CN117829550A - Solving method for batch scheduling of distributed reentrant heterogeneous mixed flow shop - Google Patents
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Abstract
The invention relates to the technical field of mixed flow shop dispatching, in particular to a solving method for dispatching batches in a distributed reentrant heterogeneous mixed flow shop. S1, analyzing problem characteristics of a batch scheduling problem of a distributed reentrant heterogeneous mixed flow shop in PCB production and manufacturing, establishing a solution target with minimum finishing time, and initializing parameters; s2, initializing a population, and generating PS individuals by using a structural heuristic algorithm; s3, a variable neighborhood descent search stage; s4, a collaborative searching stage; s5, a population reconstruction stage; and S6, updating the optimal individual, judging whether the limited maximum time is reached, ending the cycle if the limited maximum time is reached, outputting the individual with the minimum target value, otherwise, returning to S3, and executing the next searching process. The invention can continuously reduce the target value and has the positive effects of effectively improving the production efficiency and the stability of the production line.
Description
Technical Field
The invention relates to the technical field of mixed flow shop dispatching, in particular to a solving method for dispatching batches in a distributed reentrant heterogeneous mixed flow shop.
Background
In the great background of rapid development of global market economies, enterprises face increasingly aggressive market competition. The traditional single centralized production mode gradually looks at no way of mind, and cannot meet the increasingly diversified demands of the market. To accommodate this market shift, the manufacturing architecture of enterprises is evolving rapidly toward decentralization. This revolution aims at improving flexibility and better meeting the changing market trend. In this transformation process, efficient scheduling becomes a key factor in ensuring smooth enterprise operation and maximizing productivity.
With the rapid development of manufacturing industry, the problem of batch dispatch in a distributed re-entrant heterogeneous mixed flow shop has attracted a great deal of attention. This problem relates to the sequence of processing the batch and the choice of machine at the different stages of each process. At the same time, the complexity of the problem is increased in view of the selection of the factory. However, the current research on the batch scheduling problem of the distributed reentrant heterogeneous mixed flow shop has a certain limitation, and the practical requirement of the actual production scene is difficult to meet. Therefore, further intensive research is required to find a solution more suitable for practical situations.
Disclosure of Invention
The invention aims to provide a method for solving the batch scheduling of a distributed reentrant heterogeneous mixed flow shop, which solves the problem that the current research on the batch scheduling problem of the distributed reentrant heterogeneous mixed flow shop does not accord with the actual production scene, so as to achieve the purposes of ensuring more reasonable production scheduling on the premise of taking the actual production scene as the research, and effectively improving the production efficiency and the stability of a production line.
The invention provides a method for solving batch dispatch in a distributed reentrant heterogeneous mixed flow shop, which is characterized by comprising the following steps,
s1, analyzing problem characteristics of batch scheduling problems of a distributed reentrant heterogeneous mixed flow shop in PCB production and manufacturing, establishing a solution target with minimum finishing time, and initializing parameters, wherein the solution target comprises a population size PS, the maximum failure times C of a current neighborhood, the maximum times Q of current cooperative failure and the maximum times A of combined failure of neighborhood search and cooperative search;
s2, initializing a population, and generating PS individuals by using a structural heuristic algorithm;
s3, in the variable neighborhood descent search stage, searching by means of a variable neighborhood descent search strategy by using five neighborhood structures, and accepting an individual with a target value smaller than that of the original individual as a new individual;
s4, in the collaborative searching stage, the beneficial information among individuals in the population is mutually exchanged by using a collaborative searching strategy, and the individuals with smaller target values than the original individuals are accepted as new individuals;
s5, in the population reconstruction stage, each individual in the population is disturbed, three individuals are generated by three modes of sequence transposition, multipoint exchange and combination of the sequence transposition, one individual with a smaller target value in the three individuals is selected to replace the individual in the original population, and after execution, PS/2 randomly generated individuals are used to replace the worst PS/4 individuals with the target value in the population and PS/4 randomly selected individuals from the population.
And S6, updating the optimal individual, judging whether the limited maximum time is reached, ending the cycle if the limited maximum time is reached, outputting the individual with the minimum target value, otherwise, returning to S3, and executing the next searching process.
Further, each individualConsists of two parts, one part is a sorting part and is a group of F-dimensional vectors, ++>Wherein F is the total number of plants, +.> Is a factory-included->A sequence vector of the batch, representing a processing order of the first stage; in view of the re-entrant properties, the assignment to the factory +.>The batch requirement of (2) is->The occurrence of L times; the other part is a batch splitting part, which is a group of n-dimensional vectors,>where n is the total number of batches, +.>Is a lot->Is used to split the vector.
Further, the implementation of the structured heuristic algorithm comprises the steps of,
(1) The following parameters are defined in terms of the parameters,representing a factory, & lt>Representing a factory set,/->F represents the total number of factories, ">Representing a lot, +.>Representing a collection of lots, +.>N represents the total number of batches, ">Representing a certain stage of->Representing a set of phases->S represents the total number of stages, L represents the number of re-entrants,representative lot->In the factory->Is not limited, and the processing time of the device is not limited;
(2) Dividing the batch by using equal division and random division;
(3) The sum of the processing times of the batch in each factory is calculated, the calculation formula is as follows,
，
pair aggregationArranging in ascending order, collecting ++after ordering> F batches with the minimum sum of the processing time are randomly distributed to F factories, so that each factory is guaranteed to be distributed to one batch;
(4) Solving a probability of a lot being assigned to a minimum target value position in each plant using a probability formula, wherein the minimum target value position in the plant is obtained by a greedy heuristic, comprising the following process,
placing each batch in each position in each factory in turn and obtaining a target value;
comparing the target values of all the positions of each batch in each factory;
preserving the minimum target value that can be obtained in each plant And a position within the factory when the minimum target value is obtained;
the probability formula is given by the formula,
，
for the probability that the calculated lot is assigned to the minimum target value position in each plant, the sum of the probabilities that all plants are assigned is 1;
(5) Using roulette strategy and P f,i The lot is distributed into a factory, wherein the roulette strategy includes the following process,
creating a wheel disc, dividing a circular wheel disc into F sectors, wherein the size of each sector is proportional to the allocation probability of a corresponding factory;
performing roulette selection to generate a 0-1 random decimal, and mapping the random decimal onto a corresponding sector of the roulette;
determining an allocation result, and determining an allocated factory according to the selected sector;
(6) Determining the position of the residual L-1 in the factory by using one of greedy heuristic method and random selection method; the greedy heuristic method is operated in such a way that batches are put into corresponding factories, sequentially inserted into all positions in the factories, and finally put into the position with the minimum target value; the operation mode of the random selection mode is that the batch is put into the random position of the corresponding factory.
Further, the variable neighborhood descent search stage optimizes individuals in the population by adopting a variable neighborhood descent search strategy with 5 neighborhood structures, generates a plurality of individuals improved by the neighborhood structures for each individual, receives an improved individual with a smaller target value than the original individual as a new individual, wherein the five neighborhood structures are four kinds of searches about key factories, one kind is to execute sub-batch variation operation on sub-batches, the key factories refer to factories with the largest target value in all factories, the optimization of the whole production process is key, the specific processes of the 5 kinds of neighborhood operations are as follows,
inserted into the key factory: selecting a lot from a key plant and then randomly inserting it into another location within the same plant;
batch exchange in key factories: randomly selecting two batches from a key factory and exchanging, wherein the selected batches are different to avoid generating invalid operation;
inserting between a critical plant and another plant: randomly selecting one lot in the key plant and then inserting it into another randomly selected plant;
batch exchange between a key plant and another plant: randomly exchanging batches between the key plant and another randomly selected plant;
sub-batch variation: the specific operation of sub-lot variation involves selecting a lot with two or more sub-lots in a critical factory, randomly selecting two sub-lots, then generating a random integer of 1-5, subtracting the random number from one sub-lot and adding to the other sub-lot.
Further, the implementation process of the variable neighborhood descent search strategy is as follows, when each individual in the population is subjected to neighborhood search, a first neighborhood structure is firstly set as a current neighborhood structure, the number of continuous update failures of the current neighborhood structure is set as zero, then the current neighborhood structure is used for searching, if the target value of a new individual is smaller than that of an original individual, the original individual is updated as the new individual, the number of continuous update failures of the current neighborhood structure is reset to zero, and then the current neighborhood structure is continuously used for searching; if a new individual smaller than the target value of the original individual is not obtained when the current neighborhood structure is used for searching, adding one to the continuous updating failure number of the current neighborhood structure, continuing to search by using the current neighborhood structure, taking the next neighborhood structure as the current neighborhood structure when the continuous updating failure number of the current neighborhood structure reaches the set maximum failure number C, resetting the continuous updating failure number of the current neighborhood structure to zero, and repeating the process until all the neighborhood structures cannot update the current individual, switching to the next individual until all the individuals in the population complete the searching process of all the neighbors.
Further, the collaborative search strategy execution process includes selecting an individual from a population, extracting all sequences existing in the individual, assigning the batches to a sequence, then marking the batches in the sequence L times, sequentially marking the batches, recording the number of times the batches occur in the sequence, marking all the sequences sequentially, randomly selecting two different positions if the number of the batches is more than two, reserving the batches between the two positions and corresponding subscripts, selecting another different individual from the population, assigning the individual to a temporary individual, performing a marking operation only on the temporary individual, deleting the batches reserved in each sequence in the first individual and the markers from the temporary individual, the position of the sequence corresponding to the batches, the position being the number of the batches in the sequence, re-placing the corresponding batches into the temporary individual, the position being the same as the position of the first individual, randomly selecting a target value from the two batches if the position of the first individual is greater than the position of the temporary individual, replacing the target value of the two individuals, and performing a collaborative operation after the target value is replaced from the two individuals, if the number of the target values of the individuals is less than the target value, performing a collaborative operation after the two individuals are replaced, and if the target value is smaller than the target value of the individuals, performing a collaborative operation, that is, the synergy is failed, and the synergy is terminated when the number of the synergy continuous failures exceeds the set value Q.
Further, when the maximum number of joint failures of the neighborhood search and the collaborative search exceeds A, the population reconstruction is executed, and the implementation process is as follows: each individual in the population adopts sequence transposition, namely, reversing a batch sequence in a certain interval in the sequence, performing multi-point insertion, namely, inserting other positions of the sequences in a plurality of batches, and generating three disturbance individuals in a combined mode, selecting the individual with the smallest target value in the disturbance individuals to replace the individual before the disturbance is originally performed, extracting the individual with the worst target value in the PS/4 population, randomly selecting the individual in the PS/4 population, wherein the two selected individuals cannot be repeated, replacing the individual extracted in the population by the individual randomly generated by the PS/2 to finally obtain a brand new population, applying the brand new population to the next searching process, and resetting the maximum number A of joint failures of neighborhood searching and collaborative searching to zero at last.
The invention provides a method for solving batch scheduling of a distributed reentrant heterogeneous mixed flow shop, which designs an effective method for initializing population, and generates an initial population with high quality and diversity by constructing a heuristic algorithm; by introducing a variable neighborhood descent search strategy with 5 neighborhood structures, a plurality of individuals improved by the neighborhood structures are generated for the individuals, and the search efficiency of the algorithm is greatly improved. Through the collaborative search strategy, the exchange of beneficial information among individuals is performed, so that the full utilization of the information among the individuals is realized, and the search direction of the individuals is further closed towards the optimal individuals. In addition, the invention also considers a population reconstruction strategy to avoid sinking into local optimum. In summary, the invention can effectively solve the scheduling problem of double-sided PCB board in production and manufacture, and can continuously reduce the target value by optimizing the distribution of batches, the division of batches, the processing sequence of batches and the selection of machines during processing of the batches in the PCB production and scheduling process, thereby having the positive effects of effectively improving the production efficiency and the stability of the production line.
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FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a schematic illustration of an individual in accordance with the present invention;
FIG. 3 is a flow chart of a structured heuristic algorithm of the present invention.
Detailed Description
As shown in fig. 1-3, the solution method for batch scheduling in a distributed re-entrant heterogeneous mixed flow shop provided by the invention is mainly implemented through the following steps.
S1, analyzing problem characteristics of batch scheduling problems of a distributed reentrant heterogeneous mixed flow shop in PCB production and manufacturing, establishing to use minimum finishing time as a solving target, and initializing parameters, wherein the parameters comprise population size PS, maximum failure times C of a current neighborhood, maximum times Q of current cooperative failure, and maximum times A of combined failure of neighborhood search and cooperative search.
S2, initializing a population, and generating PS individuals by using a structural heuristic algorithm; each individual bodyConsists of two parts, one part is a sorting part and is a group of F-dimensional vectors, ++>Wherein F is the total number of plants, +.>Is a factory-included->A sequence vector of the batch, representing a processing order of the first stage; in view of the re-entrant properties, the assignment to the factory +.>The batch requirement of (2) is->The occurrence of L times; the other part is a batch splitting part, which is a group of n-dimensional vectors,>where n is the total number of batches, +.>Is a lot->Is used to split the vector.
The implementation process of the above-mentioned structural heuristic algorithm is realized through the following steps.
(1) The following parameters are defined in terms of the parameters,representing a factory, & lt>Representing a factory set,/->F represents the total number of factories, ">Representing a lot, +.>Representing a collection of lots, +.>N represents the total number of batches, ">Representing a certain stage of->Representing a set of phases->S represents the total number of stages, L represents the number of re-entrants,representative lot->In the factory->Is not limited, and the processing time of the device is not limited;
(2) Dividing the batch by using equal division and random division;
(3) The sum of the processing times of the batch in each factory is calculated, the calculation formula is as follows,
，
pair aggregationArranging in ascending order, collecting ++after ordering> F batches with the minimum sum of the processing time are randomly distributed to F factories, so that each factory is guaranteed to be distributed to one batch;
(4) Solving a probability of a minimum target value position of the batch distributed to each factory by utilizing a probability formula, wherein the minimum target value position is obtained by a greedy heuristic method, and the heuristic method comprises the following steps:
step 1: each batch was placed in turn at each location in each plant and the target value was found.
Step 2: the target values for all locations of each lot in each plant are compared.
Step 3: preserving the minimum target value that can be obtained in each plantAnd a position within the factory when the minimum target value is obtained.
After the above steps are completed, the probability in each factory is calculated, and the probability formula is as follows:
，
for the probability that the calculated lot is assigned to the minimum target value position in each plant, the sum of the probabilities that all plants are assigned is 1;
(5) Using roulette strategyThe lot is distributed into a factory, wherein the roulette strategy includes the following process,
step 1: a wheel is created, dividing a circular wheel into F sectors, each sector having a size proportional to the allocation probability of the corresponding plant.
Step 2: roulette selection is performed to generate a random number of 0-1, which is then mapped onto the corresponding sector of the roulette.
Step 3: and determining an allocation result, and determining an allocated factory according to the selected sector.
(6) The re-entrant times of all the lot remaining L-1 are determined at the location in the factory using one of a greedy heuristic and a random selection. The greedy heuristic method operates by placing the batch in the corresponding factory, inserting the batch into each position in the factory in turn, and finally placing the batch in the position with the minimum target value. The operation mode of the random selection mode is that the batch is put into the random position of the corresponding factory. After the whole construction heuristic algorithm is completed, a complete individual is constructed, one complete individual is shown in fig. 2, taking four batches, two factories as an example,indicating that lot 1 and lot 4 are assigned to factory 1 with lot sequences of 1, 4, 1./>Indicating that lot 2 and lot 3 are assigned to factory 2 with lot sequences 3, 2.And->Respectively represent each ofThe result of the batch division into four sub-batches. To->For example, 8, 7, 6 and 5 represent the sizes of four sub-batches, respectively.
S3, in the variable neighborhood descent search stage, individuals in the population are optimized by adopting a variable neighborhood descent search strategy with 5 neighborhood structures, a plurality of individuals improved by the neighborhood structures are generated for each individual, and the improved individuals with smaller target values than the original individuals are accepted as new individuals, wherein the five neighborhood structures are four types of search about key factories, and one type of search is to execute sub-batch variation operation on sub-batches. The above-mentioned critical plant refers to a plant having the largest target value among all plants, which plays a critical role in optimizing the entire production process. The specific procedure of the 5 neighborhood operations is as follows:
1. inserted into the key factory: a lot is selected from a key plant and then randomly inserted into another location within the same plant.
2. Batch exchange in key factories: two batches were randomly selected from the key plant and swapped. The selected lots must be different to avoid generating invalid operations.
3. Inserting between a critical plant and another plant: one batch in the key plant is randomly selected and then inserted into another randomly selected plant.
4. Batch exchange between a key plant and another plant: batches were randomly exchanged between the key plant and another randomly selected plant.
5. Sub-batch variation: the specific operation of sub-lot variation involves selecting a lot with two or more sub-lots in a critical factory, randomly selecting two sub-lots, then generating a random integer of 1-5, subtracting the random number from one sub-lot and adding to the other sub-lot.
The implementation process of the variable neighborhood descent search strategy is as follows, when each individual in the population is subjected to neighborhood search, a first neighborhood structure is firstly set as a current neighborhood structure, the number of continuous update failures of the current neighborhood structure is set as zero, then the current neighborhood structure is used for searching, if the target value of a new individual is smaller than that of an original individual, the original individual is updated as the new individual, the number of continuous update failures of the current neighborhood structure is reset to zero, and then the current neighborhood structure is continuously used for searching; if a new individual smaller than the target value of the original individual is not obtained when the current neighborhood structure is used for searching, adding one to the continuous updating failure number of the current neighborhood structure, continuing to search by using the current neighborhood structure, taking the next neighborhood structure as the current neighborhood structure when the continuous updating failure number of the current neighborhood structure reaches the set maximum failure number C, resetting the continuous updating failure number of the current neighborhood structure to zero, and repeating the process until all the neighborhood structures cannot update the current individual, switching to the next individual until all the individuals in the population complete the searching process of all the neighbors. The strategy ensures that different neighborhood structures can be flexibly switched in the neighborhood searching process, and meanwhile, the dynamic adjustment of the neighborhood structure is realized by monitoring the continuous update failure number.
And S4, in the collaborative searching stage, the beneficial information among individuals in the population is mutually exchanged by using a collaborative searching strategy, and the individuals with smaller target values than the original individuals are accepted as new individuals. The collaborative search strategy is implemented by selecting an individual from a population, extracting all sequences existing in the individual, distributing the batches to the individual, marking the batches in the sequence L times, recording the positions of the batches in the sequence, marking all the sequences sequentially, randomly selecting two different positions if the number of the batches is more than two, reserving the batches between the two positions and corresponding subscripts, selecting another different individual from the population, assigning the individual to a temporary individual, performing a marking operation on the temporary individual, performing a corresponding operation on the batches reserved in each sequence in the first individual and the temporary individual, deleting the same batches from the temporary individual, the first individual corresponds to the positions of the sequences in the batches, the positions are the same as the positions of the batches in the sequence, putting the corresponding batches into the temporary individual again, the positions of the batches in the first individual are the same as the positions of the batches, if the positions in the first individual are larger than the positions of the temporary individual, selecting the target values of the two individuals, performing a random target value after the two individuals are not matched, and performing a collaborative operation on the two individuals after the target values are replaced by the two individuals, if the number of the target values are larger than the target values, performing a collaborative operation on the individuals, and performing a collaborative operation after the two individuals are replaced by the target values, that is, the synergy is failed, and the synergy is terminated when the number of the synergy continuous failures exceeds the set value Q.
S5, when the maximum number of joint failures of neighborhood search and collaborative search exceeds A, executing population reconstruction, wherein the implementation process is as follows: each individual in the population adopts sequence transposition, namely, reversing a batch sequence in a certain interval in the sequence, performing multi-point insertion, namely, inserting other positions of the sequences in a plurality of batches, and generating three disturbance individuals in a combined mode, selecting the individual with the smallest target value in the disturbance individuals to replace the individual before the disturbance is originally performed, extracting the individual with the worst target value in the PS/4 population, randomly selecting the individual in the PS/4 population, wherein the two selected individuals cannot be repeated, replacing the individual extracted in the population by the individual randomly generated by the PS/2 to finally obtain a brand new population, applying the brand new population to the next searching process, and resetting the maximum number A of joint failures of neighborhood searching and collaborative searching to zero at last.
And S6, updating the optimal individual, judging whether the limited maximum time is reached, ending the cycle if the limited maximum time is reached, outputting the individual with the minimum target value, and otherwise, returning to S3 to execute the next searching process.
In order to better demonstrate the effectiveness of the present invention, the present invention will be further described by experimental analysis of a series of examples of the present invention.
The test data includes 144 large-scale instances created based on parameters F, n, s and machine layout. For large-scale instances, F ε {3,5,7}, n ε {40,60,80,100}, s ε {3,5,9}. The batch sizes and the setting time depending on the sequence are uniformly distributed within the range of [50-100], the unit processing time is uniformly distributed within the range of [1-10], and the batch transmission time is uniformly distributed within the range of [10-20 ]. The maximum sub-batch size is set to 5. To simulate actual plant conditions, four different types of machine layouts are considered, as follows:
type 1: in all plants, one machine is in the first stage, while three machines are in the other stages;
type 2: in all factories, there is one machine in the second stage, while there are three machines in the other stages;
type 3: in all factories, there are two machines in the second stage, while there are three machines in the other stage;
type 4: in all plants, there are three machines per stage.
The CPU time is used as termination criteria for the comparison algorithm. The termination criterion is set to t×f×n×s milliseconds, where F represents the total number of plants, n represents the total number of lots, s represents the total number of stages, and t is set to 40.
To evaluate the performance of the algorithm, for each example run 20 times independently, the relative percent increase (Relative Percentage Increase, RPI) values were calculated, along with standard deviation (Standard Deviation, SD) as an evaluation criterion.
In terms of parameter setting, ps=25, c=15, q=25, a=100, in order to better solve and optimize the distributed re-entrant heterogeneous mixed flow shop lot scheduling problem based on PCB production.
The experimental results and analyses of this example are as follows. After parameter setting is carried out on an algorithm (ICLSRA) for solving and optimizing the batch scheduling problem of the distributed reentrant heterogeneous mixed flow shop based on PCB production, the algorithm is experimentally compared with an improved artificial bee colony (DABC) algorithm and an improved effective Collaborative Iterative Greedy (CIG) algorithm. In order to adapt these algorithms to the problem being solved, the necessary modifications need to be made, including using a unified instance, employing the same target completion time, replacing the setup time with the sequence dependent preparation time, and introducing batch splitting. In the adaptation process, the details of the respective original algorithm are followed. The results of the comparison of the average relative percent increase value and the average standard deviation value are shown in tables 1-4.
Table 1 shows the results of the algorithm experiment for machine type 1 of the method of the present invention
From the data analysis results of table 1, the ICLSRA algorithm showed significant advantages in machine type 1, and superior performance was achieved in solving the various scale examples as compared to DABC and CIG algorithms. The obvious advantages are not only reflected on a single example, but also show that the ICLSRA algorithm has stronger robustness and can keep excellent performance on the problems of different scales and difficulties.
Table 2 shows the results of the algorithm of machine type 2 of the method of the present invention
From the data analysis results of table 2, it can be seen that the ICLSRA algorithm performs better than the DABC algorithm and the CIG algorithm on most problems for all scale data. Only in the 7 x 80 x 9 problem, the ICLSRA algorithm performs slightly lower than the DABC algorithm. This suggests that under certain conditions the DABC algorithm may perform slightly better on this problem scale. Overall, ICLSRA algorithm shows better performance in data analysis, especially compared to DABC algorithm and CIG algorithm.
Table 3 shows the results of the algorithm of machine type 3 of the method of the present invention
In the analysis of data under machine type 3, it is known from table 3 that the ICLSRA algorithm achieved results under this machine type that are still completely better than the DABC algorithm as well as the CIG algorithm. This shows that the ICLSRA algorithm has better performance and effect in the context of machine type 3, a more reliable and efficient choice than DABC and CIG algorithms. This emphasizes the excellent performance of the ICLSRA algorithm under certain conditions, providing a viable solution to the problem resolution under this machine type. These findings help to gain insight into the differences in performance of different algorithms in different scenarios, providing an important reference for further optimization and selection of algorithms.
Table 4 shows the results of the algorithm experiment of machine type 4 of the method of the present invention
From the results of table 4, it can be seen that the ICLSRA algorithm again performs excellently on all problems under machine type 4. By performing further stability analysis, the algorithm's excellent performance at different scales and machine layouts is enhanced. This result clearly demonstrates that the ICLSRA algorithm can ensure high quality individuals it finds in a short time due to its superior performance in initial population construction, neighborhood search based on variable neighborhood descent, and reconstruction. This further emphasizes the reliability and effectiveness of the ICLSRA algorithm in addressing various problems.
In conclusion, the ICLSRA algorithm shows excellent performance, successfully solves the problem of batch scheduling of the distributed reentrant heterogeneous mixed flow shop, provides an innovative solution to the problem of batch scheduling of the mixed flow shop, and provides powerful support for optimal scheduling in actual production scenes. Successful application of ICLSRA algorithm lays a solid foundation for research and application in similar fields in the future, and provides a feasible method for improving production efficiency and reducing cost. Overall, the successful application of ICLSRA algorithm to complex scheduling problems makes it an effective tool worthy of intensive research and widespread use.
Claims (7)
1. A method for solving batch dispatch in a distributed reentrant heterogeneous mixed flow shop is characterized by comprising the following steps,
s1, analyzing problem characteristics of batch scheduling problems of a distributed reentrant heterogeneous mixed flow shop in PCB production and manufacturing, establishing a solution target with minimum finishing time, and initializing parameters, wherein the solution target comprises a population size PS, the maximum failure times C of a current neighborhood, the maximum times Q of current cooperative failure and the maximum times A of combined failure of neighborhood search and cooperative search;
s2, initializing a population, and generating PS individuals by using a structural heuristic algorithm;
s3, in the variable neighborhood descent search stage, searching by means of a variable neighborhood descent search strategy by using five neighborhood structures, and accepting an individual with a target value smaller than that of the original individual as a new individual;
s4, in the collaborative searching stage, the beneficial information among individuals in the population is mutually exchanged by using a collaborative searching strategy, and the individuals with smaller target values than the original individuals are accepted as new individuals;
s5, in a population reconstruction stage, firstly, each individual in the population is disturbed, three individuals are generated by using three modes of sequence transposition, multipoint exchange and combination of the sequence transposition, one individual with a smaller target value in the three individuals is selected to replace the individual in the original population, and after execution, PS/2 randomly generated individuals are used to replace the worst PS/4 individuals with the target value in the population and PS/4 randomly selected individuals from the population;
and S6, updating the optimal individual, judging whether the limited maximum time is reached, ending the cycle if the limited maximum time is reached, outputting the individual with the minimum target value, otherwise, returning to S3, and executing the next searching process.
2. The method of claim 1, further characterized by each individualConsists of two parts, one part is a sorting part and is a group of F-dimensional vectors,wherein F is the total number of plants, +.>Is a factory-included->A sequence vector of the batch, representing a processing order of the first stage; in view of the re-entrant properties, the assignment to the factory +.>The batch requirement of (2) is->The occurrence of L times; the other part is a batch splitting part, which is a group of n-dimensional vectors,>where n is the total number of batches, +.>Is a lot->Is used to split the vector.
3. The method for solving a batch schedule in a distributed reentrant heterogeneous hybrid flow shop according to claim 2, further characterized by the implementation of a structured heuristic algorithm comprising the steps of,
(1) The following parameters are defined in terms of the parameters,representing a factory, & lt>Representing a factory set,/->F represents the total number of factories, ">Representing a lot, +.>Representing a collection of lots, +.>N represents the total number of batches,jrepresenting a certain stage of->Representing a set of phases->S represents the total number of stages, L represents the number of re-entrant times,>representative lot->In the factory->Is not limited, and the processing time of the device is not limited;
(2) Dividing the batch by using equal division and random division;
(3) The sum of the processing times of the batch in each factory is calculated, the calculation formula is as follows,
，
pair aggregationArranging in ascending order, collecting ++after ordering>F batches with the minimum sum of the processing time are randomly distributed to F factories, so that each factory is guaranteed to be distributed to one batch;
(4) Solving a probability of a lot being assigned to a minimum target value position in each plant using a probability formula, wherein the minimum target value position in the plant is obtained by a greedy heuristic, comprising the following process,
placing each batch in each position in each factory in turn and obtaining a target value;
comparing the target values of all the positions of each batch in each factory;
preserving the minimum target value that can be obtained in each plantAnd a position within the factory when the minimum target value is obtained;
the probability formula is given by the formula,
，
for the probability that the calculated lot is assigned to the minimum target value position in each plant, the sum of the probabilities that all plants are assigned is 1;
(5) Using roulette strategyThe lot is distributed into a factory, wherein the roulette strategy includes the following process,
creating a wheel disc, dividing a circular wheel disc into F sectors, wherein the size of each sector is proportional to the allocation probability of a corresponding factory;
performing roulette selection to generate a 0-1 random decimal, and mapping the random decimal onto a corresponding sector of the roulette;
determining an allocation result, and determining an allocated factory according to the selected sector;
(6) Determining the position of the residual L-1 in the factory by using one of greedy heuristic method and random selection method; the greedy heuristic method is operated in such a way that batches are put into corresponding factories, sequentially inserted into all positions in the factories, and finally put into the position with the minimum target value; the operation mode of the random selection mode is that the batch is put into the random position of the corresponding factory.
4. The method according to claim 3, wherein the variable neighborhood descent search stage optimizes individuals in the population by using a variable neighborhood descent search strategy having 5 neighborhood structures, generates a plurality of individuals improved by neighborhood structures for each individual, receives an improved individual having a smaller target value than the original individual as a new individual, wherein five neighborhood structures are four searches for critical factories, one performs sub-lot variation operation on sub-lots, the critical factory is a factory having the largest target value among all factories, which plays a critical role in optimizing the whole production process, the specific process of the 5 neighborhood operations is as follows,
inserting into a key factory; selecting a lot from a key plant and then randomly inserting it into another location within the same plant;
batch exchange in a key factory; randomly selecting two batches from a key factory and exchanging, wherein the selected batches are different to avoid generating invalid operation;
inserting between a critical factory and another factory; randomly selecting one lot in the key plant and then inserting it into another randomly selected plant;
batch exchange between a critical plant and another plant; randomly exchanging batches between the key plant and another randomly selected plant;
sub-batch variation: the specific operation of sub-lot variation involves selecting a lot with two or more sub-lots in a critical factory, randomly selecting two sub-lots, then generating a random integer of 1-5, subtracting the random number from one sub-lot and adding to the other sub-lot.
5. The method for solving batch scheduling in a distributed re-entrant heterogeneous mixed flow shop according to claim 1, further characterized in that the implementation process of the variable neighborhood descent search strategy is as follows, when each individual in the population is subjected to neighborhood search, the first neighborhood structure is set as the current neighborhood structure, the number of continuous update failures of the current neighborhood structure is set as zero, then, by searching using the current neighborhood structure, if the target value of the new individual is smaller than that of the original individual, the original individual is updated as the new individual, the number of continuous update failures of the current neighborhood structure is reset to zero, and then searching is continued using the current neighborhood structure; if a new individual smaller than the target value of the original individual is not obtained when the current neighborhood structure is used for searching, adding one to the continuous updating failure number of the current neighborhood structure, continuing to search by using the current neighborhood structure, taking the next neighborhood structure as the current neighborhood structure when the continuous updating failure number of the current neighborhood structure reaches the set maximum failure number C, resetting the continuous updating failure number of the current neighborhood structure to zero, and repeating the process until all the neighborhood structures cannot update the current individual, switching to the next individual until all the individuals in the population complete the searching process of all the neighbors.
6. The method according to claim 1, wherein the collaborative search strategy execution process comprises selecting an individual from a population, extracting all sequences existing in the individual, assigning the lot to a sequence, marking the lot in the sequence L times, recording the number of occurrences of the lot in the sequence, marking all the sequences sequentially, randomly selecting two different positions if the number of the sequences is greater than two, reserving the lot between the two positions and a corresponding index, selecting another different individual from the population, assigning the individual to a temporary individual, marking only the temporary individual, deleting the reserved lot and the index from the temporary individual in each sequence of the first individual, the first individual is in the sequence, resetting the corresponding temporary individual to the position of the lot, replacing the target value in the first individual by the target value in the sequence, and then comparing the number of the two temporary individuals with the target value in the sequence if the number of the temporary individual is greater than the target value in the first individual, and the number of the individual is greater than the target value in the sequence, thus, an effective synergy is performed, and if the individuals after synergy cannot replace any one of the two individuals, the synergy is failed, and the synergy is terminated if the continuous synergy failure times exceed the set value Q.
7. The method of claim 1, wherein when the maximum number of joint failure of neighborhood search and collaborative search exceeds a, performing population reconstruction, the implementation process is as follows: each individual in the population adopts sequence transposition, namely, reversing a batch sequence in a certain interval in the sequence, performing multi-point insertion, namely, inserting other positions of the sequences in a plurality of batches, and generating three disturbance individuals in a combined mode, selecting the individual with the smallest target value in the disturbance individuals to replace the individual before the disturbance is originally performed, extracting the individual with the worst target value in the PS/4 population, randomly selecting the individual in the PS/4 population, wherein the two selected individuals cannot be repeated, replacing the individual extracted in the population by the individual randomly generated by the PS/2 to finally obtain a brand new population, applying the brand new population to the next searching process, and resetting the maximum number A of joint failures of neighborhood searching and collaborative searching to zero at last.
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