CN115169798A - Distributed flexible job shop scheduling method and system with preparation time - Google Patents
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Abstract
The invention discloses a method and a system for dispatching a distributed flexible job shop with preparation time. The invention adopts a procedure-machine-workshop three-layer coding mode; improving the population initialization and population updating modes; simultaneously introducing cross variation of a genetic algorithm and a Metropolis criterion of a simulated annealing algorithm to improve the global search capability of the algorithm; a three-layer variable neighborhood structure of a process, a machine and a workshop is designed, and the local search capability of the algorithm is improved. The mixed sparrow algorithm improves the efficiency and quality of the solution convergence in the evolution process.
Description
Technical Field
The invention belongs to the technical field of distributed flexible job shop scheduling, relates to a distributed flexible job shop scheduling method and system, and particularly relates to a mixed sparrow algorithm-based distributed flexible job shop scheduling method with preparation time and a system.
Background
With the increasing globalization trend, the market changes frequently, new technologies emerge continuously, and the number of competitors increases dramatically worldwide. Distributed production is developed, and the distributed production can enable enterprises to be closer to clients and suppliers, more effectively produce and sell products, quickly cope with market changes, reduce management difficulty and risk, save cost and improve resource utilization rate.
The distributed flexible operation workshop mainly relates to three subproblems, namely, a workshop to which workpieces are distributed, how to sequence the work procedures of the workpieces in each workshop, and which machine is selected for each work procedure. The distributed flexible job shop is also an NP-hard problem, since the flexible job shop scheduling problem has proven to be an NP-hard problem. The problem of dispatching of the distributed flexible job shop is solved, and an efficient intelligent optimization algorithm is needed.
There are several situations in a distributed plant: for a factory, two categories exist, namely isomorphic workshops, and the production environment of all workshops is completely the same; the production environments of the heterogeneous workshops and the workshops are not completely the same. For the machining of workpieces, there are two possibilities, namely that all the processes of the workpiece are machined in the same workshop; or the workpiece may be processed in a different shop. For a machine, the method can be divided into a same-speed parallel machine and a different-speed parallel machine.
The scholars at home and abroad aim at the distributed flexible job shops under different conditions to improve the solving speed, precision and quality by improving the hybrid intelligent optimization algorithm. Such as: INSGAII, GOGA, GA-TS \8230.
The sparrow algorithm has good capability of balancing global search and local search by simulating the foraging behavior and the anti-predation behavior of sparrows. The algorithm can well integrate the characteristics of the population, so that the population approaches to the global optimal solution.
The simulated annealing algorithm has the advantages that the local optimal solution can be well jumped out in the early stage of the algorithm, so that the search range is larger; the genetic algorithm has the advantage of strong global search capability. The two algorithms can be well fused with other algorithms to complete population evolution.
Disclosure of Invention
The method aims at the characteristics of low efficiency, poor solution set quality and the like of the existing algorithm for solving the distributed flexible job shop. The invention provides a hybrid sparrow algorithm-based distributed flexible job shop scheduling method and system with preparation time, which meet the preparation time constraint, simultaneously design a three-layer field structure, integrate a simulated annealing algorithm and a genetic algorithm and improve the performance of a sparrow algorithm.
The method adopts the technical scheme that: a distributed flexible job shop scheduling method with preparation time comprises the following steps:
step 1: constructing a distributed flexible job shop scheduling model with preparation time, wherein the model comprises maximum completion time, maximum carbon emission, maximum delay time and constraint conditions;
the maximum completion time is:
min C max ＝max(C i ),i∈[1,n]；
the maximum carbon emission is as follows:
the maximum delay time is:
min L max ＝max{|C i -G i |Z i l },i∈[1,n]；
the constraint conditions are as follows:
in the above formulas, n is the number of workpieces, i is the workpiece number, C i Finishing time for workpiece i; j is the process number, l is the workshop number, k is the machine number, q is the workshop number, m l As to the number of machines in the plant,
the processing time of the jth procedure of the workpiece i on the kth machine in the workshop is shown,
preparing time of a jth procedure of a workpiece i in a workshop l;
if it is not
Then the first of the workpiece ij processes are processed in a workshop l; if not, then the mobile terminal can be switched to the normal mode,
if it is used
The jth procedure of the workpiece i is processed by a kth machine in a workshop; if not, then,
TC is the total carbon emission of all machines, EF is the conversion coefficient of processing time and energy consumption, CEF is the conversion coefficient of energy consumption and carbon emission, L max Maximum delay time for all workpieces, C max Maximum completion time for all workpieces; g i A planned completion time for workpiece i;
if it is not
The completion time of the workpiece i is greater than the planned completion time; if not, then the mobile terminal can be switched to the normal mode,
the beginning time of the jth procedure of the workpiece i on the kth machine of the workshop I,
the processing end time of the jth procedure of the workpiece i on the kth machine in the workshop is set; i is an infinite number; e is a workpiece marked with the reference number e, f is the f-th process of the workpiece e, P e The total number of processes of the workpiece e;
step 2: subjecting the mixture obtained in step 1
n、q、m l 、
EF、CEF、G i Inputting the number of processes of each workpiece, the discoverer proportion of the sparrow algorithm and the alerter proportion into the mixed sparrow algorithm; and (3) performing iterative calculation according to the constraints and the objective function established in the step (1) until the iteration times are reached, and outputting a section of approximately optimal process sequence as an optimal scheduling scheme. The method specifically comprises the following substeps:
step 2.1: initializing population size, determining maximum iteration times and proportion of finders and cautionars of sparrow algorithm, and defining step 1
n、q、m l 、
EF、CEF、G i And the number of processes of each workpiece, thereby initializing a sparrow population;
step 2.2: calculating the fitness value of each sparrow individual;
step 2.3: performing non-inferior ranking on the initial sparrow population, wherein n grades are provided in total;
step 2.4: calculating the crowding value of each sparrow individual in each grade;
step 2.5: the sparrow populations are sorted according to the grades firstly and then sorted according to the crowding degree; according to the sorting result, the first N% of individuals are set as discoverers, and the rest individuals are followers; wherein N is a preset value;
step 2.6: the finder and the follower are updated, and the updated solution is subjected to inter-vehicle layer variable neighborhood search, process layer variable neighborhood search and machine layer variable neighborhood search in sequence to become a new solution; if the new solution dominates the old solution, the new solution is accepted with a certain probability, and the acceptance probability is increased along with the increase of the iteration times; if the old solution dominates the new solution, the new solution is not accepted; if the new solution and the old solution are not mutually independent, the new solution is accepted with a probability of 50%;
step 2.7: respectively randomly extracting 10% of the updated discoverer and the updated follower to become an alarmer, and updating; after updating, carrying out cross mutation; deleting the extracted individuals from the finder and the follower;
step 2.8: combining the updated discoverer, the follower and the alerter together to form a new population; judging whether the current algebra is larger than the maximum iteration number, if so, outputting a section of approximately optimal procedure sequence; otherwise, the slew performs step 2.2.
The technical scheme adopted by the system of the invention is as follows: a distributed flexible job shop scheduling system with preparation time comprises the following modules:
the system comprises a module 1, a module and a module, wherein the module 1 is used for constructing a distributed flexible job shop scheduling model with preparation time, and comprises maximum completion time, maximum carbon emission, maximum delay time and constraint conditions;
the maximum completion time is:
min C max ＝max(C i ),i∈[1,n]；
the maximum carbon emission is:
the maximum delay time is:
the constraint conditions are as follows:
in the above formulas, n is the number of workpieces, i is the workpiece number, C i The finishing time of the workpiece i; j is the process number, l is the workshop number, k is the machine number, q is the workshop number, m l As to the number of machines in the plant,
the processing time of the jth procedure of the workpiece i on the kth machine in the workshop is shown,
preparing time of a jth procedure of a workpiece i in a workshop l;
if it is not
The jth procedure of the workpiece i is processed in the workshop l; if not, then,
if it is not
The jth procedure of the workpiece i is processed by a kth machine in a workshop; if not, then the mobile terminal can be switched to the normal mode,
TC is the total carbon emission of all machines, EF is the conversion coefficient of processing time and energy consumption, CEF is the conversion coefficient of energy consumption and carbon emission, L max Maximum delay time for all workpieces, C max Maximum completion time for all workpieces; g i A planned completion time for workpiece i;
if it is used
The completion time of the workpiece i is greater than the planned completion time; if not, then the mobile terminal can be switched to the normal mode,
the beginning time of the jth procedure of the workpiece i on the kth machine of the workshop,
the processing end time of the jth procedure of the workpiece i on the kth machine in the workshop is set; i is an infinite number; e is a workpiece marked with the reference number e, f is the f-th process of the workpiece e, P e For the assembly of work eOrdinal number;
module 2.1, initializing population size, determining maximum iteration number and sparrow algorithm finder to alert ratio, and defining module 1
n、q、m l 、
EF、CEF、G i The number of the processes of each workpiece is calculated, so that a sparrow population is initialized;
a module 2.2 for calculating the fitness value of each sparrow individual;
a module 2.3, for performing non-inferior ranking on the initial sparrow population, wherein n grades are provided;
a module 2.4 for calculating the crowding value of sparrow individuals in each rank;
the module 2.5 is used for sorting sparrow populations according to the grades and the crowdedness; according to the sorting result, the first N% of individuals are set as discoverers, and the rest individuals are followers; wherein N is a preset value;
the module 2.6 is used for updating the finder and the follower, and sequentially performing inter-vehicle layer variable neighborhood search, process layer variable neighborhood search and machine layer variable neighborhood search on the updated solution to form a new solution; if the new solution dominates the old solution, the new solution is accepted with a certain probability, and the acceptance probability is increased along with the increase of the iteration times; if the old solution dominates the new solution, the new solution is not accepted; if the new solution and the old solution are not mutually dominant, the new solution is accepted with the probability of 50 percent;
a module 2.7, which is used for randomly drawing 10% of the updated discoverer and the updated follower respectively to become an alert person for updating; after updating, carrying out cross mutation; deleting the extracted individuals from the finder and the follower;
a module 2.8, which is used for combining the updated discoverer, the follower and the alert together to form a new population; judging whether the current algebra is larger than the maximum iteration times, if so, outputting a section of approximately optimal procedure sequence; otherwise, the execution module 2.2 is turned around.
The invention has the advantages that:
(1) Aiming at a distributed flexible job shop model and a three-layer coding mode, the solution set space is huge, the Metropolis criterion and the cross variation strategy are adopted, and the global searching capability of the algorithm is improved;
(2) A three-layer variable neighborhood structure is designed, so that the local searching capability of the algorithm is greatly enhanced;
(3) The use of multiple hybrid initialization strategies improves population quality.
Drawings
FIG. 1 is a flow chart of a method of an embodiment of the present invention;
FIG. 2 is a Gantt chart of two factories obtained by solving an arithmetic example through a mixed sparrow algorithm in the embodiment of the invention;
FIG. 3 is a Gantt chart of three factories obtained by solving an arithmetic example through a mixed sparrow algorithm in the embodiment of the invention;
FIG. 4 is a spatial distribution of solution sets over 10 examples for the hybrid sparrow algorithm and 4 comparison algorithms in an embodiment of the present invention;
FIG. 5 is an IGD three-dimensional box plot of a solution set solved on 10 examples by a hybrid sparrow algorithm and 4 comparison algorithms in an embodiment of the present invention.
Detailed Description
In order to facilitate the understanding and implementation of the present invention for those of ordinary skill in the art, the present invention is further described in detail with reference to the accompanying drawings and examples, it is to be understood that the embodiments described herein are merely illustrative and explanatory of the present invention and are not restrictive thereof.
Referring to fig. 1, the method for scheduling a distributed flexible job shop with preparation time provided by the present invention includes the following steps:
step 1: constructing a distributed flexible job shop scheduling model with preparation time;
step 1.1: making necessary assumptions by a distributed flexible job shop scheduling model with preparation time;
step 1.2: setting related parameters;
step 1.3: setting a constraint condition;
step 1.4: determining an objective function;
step 2: designing and realizing a hybrid sparrow algorithm;
step 2.1: encoding and decoding of the population individuals;
step 2.2: a population initialization mode;
step 2.3: calculating the fitness of each individual, and performing non-inferior sorting and crowding calculation on the initial population by using a Pareto method and sorting;
step 2.4: according to the sorting result, the first 20 percent of individuals are set as discoverers, and the rest individuals are followers;
step 2.5: the finder and the follower update according to different formulas, three-layer variable neighborhood search is carried out on the updated solution to form a new solution, if the new solution dominates the old solution, the new solution is accepted with a certain probability, and the acceptance probability is increased along with the increase of the iteration times; if the old solution dominates the new solution, the new solution is not accepted; if the new solution and the old solution are not mutually independent, the new solution is accepted with a probability of 50%;
step 2.6: respectively randomly extracting 10% of the updated finder and follower to become the alert person, updating, and performing cross variation after updating; the extracted individuals are deleted from the finder and the follower.
Step 2.7: combining the updated finder, follower and alerter together to form a new population; and judging whether the current algebra is larger than the maximum iteration number, if so, outputting a result, and otherwise, circulating for 2.3-2.6.
The preparation time distribution-considered flexible job shop scheduling model constructed by the invention makes the following assumptions:
(1) The workpieces may be selected for processing in different workshops, and once assigned to a certain workshop, all the processes of the workpiece must be processed in the workshop.
(2) Each process of each workpiece has at least one machine for selection.
(3) The processing routes of different workpieces are different, and different procedures of the same workpiece are constrained by a processing sequence.
(4) All the first working procedures of the workpieces and the first machining procedure of the machine can be machined from zero time.
(5) Each machine in each factory can only process one workpiece at a time.
(6) The same workpiece can only be machined on one machine at the same time.
(7) Only the carbon emissions produced by the machine during the processing phase are taken into account.
(8) Each plant can process any workpiece. The machine performance within each plant is not the same. Each shop can process any workpiece. The machine performance within each plant is not the same.
(9) Once the workpiece is machined, it cannot be stopped.
(10) Regardless of transit time, assistance time, etc.
The parameters of the scheduling model of the distributed flexible job shop taking the preparation time into consideration are set as follows: n is the number of workpieces;
q is the number of workshops;
i, numbering the workpieces;
j is the process number;
l, numbering the workshop;
k: machine numbering;
e: a workpiece labeled e;
f: f, the f process of the workpiece e;
P e : the total number of processes for workpiece e;
m l : workshopThe number of machines of (a);
J i an i-th workpiece;
p i workpiece J i The number of steps of (2);
i: an infinite number;
O ij the jth procedure of a workpiece i;
F l the first workshop;
M lk the kth machine in the workshop l;
M l the number of machines in the plant l;
MS l a set of machines in a shop floor;
M ij optional machine set of the jth procedure of the workpiece i;
EF is the conversion coefficient of processing time and energy consumption;
CEF is energy consumption conversion and carbon emission conversion coefficient;
C i finishing time of a workpiece i;
G i planned completion time of a workpiece i;
L i delay time of workpiece i;
L max maximum delay time for all workpieces;
C max maximum completion time for all workpieces;
TC: total carbon emissions of all machines;
the constraint conditions of the distributed flexible job shop scheduling model considering the preparation time are set as follows:
at the same time, the workpiece can only be processed on one machine, and the formula is as follows:
during the processing of the workpiece, the interruption of the processing is not allowed to occur, and the formula is as follows:
the workpiece has sequence requirements in the machining process, and each procedure has preparation time before machining, and the formula is as follows:
once a workpiece is assigned to a plant, all of its processes must be processed in that plant, with the following formula:
the first procedure of the workpiece, the first procedure of the machine and a factory can start processing from zero time, and the formula is as follows:
the same machine of the same factory can only process one procedure at the same time, and the formula is as follows:
the objective function of the scheduling model of the distributed flexible job shop considering the preparation time is set as follows:
minimum maximum completion time:
min C max ＝max(C i ),i∈[1,n]，
minimum maximum carbon emission:
minimum maximum pull-out period:
the mixed sparrow algorithm is realized by the following steps:
initializing parameters including population scale, maximum iteration times of the algorithm, the number of workshops, the ratio of discoverers in the sparrow algorithm, the ratio of followers and the ratio of cautionars;
wherein the population size is set to 100; the number of workshops is set to 2 and 3; the maximum number of iterations is set to 200; the finder ratio is set to 20%; the proportion of the alert is set as 10 percent;
the first step is as follows: the method comprises the steps of constructing a structural body, wherein the structural body has 6 attributes, namely Position, cost, dominatecount, domination set, rank and CrowdingDistance, and sequentially represents a process sequence, a target value, the number of dominant solutions, a set of dominant solutions, a grade level and a crowding degree.
The second step: firstly, determining the number of workpieces, the number of processes of each workpiece, the number of workshops and the number of machines of each workshop, and initializing a sparrow population; secondly, calculating 6 attribute values of each sparrow individual according to the constraint and the objective function constructed in the step 1; and finally, sorting the sparrow populations according to the grade and crowding degree of each sparrow individual.
The third step: firstly, dividing the sparrow population into discoverers and followers according to a set discoverer proportion, wherein an updating formula of the discoverers is as follows:
wherein
Represents the ith finder in the population of t generations, and alpha is [0.1 ]]A random number; iter (R) max Is the maximum iteration number; r 2 Is a warning value (R) 2 ∈[0,1][, ST is a safety value (ST ∈ [0.5.1 ]][; q is a random number following a normal distribution; l is a 1xd matrix, where each element is 1.
The follower update formula is as follows:
wherein
Representing the ith follower in the population of the t generation; n represents the total number of followers in the current population;
representing the best location found by the current finder;
represents the worst individual in the contemporary population; a is a 1xd matrix, where each element is randomly assigned a value of 1 or-1.
Secondly, the discoverer and the follower respectively carry out variable neighborhood search of workshops, processes and machine parts. Selecting a workshop with the largest completion time as a key workshop, taking out any workpiece in the key workshop and putting the workpiece into other workshops to complete the variable neighborhood search of the workshop part; secondly, selecting the longest process section from the scheduling scheme of each workshop, wherein the process section is continuous in time and the process of section ending is the last process, the selected process set is used as a key path, the key path is divided into a plurality of key process blocks, the first process block only exchanges the first two processes, the ending process block only exchanges the last two processes, and the first two processes and the ending process blocks of the rest process blocks are exchanged; and finally, each procedure sequentially traverses different machines aiming at the selectable machine set.
Then, an elite selection strategy is adopted: if the new solution dominates the old solution, the new solution is accepted with a certain probability, and the acceptance probability is increased along with the increase of the iteration times; if the old solution dominates the new solution, the new solution is not accepted; if the new solution and the old solution are not dominant, the new solution is accepted with a probability of 50%.
And finally, randomly extracting 10% of individuals from the discoverer and the follower according to the proportion of the alert, forming the alert, and deleting the selected individuals from the discoverer and the follower, wherein the alert updating formula is as follows:
wherein
Representing the ith alerter in the t generation population;
represents the best individual in the contemporary population; f. of g ,f w Respectively representing the best and worst fitness values in the contemporary population; f. of i A fitness value representing the ith alertness; ε is a small constant, avoiding the denominator being 0; beta is a step size control parameter and is a random number which follows a standard normal distribution. K represents [ -1,1]The random number represents the moving direction of the sparrows and is also a step size control parameter.
The updated alerter adopts PMX crossover operator in the process layer and UC crossover operator in the machine layer and the inter-vehicle layer in the crossover stage; in the mutation stage, gaussian mutation operators are adopted in the three layers. And combining the updated discoverer, follower and alertor into a new sparrow population to replace the original sparrow population.
The fourth step: and judging whether the iteration times are greater than the total iteration times, if so, terminating the cycle and outputting an approximate optimal procedure sequence, otherwise, cycling the third step.
The hybrid sparrow algorithm designed by the invention comprises the following steps:
(1) The invention adopts an OPS three-layer coding mode, namely a process layer, a machine layer and an inter-vehicle layer, and an individual code is the process layer, the machine layer and the inter-vehicle layer. Each layer length is D.
(2) The initialization strategy adopted by the invention is as follows: 30% of individuals are randomly generated, 30% of individuals are generated by adopting an SPT scheduling rule, and the rest 40% of individuals are generated by adopting a chaotic mapping initialization strategy.
(3) The three-layer variable neighborhood searching process adopted by the invention is as follows: firstly, selecting key workshops (the workshop with the largest completion time [, taking out any workpiece in the key workshop and placing the workpiece in other workshops to complete the variable neighborhood search of the workshop part), secondly, selecting the longest process section from the scheduling scheme of each workshop, wherein the process section must be continuous in time and the section-end process is the last process, the selected process set is used as a key path, and dividing the key path into a plurality of key process blocks, the first process block only exchanges the first two processes of the blocks, the last process block only exchanges the last two processes of the blocks, the first and last processes of the rest processes are exchanged, and finally, each process sequentially traverses different machines aiming at the selectable machine set.
(4) In the crossing stage, a working procedure layer adopts a PMX crossing operator, and a machine layer and an inter-vehicle layer adopt a UC crossing operator; in the mutation stage, gaussian mutation operators are adopted in all three layers.
(5) The method adopts the Metropolis criterion, the new solution replaces the old solution with a certain probability after the discoverer and the follower are updated, and the probability is increased as the iteration times of the followers are increased.
In order to verify the effectiveness of the algorithm, 10 examples, 3 indexes and 4 comparison algorithms are selected, wherein the 10 examples are all extension examples of Brandumart standard examples, the 4 indexes are IGD, SP and GD, and the 4 algorithms are respectively NSGAII, MOPSO, IGWO and SCA.
Table 1 records the hybrid sparrow algorithm (HSSA [ and IGD values for 4 comparative algorithms, denoted HSSA by A1, NSGAII by A2, MOPSO by A3, IGWO by A4, SCA by A5;
TABLE 1
Table 2 records the SP values of the hybrid sparrow algorithm (HSSA [ and 4 comparative algorithms;
TABLE 2
Table 3 records the GD values for the hybrid sparrow algorithm (HSSA [ and 4 comparative algorithms;
TABLE 3
It can be seen from table 1 that the IGD values obtained by the hybrid sparrow algorithm in the solution of 10 examples are smaller, and it can be seen from fig. 5 that the IGD values obtained by the hybrid sparrow algorithm are more uniformly distributed. This shows that the hybrid sparrow algorithm solves the solution set to obtain high comprehensive quality.
It can be seen from table 2 that the SP value obtained by solving 10 examples by the mixed sparrow algorithm is basically minimum, which indicates that the spatial diversity of the solution set obtained by the mixed sparrow algorithm is higher.
It can be seen from table 3 that the mixed sparrow algorithm obtains smaller GD in solving 10 examples, which indicates that the solution set obtained by the mixed sparrow algorithm has better convergence.
FIG. 2 shows a Gantt chart corresponding to the optimal value of the HSSA solution j30c11m15-2 example. FIG. 3 shows a Gantt chart corresponding to the optimal solution of the HSSA solution j30c11m15-3 example. Fig. 4 shows the spatial distribution of the optimal solution set under the condition of solving 10 calculation examples of HSSA, NSGAII, MOPSO, IGWO and SCA, and the superiority and the validity of HSSA in solving the DFJSP problem are verified because the maximum completion time, the maximum carbon emission and the lag period selected by the patent are all smaller and more superior.
It should be understood that the above description of the preferred embodiments is illustrative, and not restrictive, and that various changes and modifications may be made therein by those skilled in the art without departing from the scope of the invention as defined in the appended claims.
Claims (6)
1. A distributed flexible job shop scheduling method with preparation time is characterized by comprising the following steps:
step 1: constructing a distributed flexible job shop scheduling model with preparation time, wherein the model comprises maximum completion time, maximum carbon emission, maximum delay time and constraint conditions;
the maximum completion time is:
minC max ＝max(C i ),i∈[1,n]；
the maximum carbon emission is as follows:
the maximum delay time is:
the constraint conditions are as follows:
in the above formulas, n is the number of workpieces, i is the workpiece number, C i Finishing time for workpiece i; j is the process number, l is the workshop number, k is the machine number, q is the workshop number, m l The number of machines in the plant room is,
the processing time of the jth procedure of the workpiece i on the kth machine in the workshop is shown,
preparing time of a jth procedure of a workpiece i in a workshop l;
if it is not
The jth procedure of the workpiece i is processed in a workshop l; if not, then,
if it is used
The jth procedure of the workpiece i is processed by a kth machine in a workshop; if not, then,
TC is the total carbon emission of all machines, EF is the conversion coefficient of processing time and energy consumption, CEF is the conversion coefficient of energy consumption and carbon emission, L max Maximum delay time for all workpieces, C max Maximum completion time for all workpieces; g i A planned finishing time for a workpiece i;
if it is not
The completion time of the workpiece i is greater than the planned completion time; if not, then the mobile terminal can be switched to the normal mode,
the beginning time of the jth procedure of the workpiece i on the kth machine of the workshop,
the processing end time of the jth procedure of the workpiece i on the kth machine in the workshop is set; i is an infinite number; e is a workpiece marked with the reference number e, f is the f-th process of the workpiece e, P e The total process number of the workpiece e;
step 2: subjecting the mixture obtained in step 1
n、q、m l 、
EF、CEF、G i Inputting the number of processes of each workpiece, the discoverer proportion and the alertness proportion of the sparrow algorithm into a mixed sparrow algorithm; the algorithm is iteratively calculated according to the constraints and the objective function established in the step 1 until the iteration times are reached, and a section of approximately optimal procedure sequence is output as an optimal scheduling scheme;
the method specifically comprises the following substeps:
step 2.1: initializing population size, determining maximum iteration times, and finder proportion and alarm proportion of sparrow algorithm, and making clear
n、q、m l 、
EF、CEF、G i And the number of steps of each workpiece, thereby initializing a sparrow population;
step 2.2: calculating the fitness value of each sparrow individual;
step 2.3: performing non-inferior ranking on the initial sparrow population, wherein n grades are provided in total;
step 2.4: calculating the crowding value of each sparrow individual in each grade;
step 2.5: the sparrow populations are sorted according to the grades, and then sorted according to the crowding degree; according to the sorting result, the first N% of individuals are set as discoverers, and the rest individuals are followers; wherein N is a preset value;
step 2.6: the finder and the follower are updated, and the updated solution is subjected to inter-vehicle layer variable neighborhood search, process layer variable neighborhood search and machine layer variable neighborhood search in sequence to become a new solution; if the new solution dominates the old solution, the new solution is accepted with a certain probability, and the acceptance probability is increased along with the increase of the iteration times; if the old solution dominates the new solution, the new solution is not accepted; if the new solution and the old solution are not mutually independent, the new solution is accepted with a probability of 50%;
step 2.7: respectively randomly extracting 10% of the updated discoverer and the updated follower to become an alarmer, and updating; after updating, carrying out cross mutation; deleting the extracted individuals from the finder and the follower;
step 2.8: combining the updated discoverer, the follower and the alerter together to form a new population; judging whether the current algebra is larger than the maximum iteration times, if so, outputting a section of approximately optimal procedure sequence; otherwise, the slew performs step 2.2.
2. The distributed flexible job shop scheduling method with preparation time according to claim 1, wherein: in the step 2.1, 30% of sparrows are randomly generated, 30% of sparrows are generated by adopting an SPT scheduling rule, and the rest 40% of sparrows are generated by adopting a chaotic mapping initialization strategy.
3. The distributed flexible job shop scheduling method with preparation time according to claim 1, characterized in that: in step 2.6, firstly, selecting a workshop with the largest completion time as a key workshop, taking out any workpiece in the key workshop and putting the workpiece into other workshops to complete the variable neighborhood search of the workshop part; secondly, selecting the longest process section from the scheduling scheme of each workshop, wherein the process section is continuous in time and the process of section ending is the last process, the selected process set is used as a key path, the key path is divided into a plurality of key process blocks, the first process block only exchanges the first two processes, the ending process block only exchanges the last two processes, and the first two processes and the ending process blocks of the rest process blocks are exchanged; and finally, each process sequentially traverses different machines aiming at the selectable machine set.
4. The distributed flexible job shop scheduling method with preparation time according to claim 1, characterized in that: in the step 2.7, in the cross mutation, in the cross stage, a PMX cross operator is adopted in a process layer, and a UC cross operator is adopted in a machine layer and an inter-vehicle layer; in the mutation stage, gaussian mutation operators are adopted in the three layers.
5. The distributed flexible job shop scheduling method with preparation time according to any one of claims 1 to 4, wherein: in step 2.6, an OPS coding mode is adopted, and a three-layer coding strategy is adopted, wherein the first layer is a process layer and is used for process sequencing; the second layer is a machine layer used for machine selection; the third layer is a vehicle interlayer used for selecting a workshop; the three layers are all D in programming length.
6. A distributed flexible job shop scheduling system with preparation time is characterized by comprising the following modules:
the system comprises a module 1, a module and a module, wherein the module 1 is used for constructing a distributed flexible job shop scheduling model with preparation time, and comprises maximum completion time, maximum carbon emission, maximum delay time and constraint conditions;
the maximum completion time is:
minC max ＝max(C i ),i∈[1,n]；
the maximum carbon emission is as follows:
the maximum delay time is:
the constraint conditions are as follows:
in the above formulas, n is the number of workpieces, i is the workpiece number, C i The finishing time of the workpiece i; j is the process number, l is the workshop number, k is the machine number, q is the workshop number, m l As to the number of machines in the plant,
the processing time of the jth procedure of the workpiece i on the kth machine in the workshop is shown,
preparing time of a jth procedure of a workpiece i in a workshop l;
if it is not
The jth procedure of the workpiece i is processed in the workshop l; if not, then the mobile terminal can be switched to the normal mode,
if it is not
The jth procedure of the workpiece i is processed by a kth machine in a workshop; if not, then,
TC is the total carbon emission of all machines, EF is the processing time and energy consumption conversion coefficient, CEF is the energy consumption conversion and carbon emission conversionCoefficient, L max Maximum delay time for all workpieces, C max Maximum completion time for all workpieces; g i A planned completion time for workpiece i;
if it is not
The completion time of the workpiece i is greater than the planned completion time; if not, then the mobile terminal can be switched to the normal mode,
the beginning time of the jth procedure of the workpiece i on the kth machine of the workshop I,
the processing end time of the jth procedure of the workpiece i on the kth machine in the workshop is set; i is an infinite number; e is a workpiece marked with the reference number e, f is the f-th process of the workpiece e, P e The total number of processes of the workpiece e;
module 2, module 1
n、q、m l 、
EF、CEF、G i Inputting the number of processes of each workpiece, the discoverer proportion and the alertness proportion of the sparrow algorithm into a mixed sparrow algorithm; after iterative computation is performed according to the constraint and the objective function constructed by the module 1, the algorithm outputs a section of procedure sequence.
The method specifically comprises the following sub-modules:
module 2.1, initialise the population size, determine the maximum number of iterations and the proportion of finders and caudators in the sparrow algorithm, and make sure thatIn the module 1
n、q、m l 、
EF、CEF、G i And the number of processes of each workpiece, thereby initializing a sparrow population;
a module 2.2 for calculating the fitness value of each sparrow individual;
a module 2.3, for performing non-inferior ranking on the initial sparrow population, wherein n grades are provided in total;
a module 2.4 for calculating the crowding value of sparrow individuals in each rank;
the module 2.5 is used for sorting sparrow populations according to the grades and the crowdedness; according to the sorting result, the first N% of individuals are set as discoverers, and the rest individuals are followers; wherein N is a preset value;
the module 2.6 is used for updating the finder and the follower, and sequentially carrying out inter-vehicle layer variable neighborhood search, process layer variable neighborhood search and machine layer variable neighborhood search on the updated solution to form a new solution; if the new solution dominates the old solution, the new solution is accepted with a certain probability, and the acceptance probability is increased along with the increase of the iteration times; if the old solution dominates the new solution, the new solution is not accepted; if the new solution and the old solution are not mutually independent, the new solution is accepted with a probability of 50%;
a module 2.7, which is used for randomly extracting 10% of the updated finder and follower respectively to become the alerter for updating; after updating, carrying out cross mutation; deleting the extracted individuals from the finder and the follower;
a module 2.8, which is used for combining the updated discoverer, the follower and the alert together to form a new population; judging whether the current algebra is larger than the maximum iteration number, if so, outputting a section of approximately optimal procedure sequence; otherwise, the execution module 2.2 is turned around.
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| CN116755393A (en) * | 2023-05-06 | 2023-09-15 | 成都飞机工业（集团）有限责任公司 | Large-scale flexible job shop scheduling method, system, equipment and medium |
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| CN115542944A (en) * | 2022-10-24 | 2022-12-30 | 广东电网有限责任公司云浮供电局 | Multi-unmanned aerial vehicle path planning method based on power distribution network environment and related device |
| CN116755393A (en) * | 2023-05-06 | 2023-09-15 | 成都飞机工业（集团）有限责任公司 | Large-scale flexible job shop scheduling method, system, equipment and medium |
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