in a better condition after repair.

[0079] Therefore, assume that the state probability distribution of unit l at the beginning of the task interval is P l , then the state probability distribution P after executing maintenance measure v l 'for:

[0080] P l '=P l A v

[0081] During the task interval, each unit has multiple maintenance measures to choose from. Let V represent the number of executable maintenance measures, A v ,v=1,2,…,V represents the maintenance effect of maintenance measure v, where v=1 represents no maintenance, v=V represents complete maintenance, and v=2,…,V-1 represents incomplete maintenance. The state probability distribution P of unit l after executing maintenance measure v is l ' can be calculated by the formula.

[0082] Let the decision variable X l,v Indicates whether maintenance action v is taken on unit l during the task interval. X l,v =1 means maintenance measure v has been taken, otherwise X l,v = 0. The total maintenance cost during the task interval is:

[0083]

[0084] Where N is the total number of units, c v represents the cost of performing repair action v. Performing a complete repair has the highest cost. Choosing no repair incurs no cost, i.e., c1 = 0. Repair costs vary for non-complete repair actions with different effects, and the better the repair effect, the higher the cost.

[0085] However, only one maintenance action can be taken at any unit, so the following constraints apply:

[0086]

[0087] Since the next stage mission contains multiple subtasks, the decision maker needs to assign each type of unit to different subtasks according to the status and maintenance of each unit before the mission begins to meet the needs of the combat mission. Let M represent the number of subtasks, N m,j ,m=1,2,…,M,j=1,2,…,J represents the demand of subtask m for the j-th type of unit, then the total demand of subtask m is:

[0088]

[0089] Let the decision variable Y l,m Indicates whether unit l is assigned to subtask m. Y l,m =1 means unit l is assigned to subtask m, otherwise Y l,m =0.

[0090] The final task allocation strategy must meet the requirements of each subtask, namely:

[0091]

[0092] Among them, J j is the set of units of type j.

[0093] However, any unit can only be assigned to one subtask, so the following constraints apply:

[0094]

[0095] In addition, due to the different working environments of different subtasks, the degradation laws of the same unit when performing different subtasks are different. Therefore, in order to describe the differences between the working environments of this subtask, this study introduces an environmental coefficient α m To characterize the influence of the subtask working environment on the unit state degradation, the state transition intensity matrix Λ of unit l when executing subtask m is l,m for:

[0096] Λ l,m =α m Λl

[0097] Among them, Λ l represents the basic state transition strength matrix of unit l, α m is the environmental coefficient of subtask m, and α m ≥1, which represents the accelerated degradation effect of the task's working environment on unit l.

[0098] Assume that unit l is assigned to task m, and the state transfer strength matrix Λ of unit l is l,m Substituting this into the formula, we can get the state probability distribution of unit l after completing the task: Where T is the duration of the task. Then, the probability r that unit l completes the task l for:

[0099]

[0100] Furthermore, according to the requirements of subtask m, N m Each unit has at least K m The units complete the task, and the task completion probability R of subtask m can be evaluated. m .

[0101] Based on the description of the selective maintenance decision-making and equipment task allocation problem above, the joint optimization model of selective maintenance decision-making and task allocation is finally established with the goal of maximizing the completion probability of the entire task as follows:

[0102] max R=R1R2…R M (1-1)

[0103]

[0104]

[0105]

[0106]

[0107]

[0108]

[0109] Among them, formula (1-1) is the objective function, which represents maximizing the probability of task completion, which is equal to the product of the completion probabilities of each subtask; formula (1-2) indicates that the maintenance cost cannot exceed the maintenance budget C0; formula (1-3) indicates that any unit can only take one maintenance measure; formula (1-4) indicates that any unit can only be assigned to one subtask; formula (1-5) indicates that the task allocation plan must meet the quantity requirements of each subtask for each type of unit; formulas (1-6) and (1-7) indicate that the decision variables are 0-1 integer variables;

[0110] The above-mentioned joint optimization model of selective decision-making and task allocation includes two sub-problems: maintenance decision-making and task allocation. For the above-mentioned model, the present invention provides a genetic algorithm based on random keys to solve it. The genetic algorithm process is as follows: Figure 1 As shown, the key steps are as follows:

[0111] (1) Chromosome encoding

[0112] In this problem, there are two sub-problems: maintenance decision and task allocation. For the problem with N units, the traditional chromosome encoding method needs to encode the two sub-problems separately, as shown in the following figure. Figure 3 As shown in Figure 2 . This encoding method requires a code length of 2N, resulting in low coding efficiency and thus impacting the performance of the genetic algorithm. Therefore, this paper adopts a random key encoding method, randomly generating the value of each gene bit between [0, 1] to simultaneously encode the maintenance strategy and task allocation strategy. These strategies are then parsed using a special decoding method. This encoding and decoding method reduces the chromosome code length to N, improving coding efficiency.

[0113] Random key encoding generates a random key r between [0,1] for each unit l , the key decoding mainly includes the following steps:

[0114] Step 1: Divide the interval [0,1] into V intervals of equal length, where V represents the number of maintenance measures that can be taken for each unit. Therefore, different intervals represent different maintenance measures, as shown in the following figure. Figure 4 As shown. If r l If the value of is in the vth interval, it means that maintenance measure v is taken for unit l. Similarly, the maintenance strategy for all units can be obtained.

[0115] Step 2: After parsing the unit maintenance strategy, the key r l Normalize according to the interval where its value is located to obtain the normalized key r l ',Right now:

[0116]

[0117] Step 3: Sort the units using the normalized key, and then assign each subtask based on the unit sorting results. For example, if subtask 1 and subtask 2 require two and three type 1 units, respectively, the top two type 1 units are assigned to subtask 1, the next three are assigned to subtask 2, and so on. This provides the task allocation strategy.

[0118] (2) Fitness function

[0119] Fitness is a criterion for judging the quality of individuals in a population. In this problem, the optimization goal is to maximize the probability of task completion within a limited maintenance budget. To comprehensively evaluate individual performance within the maintenance budget constraint, a penalty function is introduced to penalize individuals that violate the constraint. This reduces the fitness of individuals that violate the constraint during fitness evaluation, improving the algorithm's ability to filter out inferior solutions. The penalty function is set as follows:

[0120]

[0121] Among them, p s is the penalty value for individual s; G is the penalty factor, which is a large positive real number; C0 is the maintenance budget; C s The maintenance cost required for individual s to represent the solution. Then the fitness function is:

[0122] f s =R s -p s

[0123] Among them, f s is the fitness value of individual s; R s is the task completion probability corresponding to individual s.

[0124] (3) Select operation

[0125] The goal of selection is to preserve the best genes during the swarm iteration process and screen the best individuals in the current population for subsequent crossover and mutation operations. This algorithm uses a tournament approach for individual selection, selecting a certain number of individuals from the current population, comparing their fitness values, and retaining the best individuals. This process is repeated until a parent population of the required size is generated.

[0126] (4) Crossover and mutation operations

[0127] The crossover operation, a key component of a genetic algorithm, aims to generate a new population by randomly combining parent populations. This algorithm employs a single-point crossover method, first randomly determining the starting point of the gene segment to be crossed, then swapping the two parent chromosomes from that location to the end of the chromosome to produce the daughter chromosome. Mutation aims to increase population diversity. This process of randomly perturbing the daughter population with each iteration to generate new individuals effectively enhances the algorithm's local search capabilities. In this problem, mutation is accomplished by mutating each gene position to a random value within the feasible domain with a certain probability.

[0128] (5) Elite retention strategy

[0129] In order to prevent the loss of excellent individuals during the algorithm iteration process, an elite retention strategy is introduced. That is, each time the population evolves to generate a sub-population, the k individuals with the highest fitness values ​​in the parent population are selected and retained in the sub-population to participate in the next iteration, fully ensuring the high quality of the population during the iteration process and preventing the loss of excellent genes during the crossover mutation process.

[0130] The following two different examples demonstrate the correctness and effectiveness of the proposed joint optimization method for selective maintenance decision-making and task allocation. The units in each example are all four-state units, where state 4 is intact, state 1 is a failed state, and states 2 and 3 are intermediate states. Each unit has a different state probability distribution at the beginning of the maintenance period. Furthermore, it is assumed that the basic state transition intensity matrix of each unit is the same:

[0131]

[0132] The actual state transition intensity matrix of the unit is determined by the basic state transition intensity matrix and the environmental coefficient of the combat mission.

[0133] Each unit has 4 optional repair measures, and the corresponding repair effects are:

[0134]

[0135]

[0136]

[0137]

[0138] Among them, maintenance measures 1 and 4 are no maintenance and complete maintenance respectively, maintenance measures 2 and 3 are two degrees of non-complete maintenance, and the maintenance costs corresponding to the four maintenance measures are 0, 20, 40, and 60,000 yuan respectively.

[0139] The following are two sets of experimental examples based on the above method combined with genetic algorithm;

[0140] Experimental Example 1:

[0141] In this embodiment, a total of 6 units of 2 types need to jointly perform the next combat mission, which contains 2 subtasks and lasts for 10 hours. The parameters of each subtask are shown in Table 1-1. m is the working environment coefficient of each subtask, N m,1 and N m,2 The number of these two types of units required for each subtask, N m is the total quantity required for each subtask, K m The minimum number of units that need to survive in the subtask.

[0142] Table 1-1 Task parameters

[0143]

[0144] Each unit is a 4-state unit, with state 4 being the intact state and state 1 being the failed state. Table 1-2 lists the type of each unit and the state probability distribution of each unit at the beginning of the maintenance period.

[0145] Table 1-2 Parameters of each unit

[0146]

[0147]

[0148] When the maintenance budget C0 = 180,000 yuan, a genetic algorithm is used to solve the problem. The basic parameters of the algorithm are set as follows: population size of 50, crossover probability and mutation probability of 0.9 and 0.1 respectively, and the number of elite strategies retained is 5. To verify the solution effect of the algorithm, the maximum number of iterations is set to 50, 100, 150 and 200 respectively, and the operation is repeated 20 times. In this example, for the selective maintenance decision, each of the 6 units contains 4 optional maintenance measures, so there are 4 6 = 4096 maintenance strategies; for task allocation, 3 type 1 units need to allocate 1 to subtask 1, and 3 type 2 units need to allocate 2 to subtask 1, totaling The number of solutions to the joint optimization model is 4096 × 9 = 36864, and the exact solution can be obtained by enumeration. The calculation results of the enumeration method and the genetic algorithm are shown in Table 1-3.

[0149] Table 1-3 Comparison of calculation results of two algorithms

[0150]

[0151] Tables 1-3 show that the enumeration method can quickly find the optimal solution for this example, with a corresponding task completion probability of 0.8872. For the genetic algorithm, the optimization effect is reflected by calculating the optimal value, mean, and standard deviation of the results from 20 runs. It can be seen that with 50 iterations, the optimal solution can still be found, and the runtime is only 0.1104 seconds. However, the low mean and high standard deviation indicate that the algorithm is not yet stable. As the number of iterations increases, the mean increases and the standard deviation decreases, indicating that the algorithm is converging. When the number of iterations reaches 200, the standard deviation reaches 0, indicating that the optimal solution was found in all 20 runs. The runtime is also only 0.4365 seconds, far lower than the 1.2078 seconds of the enumeration method. Furthermore, the solution space for joint optimization problems grows exponentially with the number of units. For medium- to large-scale problems, the enumeration method cannot perform computations due to runtime constraints, while the genetic algorithm can still find a satisfactory solution within a reasonable time.

[0152] Tables 1-4 and 1-5 list the maintenance costs and subtask completion probabilities for the optimal solution, respectively. Table 1-4 shows that, through reasonable maintenance and task allocation, the demands of both subtasks were ultimately balanced, with task completion rates exceeding 0.94. In Tables 3-5, C1 and C2 represent the maintenance costs invested by the units assigned to the two subtasks, respectively. It can be seen that the two subtasks received similar maintenance costs. Because Subtask 1 has a higher environmental coefficient, meaning that the unit degradation rate is greater when performing this task, Subtask 1 receives more maintenance resources.

[0153] Table 1-4 Completion probability of each subtask corresponding to the optimal solution

[0154]

[0155] Table 1-5 Maintenance costs allocated to each subtask corresponding to the optimal solution (10,000 yuan)

[0156]

[0157] To further explore the effects of considering non-perfect repairs and task allocation, four models were compared. Model I is the proposed joint optimization model for selective maintenance and task allocation that considers the effects of non-perfect repairs. Model II is the joint optimization model for selective maintenance and task allocation that does not consider the effects of non-perfect repairs. Model III is the selective maintenance decision-making model that considers the effects of non-perfect repairs. Model IV is the selective maintenance decision-making model that does not consider the effects of non-perfect repairs. In Models III and IV, each unit is assigned to each subtask in numerical order. The selective maintenance strategies and task allocation strategies optimized by each model are shown in Tables 1-6.

[0158] As shown in Tables 1-6, Model I achieves the highest task completion probability, demonstrating the effectiveness of the combined optimization of selective maintenance and task allocation by considering the effects of non-perfect repairs. A comparison of Model I with Model II, and Model III with Model IV, shows that considering the effects of non-perfect repairs leads to better optimization results than not considering the effects of intact repairs. A comparison of Model I with Model III, and Model II with Model IV, shows that considering the unit's combat task allocation in the selective maintenance problem better meets combat mission requirements and effectively increases the task completion probability. Furthermore, considering the subtask completion probabilities, task allocation (Models I and III) can reasonably balance the requirements of the two subtasks while simultaneously improving their completion probabilities.

[0159] Table 1-6 Optimal selective maintenance strategy and task allocation strategy

[0160]

[0161]

[0162] Generally speaking, as the maintenance budget increases, the probability of task completion will increase accordingly. The corresponding relationship is shown in the attached figure. Figure 5 As shown in Figure 2, under different maintenance budgets, the combined optimization of selective maintenance and task allocation, which considers the effects of non-perfect maintenance, achieves the best optimization results. Furthermore, when the maintenance budget is zero, meaning no maintenance measures can be taken, Models I and II improve the probability of task completion by rationally allocating tasks.

[0163] In this example, the environmental coefficients α1 and α2 of the two subtasks describe the different state transitions of the same unit under different subtask operating environments, resulting in different task completion probabilities. Furthermore, α1 > α2 indicates a higher degradation rate when the unit is assigned to subtask 1. To explore the impact of different environmental coefficients on the optimal strategy, we solved the optimal selective maintenance strategy and task allocation strategy with α1 held constant at 1.4 and α2 set to 1.0, 1.2, 1.4, 1.6, and 1.8, respectively. The results are shown in Tables 3-7 and 3-8.

[0164] Table 1-7 shows the optimal selective maintenance strategy and task allocation strategy when α1 ≥ α2. It can be seen that when α2 = 1.0 and α2 = 1.2, the environmental coefficient of subtask 1 is greater than that of subtask 2, so more maintenance costs are allocated to the units performing subtask 1. Furthermore, the maintenance strategy for the units in both cases is the same, and the optimal strategy simply adapts to the increase in the environmental coefficient of subtask 2 by changing the unit's task allocation. When α2 = 1.4, meaning that the units have the same degradation rate in both subtasks, more maintenance costs are allocated to the units performing subtask 2. Furthermore, the task allocation strategy when α2 = 1.4 is the same as when α2 = 1.0, and the optimal strategy responds to the change in the subtask's environmental coefficient by adjusting the maintenance measures of units 4 and 6.

[0165] Table 1-7 Optimal selective maintenance strategies and task allocation strategies under different environmental coefficients (α1≥α2)

[0166]

[0167]

[0168] Table 1-8 shows the optimal selective maintenance strategy and task allocation strategy when α1 ≤ α2. It can be seen that because subtask 2 has a larger environmental coefficient, meaning the unit degradation rate is greater in subtask 2, more maintenance costs are allocated to subtask 2. Furthermore, when α2 = 1.8, maintenance costs are even more likely to be allocated to subtask 2. Furthermore, the unit maintenance strategy for α2 = 1.8 is once again identical to that for α2 = 1.4. The optimal strategy adjusts the maintenance cost distribution of units within each subtask by changing the task allocation strategy for each unit.

[0169] Combining Tables 1-7 and 1-8, we can see that as the relative size relationship of the two subtask environmental coefficients changes, the optimal strategy needs to adjust both the unit maintenance strategy and the task allocation strategy to meet the needs of different task environments.

[0170] Table 1-8 Optimal selective maintenance strategies and task allocation strategies under different environmental coefficients (α1≤α2)

[0171]

[0172] Experimental Example 2:

[0173] The problem considered in this example involves 16 combat units of three types, which need to jointly perform a combat mission consisting of three subtasks. The mission duration is 10 hours, and the parameters of each subtask are shown in Table 1-9. m is the working environment coefficient of each subtask, N m,1 、N m,2 and Nm,3 The number of 3 types of units required for each subtask, N m is the total quantity demanded, K m The minimum number of units that need to survive in the subtask.

[0174] Table 1-9 Task parameters

[0175]

[0176] Each unit is a 4-state unit, with state 4 being the intact state and state 1 being the failed state. Table 1-10 lists the type of each unit and the state probability distribution at the beginning of the mission interval.

[0177] Table 1-10 Parameters of each unit

[0178]

[0179] With a maintenance budget of C0 = 500,000 yuan, a genetic algorithm was used to solve the problem. The algorithm parameters were: population size of 100, maximum number of iterations of 200, crossover and mutation probabilities of 0.9 and 0.1, respectively, and the number of elite strategies retained of 10. The optimized selective maintenance and task allocation strategies are shown in Table 1-11. Model I is a joint optimization model for selective maintenance and task allocation that considers the effects of non-intact maintenance, while Model II is a joint optimization model for selective maintenance and task allocation that does not consider these effects.

[0180] As shown in Table 1-11, when considering the effects of suboptimal repairs, all 13 units received a certain degree of repair. Optimizing task allocation based on the unit's status and repair status resulted in a higher probability of task completion, and the completion probability of each subtask was greater than that of the model without considering the effects of suboptimal repairs. However, when the effects of suboptimal repairs were not considered, only 8 units could be repaired, resulting in an imbalance in the demands of each subtask, ultimately affecting the task completion probability.

[0181] The maintenance costs allocated to each subtask corresponding to the optimal solution of Model I are shown in Table 1-12, where C1, C2, and C3 represent the maintenance costs invested by the units allocated to each subtask. It can be seen that although both Task 1 and Task 2 require six units to participate, the different completion requirements (Task 1 requires at least three units to survive, while Task 2 requires at least four units to survive) lead to significant differences in the final allocated maintenance resources. Furthermore, although Task 3 only requires four units to participate, due to its high completion requirement (at least three units must survive), it is allocated a maintenance budget of 200,000 yuan, resulting in the highest average maintenance cost per unit.

[0182] Table 1-11 Optimal selective maintenance strategy and task allocation strategy

[0183]

[0184] Table 1-12 Maintenance costs allocated to each subtask corresponding to the optimal solution (10,000 yuan)

[0185]

[0186] To verify the effectiveness of the proposed joint optimization of selective maintenance decisions and task allocation, we compared the joint optimization method with a two-stage optimization approach. The results are shown in Tables 1-13. The two-stage optimization approach optimizes selective maintenance decisions and task allocation independently: in the first stage, the unit's maintenance strategy is optimized; in the second stage, the unit's task allocation strategy is optimized based on the optimized maintenance strategy. As shown in Tables 1-13, compared to the two-stage optimization approach, which optimizes the two problems independently, the joint optimization approach comprehensively considers the relationship between the two optimization problems, resulting in superior results and an increased probability of completion for each subtask.

[0187] Table 1-13 Optimal selective maintenance strategy and task allocation strategy for joint optimization and two-stage optimization

[0188]

[0189] Attachment Figure 6 The results of four optimization models are presented under different maintenance budget conditions: a joint optimization model for selective maintenance and task allocation that considers the effects of suboptimal repairs, a joint optimization model for selective maintenance and task allocation that does not consider the effects of suboptimal repairs, a selective maintenance decision-making model that considers the effects of suboptimal repairs, and a selective maintenance decision-making model that does not consider the effects of suboptimal repairs. It can be seen that the joint optimization model for selective maintenance and task allocation that considers the effects of suboptimal repairs achieves the best results under different maintenance budgets. Furthermore, when no maintenance measures can be taken for a unit (i.e., when the maintenance budget is zero), optimizing the unit's task allocation strategy alone still improves the probability of task completion.

[0190] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A joint optimization method for equipment selective maintenance decision-making and task allocation, characterized in that: The following steps are involved: Step S001: Assume that each unit has S states, where state 1 is a completely failed state, state S is a fully working state, and the remaining states are intermediate states. The state degradation process of each unit is described using a homogeneous Markov model, a unit state transition intensity matrix is ​​established, and the state distribution probability of the unit is obtained by solving the Kolmogorov differential equation; Step S002: Classify maintenance measures into three categories according to maintenance effects: no maintenance, complete maintenance, and incomplete maintenance, and define a maintenance matrix based on the maintenance effects; Step S003: Based on the state transition intensity matrix and the maintenance matrix, the optimal maintenance strategy and equipment task allocation strategy are formulated for each unit in combination with the maintenance cost and the working environment. Each unit is then assigned to different subtasks to collaboratively execute the next phase of combat missions, maximizing the probability of mission completion. Step S004: combining the maintenance strategy and the equipment task allocation strategy to establish a joint optimization model of selective maintenance decision and task allocation; Step S005: A random key-based genetic algorithm is used to solve the joint optimization model of selective maintenance decision and task allocation to obtain the optimal maintenance decision and task allocation method; In step S001, the entire state transfer process of a single unit l can be represented by the state transfer intensity matrix Λ l express: is the transition strength of unit l from state i to state j, and In step S002, define the maintenance effect matrix A v as follows: in, A represents the probability that the unit will recover to state j after taking maintenance measure v if it is in state i. v Describes the maintenance effect of maintenance measure v, that is, the state transition of the unit after maintenance; When the selected unit does not take maintenance, the maintenance effect matrix A v is the identity matrix; When the selected unit is repaired in good condition, the maintenance effect matrix A v for When the selected unit is not repaired properly, there is and restrictions.

2. The joint optimization method for equipment selective maintenance decision and task allocation according to claim 1 is characterized in that: In step S005, the algorithm process includes the following steps: Step A001: population initialization; Step A002: Generate a random key and decode it; Step A003: Perform fitness evaluation; Step A004: Perform selection, crossover, and mutation to produce offspring populations; Step A005: retain elite individuals; Step A006: Determine whether the maximum number of iterations has been reached. If so, end the process. If not, return to step A002 and repeat the process.

3. The joint optimization method for equipment selective maintenance decision and task allocation according to claim 2 is characterized in that: In step A002, the random key encoding generates a random key r between [0,1] for each unit. l , key decoding includes the following steps: Step B001: Divide the interval [0,1] into V intervals of equal length, where V represents the number of maintenance measures that can be taken for each unit, and different intervals represent different maintenance measures; Step B002: Analyze the unit maintenance strategy, and after the analysis is completed, the key r l Normalize according to the interval where its value is located to obtain the normalized key r l '; Step B003: Sort the units in order using the normalized key, and then assign each subtask according to the unit sorting result.

4. The joint optimization method for equipment selective maintenance decision and task allocation according to claim 2 is characterized in that: In step A004, individual selection is performed using a tournament method.

5. The joint optimization method for equipment selective maintenance decision and task allocation according to claim 2 is characterized in that: In step A004, a single-point crossover method is used to perform a crossover operation.

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