A Method for Optimizing Equipment Maintenance Workshop Scheduling and a Computer Readable Medium

Abstract

The present invention relates to a method for optimizing the scheduling of an equipment maintenance workshop and a computer-readable medium. Input the time type and cost type parameters of each piece of equipment, and obtain the actual processing time of each process of each workpiece on each piece of equipment; calculate the service age and processing end time of each piece of equipment after each processing, and the processing start and completion times of each process of each workpiece; obtain the processing completion time of each workpiece according to the processing start and completion times of each process of each workpiece and the end time of each processing of each piece of equipment, and construct a dual optimization objective model of the total system completion time and the total system maintenance cost; construct the constraint conditions of the optimization objective model; taking the minimization of the optimization objective model as the optimization objective, combining the constraint conditions of the optimization objective model, and performing optimization solution through a hybrid artificial bee colony method to obtain the optimized processing plan selected for each process of each workpiece; the processing plan obtained by the present invention can significantly reduce the equipment maintenance time and maintenance cost and improve production coordination.

Description

Technical Field

[0001] The present invention belongs to the technical field of equipment maintenance and processing scheduling, and in particular relates to an equipment maintenance workshop scheduling optimization method and a computer-readable medium. Background Art

[0002] Production scheduling and preventive maintenance (PM) are two key technologies that impact manufacturing production. Production scheduling involves rationally arranging processing plans while meeting process constraints and ensuring equipment availability, in order to shorten construction times and reduce costs. Many studies on equipment maintenance scheduling base maintenance decisions on the current state of the equipment, assuming that the equipment has an initial service life of zero, and that maintenance can restore it to its original condition. This contradicts reality, as this approach makes it difficult to guarantee that the equipment's reliability remains above a threshold for every workpiece processed.

[0003] Therefore, the present invention proposes a dynamic maintenance decision-making method, namely, whether the equipment is currently maintained depends on its reliability when the next workpiece is processed. At the same time, the equipment degradation effect and the situation of imperfect maintenance are taken into account. The decision-making takes into account both production and equipment needs, and minimizes the maximum completion time and maintenance cost as the optimization goal. According to the actual situation, the reliability threshold and other maintenance parameters are preset for each equipment, and an improved hybrid artificial bee colony algorithm (HABC) is designed to solve the model and resolve the problem of incoordination between production scheduling and equipment maintenance in the production process. Summary of the Invention

[0004] In order to solve the problem of incoordination between production scheduling and equipment maintenance during the production process, the present invention proposes an equipment maintenance workshop scheduling optimization method and a computer-readable medium.

[0005] The technical solution of the method of the present invention is a method for optimizing equipment maintenance workshop scheduling, comprising the following steps:

[0006] Step 1: Input the single maintenance time required for each device, the single maintenance cost required for each device, and the maintenance age threshold for each device to obtain the actual processing time of each process for each workpiece on each device;

[0007] Step 2: Calculate the age of each device after each processing, the end time of each processing of each device, the start processing time and completion time of each process of each workpiece; obtain the processing completion time of each workpiece according to the start processing time and completion time of each process of each workpiece and the end time of each processing of each device, and construct a dual-optimization objective model of the total system completion time and the total system maintenance cost; construct the processing equation constraint conditions of the optimization objective model, the process constraint conditions of each workpiece, and the maintenance strategy constraint conditions of each device.

[0008] Step 3: Taking the minimization of the total completion time and the total maintenance cost objective function model as the optimization objective, combined with the processing equation constraint conditions of the optimization objective model, the process constraint conditions of each workpiece, and the maintenance strategy constraint conditions of each device, perform optimization and solution through the hybrid artificial bee colony method to obtain the optimized processing plan selected for each process of each workpiece.

[0009] Preferably, the single maintenance time of each device described in Step 1 is defined as:

[0010] time i ,i∈[1,M]

[0011] where, time i represents the single maintenance time required for the i-th device, and M represents the number of devices;

[0012] The single maintenance cost required for each device described in Step 1 is defined as:

[0013] Pm i ,i∈[1,M]

[0014] where, Pm i represents the single maintenance cost of the i-th device, and M represents the number of devices;

[0015] The maintenance age threshold of each device described in Step 1 is defined as:

[0016] θ i ,i∈[1,M]

[0017] where, θ i represents the maintenance age threshold of the i-th device, and M represents the number of devices;

[0018] The standard processing time of each process of each workpiece on each device described in Step 1 is defined as:

[0019] p j,k,i

[0020] i∈[1,M],j∈[1,N],k∈[1,K j ​

[0021] Among them, p j,k,i represents the standard processing time of the k-th process of the j-th workpiece on the selected i-th device, N represents the number of workpieces, and K j represents the number of processes of the j-th workpiece;

[0022] The actual processing time of each process of each workpiece described in Step 1 on each device is specifically

[0023] u j,k,i = p j,k,i + δ i · p j,k,i

[0024] i ∈ [1, M], j ∈ [1, N], k ∈ [1, K j

[0025] Among them, u j,k,i represents the actual processing time of the k-th process of the j-th workpiece on the selected i-th device, p j,k,i represents the standard processing time of the k-th process of the j-th workpiece on the selected i-th device, M represents the number of devices, N represents the number of workpieces, and K j represents the number of processes of the j-th workpiece;

[0026] δ i represents the growth rate of the processing time of the i-th device, and the specific calculation is as follows:

[0027]

[0028] Among them, θ i is the maintenance service age threshold of the i-th device, and ρ is the degradation weight; is the service age of the i-th device before processing the k-th process of the j-th workpiece, that is, the service age after the i-th device completed the previous processing. If the current processing is the first processing of the i-th device, then is 0;

[0029] Preferably, the start processing time of the k-th process of the j-th workpiece described in Step 2 is:

[0030]

[0031] i ∈ [1, M], j ∈ [1, N], k ∈ [1, K j

[0032] Among them, time i represents the single duration of the maintenance implemented by the i-th device, and y j,k,i represents whether the i-th device is maintained before processing the k-th process of the j-th workpiece, and y j,k,i ​​= 1 means that the i-th device performs maintenance before the k-th process of the j-th workpiece, otherwise y j,k,i = 0; represents the end time of the last processing on the i-th device selected for the k-th process of the j-th workpiece. If the current processing is the first processing on the i-th device, then C j,(k-1) represents the completion time of the (k - 1)-th process of the j-th workpiece.

[0033] The completion time of the k-th process of the j-th workpiece described in Step 2 is:

[0034] C j,k = S j,k + u j,k,i

[0035] i ∈ [1, M], j ∈ [1, N], k ∈ [1, K j

[0036] where S j,k is the start processing time of the k-th process of the j-th workpiece, and u j,k,i is the actual processing time of the k-th process of the j-th workpiece on the selected i-th device;

[0037] The end time for each device to complete each processing described in Step 2 is:

[0038] T j,k,i = C j,k

[0039] i ∈ [1, M], j ∈ [1, N], k ∈ [1, K j

[0040] where T j,k,i represents the end time of the k-th process of the j-th workpiece processed by the i-th device;

[0041] The dual-objective function model of the total system completion time and the total system maintenance cost described in Step 2 is specifically defined as follows:

[0042] f = (C, Cost)

[0043] where Cost represents the total system maintenance cost, and C represents the total system completion time;

[0044] The total system completion time is specifically defined as follows;

[0045]

[0046] where C represents the total system completion time, represents the K-th of the j-th workpiece j ​​The completion time of the j-th operation, that is, the completion time of the processing of the j-th workpiece;

[0047] The total maintenance cost of the system is specifically defined as follows;

[0048]

[0049] Among them, Pm i represents the cost of the i-th equipment, and np i represents the total number of maintenance times of the i-th equipment;

[0050] The processing equation constraint conditions described in step 2 are specifically defined as follows:

[0051] The number of equipment processing times is equal to the total number of all workpiece operations, specifically as follows:

[0052]

[0053] i ∈ [1, M], j ∈ [1, N]

[0054] Among them, n i represents the total number of processing times required for the i-th equipment to complete the production task, M represents the number of equipment, N represents the number of workpieces, and K j represents the number of operations of the j-th workpiece;

[0055] The process constraint conditions for each workpiece described in step 2 are as follows:

[0056] C j,(k-1) ≤ S j,k

[0057] j ∈ [1, N], k ∈ [2, K j

[0058] Among them, C j,(k-1) represents the completion time of the (k - 1)-th operation of the j-th workpiece, and S j,k represents the start time of the k-th operation of the j-th workpiece, N represents the number of workpieces, and K j represents the number of operations of the j-th workpiece;

[0059] The maintenance strategy constraint conditions for each equipment described in step 2 are specifically defined as follows:

[0060]

[0061] i ∈ [1, M], j ∈ [1, N], k ∈ [1, K j

[0062] Among them, t j,k,i represents the age of the i-th equipment after processing the k-th operation of the j-th workpiece; θ iRepresents the maintenance age threshold of the $i$-th device; $y$ j,k,i Represents the maintenance flag of the $i$-th device before the $k$-th process of processing the $j$-th workpiece. If $y$ j,k,i $= 1$, it means that the $i$-th device performs maintenance before the $k$-th process of processing the $j$-th workpiece. Otherwise, the $i$-th device does not perform maintenance before the $k$-th process of processing the $j$-th workpiece;

[0063] The age of each device after each processing described in Step 2 is as follows:

[0064]

[0065] $i\in[1,M], j\in[1,N], k\in[1,K j

[0066] where $t$ j,k,i Represents the age of the $i$-th device after the $k$-th process of processing the $j$-th workpiece, Represents the age of the $i$-th device before the $k$-th process of processing the $j$-th workpiece, that is, the age of the $i$-th device after the last processing; $y$ j,k,i Represents whether the $i$-th device performs maintenance before the $k$-th process of processing the $j$-th workpiece. $y$ j,k,i $= 1$ means that the $i$-th device performs maintenance before the $k$-th process of processing the $j$-th workpiece. $y$ j,k,i $= 0$ means that the $i$-th device does not perform maintenance before the $k$-th process of processing the $j$-th workpiece; Is the device improvement factor; $u$ j,k,i Represents the actual processing time of the $k$-th process of the $j$-th workpiece on the selected $i$-th device;

[0067] Preferably, the optimized device selected for each process of each workpiece obtained by the hybrid artificial bee colony method in Step 3 is specifically as follows:

[0068] Step 3.1: Set the convergence iteration number of the method to Ite, the population size to $N$ P , the number of employed bee colonies to $N$ eB , the number of follower bee colonies to $N$ fB , the number of scout bee colonies to $N$ oB , the capacity of the archive set to $N$ D , the update upper limit to limit, the update stagnation value to LM, and the acceptance probability to $pt$;

[0069] Construct a workpiece set vector, a process set vector, a device set vector, and a maintenance strategy set vector in sequence;

[0070] The workpiece set vector is defined as:

[0071] ​

[0072] Among them, represents the workpiece set vector, j represents the j-th workpiece, and the number of j is its number of processes K j , and N represents the number of workpieces;

[0073] The process set vector is defined as:

[0074]

[0075] Among them, represents the process set vector, where k is the same index in the array where the number of times j appears at the same index, representing the k-th process of the j-th workpiece, K j represents the number of processes of the j-th workpiece;

[0076] The equipment set vector is defined as:

[0077]

[0078] o j,k ∈[1, M], j ∈[1, N], k ∈[1, K j

[0079] Among them, represents the equipment set vector selected for each process of each workpiece, o j,k represents the equipment selected for the k-th process of the j-th workpiece, M represents the number of equipment, N represents the number of workpieces, K j represents the number of processes of the j-th workpiece;

[0080] The maintenance strategy set vector is defined as:

[0081]

[0082] o j,k ∈[1, M], j ∈[1, N], k ∈[1, K j

[0083] Among them, represents the maintenance strategy set vector for each equipment before processing each process of each part, where represents the maintenance strategy before processing the k-th process of the j-th workpiece on the selected equipment o j,k ; represents maintenance before processing, otherwise no maintenance; M represents the number of equipment, N represents the number of workpieces, K j represents the number of processes of the j-th workpiece;

[0084] Generate a population randomly through the workpiece set vector, process set vector, equipment set vector, and maintenance strategy set vector, specifically as follows ​​

[0085] Random permutation The workpiece set vector of the x-th individual solution in the population at the z-th iteration is obtained according to the numerical order in According to The operation set vector of the x-th individual solution in the population at the z-th iteration is obtained according to the number of occurrences of each value in According to and The processing equipment for each operation of each workpiece is selected in turn to obtain the equipment set vector of the x-th individual solution in the population at the z-th iteration, defined as Among them, the first X% of the elements select equipment with the shortest standard processing time p j,k,i The Y% of the elements select equipment with the shortest time time i required for single equipment maintenance, and the remaining Z% of the elements randomly select equipment; after obtaining According to the maintenance strategy constraint conditions of each equipment in step 2, calculate The maintenance strategy set vector of the x-th individual solution in the population at the z-th iteration is obtained, defined as Among them represents the maintenance strategy before processing the k-th operation of the j-th workpiece on the selected equipment o j,k , represents maintenance before processing, otherwise no maintenance; from The x-th individual solution in the population at the z-th iteration is obtained, defined as

[0086]

[0087] Among them, z represents the current iteration number; represents the x-th individual solution in the population at the z-th iteration; the processing method of the k-th operation of the j-th workpiece in the x-th individual solution in the population at the z-th iteration is defined as

[0088]

[0089] o j,k ∈[1, M], j ∈[1, N], k ∈[1, K j

[0090] Among them represents that the k-th operation of the j-th workpiece in the x-th individual solution in the population at the z-th iteration is selected to be processed on o j,k , represents the maintenance strategy before processing the k-th operation of the j-th workpiece on the selected equipment o j,k , represents maintenance before processing, otherwise no maintenance;​

[0091] Step 3.2: Initialize the population fitness value and the archive set;

[0092] The fitness value consists of two parts: non-dominated rank and crowding degree, and its evaluation method is as follows:

[0093] Calculate the objective function values of all individuals in the population, and use the objective function model of minimizing the total completion time and the total maintenance cost as the optimization objective:

[0094] minf = min(C, Cost)

[0095] where C represents the total system completion time, Cost represents the total system maintenance cost, and min represents minimization; the smaller the objective function value of an individual, the better:

[0096] Perform non-dominated sorting on all individual solutions in the current population according to the Pareto non-dominated rule, and each individual obtains a non-dominated rank. The smaller the non-dominated rank of an individual, the better; the non-dominated rank to which the x-th individual in the population belongs in the z-th iteration is defined as Calculate the crowding degree between different individuals in each rank. Among individuals in the same rank, the smaller the crowding degree, the better. The crowding degree of individual I is determined by its two adjacent individuals, and the calculation method of the crowding degree is as follows:

[0097]

[0098] where represents the crowding degree of the x-th individual in the z-th iteration, represents the maximum value of the total system maintenance cost Cost among all individuals with non-dominated rank in the z-th iteration, represents the minimum value of the total system maintenance cost Cost among all individuals with non-dominated rank in the z-th iteration, and respectively represent the two adjacent values of the total system maintenance cost Cost that are higher and lower than that of the x-th individual among all individuals with non-dominated rank in the z-th iteration; represents the maximum value of the total system completion time C among all individuals with non-dominated rank in the z-th iteration, represents the minimum value of the total system completion time C among all individuals with non-dominated rank in the z-th iteration, and respectively represent the two adjacent values of the total system completion time C that are higher and lower than that of the x-th individual among all individuals with non-dominated rank in the z-th iteration; In the same non-dominated rank The crowding degree of the two boundary individuals with the maximum and minimum objective function values is infinite, that is

[0099] Step 3.3: Iteratively execute the employed bee search step N eB times. The specific steps of the employed bee search are as follows:

[0100] Generate a random integer r, where N is the number of workpieces, and K j is the number of processes of the jth workpiece;

[0101] Randomly select two individuals from the population at the current zth iteration and Select r randomly from and put them into the same index columns of the empty set , where represents the ath individual randomly selected from the population at the zth iteration, represents the processing method of the kth process of the jth workpiece in represents the new1th individual generated in the employed bee search step at the zth iteration; select from and put them into the remaining index columns of ; similarly, select r randomly from and put them into the same index columns of the empty set where represents the bth individual randomly selected from the population at the zth iteration, represents the processing method of the kth process of the jth workpiece in represents the new2th individual generated in the employed bee search step at the zth iteration, and select from and put them into

[0102] According to the maintenance strategy constraint conditions of each device in Step 2 and the generation method of the maintenance strategy set vector in Step 3.1, correct the maintenance strategy set vectors and of and where It represents the maintenance strategy set vector of the new1-th individual generated in the employed bee search step of the z-th iteration. It represents the maintenance strategy set vector of the new2-th individual generated in the employed bee search step of the z-th iteration;

[0103] According to the non-dominated rank and crowding degree calculation method in step 3.2, Compare them. If the new individual is better than the old individual, replace the old individual with the new individual, and at the same time change the employed bee into a follower bee, and update the number of employed bee colonies and the number of follower bee colonies:

[0104]

[0105]

[0106] Among them, and respectively represent the number of employed bee colonies and the number of follower bee colonies in the z-th iteration, and respectively represent the number of employed bee colonies and the number of follower bee colonies in the updated (z + 1)-th iteration;

[0107] After completing the employed bee search, the updated stagnation values corresponding to the indices of all individuals in the population that have not been replaced Among them, represents the updated stagnation value corresponding to the x-th individual in the population at the z-th iteration;

[0108] Step 3.4, Follower bee search stage, introduce the tournament selection strategy and local search based on simulated annealing, specifically:

[0109] Repeat N fB times. Each time, randomly select RM individuals from the population, defined as:

[0110]

[0111] where ceil is rounding up, and N fB is the number of follower bee colonies; Select the best individual among them according to the non-dominated rank and crowding degree calculation method in step 3.2, and define the best individual selected for the f-th time in the z-th iteration as After completing all selections, N fB individuals are obtained;

[0112] Repeat N fB times. Each time, perform local search based on simulated annealing on these N fB individuals, and define the new individual obtained from the f-th local search in the z-th iteration as According to the non-dominated rank and crowding degree calculation method in step 3.2, and For comparison, if Better, then replace the Otherwise generate a random number r f , r f ∈[0,1], if r f >pt, then use Replace the population If r f If ≤pt, no replacement is performed, and the following bees are converted into scout bees, and the number of following bee swarms and scout bee swarms are updated:

[0113]

[0114]

[0115] in, and denote the number of following swarms and the number of swarm scouts in the zth iteration, and They represent the number of following swarms and the number of scout swarms in the updated z+1th iteration respectively;

[0116] After completing the follow-up bee search phase, update the hysteresis value corresponding to all the unreplaced individual indexes in the population Add 1 and select the optimal N from the population according to the non-dominated level and crowding calculation method in step 3.2 d Individuals constitute the archive set SOR;

[0117] Step 3.5, the scout bee update phase, uses the archive set replacement strategy to update the population to avoid the method falling into a local optimum. Specifically:

[0118] Repeat N times oB times, each time find an individual from the population whose update hysteresis value exceeds the update upper limit limit, recorded as Randomly select an individual from the archive set SOR, denoted as use Replace the population Reset the update hysteresis value of the position in the population to 0, convert the scout bees into hired bees, and update the number of scout bee colonies and hired bee colonies:

[0119]

[0120]

[0121] in, and denote the number of scout swarms and employed swarms in the z-th iteration, and respectively represent the number of scout bee colonies and employed bee colonies in the (z + 1)-th iteration after update;

[0122] If there is no individual in the population whose update stagnation value exceeds the update upper limit limit, the scout bee stage ends;

[0123] Step 3.6, the iterative update of the method converges, specifically:

[0124] If the iteration number z of the current method is less than Ite, then z = z + 1, add 1 to the iteration number of all individuals in the current population, and add 1 to the iteration number of all update stagnation values, complete the iterative update, and jump to Step 3.3 to continue execution:

[0125]

[0126]

[0127] Among them, represents the solution of the x-th individual in the population at the z-th iteration, represents the update stagnation value corresponding to the x-th individual in the population at the z-th iteration, represents the solution of the x-th individual in the population at the (z + 1)-th iteration after completing the z-th iterative update, represents the update stagnation value corresponding to the x-th individual in the population at the (z + 1)-th iteration after completing the z-th iterative update.

[0128] If the iteration number z of the current method is equal to Ite, the method terminates, and the optimal individual is selected from the current population according to the non-dominated rank and crowding degree calculation method in Step 3.2 as the optimal solution of the method, denoted as

[0129]

[0130]

[0131]

[0132] Among them, is the optimized processing plan selected for each process of each workpiece, is the processing plan selected for the k-th process of the j-th workpiece, represents that the k-th process of the j-th workpiece is processed on the selected equipment,

[0133] represents the maintenance strategy before processing the k-th process of the j-th workpiece on the selected equipment ; represents maintenance before processing, otherwise no maintenance.

[0134] The present invention also provides a computer-readable medium storing a computer program executed by an electronic device. When the computer program runs on the electronic device, the electronic device is caused to execute the steps of the device maintenance workshop scheduling optimization method.

[0135] The advantages of the present invention are as follows: The established production scheduling optimization model takes into account the degradation of equipment and imperfect maintenance, and can more accurately reflect actual production factors; compared with the traditional fixed-cycle independent maintenance strategy, the proposed dynamic maintenance strategy can effectively improve the accuracy of equipment maintenance and reduce the number of unnecessary equipment maintenance; the proposed improved artificial bee colony method has stronger neighborhood search ability than the standard artificial bee colony method and the improved particle swarm method, and has a better effect in preventing the method from falling into local optimum. Under various different production scales, compared with the traditional maintenance strategy and other methods, the production plan obtained by the present invention can significantly reduce the equipment maintenance time and maintenance cost in production and improve production coordination. BRIEF DESCRIPTION OF THE DRAWINGS

[0136] Figure 1 : Flowchart of the method according to an embodiment of the present invention;

[0137] Figure 2 : Schematic diagram of the workpiece processing sequence according to an embodiment of the present invention;

[0138] Figure 3 : Gantt chart of example scheduling according to an embodiment of the present invention;

[0139] Figure 4 : Schematic diagram of initialization according to an embodiment of the present invention;

[0140] Figure 5 : Schematic diagram of the employed bee search operation according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0141] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0142] Specifically, when implemented, the method proposed by the technical solution of the present invention can be automatically run by those skilled in the art using computer software technology. The system device for implementing the method, such as a computer-readable storage medium storing the corresponding computer program of the technical solution of the present invention and a computer device including running the corresponding computer program, should also fall within the protection scope of the present invention.

[0143] Now assume an instance with 10 workpieces to be processed on 6 devices. Each workpiece requires multiple processing operations, and there are significant process differences.

[0144] As Figure 1 shown, it is the flowchart of the method of the present invention.

[0145] Next, in combination with Figures 1-5 the technical solution of the method of the embodiment of the present invention is introduced as an equipment maintenance shop scheduling optimization method, and the specific steps are as follows:

[0146] Step 1: Input the time required for single maintenance of each device, the cost required for single maintenance of each device, and the maintenance service life threshold of each device, and obtain the actual processing time of each process of each workpiece on each device;

[0147] The single maintenance time of each device in Step 1 is defined as:

[0148] time i , i ∈ [1, M]

[0149] where time i represents the time required for single maintenance of the i-th device, and M = 6 represents the number of devices;

[0150] The cost required for single maintenance of each device in Step 1 is defined as:

[0151] Pm i , i ∈ [1, M]

[0152] where Pm i represents the single maintenance cost of the i-th device, and M = 6 represents the number of devices;

[0153] The maintenance service life threshold of each device in Step 1 is defined as:

[0154] θ i , i ∈ [1, M]

[0155] where θ i represents the maintenance service life threshold of the i-th device, and M = 6 represents the number of devices;

[0156] The standard processing time of each process of each workpiece on each device in Step 1 is defined as:

[0157] p j,k,i

[0158] i ∈ [1, M], j ∈ [1, N], k ∈ [1, K j

[0159] where p j,k,i ​Denote the standard processing time of the $k$-th process of the $j$-th workpiece on the selected $i$-th device. $N$ represents the number of workpieces, and $K$ j represents the number of processes of the $j$-th workpiece;

[0160] The actual processing time of each process of each workpiece in Step 1 on each device is specifically

[0161] u j,k,i = p j,k,i + δ i ·p j,k,i

[0162] where $i\in[1, M], j\in[1, N], k\in[1, K j

[0163] where, $u j,k,i represents the actual processing time of the $k$-th process of the $j$-th workpiece on the selected $i$-th device, $p j,k,i represents the standard processing time of the $k$-th process of the $j$-th workpiece on the selected $i$-th device, $M = 6$ represents the number of devices, $N = 10$ represents the number of workpieces, and $K j represents the number of processes of the $j$-th workpiece;

[0164] δ i represents the growth rate of the processing time of the $i$-th device, and the specific calculation is as follows:

[0165]

[0166] where, $\theta i is the maintenance age threshold of the $i$-th device, and $\rho = 0.01$ is the degradation weight; is the age of the $i$-th device before processing the $k$-th process of the $j$-th workpiece, that is, the age of the $i$-th device after the last processing. If the current processing is the first processing of the $i$-th device, then it is 0;

[0167] Step 2: Calculate the age of each device after each processing, the end time of each processing of each device, the start processing time and completion time of each process of each workpiece; obtain the processing completion time of each workpiece according to the start processing time and completion time of each process of each workpiece and the end time of each processing of each device, and construct a double-optimization objective model of the total system completion time and the total system maintenance cost; construct the processing equality constraint conditions, the process constraint conditions of each workpiece, and the maintenance strategy constraint conditions of each device for the optimization objective model;

[0168] The start processing time of the $k$-th process of the $j$-th workpiece in Step 2 is:

[0169] ​

[0170] where \(i\in[1,M]\), \(j\in[1,N]\), \(k\in[1,K j

[0171] where \(time i represents the single duration of maintenance implemented by the \(i\)-th device, and \(y j,k,i represents whether maintenance is performed before the \(k\)-th process of the \(j\)-th workpiece on the \(i\)-th device. \(y j,k,i = 1\) indicates that the \(i\)-th device performs maintenance before the \(k\)-th process of the \(j\)-th workpiece, otherwise \(y j,k,i = 0;\) represents the end time of the previous processing on the \(i\)-th device selected for the \(k\)-th process of the \(j\)-th workpiece. If the current processing is the first processing on the \(i\)-th device, then C j,(k-1) represents the completion time of the \((k - 1)\)-th process of the \(j\)-th workpiece.

[0172] The completion time of the \(k\)-th process of the \(j\)-th workpiece described in step 2 is:

[0173] C j,k = S j,k + u j,k,i

[0174] where \(i\in[1,M]\), \(j\in[1,N]\), \(k\in[1,K j

[0175] where \(S j,k is the start processing time of the \(k\)-th process of the \(j\)-th workpiece, and \(u j,k,i is the actual processing time of the \(k\)-th process of the \(j\)-th workpiece on the selected \(i\)-th device;

[0176] The end time of each device to complete each processing described in step 2 is:

[0177] T j,k,i = C j,k

[0178] where \(i\in[1,M]\), \(j\in[1,N]\), \(k\in[1,K j

[0179] where \(T j,k,i represents the end time of the \(k\)-th process of the \(j\)-th workpiece processed by the \(i\)-th device;

[0180] The bi-objective function model of the total system completion time and the total system maintenance cost described in step 2 is specifically defined as follows:

[0181] f=(C,Cost)

[0182] ​​​Among them, Cost represents the total system maintenance cost, and C represents the total system completion time;

[0183] The total system completion time is specifically defined as follows;

[0184]

[0185] Among them, C represents the total system completion time, represents the completion time of the K j th process of the jth workpiece, that is, the processing completion time of the jth workpiece;

[0186] The total system maintenance cost is specifically defined as follows;

[0187]

[0188] Among them, Pm i represents the cost of the ith device, and np i represents the total number of maintenance times of the ith device;

[0189] The processing equality constraint conditions described in step 2 are specifically defined as follows:

[0190] The number of device processing times is equal to the total number of all workpiece processes, specifically as follows:

[0191]

[0192] i ∈ [1, M], j ∈ [1, N]

[0193] Among them, n i represents the total number of processing times required for the ith device to complete the production task, M = 6 represents the number of devices, N = 10 represents the number of workpieces, and K j represents the number of processes of the jth workpiece;

[0194] The process constraint conditions of each workpiece described in step 2 are as follows:

[0195] C j,(k-1) ≤ S j,k

[0196] j ∈ [1, N], k ∈ [2, K j

[0197] Among them, C j,(k-1) represents the completion time of the (k - 1)th process of the jth workpiece, and S j,k represents the start time of the kth process of the jth workpiece, N = 10 represents the number of workpieces, and K j represents the number of processes of the jth workpiece;

[0198] ​The maintenance strategy constraint conditions of each device described in Step 2 are specifically defined as follows:

[0199]

[0200] i ∈ [1, M], j ∈ [1, N], k ∈ [1, K j

[0201] where t j,k,i represents the age of the i-th device after processing the k-th process of the j-th workpiece; θ i represents the maintenance age threshold of the i-th device; y j,k,i represents the maintenance flag of the i-th device before processing the k-th process of the j-th workpiece. If y j,k,i = 1, it means that the i-th device is maintained before processing the k-th process of the j-th workpiece; otherwise, the i-th device is not maintained before processing the k-th process of the j-th workpiece;

[0202] The age of each device after each processing described in Step 2 is as follows:

[0203]

[0204] i ∈ [1, M], j ∈ [1, N], k ∈ [1, K j

[0205] where t j,k,i represents the age of the i-th device after processing the k-th process of the j-th workpiece, represents the age of the i-th device before processing the k-th process of the j-th workpiece, that is, the age of the i-th device after the previous processing; y j,k,i represents whether the i-th device is maintained before processing the k-th process of the j-th workpiece. y j,k,i = 1 means that the i-th device performs maintenance before processing the k-th process of the j-th workpiece, and y j,k,i = 0 means that the i-th device does not perform maintenance before processing the k-th process of the j-th workpiece; is the device improvement factor; u j,k,i represents the actual processing time of the k-th process of the j-th workpiece on the selected i-th device;

[0206] Step 3: Taking the objective function model of minimizing the total completion time and the total maintenance cost as the optimization objective, combining the processing equality constraint conditions of the optimization objective model, the process constraint conditions of each workpiece, and the maintenance strategy constraint conditions of each device, the optimized device selected for each process of each workpiece is obtained through the hybrid artificial bee colony method;

[0207] ​​In step 3, the equipment selected after optimization of each process of each workpiece is obtained by using the hybrid artificial bee colony method, as follows:

[0208] Step 3.1: Set the number of method convergence iterations to Ite=200 and the population size to N P =50, the number of employed bee colonies is N eB , the number of following bee colonies is N fB , the number of swarms is N oB , the file set capacity is N D =30, the update upper limit is limit=20, the update hysteresis value is LM, and the acceptance probability is pt=0.5;

[0209] Construct the workpiece set vector, process set vector, equipment set vector, and maintenance strategy set vector in sequence;

[0210] The workpiece set vector is defined as:

[0211]

[0212] in, Represents the workpiece set vector, j represents the jth workpiece, and the number of j is the number of processes K j , N = 10 represents the number of workpieces;

[0213] The process set vector is defined as:

[0214]

[0215] in, Represents the process set vector, where k is an array The number of times j appears at the same index in represents the kth process of the jth workpiece, K j represents the number of processes for the jth workpiece;

[0216] The device set vector is defined as:

[0217]

[0218] o j,k ∈[1,M],j∈[1,N],k∈[1,K j ]

[0219] in, Represents the equipment set vector selected for each process of each workpiece, o j,k represents the equipment selected for the kth process of the jth workpiece, M=6 represents the number of equipment, N=10 represents the number of workpieces, K j represents the number of processes for the jth workpiece;

[0220] The maintenance strategy set vector is defined as:

[0221]

[0222] o j,k ∈[1,M], j∈[1,N], k∈[1,K j

[0223] where represents the maintenance strategy set vector before each process of each part processed by each device, where represents the maintenance strategy before the k-th process of the j-th workpiece is processed on the selected device o j,k ; represents maintenance before processing, otherwise no maintenance; M = 6 represents the number of devices, N = 10 represents the number of workpieces, and K j represents the number of processes of the j-th workpiece;

[0224] The following gives an example to illustrate the workpiece set vector process set vector device set vector maintenance strategy set vector The relevant data of this example are shown in Tables 1, 2, and 3.

[0225] Table 1 Device Processing Table

[0226]

[0227] Table 2 Processing Time Table

[0228]

[0229] Table 3 Device Data

[0230]

[0231] Workpiece set vector Determine the workpiece processing order, as Figure 2 shown, [1 3 1 2 3 2 2 3] respectively represent the 1st workpiece, the 3rd workpiece, the 1st workpiece, the 2nd workpiece, the 3rd workpiece, the 2nd workpiece, the 2nd workpiece, and the 3rd workpiece.

[0232] Process set vector Determine the processes of the workpiece and correspond one-to-one with the workpiece set vector ; as Figure 2 shown, in [1 1 2 1 2 2 3 3], the first 1 represents the 1st process of the 1st workpiece, the second 1 represents the 1st process of the 3rd workpiece, and the first 2 represents the 2nd process of the 1st workpiece. ​

[0233] Device set vector Determine the processing device, corresponding to the workpiece set vector Process set vector Correspondingly, as Figure 2 shown, in [2 1 1 3 3 2 2 1], the first 2 means that the first process of the first workpiece selects the second device for processing, and the second 1 means that the first process of the third workpiece selects the first device for processing.

[0234] Maintenance strategy set vector Determine whether maintenance is required before each process of the device, corresponding to the workpiece set vector Process set vector Device set vector Correspondingly, as Figure 2 shown, in [0 0 0 0 0 0 1 0], the first 0 means that the second device does not require maintenance before processing the first process of the first workpiece, and the first 1 means that the second device requires maintenance before processing the third process of the second workpiece, and its value is determined by the maintenance strategy constraint conditions of each device in step 2.

[0235] From the workpiece set vector Process set vector Device set vector Maintenance strategy set vector The instance scheduling Gantt chart can be obtained as Figure 3 shown, the vertical axis represents the processing device, the horizontal axis represents time, the rectangle represents the production activity of the device corresponding to the vertical axis, the number in the rectangle represents the time spent on processing or maintenance, the number above the rectangle represents the workpiece and process being processed, and the letter PM represents the execution of the maintenance operation. For example, the number 021 and its matrix represent the first process of the second workpiece processed by the third device, which takes 4 man-hours, and the letter PM and its matrix represent the maintenance of the second device, which takes 3 man-hours; from Figure 3 it can be intuitively seen the production activity of each device;

[0236] Randomly generate a population through the workpiece set vector, process set vector, device set vector, and maintenance strategy set vector, specifically as follows

[0237] Random permutation The numerical order in to obtain the workpiece set vector of the x-th individual solution in the population at the z-th iteration, defined as According to the number of occurrences of each value in to obtain the process set vector of the x-th individual solution in the population at the z-th iteration, defined as According to and Select the processing equipment for each process of each workpiece in sequence to obtain the equipment set vector of the x-th individual solution in the population at the z-th iteration, which is defined as Among them, the first X = 50% of the elements select equipment with the standard processing time p j,k,i being the shortest, Y = 20% of the elements select equipment with the shortest time time required for single equipment maintenance i being the shortest, and the remaining Z = 30% of the elements randomly select equipment. As Figure 4 shown, the number 1 in the 4th column is obtained by the 2nd process of the 2nd workpiece selecting the 1st equipment with the shortest standard processing time, and the number 2 in the 8th column is obtained by the 3rd process of the 2nd workpiece selecting the 2nd equipment with the shortest single maintenance time. Finally, the equipment selected for each process of each workpiece is obtained as [1 2 2 12 3 1 2 2 1]; after obtaining , calculate according to the maintenance strategy constraint conditions of each equipment in step 2 to obtain the maintenance strategy set vector of the x-th individual solution in the population at the z-th iteration, which is defined as where represents the maintenance strategy before processing the k-th process of the j-th workpiece on the selected equipment o j,k , indicating maintenance before processing, otherwise no maintenance; from obtain the x-th individual solution in the population at the z-th iteration, which is defined as

[0238]

[0239] where z represents the current iteration number; represents the x-th individual solution in the population at the z-th iteration; the processing method of the k-th process of the j-th workpiece in the x-th individual solution in the population at the z-th iteration is defined as

[0240]

[0241] o j,k ∈[1, M], j ∈[1, N], k ∈[1, K j

[0242] where represents that the k-th process of the j-th workpiece in the x-th individual solution in the population at the z-th iteration is selected to be processed on o j,k , represents the maintenance strategy before processing the k-th process of the j-th workpiece on the selected equipment o j,k , indicating maintenance before processing, otherwise no maintenance;

[0243] ​Step 3.2: Initialize the population fitness value and the archive set;

[0244] The fitness value consists of two parts: the non-dominated rank and the crowding degree, and its evaluation method is as follows:

[0245] Calculate the objective function values of all individuals in the population, and take the objective function model of minimizing the total completion time and the total maintenance cost as the optimization objective:

[0246] minf = min(C, Cost)

[0247] where C represents the total system completion time, Cost represents the total system maintenance cost, and min represents minimization; the smaller the objective function value of an individual, the better:

[0248] Perform non-dominated sorting on all individual solutions in the current population according to the Pareto non-dominated rule, and each individual obtains a non-dominated rank. The smaller the non-dominated rank of an individual, the better; the non-dominated rank to which the x-th individual in the population belongs in the z-th iteration is defined as Calculate the crowding degree between different individuals in each rank. The smaller the crowding degree of an individual in the same rank, the better. The crowding degree of individual I is determined by its two adjacent individuals, and the calculation method of the crowding degree is as follows:

[0249]

[0250] where represents the crowding degree of the x-th individual in the z-th iteration, represents the maximum value of the total system maintenance cost Cost among all individuals with the non-dominated rank of in the z-th iteration, represents the minimum value of the total system maintenance cost Cost among all individuals with the non-dominated rank of in the z-th iteration, and respectively represent the two adjacent values of the total system maintenance cost Cost that are higher and lower than the x-th individual among all individuals with the non-dominated rank of in the z-th iteration; represents the maximum value of the total system completion time C among all individuals with the non-dominated rank of in the z-th iteration, represents the minimum value of the total system completion time C among all individuals with the non-dominated rank of in the z-th iteration, and respectively represent the two adjacent values of the total system completion time C that are higher and lower than the x-th individual among all individuals with the non-dominated rank of in the z-th iteration; the same non-dominated rank The crowding degrees of the two boundary individuals with the maximum and minimum objective function values are infinite, that is

[0251] Step 3.3: Iteratively execute the employed bee search step N eB times. The specific steps of the employed bee search are as follows:

[0252] Generate a random integer r, where N is the number of workpieces, and K j is the number of processes of the jth workpiece;

[0253] Randomly select two individuals from the current population at the zth iteration and Randomly select r from and put them into the empty set in the same index columns, where represents the ath individual randomly selected from the population at the zth iteration, represents the processing method of the kth process of the jth workpiece in and represents the new1th individual generated in the employed bee search step at the zth iteration; Select from the and put them into the remaining index columns of, as shown in Figure 5 . In the example, based on the processing equation constraints in Step 2 and the process constraints of each workpiece, it is composed of the 2nd, 4th, 8th, and 9th columns of and the remaining index columns in excluding these 4 processes Similarly, randomly select r from and put them into the empty set in the same index columns, where represents the bth individual randomly selected from the population at the zth iteration, represents the processing method of the kth process of the jth workpiece in and represents the new2th individual generated in the employed bee search step at the zth iteration. Select from the and put them into the remaining index columns; that is, the new individual

[0254] According to the maintenance policy constraints of each device in step 2 and the maintenance policy set vector in step 3.1 The generation method of and Maintenance strategy set vector and Make corrections, including represents the maintenance strategy set vector of the new1th individual generated in the employed bee search step of the zth iteration, represents the maintenance strategy set vector of the new2th individual generated in the employed bee search step of the zth iteration; Figure 5 As shown, [0 0 0 0 0 0 1 0 00] is the corrected result;

[0255] According to the non-dominated level and congestion calculation method in step 3.2, Compare and if the new individual is better than the old one, replace the old one with the new one, and transform the employed bees into follower bees, and update the number of employed bee colonies and the number of follower bee colonies:

[0256]

[0257]

[0258] in, and denote the number of employed bee swarms and the number of following bee swarms in the z-th iteration, and They represent the number of employed bee swarms and the number of following bee swarms in the updated z+1th iteration respectively;

[0259] After the hired bee search is completed, the updated hysteresis value corresponding to the index of all unreplaced individuals in the population is in, Indicates the updated hysteresis value corresponding to the x-th individual in the population at the z-th iteration;

[0260] Step 3.4, the bee search phase, introduces the tournament selection strategy and local search based on simulated annealing, specifically:

[0261] Repeat with the number of bee colonies N fB times, each time randomly selecting RM individuals from the population, defined as:

[0262]

[0263] Where ceil is rounded up, N fBLet it be the number of follower bees; Select the optimal individual among them according to the non-dominated ranking and crowding degree calculation method in Step 3.2, and define the optimal individual selected for the f-th time in the z-th iteration as After all selections are completed, N fB individuals are obtained;

[0264] Repeat for the number of follower bees N fB times. Each time, perform local search of simulated annealing on these N fB individuals, and define the new individual obtained from the f-th local search in the z-th iteration as According to the non-dominated ranking and crowding degree calculation method in Step 3.2, compare and . If is better, then replace in the population. Otherwise, generate a random number r f , r f ∈[0,1]. If r f >pt, then use to replace in the population. f If r ≤pt, then no replacement is made, and at the same time, the follower bees turn into scout bees, updating the number of follower bees and the number of scout bees:

[0265]

[0266]

[0267] and respectively represent the number of follower bees and the number of scout bees in the z-th iteration, and respectively represent the number of follower bees and the number of scout bees in the updated (z + 1)-th iteration;

[0268] After the follower bee search stage is completed, increment by 1 the updated stagnation value corresponding to the indices of all individuals in the population that have not been replaced, and select the optimal N = 30 individuals from the population according to the non-dominated ranking and crowding degree calculation method in Step 3.2 to form the archive set SOR; d = 30 individuals to form the archive set SOR;

[0269] Step 3.5, Scout bee update stage, adopt the strategy of archive set replacement to achieve population update to avoid the method falling into local optimum. Specifically:

[0270] Repeat N oB times. Each time, find an individual in the population whose updated stagnation value exceeds the update upper limit limit = 20, denoted as Randomly select an individual from the archive set SOR, denoted as​ use Replace the population Reset the update hysteresis value of the position in the population to 0, convert the scout bees into hired bees, and update the number of scout bee colonies and hired bee colonies:

[0271]

[0272]

[0273] in, and denote the number of scout swarms and employed swarms in the z-th iteration, and They represent the number of scout swarms and employed swarms in the updated z+1th iteration respectively;

[0274] If there is no individual in the population whose update hysteresis value exceeds the update upper limit limit = 20, the scout bee stage ends;

[0275] Step 3.6, the iterative update of the method converges, specifically:

[0276] If the number of iterations of the current method is z <Ite,则z=z+1,将当前种群所有个体迭代次数加1,所有更新滞化值迭代次数加1,完成迭代的更新,跳转到步骤3.3继续执行:

[0277]

[0278]

[0279] in, represents the x-th individual solution in the population at the z-th iteration, Indicates the updated hysteresis value corresponding to the x-th individual in the population at the z-th iteration, It means the xth individual solution in the population at the z+1th iteration after the zth iteration update is completed. It represents the updated hysteresis value corresponding to the xth individual in the population at the z+1th iteration after the zth iterative update is completed.

[0280] If the number of iterations of the current method z = Ite, the method terminates, and the best individual is selected from the current population according to the non-dominated level and crowding calculation method in step 3.2 as the optimal solution of the method, which is recorded as

[0281]

[0282]

[0283]

[0284] Among them, is the selected processing plan optimized for each process of each workpiece, is the selected processing plan for the k-th process of the j-th workpiece in the optimized plan, indicates that the k-th process of the j-th workpiece is processed on the selected equipment, indicates the maintenance strategy before the k-th process of the j-th workpiece is processed on the selected equipment for maintenance before processing, otherwise no maintenance. It indicates maintenance before processing, otherwise no maintenance.

[0285] The solution obtained by the optimization scheduling of the present invention can significantly reduce the number of equipment maintenance, shorten the maintenance time, improve the efficiency of equipment maintenance, reduce the resource consumption caused by redundant maintenance, improve the accuracy of maintenance decision-making, significantly shorten the overall completion time of the solution, and improve the overall coordination of production.

[0286] The specific embodiment of the present invention also provides a computer-readable medium.

[0287] The computer-readable medium is a server workstation;

[0288] The server workstation stores a computer program executed by an electronic device. When the computer program runs on the electronic device, the electronic device is caused to execute the steps of the equipment maintenance workshop scheduling optimization method of the embodiment of the present invention.

[0289] It should be understood that the parts not elaborated in detail in this specification all belong to the prior art.

[0290] It should be understood that the above description of the preferred embodiment is relatively detailed, and it should not be considered as a limitation to the protection scope of the present invention patent. Under the inspiration of the present invention, those of ordinary skill in the art can also make substitutions or deformations without departing from the protection scope defined by the claims of the present invention, and all fall within the protection scope of the present invention. The scope of protection requested by the present invention shall be subject to the appended claims.

Claims

1. An optimization method for equipment maintenance workshop scheduling, characterized in that, It includes the following steps: Step 1: Input the time required for single maintenance of each device, the cost required for single maintenance of each device, and the maintenance age threshold of each device, and obtain the actual processing time of each process of each workpiece on each device; Step 2: Calculate the age of each device after each processing, the end time of each processing of each device, the start processing time and completion time of each process of each workpiece; obtain the processing completion time of each workpiece according to the start processing time and completion time of each process of each workpiece and the end time of each processing of each device, and construct a double-optimization objective model of the total system completion time and the total system maintenance cost; construct the processing equation constraint conditions of the optimization objective model, the process constraint conditions of each workpiece, and the maintenance strategy constraint conditions of each device; Step 3: Taking the objective function model of minimizing the total completion time and the total maintenance cost as the optimization objective, combining the processing equation constraint conditions of the optimization objective model, the process constraint conditions of each workpiece, and the maintenance strategy constraint conditions of each device, and performing optimization and solution through the hybrid artificial bee colony method to obtain the optimized processing plan selected for each process of each workpiece, including: Step 3.1: Set the number of method convergence iterations as Ite, the population size as N P , the number of employed bee colonies as N eB , the number of onlooker bee colonies as N fB , the number of scout bee colonies as N oB , the capacity of the archive set as N D , the update upper limit as limit, the update stagnation value as LM, and the acceptance probability as pt; Successively construct a workpiece set vector, a process set vector, a device set vector, and a maintenance strategy set vector; Generate a population randomly through the above vectors, specifically as follows: Random arrangement The workpiece set vector of the x-th individual solution in the population at the z-th iteration is obtained by arranging the numerical order in According to The process set vector of the x-th individual solution in the population at the z-th iteration is obtained according to the number of occurrences of each value in According to And The processing equipment for each process of each workpiece is selected in turn to obtain the equipment set vector of the x-th individual solution in the population at the z-th iteration, defined as Among them, the first X% of the elements select the equipment with the shortest standard processing time p j,k,i The Y% of the elements select the equipment with the shortest time required for single equipment maintenance time i The remaining Z% of the elements randomly select the equipment; obtain After that, calculate according to the maintenance strategy constraint conditions of each equipment in step 2 The maintenance strategy set vector of the x-th individual solution in the population at the z-th iteration is obtained, defined as Among them Indicates the maintenance strategy before processing the k-th process of the j-th workpiece on the selected equipment o j,k For processing, Indicates maintenance before processing, otherwise no maintenance; from The x-th individual solution in the population at the z-th iteration is obtained, defined as where z represents the current iteration number; represents the x-th individual solution in the population at the z-th iteration; the processing method of the k-th process of the j-th workpiece in the x-th individual solution in the population at the z-th iteration is defined as Among them It means that the k-th process of the j-th workpiece in the x-th individual solution in the population at the z-th iteration is selected to be processed on o j,k for processing It means the maintenance strategy before the k-th process of the j-th workpiece is processed on the selected equipment o j,k for maintenance It means to perform maintenance before processing, otherwise no maintenance 2. The equipment maintenance workshop scheduling optimization method according to claim 1, wherein: The single maintenance time of each device described in Step 1 is defined as: time i , where \(i\in[1,M]\) Among them, time i represents the time required for a single maintenance of the i-th device, and M represents the number of devices; The cost required for single maintenance of each device described in Step 1 is defined as: Pm i , where \(i\in[1,M]\) Among them, Pm i represents the single maintenance cost of the i-th device, and M represents the number of devices; The maintenance age threshold of each device described in Step 1 is defined as: θ i , i ∈ [1, M] where θ i represents the maintenance age threshold of the i-th device, and M represents the number of devices; The standard processing time of each process of each workpiece on each device described in Step 1 is defined as: p j,k,i i ∈ [1, M], j ∈ [1, N], k ∈ [1, K j ​ where p j,k,i represents the standard processing time of the k-th process of the j-th workpiece on the selected i-th device, N represents the number of workpieces, and K j represents the number of processes of the j-th workpiece; The actual processing time of each process of each workpiece on each device described in Step 1 is specifically u j,k,i = p j,k,i + δ i · p j,k,i i ∈ [1, M], j ∈ [1, N], k ∈ [1, K j ​ where, u j,k,i represents the actual processing time of the k-th process of the j-th workpiece on the selected i-th device, p j,k,i represents the standard processing time of the k-th process of the j-th workpiece on the selected i-th device, M represents the number of devices, N represents the number of workpieces, K j represents the number of processes of the j-th workpiece; δ i represents the growth rate of the processing time of the i-th device, and the specific calculation is as follows: where, θ i is the maintenance service age threshold of the i-th device, and ρ is the degradation weight; is the service age before the k-th process of the j-th workpiece processed by the i-th device, that is, the service age after the i-th device completed the last processing. If the current processing is the first processing of the i-th device, then is 0.

3. The equipment maintenance workshop scheduling optimization method according to claim 2, wherein: The start processing time of the kth process of the jth workpiece described in Step 2 is: Among them, time i represents the single duration of maintenance performed by the i-th device, y j,k,i represents whether maintenance is performed before the k-th process of the j-th workpiece processed by the i-th device, y j,k,i = 1 indicates that the i-th device performs maintenance before the k-th process of the j-th workpiece, otherwise y j,k,i = 0; represents the end time of the previous processing on the i-th device selected for the k-th process of the j-th workpiece. If the current processing is the first processing on the i-th device, then C j,(k-1) represents the completion time of the (k - 1)-th process of the j-th workpiece; The completion time of the kth process of the jth workpiece described in Step 2 is: C j,k = S j,k + u j,k,i i ∈ [1, M], j ∈ [1, N], k ∈ [1, K j ​ Among them, S j,k is the start processing time of the k-th process of the j-th workpiece, and u j,k,i is the actual processing time of the k-th process of the j-th workpiece on the selected i-th device; The end time of each device to complete each processing described in Step 2 is: T j,k,i = C j,k i ∈ [1, M], j ∈ [1, N], k ∈ [1, K j ​ Among them, T j,k,i represents the end time of the k-th process of the j-th workpiece processed by the i-th device.

4. The equipment maintenance workshop scheduling optimization method according to claim 3, wherein: The double-objective function model of the total system completion time and the total system maintenance cost described in Step 2 is specifically defined as follows: f = (C, Cost) Wherein, Cost represents the total system maintenance cost, and C represents the total system completion time; The total system completion time is specifically defined as follows; Among them, C represents the total system completion time, represents the completion time of the K j th process of the jth workpiece, that is, the processing completion time of the jth workpiece; The total system maintenance cost is specifically defined as follows; Among them, Pm i represents the cost of the i-th device, and np i represents the total number of maintenance times of the i-th device; The processing equation constraint conditions described in Step 2 are specifically defined as follows: The number of device processing times is equal to the total number of all workpiece processes, specifically as follows: Among them, n i represents the total number of processing times required for the i-th device to complete the production task, M represents the number of devices, N represents the number of workpieces, and K j represents the number of processes of the j-th workpiece; The process constraint conditions of each workpiece described in Step 2 are as follows: C j,(k-1) ≤S j,k j ∈ [1, N], k ∈ [2, K j ​ Among them, C j,(k-1) represents the completion time of the (k - 1)-th process of the j-th workpiece, and S j,k represents the start time of the k-th process of the j-th workpiece. N represents the number of workpieces, and K j represents the number of processes of the j-th workpiece; The maintenance strategy constraint conditions of each device described in Step 2 are specifically defined as follows: where t j,k,i represents the age of the i-th device after the k-th process of the j-th workpiece is processed; θ i represents the maintenance age threshold of the i-th device; y j,k,i represents the maintenance flag of the i-th device before the k-th process of the j-th workpiece. If y j,k,i = 1, it means that the i-th device is maintained before the k-th process of the j-th workpiece. Otherwise, the i-th device is not maintained before the k-th process of the j-th workpiece; The age of each device after each processing described in Step 2 is as follows: Among them, t j,k,i represents the age of the i-th device after the k-th process of the j-th workpiece is processed, represents the age of the i-th device before the k-th process of the j-th workpiece, that is, the age of the i-th device after the last processing is completed; y j,k,i represents whether maintenance is carried out on the i-th device before the k-th process of the j-th workpiece, y j,k,i = 1 indicates that the i-th device performs maintenance before the k-th process of the j-th workpiece, y j,k,i = 0 indicates that the i-th device does not perform maintenance before the k-th process of the j-th workpiece; is the equipment improvement factor; u j,k,i represents the actual processing time of the k-th process of the j-th workpiece on the selected i-th device.

5. The equipment maintenance workshop scheduling optimization method according to claim 4, wherein: The optimized equipment selected for each process of each workpiece obtained by optimizing and solving through the hybrid artificial bee colony method described in step 3 is specifically as follows: The workpiece set vector is defined as: Among them, represents the workpiece set vector, j represents the j-th workpiece, and the number of j is its number of processes K j , N represents the number of workpieces; The process set vector is defined as: Among them, represents the process set vector, where k is the array the number of occurrences of j at the same index in, representing the k-th process of the j-th workpiece, K j represents the number of processes of the j-th workpiece; The equipment set vector is defined as: Among them, represents the set vector of equipment selected for each process of each workpiece, o j,k represents the equipment selected for the k-th process of the j-th workpiece, M represents the number of equipment, N represents the number of workpieces, K j represents the number of processes of the j-th workpiece; The maintenance strategy set vector is defined as: Among them, represents the vector of maintenance strategy sets before each process of each part by each device, where represents the maintenance strategy before processing the k-th process of the j-th workpiece on the selected device o j,k ; represents maintenance before processing, otherwise no maintenance; M represents the number of devices, N represents the number of workpieces, and K j represents the number of processes of the j-th workpiece.

6. The equipment maintenance shop scheduling optimization method according to claim 5, characterized in that: Initialize the population fitness value and the archive set; The fitness value consists of two parts: non-dominated rank and crowding degree, and its evaluation method is: Calculate the objective function values of all individuals in the population, and use the objective function model of minimizing the total completion time and the total maintenance cost as the optimization objective: minf = min(C, Cost) where C represents the total system completion time, Cost represents the total system maintenance cost, and min represents minimization; the smaller the objective function value of an individual, the better: All individual solutions in the current population are non-dominated sorted according to the Pareto non-dominance rule, and each individual obtains a non-dominated rank. The smaller the non-dominated rank, the better the individual. The non-dominated rank to which the x-th individual in the population belongs in the z-th iteration is defined as Calculate the crowding degree between different individuals in each rank. The smaller the crowding degree in the same rank, the better the individual. The crowding degree of individual I is determined by its two adjacent individuals. The calculation method of the crowding degree is as follows: Among them, represents the crowding degree of the x-th individual in the z-th iteration, represents the maximum value of the total system maintenance cost Cost among all individuals with non-dominated rank in the z-th iteration, represents the minimum value of the total system maintenance cost Cost among all individuals with non-dominated rank in the z-th iteration, and respectively represent two adjacent values of the total system maintenance cost Cost that are higher and lower than the x-th individual among all individuals with non-dominated rank in the z-th iteration; represents the maximum value of the total system completion time C among all individuals with non-dominated rank in the z-th iteration, represents the minimum value of the total system completion time C among all individuals with non-dominated rank in the z-th iteration, and respectively represent two adjacent values of the total system completion time C that are higher and lower than the x-th individual among all individuals with non-dominated rank in the z-th iteration; The crowding degrees of the two boundary individuals with the maximum and minimum objective function values in the same non-dominated rank are infinite, that is, 7. The equipment maintenance shop scheduling optimization method according to claim 6, characterized in that: Iteratively execute the employed bee search step N eB times. The specific steps of the employed bee search are as follows: Generate a random integer where N is the number of workpieces, and K j is the number of processes for the j-th workpiece; Randomly select two individuals from the current population at the z-th iteration and Randomly select r from and put them into the empty set for the same index columns, where represents the a-th individual randomly selected from the population at the z-th iteration, represents the processing method for the k-th process of the j-th workpiece in ; represents the new1-th individual generated in the employed bee search step at the z-th iteration; select according to the processing equation constraint conditions in step 2 and the process constraint conditions of each workpiece from the and put them into the remaining index columns of; similarly, randomly select r from and put them into the empty set for the same index columns, where represents the b-th individual randomly selected from the population at the z-th iteration, represents the processing method for the k-th process of the j-th workpiece in ; represents the new2-th individual generated in the employed bee search step at the z-th iteration, and select according to the processing equation constraint conditions in step 2 and the process constraint conditions of each workpiece from the and put them into the remaining index columns of; thus obtaining the new individual According to the maintenance strategy constraint conditions of each device in step 2 and the generation method of the maintenance strategy set vector in step 3.1 to and the maintenance strategy set vectors and are corrected, where represents the maintenance strategy set vector of the new1-th individual generated in the employed bee search step of the z-th iteration, represents the maintenance strategy set vector of the new2-th individual generated in the employed bee search step of the z-th iteration; According to the non-dominated ranking and crowding distance calculation method, compare them. If the new individual is better than the old individual, replace the old individual with the new individual. At the same time, change the employed bee into a follower bee, and update the number of employed bee colonies and the number of follower bee colonies: Among them, and represent the number of employed bee colonies and the number of onlooker bee colonies in the z-th iteration respectively, and represent the number of employed bee colonies and the number of onlooker bee colonies in the updated (z + 1)-th iteration respectively; After completing the employed bee search, the updated stagnation values corresponding to the indices of all individuals in the population that have not been replaced where represents the updated stagnation value corresponding to the x-th individual in the population at the z-th iteration.

8. The equipment maintenance shop scheduling optimization method according to claim 7, characterized in that: In the onlooker bee search stage, introduce the tournament selection strategy and local search based on simulated annealing, specifically: Repeatedly with the number of bee colonies N fB times, each time randomly select RM individuals from the population, defined as: where ceil is rounding up, and N fB is the number of bee swarms; the optimal individuals are selected according to the non-dominated rank and crowding degree calculation method, and the optimal individual selected for the f-th time in the z-th iteration is defined as After all the selections are completed, N fB individuals are obtained; Repeat with the number of bee colonies N fB times, and perform local search of simulated annealing on these N fB individuals each time. Define the new individual obtained from the f - th local search in the z - th iteration as According to the non - domination rank and crowding degree calculation method, compare and If is better, then replace in the population. Otherwise, generate a random number r f , r f ∈[0, 1]. If r f > pt, then use to replace in the population. If r f ≤pt, then no replacement is made, and at the same time, the follower bees turn into scout bees, updating the number of follower bee colonies and the number of scout bee colonies: Among them, and represent the number of follower bee swarms and the number of scout bee swarms in the z-th iteration respectively, and represent the number of follower bee swarms and the number of scout bee swarms in the updated (z + 1)-th iteration respectively; After completing the following bee search stage, increment the updated stagnation value corresponding to the indices of all individuals in the population that have not been replaced by 1, and select the optimal N d individuals from the population according to the non-dominated ranking and crowding distance calculation method to form the archive set SOR.

9. The equipment maintenance shop scheduling optimization method according to claim 8, characterized in that: In the scout bee update stage, adopt the strategy of replacing the archive set to update the population to avoid the method falling into local optimum, specifically: Execute N oB times. Each time, find an individual in the population whose update stagnation value exceeds the update upper limit limit, and denote it as Randomly select an individual from the archive set SOR and denote it as Use to replace in the population. Reset the update stagnation value at the position of this individual in the population to 0. The scout bees are converted into employed bees to update the number of scout bee colonies and the number of employed bee colonies: Among them, and respectively represent the number of scout bee colonies and employed bee colonies in the z-th iteration, and respectively represent the number of scout bee colonies and employed bee colonies in the updated (z + 1)-th iteration; If there is no individual in the population whose update stagnation value exceeds the update upper limit limit, the scout bee stage ends; The iterative update of the method converges, specifically: If the current iteration number z of the method < Ite, then z = z + 1, add 1 to the iteration number of all individuals in the current population, and add 1 to the iteration number of all update stagnation values, complete the iterative update, and jump to the employed bee search step to continue execution: Among them, represents the x-th individual solution in the population at the z-th iteration, represents the updated stagnation value corresponding to the x-th individual in the population at the z-th iteration, represents the x-th individual solution in the population at the (z + 1)-th iteration after completing the update at the z-th iteration, represents the updated stagnation value corresponding to the x-th individual in the population at the (z + 1)-th iteration after completing the update at the z-th iteration; If the iteration number z of the current method is equal to Ite, the method terminates, and the optimal individual is selected from the current population according to the non-dominated rank and crowding degree calculation method as the optimal solution of the method, denoted as Among them, is the selected processing plan optimized for each process of each workpiece, is the selected processing plan for the k-th process of the j-th workpiece, indicates that the k-th process of the j-th workpiece is processed on the selected equipment, indicates the k-th process of the j-th workpiece on the selected equipment maintenance strategy before processing, indicates maintenance before processing, otherwise no maintenance.

10. A computer-readable medium, characterized in that, The computer program executed by its storage electronic device, when the computer program runs on the electronic device, enables the electronic device to execute the steps of the method described in claims 1-9.

Images