CN110865617B - Equipment opportunity maintenance and production scheduling integrated optimization method under time-varying working condition - Google Patents
Equipment opportunity maintenance and production scheduling integrated optimization method under time-varying working condition Download PDFInfo
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Abstract
Maintenance of some equipment in engineering practice can only restore it to a degraded state and not repair it as new. Furthermore, in mass production systems, production processing tasks are often not interrupted, and therefore maintenance activities can only be moved to be performed before or after a processing task. In addition, the influence on the reliability degradation of the equipment is different in consideration of different working conditions of different production and processing tasks. Aiming at the problems, the invention provides a method for integrating and optimizing equipment opportunity maintenance and production scheduling under the time-varying working condition. The invention considers the equipment maintenance and the production scheduling integrated optimization under different production systems and different maintenance effects, ensures the reliability of the equipment and improves the production efficiency of the production system.
Description
Technical Field
The invention relates to an equipment maintenance and production scheduling integrated optimization technology. Specifically, under the condition of considering the operation conditions of different processing tasks, the method combines the characteristics of a batch production system and establishes an opportunistic non-perfect preventive maintenance and production scheduling integrated optimization model of equipment in the batch production system.
Background
In production practice, a product often needs to be processed on a plurality of different devices to complete the production task. Failure or maintenance of any one device in the system can affect production of the production system, so that integrated optimization of device maintenance and production scheduling is necessary. In the optimization, the influence of various aspects such as maintenance strategy, maintenance effectiveness, maintenance time and maintenance cost needs to be considered. In addition, different production modes require different equipment maintenance modes, so that when the equipment is maintained and optimized in production scheduling integration, not only the current state of the equipment, but also the state of the equipment after maintenance and the degradation track of the equipment after maintenance are required to be considered, and time factors (maintenance time, processing time, equipment start and stop time, and operation switching time), cost factors (maintenance cost, processing cost and delivery delay cost), the characteristics of the production task, the production mode and the production system characteristics are also required to be considered.
Disclosure of Invention
The purpose of the invention is: and establishing an opportunistic imperfect preventive maintenance and production scheduling integrated optimization model of the equipment in the batch production system.
In order to achieve the above object, the technical solution of the present invention is to provide an integrated optimization method for equipment opportunity maintenance and production scheduling under a time-varying working condition, which is characterized by comprising the following steps:
first step, determining problems and assumptions
Assuming that a job-shop contains M devices, a processing task comprising N batches is to be processed on the job-shop, all the batches are ready before the processing task is started, and the N batches are independent from each other; there is a delivery deadline for each lot, and if the completion time of the lot lags behind the corresponding delivery deadline, a delay cost is incurred as a cost; the starting time for converting different batches and the transfer time between batches are ignored; if the equipment fails, performing minor repair on the equipment to restore the equipment to a state capable of running without changing the risk rate of the equipment, and neglecting the minor repair time of the equipment; assuming a mass production mode is performed on the equipment, but the preventive maintenance PM activity cannot interrupt an equipment that is being processed, so the preventive maintenance PM activity has to be advanced to before or postponed after the processing task;
second, determining an optimization objective
The goal of the integration optimization is to minimize the total cost by determining the order of processing on each device on the job-shop and the execution time of the preventive maintenance PM, the total cost including the delay cost, the preventive maintenance PM cost and the expected minor repair cost, the delay cost of a lot being related to its completion time, the preventive maintenance PM cost and the minor repair cost being related to the execution times and time of the preventive maintenance PM, the objective function being:
min C total ＝C T +C P +C F
in the formula, C total Is the total cost;
C T in order to account for the total delay cost,
n is the total number of batches, T n For the delay cost of the batch n,
L n for the delay of the batch n,
E m,n for the completion time of batch n on device m, D n For a given projected completion time of batch n,
delay cost per unit time for batch n;
C P PM cost for total preventative maintenance:
C F for the total desired minor repair cost:
thirdly, determining the batch completion time
The completion time of a batch on a piece of equipment is related to four factors: (1) the completion time of the previous batch on the equipment; (2) the processing time of the batch on the equipment; (3) the completion time of the batch on the previous equipment; (4) Execution time of maintenance if preventative maintenance PM is required before processing the lot;
fourth, determining the reliability of the equipment in the PM period of preventive maintenance
The cost rate function for the time to initially perform preventative maintenance PM is determined as follows:
in the formula,
the maintenance cost rate for device m in the ith preventative maintenance PM cycle,
the time required to perform a preventive maintenance PM for the equipment m;
suppose there is already in the ith cycle of device m
For a finished or in-process lot, the risk rate function for the equipment during that cycle is written as:
in the formula,
is a variable from 0 to 1, 1 if the jth process in the ith preventative maintenance PM cycle on device m is lot n;
a risk rate function for the equipment m in the jth process in the ith preventative maintenance PM cycle;
the equipment reliability of the equipment in the 1 st preventive maintenance PM period when the equipment carries out the 1 st processing is as follows:
in the formula,
indicating the reliability of the equipment at the time of the 1 st process in the 1 st preventive maintenance PM cycle,
is the equivalent reliability of the plant under the reference operating conditions,
is a working condition adjusting parameter in the k-th processing on the equipment m,
is a function of the risk of the device m in the ith preventive maintenance PM cycle under the reference condition;
the risk rate function of the equipment m during the 1 st process in the 1 st preventive maintenance PM cycle is:
in the 1 st preventive maintenance PM cycle, the reliability of the equipment m when performing the 2 nd machining is as follows:
wherein:
wherein S is m,n,k The processing start time of the equipment m if the kth processing on the equipment m is the batch n;
the risk rate function of the equipment m at the 2 nd process in the 1 st preventative maintenance PM cycle is:
the reliability of the equipment m in the k processing in the 1 st preventive maintenance PM period is as follows:
the risk rate function for the equipment m during the kth process in the 1 st preventive maintenance PM cycle is:
due to the foregoing assumptions that preventative maintenance PM is non-perfect, introducing a reduction of service life factor and an increase of failure rate factor, the baseline risk rate function for equipment m during the ith preventative maintenance PM cycle is:
and fifthly, performing integrated optimization by using a random key genetic algorithm GA.
Preferably, the completion time of other batches in the job-shop is calculated by calculating the completion time of the first process on each equipment, and then:
if the first processing batches allocated to each equipment in the job-shop are different from each other, the completion time of the first processing on the equipment is as follows:
in the formula, E m,n,1 If the 1 st process is a batch n, its completion time on equipment m; x is a radical of a fluorine atom m,n,1 Is a variable from 0 to 1, x if the 1 st process on plant m is a batch n m,n,1 Has a value of 1; p is a radical of formula m,n Is the processing time of batch n on the equipment m;
if the first processing batch allocated to each equipment on the job-shop is the same, the completion time of the first processing on the equipment is:
if the kth process on tool m is a lot n, its completion time is inferred from the following: the time it takes to complete if the batch has been processed on other equipment; finish time of the (k-1) th process on the equipment m; if the preventive maintenance PM is to be executed, the execution time of the preventive maintenance PM is calculated by the following formula:
in the formula,
the time required to perform a preventive maintenance PM on device m, k being equal or not equal to k ', if k = k', it means that the order in which the batch n is placed on device m and device m 'is the same, otherwise, the order in which the batch n is placed on device m and device m' is not the same.
Preferably, the fifth step includes the steps of:
firstly, defining chromosome type, wherein a chromosome group is composed of two parts, the part 1 is the batch distribution on equipment and is a sequencing problem, therefore, random keys are generated and are sequenced according to sizes, and further, the processing sequence is obtained; part 2 is a preventative maintenance PM decision, which is not a ranking problem;
subsequently, a crossover is performed: calculating the fitness of each chromosome group after coding, taking a target function as a fitness function, adopting an elite strategy to keep the evolution of the random key genetic algorithm GA as monotonous non-reducibility, recording elite in each iteration process, putting the elite back into a mating pool, and only performing cross operation on a processing sequence part; the cross operation is not carried out in a preventive maintenance PM decision part, the minimum maintenance cost rate is related to the service time of the equipment after the execution of the previous preventive maintenance PM, a preventive maintenance PM decision matrix is related to a processing sequence part, and the cross operation only acts on a random key part; all the chromosomes and their bonds are divided into two parts: one part is an elite group, the other part is a non-elite group, and a chromosome group in the elite group and a chromosome group in the non-elite group are mated, a single-point crossing is carried out, and convergence of a convex set theory acceleration algorithm is entered; in the crossing process, the crossing points are randomly selected, the parents keep unchanged at the left sides of the crossing points, the parts at the right sides are exchanged with each other, and the numerical values of the crossing points are obtained by using a linear connection method;
then, mutation was performed: mutation occurs in a processing sequence part and a preventive maintenance PM decision part, two genes are randomly selected on a chromosome, convex connection mutation is then executed, mutation is only carried out on random keys as with a crossover operator, mutation is carried out in the preventive maintenance PM decision part for the case that mutation occurs in the preventive maintenance PM decision part, and a certain non-zero position is selected in the preventive maintenance PM decision part because the non-zero position is the time for theoretically executing preventive maintenance PM; at the mutation site, the result after mutation was 1 minus the original value.
The invention has the following advantages:
1) The method can optimize the processing sequence of the batch on the equipment on the premise of keeping higher reliability of the equipment.
2) Compared with the advance and lag fixed period preventive maintenance strategy commonly used in engineering practice, the method has better effect.
Drawings
FIG. 1 is a graph of device reliability at different batches during a task cycle;
FIG. 2 is a plot of batch and PM lead and PM lag in a finite time;
FIG. 3 is a flowchart illustrating the opportunistic maintenance proposed herein verified for a given process sequence;
FIG. 4 is a verification of an integrated optimization model.
Detailed Description
The invention will be further illustrated with reference to the following specific examples. It should be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the present invention. Further, it should be understood that various changes or modifications of the present invention may be made by those skilled in the art after reading the teaching of the present invention, and such equivalents may fall within the scope of the present invention as defined in the appended claims.
Suppose a jobshop contains M devices. A processing job comprising N batches is processed on this job-shop. For each batch, it requires different conditions for the equipment, but the conditions of the equipment are fixed when a particular batch is processed. The reliability changes of the equipment caused by different batches processed by the equipment during a fixed period Preventive Maintenance (PM) period are shown in fig. 1. In fig. 1, the broken line indicates the reliability of the equipment under the reference condition, and the red and green lines respectively indicate the reliability variation of the equipment under different lots.
All batches are ready before the start of the processing task. The batches are independent of each other. There is a delivery deadline for each lot, and if the completion time of the lot lags behind the corresponding delivery time, a delay cost is incurred as a cost. The start-up time of the apparatus for converting different batches is negligible. In addition, the transfer time between batches is negligible.
If the equipment fails, the equipment is repaired to restore the equipment to a state in which the equipment can operate but the risk rate of the equipment is not changed. To simplify the calculation, the minor repair time of the device is ignored. It is assumed that a batch mode is in progress on the equipment, but preventative maintenance PM cannot interrupt an in-progress piece of equipment. Maintenance has to be advanced to the machining task or postponed to the machining task as shown in fig. 2.
The basic assumptions and symbolic descriptions in the present invention are shown in table 1 below:
table 1: equipment opportunity maintenance and production scheduling integrated optimization model data specification
A1: at the beginning of the processing task, all equipment is new.
A2: if the device fails, the device is minor repaired and the minor repair can only make the device "as bad as old". Preventative maintenance PM is imperfect and can restore the device to a better, but not new, state.
A3: PM must be performed before or after batch processing.
A4: minor repair time, equipment start-up time, batch changeover and shipping time are negligible.
A5: at the start of a processing task, all batches are ready, it being not permissible to cancel one batch being processed and process other batches.
A6: the different batches require different conditions, but the conditions are not the same in one batch.
A7: at one time, the installation can only be occupied by one batch and one batch can be processed on only one installation.
TABLE 1
The integrated optimization of the present invention means minimizing the total cost by determining the processing order and the execution time of the PM on each device on the job-shop. The total cost includes the delay cost, the PM cost, and the expected repair cost. The delay cost of a batch is related to its completion time. The PM cost and the minor repair cost are related to the execution times and time of the PM. The objective function herein can be written as:
min C total ＝C T +C P +C F equation 1
In the formula, C total To total cost after completion of all production tasks, C T To total delay cost, C P To total PM cost, C F To total desired minor repair costs.
Wherein N is in bulkTotal number, T n Is the delay cost of batch n.
Is the delay cost per unit time of batch n.
Wherein L is n Is the delay of batch n.
In the formula, E m,n Is the completion time of batch n on device m. D n Predicted completion time for a given batch n
In the formula I m For the total number of times the preventive maintenance PM is performed on the device m during the task period,
PM costs for one preventive maintenance.
In the formula,
for an equivalent machining time of the machine m in the ith preventive maintenance PM cycle at the base condition,
in order to achieve equivalent machining time after the equipment m performs the last preventive maintenance of PM under the reference working condition,
a baseline failure rate function for the device m during the ith preventive maintenance PM cycle.
The time to complete a batch on a piece of equipment is complex. It is mainly related to four factors: (1) the completion time of the last batch on the equipment; (2) the processing time of the batch on the equipment; (3) the completion time of the batch on the previous equipment; (4) If PM needs to be performed before processing the lot, execution time of PM.
The completion time of the first process on each tool is the basis for calculating the completion time of other lots in this job-shop. Two scenarios need to be considered. One is that the first process batch allocated to each device on this job-shop is different from each other. Another scenario is that the first process batch allocated to each piece of equipment on this job-shop is the same. For the first scenario, the completion time of the first process is:
wherein E is m,n,1 If the 1 st process is a batch n, its completion time on equipment m; x is the number of m,n,1 Is a variable from 0 to 1, x if the 1 st process on plant m is a batch n m,n,1 Has a value of 1; p is a radical of formula m,n Is the processing time of the batch n on the apparatus m. The constraint of equation 7 illustrates that at one time, a device can only be occupied by one lot and one lot can only occupy one device.
For the second scenario, the 1 st processing completion time on one device is related to the completion time of the batch on the other device, as shown in equation 8.
If the kth process on the machine m is a batch n, its completion time can be inferred from the following: the time it takes to complete if the batch has been processed on other equipment; finish time of the (k-1) th process on the equipment m; if PM is to be executed, execution time of PM. The calculation formula is shown in formula 9:
wherein,
the time required to perform a preventive maintenance PM on device m, k being equal or not equal to k ', if k = k', it means that the order in which the batch n is placed on device m and device m 'is the same, otherwise, the order in which the batch n is placed on device m and device m' is not the same.
The initial time to perform a PM is determined based on a minimum maintenance cost rate on the device. A piece of equipment that is processing cannot be interrupted for executing a PM, so the PM has to be advanced or pushed back until the processing task is completed. Determining the cost rate function for the initial execution of PM time as equation 10
Wherein,
the maintenance cost rate for the device m during the ith preventative maintenance PM cycle,
the time required to perform a preventive maintenance PM on the device m.
Because the equipment works under different working conditions, the risk rate of the equipment also varies with different processing batches. Suppose that in the i-th cycle of device mAlready has
For each processed or processing lot, the risk rate function for the equipment during that cycle is written as:
in the formula,
is a variable from 0 to 1, 1 if the jth process in the ith preventative maintenance PM cycle on device m is lot n;
as a function of the risk rate of the equipment m in the jth process in the ith preventive maintenance PM cycle.
The time-varying operating conditions may be converted to baseline operating conditions by AFTM. Taking the 1 st PM cycle as an example, the reliability of the apparatus when performing the 1 st processing in the 1 st PM cycle is:
wherein,
indicating the reliability of the equipment at the time of item 1 processing during the 1 st preventive maintenance PM cycle,
is the equivalent reliability of the plant under the reference operating conditions,
is a working condition adjusting parameter during the kth processing on the equipment m,
is a function of the risk rate of the plant m in the ith preventive maintenance PM cycle under the reference condition.
Then, the risk rate function that the equipment m is performing the 1 st process in the 1 st PM cycle is:
in the 1 st PM period, the reliability of the equipment m in the 2 nd processing is as follows:
wherein,
wherein S is m,n,k The processing start time for tool m if the kth process on tool m is batch n. The risk rate function for the equipment m at the 2 nd process in the 1 st PM cycle is:
the reliability of the apparatus m at the kth processing time in the 1 st PM period is as follows:
the risk ratio function of the equipment m in the kth machining process in the 1 st PM period is as follows:
due to the foregoing assumptions, PM is imperfect, introducing a work-age decreasing factor and a failure rate increasing factor. The benchmark risk rate function of the device m in the ith PM period is as follows:
First, a chromosome type is defined. Considering this as a multi-device multi-batch problem, the concept of genome was introduced. The genome is composed of two parts, part 1 is the batch distribution on the equipment, which is a sorting problem, therefore, random keys are generated and sorted according to size, and further a processing sequence is obtained; part 2 is the PM decision, which is not a sorting problem, so it is not necessary to assign random keys to them.
Subsequently, interleaving is performed. And calculating the fitness of each chromosome set after coding, and taking the target function of the method as a fitness function. To keep the evolution of GA monotonic non-decreasing, an elite strategy was used. Elite was recorded and placed back into the mating pool during each iteration. The crossover operation is performed only during the portion of the process sequence. Since the opportunity for PM is obtained based on the minimum cost to repair rate, no crossover operations are performed in the PM decision section. The minimum cost to repair rate is related to the length of service of the equipment after the execution of the previous PM. That is, it relates to the processing sequence after PM. The PM decision matrix is therefore related to the process sequence part. The crossover operation only works on random key portions. All the chromosomes and their bonds are divided into two parts: one part is the elite group and one part is the non-elite group. The chromosome set in the elite group and the chromosome set in the non-elite group are mated. And performing single-point crossing and entering the convergence of a convex set theory acceleration algorithm. During the crossing process, the crossing points are randomly selected. The parents remain unchanged on the left side of the intersection and the parts on the right side are swapped with each other. The value of the cross-over point is obtained using a linear connection method.
Thereafter, mutation was performed. The variation may occur in the process sequence part and the PM decision part. Two genes were randomly selected on one chromosome, and then convex junction mutation was performed. Like the crossover operator, mutation is only performed on random bonds. For the second case, the mutation is made in the PM decision section. In the PM decision section, a certain non-zero position is selected, since the non-zero position is the time at which PM is theoretically performed. At the mutation site, the result after mutation was 1 minus the original value.
It should be noted that, if a sudden change occurs in the PM decision section, the processing sequence on the equipment remains unchanged, and after the sudden change occurs, the fitness is recalculated. And repeating the processes of selection, crossing and mutation until the current iteration number exceeds the limit of the maximum iteration number.
Claims (3)
1. A method for integrating and optimizing equipment opportunity maintenance and production scheduling under a time-varying working condition is characterized by comprising the following steps:
first step, determining problems and assumptions
Assuming that a job contains M devices, a processing task comprising N batches is to be processed on the job, all the batches are ready before the processing task is started, and the N batches are independent; there is a delivery deadline for each lot, and if the completion time of the lot lags behind the corresponding delivery deadline, a delay cost is incurred as a cost; the starting time for converting different batches and the transfer time between batches are ignored; if the equipment fails, performing minor repair on the equipment to restore the equipment to a state capable of running without changing the risk rate of the equipment, and neglecting the minor repair time of the equipment; assuming a batch mode is in progress on the equipment, but the preventative maintenance PM cannot interrupt an equipment that is in process, so the preventative maintenance PM has to be advanced to before or deferred to after the process job;
second, determining an optimization objective
The integration optimization means that the total cost is minimized by determining the processing sequence of each device on the job-shop and the execution time of the preventive maintenance PM, wherein the total cost comprises delay cost, preventive maintenance PM cost and expected minor repair cost, the delay cost of one batch is related to the completion time of the batch, the preventive maintenance PM cost and the minor repair cost are related to the execution times and time of the preventive maintenance PM, and the objective function is as follows:
min C total ＝C T +C P +C F
in the formula, C total Is the total cost;
C T in order to account for the total delay cost,
n is the total number of batches, T n For the delay cost of the batch n,
L n is a delay of the batch n and,
E m,n for the completion time of batch n on device m, D n For a given projected completion time of batch n,
delay cost per unit time for batch n;
C P PM cost for total preventative maintenance:
C F for the total desired minor repair cost:
thirdly, determining the batch completion time
The completion time of a batch on a piece of equipment is related to four factors: (1) the completion time of the last batch on the equipment; (2) the processing time of the batch on the equipment; (3) the completion time of the batch on the previous equipment; (4) An execution time for preventively maintaining the PM if the preventive maintenance PM is required before the lot is processed;
step four, determining the equipment reliability in the PM period of preventive maintenance
The cost rate function for determining the time to initially perform preventative maintenance PM is given by:
in the formula,
the maintenance cost rate for the device m during the ith preventative maintenance PM cycle,
the time required to perform a preventive maintenance PM for the equipment m;
suppose there is already an i-th cycle of device m
For a finished or in-process lot, the risk rate function for the equipment during that cycle is written as:
in the formula,
is a variable from 0 to 1, 1 if the jth process in the ith preventative maintenance PM cycle on device m is lot n;
as a function of the risk of equipment m in the jth process in the ith preventive maintenance PM cycle;
the reliability of the equipment in the 1 st preventive maintenance PM period when the equipment carries out the 1 st processing is as follows:
in the formula,
indicating the reliability of the equipment at the time of the 1 st process in the 1 st preventive maintenance PM cycle,
is the equivalent reliability of the device under the baseline conditions,
is a working condition adjusting parameter in the k-th processing on the equipment m,
is a risk rate function of the equipment m in the 1 st preventive maintenance PM period under the reference condition;
the risk rate function of the equipment m during the 1 st process in the 1 st preventive maintenance PM cycle is:
in the 1 st preventive maintenance PM period, the reliability of the equipment m when performing the 2 nd processing is as follows:
wherein:
wherein S is m,n,k The processing start time of the equipment m if the kth processing on the equipment m is the batch n; the risk rate function of the equipment m at the 2 nd process in the 1 st preventative maintenance PM cycle is:
the reliability of the apparatus m at the kth processing in the 1 st preventive maintenance PM cycle is:
the risk rate function for the equipment m during the kth process in the 1 st preventive maintenance PM cycle is:
m＝1,2,…,M n＝1,2,…,N n'＝1,2,…,N
preventive maintenance PM is non-perfect, introducing a work-age decreasing factor and a failure rate increasing factor, and the benchmark risk rate function for equipment m during the ith preventive maintenance PM cycle is:
and fifthly, performing integrated optimization by using a random key genetic algorithm GA.
2. The method for integrated optimization of equipment opportunity maintenance and production scheduling under the time-varying working condition of claim 1, wherein the completion time of other batches in the job is calculated by calculating the completion time of the first process on each equipment, and the following steps are carried out:
if the first processing batches allocated to each equipment in the job-shop are different from each other, the completion time of the first processing on the equipment is as follows:
in the formula, E m,n,1 If the 1 st process is a batch n, its completion time on equipment m; x is the number of m,n,1 Is a variable from 0 to 1, x if the 1 st process on plant m is a batch n m,n,1 Has a value of 1; p is a radical of formula m,n Is the processing time of batch n on the equipment m;
if the first processing batch allocated to each equipment on the job-shop is the same, the completion time of the first processing on the equipment is as follows:
if the kth processing on machine m is a batch n, its completion time is inferred from the following: if the batch has been processed on other equipment, its completion time; finish time of the (k-1) th process on the equipment m; if the preventive maintenance PM is to be executed, the execution time of the preventive maintenance PM is calculated by the following formula:
in the formula,
the time required to perform a preventive maintenance PM on device m, k being equal or not equal to k ', if k = k', it means that the order in which the batch n is placed on device m and device m 'is the same, otherwise, the order in which the batch n is placed on device m and device m' is not the same.
3. The time-varying operating condition equipment opportunity maintenance and production scheduling integrated optimization method of claim 1, wherein the fifth step comprises the steps of:
firstly, defining chromosome type, wherein a chromosome group is composed of two parts, the part 1 is the batch distribution on equipment and is a sequencing problem, therefore, random keys are generated and are sequenced according to sizes, and further, the processing sequence is obtained; part 2 is a preventative maintenance PM decision, which is not a ranking problem;
subsequently, a crossover is performed: calculating the fitness of each chromosome set after coding, taking a target function as a fitness function, adopting an elite strategy to keep the evolution of a random key genetic algorithm GA to be monotonous and non-decreasing, recording elite in each iteration process, putting the elite back into a mating pool, and only performing cross operation on a processing sequence part; the cross operation is not carried out in a PM preventive maintenance decision part, the minimum maintenance cost rate is related to the service time of the equipment after the execution of the previous PM preventive maintenance, a PM preventive maintenance decision matrix is related to a processing sequence part, and the cross operation only acts on a random key part; all the chromosomes and their bonds are divided into two parts: one part is an elite group, the other part is a non-elite group, and a chromosome group in the elite group and a chromosome group in the non-elite group are mated, a single-point crossing is carried out, and convergence of a convex set theory acceleration algorithm is entered; in the crossing process, the crossing points are randomly selected, the parents keep unchanged at the left sides of the crossing points, the parts at the right sides are exchanged with each other, and the numerical values of the crossing points are obtained by using a linear connection method;
then, mutation was performed: mutation occurs in a processing sequence part and a preventive maintenance PM decision part, two genes are randomly selected on a chromosome, convex connection mutation is then executed, mutation is only carried out on random keys as with a crossover operator, mutation is carried out in the preventive maintenance PM decision part for the case that mutation occurs in the preventive maintenance PM decision part, and a certain non-zero position is selected in the preventive maintenance PM decision part because the non-zero position is the time for theoretically executing preventive maintenance PM; at the mutation site, the result after mutation was 1 minus the original value.
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