CN115310832A - Multi-population optimization algorithm double-resource constraint flexible job shop scheduling method and device - Google Patents
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Abstract
The invention relates to a method and a device for scheduling a multi-population optimization algorithm based on double-resource constraint flexible job shop, which aim at the scheduling problem of the double-resource constraint multi-target flexible job shop of time and cost, namely, consider the influence of machine and worker constraints on the scheduling problem of the flexible job shop under the condition of adjusting the time and the cost. The method is characterized in that three initialization rules are provided to generate an initial population by taking the maximum completion time, the total adjustment time and the total cost as optimization targets, the population quality is continuously improved by using a designed population communication method, in addition, a clustering ordering method is provided for improving the diversity of the population, the population is normalized to a plurality of quadrants according to the distribution of solution space individuals, the distances from the individuals to an original point are calculated for screening, so that the optimization function among the populations is realized, and the problem of scheduling the double-constraint multi-target flexible job workshop considering the time and the cost can be effectively solved.
Description
Technical Field
The invention belongs to the technical field of workshop scheduling, and particularly relates to a method and a device for scheduling a multi-population optimization algorithm based on double-resource constraint flexible job workshop.
Background
In actual production, enterprises face a plurality of problems such as flexibility of machines and workers, namely the machines can process a plurality of workpieces, and the workers can operate a plurality of machines, in addition, only the processing time of the workpieces is considered in most of researches, for example, 2021, the method is mentioned in an article of 'multi-target flexible job shop scheduling research considering transportation time' published in the journal of a small microcomputer system, but neglects auxiliary time in a workshop;
the artificial factors are also important indexes influencing production, such as a double-flexible job shop scheduling problem integrating processing time, green production and human factors, published in the clean production science report in 2018, the conditions of different flexibility, skill level and use cost of workers operating machines are considered, a hybrid genetic algorithm is used for solving, a local search strategy is adopted for DRCFJSP (distributed resource computing), an improved backtracking search algorithm for solving the multi-target flexible job shop scheduling problem, published in 2021, an improved backtracking search algorithm for solving the multi-target flexible job shop scheduling problem, the flexibility of personnel of DRJSP and the condition of uncertain processing time are considered, and a heuristic method is provided for integrating Monte Carlo simulation into the provided multi-target correction backtracking search algorithm framework;
based on the above, the scheduling problem of the double-resource constraint flexible job shop considering time and cost is more in line with production practice, and in order to make scheduling research in line with production scenes, the practicability and economy of the flexible job shop need to be considered, and even if the scheduling scheme is in line with production practice, a feasible and economical scheduling scheme can be generated.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a scheduling method and a scheduling device for a multi-population optimization algorithm dual-resource constraint flexible job shop, and solves the problems that the existing scheduling method neglects the influence of artificial factors on production, and considers the labor efficiency of workers to be the same and not to be practical.
The technical purpose of the invention is realized by the following technical scheme:
the invention content part is as follows: a double-resource constraint flexible job shop scheduling method of a multi-population optimization algorithm is characterized by comprising the following steps:
s1, establishing a mathematical model, setting relevant parameters, determining a target function and constraint conditions, and taking maximum completion time, total adjustment time and total cost as optimization targets;
s2, carrying out chromosome coding and randomly initializing a population, combining offspring generated after cross mutation with a parent population, and then carrying out non-dominated sorting and clustering sorting on the combined population;
s3, selecting various groups by using the method in S2, reserving elite individuals, combining elite individuals of other groups and eliminating individuals with poor quality of the group;
and S4, after the step S3 is executed, all the individuals are merged and randomly divided into three populations, the operations of the step S2 and the step S3 are repeated, and after the iteration is finished, a Pareto front edge is found.
The invention has the beneficial effects that:
the invention considers the scheduling problem of the double-resource-constrained flexible job workshop with adjustment time, processing time, energy cost and labor cost, takes the maximum completion time, total adjustment time and total cost as research objects, mutually exchanges elite individuals in a population among the populations through a multi-population evolution algorithm, eliminates individuals with poor quality in the population, and provides a cluster ordering method to further optimize the population quality, thereby realizing the optimization function among the populations and effectively solving the scheduling problem of the double-constrained multi-target flexible job workshop considering time and cost.
Drawings
FIG. 1 is a flow chart of the MPEA algorithm of the present invention.
Fig. 2 is a DRCFJSP data diagram of three types of workers working two workpieces on three machines of the present invention.
Fig. 3 is a gantt chart of the present invention without regard to settling time.
Fig. 4 is a gantt chart in view of the adjustment time of the present invention.
FIG. 5 is a graph of the impact of adjusting time on the scheduling scheme of the present invention.
FIG. 6 is a chromosome coding map of the present invention.
FIG. 7 is a non-dominated ranking diagram of the invention.
FIG. 8 is a diagram of the cluster ranking method of the present invention.
Detailed Description
The following description of the present invention will be made in detail with reference to the accompanying drawings 1 to 8.
In this embodiment, the flexible job shop scheduling problem may be described as processing N workpieces on M machines, where each workpiece has multiple processes and the processing time varies with the processing machine of the workpiece, each process is directly sent to the next process for processing after being processed on the machine, and the process needs to consider the adjustment time caused by machine adjustment before processing. Because different proficiencies of workers on machine operation affect the processing time of a workpiece on a machine, and workers have different compensation, energy consumed in workshop production mainly consists of processing energy consumption generated in machine processing, idle energy consumption generated in machine idling and adjustment energy consumption generated in machine adjustment, and electricity and labor costs generated by energy consumption are production costs which are not negligible for enterprises, under the condition of considering machine adjustment, a proper processing machine and a proper processing sequence are selected for the workpiece and a worker operation machine are reasonably arranged when the maximum completion time and the minimum production cost are ensured, so the following assumptions are adopted in the embodiment:
(1) All machines are ready at time zero;
(2) Each procedure can only be processed on one machine at the same time, and the processing process cannot be interrupted;
(3) Different workpieces are not sequentially constrained, and the same workpiece is sequentially constrained;
(4) Only one workpiece can be processed on one machine at the present moment;
(5) The adjustment time of adjacent working procedures of the same workpiece is zero when the same machine is used for processing; on the contrary, the machine needs to be adjusted when the workpiece is processed, and the adjustment time is determined;
(6) The machine needs to consume energy for adjustment, and the machine needs to adjust according to the characteristics of a workpiece before processing the workpiece and determine the adjustment power;
(7) The processing power and standby power of each machine are known;
(8) Each worker may operate all of the machines, but their proficiency at each machine varies;
(9) The proficiency of the worker on the machine will be classified as L 1 、L 2 、L 3 Wherein the grade L 3 The most skilled worker is in the machine.
According to the assumptions presented above, the implementation steps of the present invention include the following steps:
s1, establishing a mathematical model, setting relevant parameters, determining a target function and constraint conditions, and taking maximum completion time, total adjustment time and total cost as optimization targets;
s2, carrying out chromosome coding and randomly initializing a population, combining offspring generated after cross variation with a parent population, and then executing a non-dominated sorting and clustering sorting method on the combined population;
s4, selecting various groups by using the method in S3, reserving elite individuals, combining elite individuals of other groups and eliminating individuals with poor quality of the group;
and S5, after the step S4 is executed, all the individuals are merged and randomly divided into three populations, the operations of the step S3 and the step S4 are repeated, and after the iteration is finished, a Pareto front edge is found.
In the present embodiment, the maximum completion time, the total sorting time, and the total cost are taken as optimization targets, and the objective functions are as follows:
(1) Maximum time-out C M ：
C M ＝min(max(C i ))；
Wherein, C i I is the workpiece number; i =1,2,3.. N;
(2) Total adjustment time L A ：
Wherein A is ijk The adjustment time of the j-th procedure of the workpiece i on the machine k;
(3) Total cost L C ：
L C ＝C w +C ec ；
Wherein, C W Is the labor cost C ec The electricity charge is obtained;
C W the calculation formula of (a) is as follows:
wherein, C ijks The cost of the jth process for the worker s to machine the workpiece i with the machine k;
δ ijk for decision variables, the discrimination is as follows:
C ec the calculation formula of (c) is as follows:
C ec ＝E×Q；
wherein E is the total energy consumption of the machine, and Q is the electric charge per kilowatt hour;
e is calculated as follows:
E＝E ijk +E idlek +E adk ；
wherein, E ijk Energy consumption for processing the workpiece on machine k for ith and jth process, E idlek For idle energy consumption of machine k, E adk Adjusting energy consumption for machine k;
E ijk the calculation formula of (a) is as follows:
wherein, P ijk Machining efficiency, T, of the j-th process on the machine k for the workpiece i ijk The processing time of the jth procedure of the workpiece i on the machine k;
E idlek the calculation formula of (a) is as follows:
wherein, P idlek Is the idle power, T, of machine k ijk Is the idle time of machine k;
E ad the calculation formula of (a) is as follows:
wherein, P Aijk And adjusting the power of the j process of the workpiece i on the machine k.
The DRCFJSP constraint is as follows:
the current working procedure can only be processed on one machine;
S ijk +A ijk +T ijk ≤E ijk +M(1-δ ijk )；
wherein S is ijk The starting processing time of the ith and jth processes of the workpiece on the machine k, M is an infinite value, and each machine can only process one process at the same time;
the finishing time of the process is the sum of the adjusting time and the processing time of the process, namely, no fault occurs in the adjusting and processing processes to influence the normal operation.
To describe the problems presented therein, an example of DRCFJSP is given for three types of workers working two workpieces on three machines with reference to fig. 2, the first column representing the workpieces, the second column representing the processes of the workpieces, the third column representing the processing machines selectable for each process of the workpieces, the fourth column representing the labor costs and energy costs required for the processes working the workpieces, and the fifth column representing the processing times and adjustment times for the workers operating the machines to process the workpieces, where W is the processing time and adjustment time for the workers operating the machines to process the workpieces ijk Indicating that the worker i is proficient at operating the machine k at a level j, e.g. W 123 Indicating that the worker 1 has a proficiency level L in operating the machine 3 2 Taking the problem of fig. 2 as an example, fig. 3 shows a gantt chart without considering the adjustment time, fig. 4 shows a gantt chart with considering the adjustment of the actual gantt chart, the upper and lower dark regions are the adjustment times of the machine when processing the workpiece, and fig. 5 is a comparison of whether the adjustment times generate the scheduling scheme;
it can be seen from fig. 5 that the adjustment time is 16.1% of the scheduling time without consideration of the adjustment time, which is different from the maximum completion time without consideration of the adjustment time by 1.9 time units. The total cost differs by 3.17 cost units and is 13.63% of the total cost without regard to the adjusted time schedule. Therefore, in actual production, the influence of the adjusted time on the scheduling system cannot be ignored, and the feasibility of the produced scheduling scheme is very poor if the adjusted time is not considered.
In step S2 in this embodiment, the problem needs to be converted into a language that can be identified by a computer for encoding, and the DRCFJSP includes three sub-problems, namely, a machine selection problem, a process ordering problem, and a personnel allocation problem, taking the problem in fig. 2 as an example, the left side in fig. 6 is a set of processing processes of each workpiece and processing machines selectable for each process, and the right side is a chromosome encoding and encoding result;
wherein the machine selects the segment: this section represents the processing machine selected for each process, J from left to right 1 To J 2 The processing machine selected for each process, the machine selection results are determined in the chromosome coding result map of fig. 6;
procedure sequencing section: the segment represents the sequence of the processing of each procedure, the number i of the occurrences of the integers represents the ith procedure of the workpiece, and the sequencing result of the procedures can be determined in a chromosome coding result graph;
worker distribution section: the segment represents the worker type selected by each machine, and the worker type selected by each machine is represented from left to right, and the result can be determined in the chromosome coding result graph;
in the present embodiment, the decoding method employs plug-in decoding.
After encoding and decoding are completed, initialization, crossover and variation are required, wherein the initialization is the key for determining population quality, and three initialization rules are provided in the embodiment for maintaining diversity of a solution space;
a random generation method: the machine selection, the procedure sequencing and the worker distribution segment chromosomes are all generated in a random generation mode;
the minimum time method of first processing: the machine selection section is determined by selecting the machine with the shortest processing time from the selectable machine set in the working procedure, and the working procedure selection section and the worker distribution section are generated by adopting a random method;
the method for maximizing the residual processing time comprises the following steps: namely, the procedure sequencing section is determined by selecting the operation with the largest remaining total processing time during current sequencing, and machine allocation and procedure sequencing are generated by adopting a random method;
the parent generation realizes information exchange through cross operation to generate offspring, the offspring is arranged according to the parent gene information in a certain rule, so that individuals with better quality are generated, and similarly, the individuals generate a new combination mode through a variation mode to ensure the diversity of a scheduling scheme;
then, combining the offspring generated after cross mutation with the parent population, and then executing a non-dominated sorting method and a clustering sorting method on the combined population;
in this embodiment, the non-dominant ranking method is as follows:
(1) Finding out the individuals of non-dominant solution in the group, namely rank i =0, put it into the set F 1 Performing the following steps;
(2) Finding a set S dominated by each individual in the set i Is reduced by 1, i.e. rank l ＝rank l -1, if 0, stored in set H;
(3) Carrying out the operations of the steps (1) and (2) on the set H until all individuals are layered;
referring to FIG. 7, the non-dominant post-sort selection F 1 As a new parent P 1 If the population P 1 If the number of individuals is less than the initial population N, selecting the sorting grade as F 2 The individual continues to move to the population P 1 Filling until filling grade F m If the population size exceeds N after the individual, then F m The individuals in (1) are subjected to a clustering and sorting method.
In this embodiment, the purpose of the cluster ranking method is to discard the rank F m S individuals with poor quality in the population are shown in the figure 8 by taking the binocular standard problem as an example, and the left part in the figure is the population F m Projection in space, to ensure diversity of the population, peer F m In a subject of [ -1,1]Carrying out normalization processing inside to obtain the right part in the graph, and selecting m closer individuals according to the distances from the individuals to the origin;
the clustering sorting method comprises the following specific steps:
(1) Setting a parameter n =1;
(2) Performing normalization processing on the non-dominated sorted populations in the corresponding dimension space according to the number of research targets;
(3) Judging with R n Whether the number of individuals in the space enclosed by the circle or the ball drawn by the radius is less than a set value m or not, if so, executing R n+1 ＝R n +h n- ；
(4) Calculating the distance from the individual to the origin in the circle or sphere space;
(5) Arranging the individuals from small to large according to the distance l from the individuals to the origin, and discarding the individuals with larger distance;
(6) Repeating the steps from (2) to (5) until m individuals exist in the circle or the sphere;
wherein the content of the first and second substances,
the distance from the individual i to the origin,
The space for expansion is smaller and smaller; l i ＝{l 1 ,l 2 ...l n Is radius R i The distance from the enclosed space to the origin; r 1 Is the average of the maximum and minimum distances to the origin after normalization.
And then, selecting various groups by using the method, reserving elite individuals, combining elite individuals of other groups, eliminating individuals with poor quality of the group, combining all the individuals into three groups randomly after population information exchange, repeating the operation, and finding a Pareto frontier after iteration is completed.
Preset, an embodiment of the present invention further provides a workshop scheduling apparatus, which includes a processor, a memory, and corresponding modules for implementing the steps of any one of the workshop scheduling methods described above, and is configured to implement operations of all the steps in the workshop scheduling method described above.
It should be noted that the apparatus is an apparatus corresponding to the individual recommendation method, and all implementation manners in the method embodiments are applicable to the embodiment of the apparatus, and the same technical effect can be achieved.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (9)
1. A double-resource constraint flexible job shop scheduling method of a multi-population optimization algorithm is characterized by comprising the following steps:
s1, establishing a mathematical model, setting relevant parameters, determining a target function and constraint conditions, and taking maximum completion time, total adjustment time and total cost as optimization targets;
s2, carrying out chromosome coding and randomly initializing a population, combining offspring generated after cross variation with a parent population, and then executing a non-dominated sorting and clustering sorting method on the combined population;
s3, selecting various groups by using the method in S2, reserving elite individuals, combining elite individuals of other groups and eliminating individuals with poor quality of the group;
and S4, after the step S3 is executed, all the individuals are merged and randomly divided into three populations, the operations of the step S2 and the step S3 are repeated, and after the iteration is finished, a Pareto front edge is found.
2. The multi-population optimization algorithm double-resource constraint flexible job shop scheduling method according to claim 1, wherein the objective function in S2 is as follows:
(1) Maximum time-out C M ：
C M ＝min(max(C i ))；
Wherein, C i I is the completion time of the workpiece, i is the workpiece number; i =1,2,3.., n;
(2) Total adjustment time L A ：
Wherein A is ijk The adjustment time of the j-th procedure of the workpiece i on the machine k;
(3) Total cost L C ：
L C ＝C w +C ec ；
Wherein, C w Cost of labor, C ec The electricity charge is obtained;
C w the calculation formula of (a) is as follows:
wherein, C ijks The cost of the jth process for the worker s to machine the workpiece i with the machine k;
δ ijk for decision variables, the discrimination is as follows:
C ec the calculation formula of (a) is as follows:
C ec ＝E×Q；
wherein E is the total energy consumption of the machine, and Q is the electricity charge per kilowatt hour;
e is calculated as follows:
E＝E ijk +E idlek +E adk ；
wherein, E ijk Energy consumption for processing the workpiece i on the machine k for the j-th process step, E idlek For idle energy consumption of machine k, E adk Adjusting energy consumption for machine k;
E ijk the calculation formula of (a) is as follows:
wherein, P ijk Machining efficiency, T, of the j-th process on the machine k for the workpiece i ijk The processing time of the j-th procedure of the workpiece i on the machine k is;
E idlek the calculation formula of (a) is as follows:
wherein, P idlek Is the idle power, T, of machine k idlek Is the idle time of machine k;
E ad the calculation formula of (c) is as follows:
wherein, P Aijk And adjusting the power of the j-th procedure of the workpiece i on the machine k.
3. The multi-population optimization algorithm double-resource constraint flexible job shop scheduling method according to claim 2, wherein the constraint conditions are as follows:
the current working procedure can only be processed on one machine;
S ijk +A ijk +T ijk ≤E ijk +M(1-δ ijk )；
wherein S is ijk The starting processing time of the jth procedure of the workpiece i on the machine k, M is an infinite value, and each machine can only process one procedure at the same time;
the completion time of the process is the sum of the adjustment time and the machining time of the process.
4. The method for scheduling a multi-population optimization algorithm based on dual resource constraints as claimed in claim 1, wherein the step S2 further comprises:
s2-1, selecting machines, arranging processes and distributing segment chromosomes to workers by using a random generation method, determining a machine selection segment by selecting a machine with the shortest processing time from a selectable machine set by using a minimum processing time method, and determining a process sequencing segment by selecting an operation with the largest remaining total processing time when sequencing is performed currently by using a maximum remaining processing time method, wherein the power selection segment and worker distribution, the machine distribution and the process sequencing are all generated by using a random method;
s2-2, carrying out chromosome crossing by adopting a multipoint crossing method, and carrying out chromosome variation by adopting a multipoint variation and random transformation method;
and S2-3, combining the filial generation and the parent population generated after the cross mutation, and then executing a non-dominated sorting and clustering sorting method on the combined population.
5. The method of multi-population optimization algorithm for dual resource constrained flexible job shop scheduling according to claim 4, wherein said step of non-dominated sorting comprises:
step S2-3-1-1, finding out individual non-dominant solution, namely rank in population i =0, put it into the set F 1 The preparation method comprises the following steps of (1) performing;
step S2-3-1-2, finding F 1 Set S governed by each individual in the set i Is reduced by 1, i.e. rank l ＝rank l -1, if 0, stored in set H;
and step S2-3-1-3, performing the operations of steps S2-3-1-1 and S2-3-1-2 on the set H until all individuals are layered.
6. The method for scheduling the multi-population optimization algorithm based on the dual-resource constraint flexible job shop, according to claim 5, wherein F is selected after the non-dominated sorting 1 As a new parent P 1 If the population P 1 If the number of individuals is less than the initial population N, selecting the sorting grade as F 2 Personal relayContinued population P 1 Filling up to a filling level F m If the population size exceeds N after the individual, the pair F m The individuals in (1) are subjected to a clustering ranking method.
7. The multi-population optimization algorithm double-resource-constrained flexible job shop scheduling method according to claim 6, wherein the clustering ordering method comprises the following steps:
step S2-3-2-1, setting a parameter n =1;
s2-3-2-2, performing normalization processing on the non-dominated sorted population in a corresponding dimension space according to the number of research targets;
step S2-3-2-3, judging with R n Whether the number of individuals in the space enclosed by the circle or the ball drawn by the radius is less than a set value m or not, if so, executing R n+1 ＝R n +h n- ；
S2-3-2-4, calculating the distance l from the individual to the origin in the circle or sphere space i ；
S2-3-2-5, arranging the individuals from small to large according to the distances l from the individuals to the origin, and discarding the individuals with larger distances;
s2-3-2-6, repeating the steps from S2-3-2-2 to S2-3-2-5 until m individuals exist in the circle or the sphere;
wherein the content of the first and second substances,
the distance from the individual i to the origin,
The space for expansion is smaller and smaller; l. the i ＝{l 1 ,l 2 ,...l n Is the radius R i The distance from the enclosed space to the origin; r 1 Is the average of the maximum and minimum distances to the origin after normalization.
8. The method for scheduling a multi-population optimization algorithm based on dual resource constraints flexible job shop according to claim 1, wherein the decoding in step S2 is performed by using a plug-in decoding method.
9. A flexible job shop scheduling device comprising a processor, a memory and corresponding modules for implementing the steps of the shop scheduling method according to any one of claims 1 to 8.
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