CN114254721A - Flexible job shop scheduling method and device with interval gray processing time - Google Patents

Flexible job shop scheduling method and device with interval gray processing time Download PDF

Info

Publication number
CN114254721A
CN114254721A CN202111317709.0A CN202111317709A CN114254721A CN 114254721 A CN114254721 A CN 114254721A CN 202111317709 A CN202111317709 A CN 202111317709A CN 114254721 A CN114254721 A CN 114254721A
Authority
CN
China
Prior art keywords
job shop
flexible job
shop scheduling
processing time
operator
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202111317709.0A
Other languages
Chinese (zh)
Inventor
徐文星
吴文通
孙培勇
王兆琦
梁永文
王家泰
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Beijing Institute of Petrochemical Technology
Original Assignee
Beijing Institute of Petrochemical Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Beijing Institute of Petrochemical Technology filed Critical Beijing Institute of Petrochemical Technology
Priority to CN202111317709.0A priority Critical patent/CN114254721A/en
Publication of CN114254721A publication Critical patent/CN114254721A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/004—Artificial life, i.e. computing arrangements simulating life
    • G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
    • G06Q10/063—Operations research, analysis or management
    • G06Q10/0631—Resource planning, allocation, distributing or scheduling for enterprises or organisations
    • G06Q10/06316—Sequencing of tasks or work

Landscapes

  • Engineering & Computer Science (AREA)
  • Business, Economics & Management (AREA)
  • Human Resources & Organizations (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Economics (AREA)
  • Strategic Management (AREA)
  • Entrepreneurship & Innovation (AREA)
  • General Physics & Mathematics (AREA)
  • Game Theory and Decision Science (AREA)
  • Quality & Reliability (AREA)
  • Tourism & Hospitality (AREA)
  • Operations Research (AREA)
  • General Business, Economics & Management (AREA)
  • Marketing (AREA)
  • Development Economics (AREA)
  • Health & Medical Sciences (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Artificial Intelligence (AREA)
  • Biomedical Technology (AREA)
  • Biophysics (AREA)
  • Computational Linguistics (AREA)
  • Data Mining & Analysis (AREA)
  • Evolutionary Computation (AREA)
  • General Health & Medical Sciences (AREA)
  • Molecular Biology (AREA)
  • Computing Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Mathematical Physics (AREA)
  • Software Systems (AREA)
  • Educational Administration (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

Abstract

The application relates to a flexible job shop scheduling method and equipment with interval gray processing time, wherein the method comprises the following steps: and acquiring data to be processed, wherein the data to be processed comprises data of workpieces to be processed, processing time ranges of the workpieces and candidate machine data. And obtaining a processing scheduling scheme based on a flexible job shop scheduling model trained in advance according to the data to be processed. The flexible job shop scheduling model is provided with the load balancing step-size self-adaptive discrete particle swarm algorithm, the algorithm sets the particle updating step size as the self-adaptive parameter, the fast convergence in the early stage and the local search capability in the later stage of the algorithm are guaranteed, the local search capability of the particles is further increased by introducing the load balancing strategy, and the solving efficiency and the solving quality of the algorithm are guaranteed.

Description

Flexible job shop scheduling method and device with interval gray processing time
Technical Field
The application relates to the technical field of flexible job shop scheduling, in particular to a flexible job shop scheduling method and device with interval gray processing time.
Background
The development of the manufacturing industry is an important way for improving the national economic strength, the development trend of the manufacturing industry can directly influence the comprehensive national strength of the country, and a workshop scheduling system is the core of a production management system of the manufacturing industry. In the mechanical processing process, different work step numbers and process parameters have great influence on processing time, a processing scheduling scheme is obtained according to workpiece data to be processed and candidate machines through a flexible job shop scheduling model in the prior art, but the algorithm adopted by the flexible job shop scheduling model in the prior art is slow in convergence, and the solving efficiency and the solving quality are to be optimized.
Disclosure of Invention
In order to overcome the problems that an algorithm adopted by a flexible job shop scheduling model in the related technology is slow in convergence and the solving efficiency and the solved quality need to be optimized at least to a certain extent, the application provides a flexible job shop scheduling method and equipment with interval gray processing time.
The scheme of the application is as follows:
according to a first aspect of the embodiments of the present application, there is provided a flexible job shop scheduling method with interval gray processing time, including:
acquiring data to be processed, wherein the data to be processed comprises: data of workpieces to be processed, processing time ranges of the workpieces and candidate machine data;
obtaining a processing scheduling scheme based on a flexible job shop scheduling model trained in advance according to the data to be processed; the flexible job shop scheduling model is loaded with a step-size self-adaptive discrete particle swarm algorithm with load balancing.
Preferably, in an implementable manner of the present application, the flexible job shop scheduling model is trained with a goal of minimizing a maximum value of interval gray completion time;
the flexible job shop scheduling model comprises:
optimizing the target:
Figure BDA0003344143920000021
constraint conditions are as follows:
Figure BDA0003344143920000022
wherein J ═ { J ═ JiN represents a set of n workpieces to be machined;
M＝{Mkm denotes a set of m candidate machines;
Oi，h，h∈{1，2，...qidenotes a workpiece JiThe step (2);
M(Oi，h)＝{Me}，e＝1，2，...，li，hrepresents a step Oi，hThe available set of processing machines;
Figure BDA0003344143920000023
represents a step Oi，hAt MkUpper interval gray processing time;
and is
Figure BDA0003344143920000024
Figure BDA0003344143920000025
Figure BDA0003344143920000026
Represents a step Oi，hInterval gray start time;
Figure BDA0003344143920000027
represents a step Oi，hThe interval gray completion time of (1);
Figure BDA0003344143920000028
the maximum value of gray completion time of all the process sections is represented;
Figure BDA0003344143920000029
Figure BDA0003344143920000031
preferably, in an implementation manner of the present application, the method further includes: and solving the time parameter of the flexible job shop scheduling model based on an addition operator, a number multiplication operator, a comparison operator, a combination operator and an interpolation operator.
Preferably, in an implementable manner of the present application, the operation rule of the addition operator is defined as:
Figure BDA0003344143920000032
the operation rule of the number multiplication operator is defined as:
Figure BDA0003344143920000033
the operation rule of the comparison operator is defined as:
Figure BDA0003344143920000034
Figure BDA0003344143920000035
Figure BDA0003344143920000036
or
Figure BDA0003344143920000037
And a is+-a-＞b+-b-；
Figure BDA0003344143920000038
And a is+-a-＝b+-b-；
The operation rule of the merge operator is defined as:
Figure BDA0003344143920000039
the operation rule of the merge operator is defined as:
definition of
Figure BDA00033441439200000310
Figure BDA00033441439200000311
So that y is less than or equal to x and
Figure BDA00033441439200000312
so that x is more than or equal to y;
define the g-th idle time on machine k as
Figure BDA0003344143920000041
If and only if
Figure BDA0003344143920000042
And is
Figure BDA0003344143920000043
The process may be inserted into a free slot of a candidate machine.
Preferably, in an implementation manner of the present application, the load balancing step-size adaptive discrete particle swarm algorithm uses segmented integer coding to divide the code of each particle into a machine selection part and a procedure sorting part;
the machine selection part is arranged from small to large in sequence according to the process numbers of the candidate machines, and the numbers of the corresponding positions are the numbers of the candidate machines in the process selectable machine set; the process sequencing part represents the workpiece number by a number, and the occurrence frequency of the number represents the process channel number of the workpiece corresponding to the number.
Preferably, in an implementation manner of the present application, the load balancing step-size adaptive discrete particle swarm algorithm performs machine selection on all processes based on a global random selection initialization method, sorts all processes, and completes initialization of the machine selection part and the process sorting part.
Preferably, in an implementation manner of the present application, the load balancing step-size adaptive discrete particle swarm algorithm sets an update step size as an adaptive parameter, and introduces a load balancing strategy, where a particle position update formula of the load balancing step-size adaptive discrete particle swarm algorithm includes:
Figure BDA0003344143920000044
wherein, c1、c2Respectively expressed as a particle confidence coefficient and a particle social confidence coefficient; ω represents an inertial weight factor; i represents the ith particle in the particle group, t and t +1 represent the number of iterations,
Figure BDA0003344143920000045
representing that the historical position of the ith particle in the t generation is optimal; gBtRepresenting t generation of global optimal particles; f, p and g all represent operation operators.
Preferably, in an implementable manner of the present application, the formula for updating the particle position of the load balancing step-size adaptive discrete particle swarm algorithm further includes:
Figure BDA0003344143920000046
Figure BDA0003344143920000051
Figure BDA0003344143920000052
according to a second aspect of embodiments of the present application, there is provided a flexible job shop scheduling apparatus having an interval gray processing time, including:
a processor and a memory;
the processor and the memory are connected through a communication bus:
the processor is used for calling and executing the program stored in the memory;
the memory configured to store a program for performing at least one of the flexible job shop scheduling methods with interval gray processing time described in any of the above.
The technical scheme provided by the application can comprise the following beneficial effects: the flexible job shop scheduling method with interval gray processing time comprises the following steps: and acquiring data to be processed, wherein the data to be processed comprises data of workpieces to be processed, processing time ranges of the workpieces and candidate machine data. And obtaining a processing scheduling scheme based on a flexible job shop scheduling model trained in advance according to the data to be processed. The flexible job shop scheduling model is provided with the load balancing step-size self-adaptive discrete particle swarm algorithm, the algorithm sets the particle updating step size as the self-adaptive parameter, the fast convergence in the early stage and the local search capability in the later stage of the algorithm are guaranteed, the local search capability of the particles is further increased by introducing the load balancing strategy, and the solving efficiency and the solving quality of the algorithm are guaranteed.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the application.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present application and together with the description, serve to explain the principles of the application.
FIG. 1 is a schematic flow chart diagram illustrating a flexible job shop scheduling method with interval gray processing time according to an embodiment of the present application;
FIG. 2 is a schematic diagram of an example flexible job shop scheduling problem with interval gray processing time according to an embodiment of the present application;
FIG. 3 is a schematic diagram of a particle coding scheme corresponding to an example of a flexible job shop scheduling problem with interval gray processing time according to an embodiment of the present application;
FIG. 4 is a block diagram of a particle assembly according to an embodiment of the present application
Figure BDA0003344143920000061
A schematic diagram of replacing elements of the corresponding positions;
FIG. 5 is a block diagram of a computer system according to an embodiment of the present application
Figure BDA0003344143920000062
Sequentially filling non-zero elements of the middle OS segment into particles according to sequence
Figure BDA0003344143920000063
A schematic at zero element of the mid-OS segment;
FIG. 6 is a gray gantt chart derived from the data in FIG. 2 as provided by one embodiment of the present application;
FIG. 7 is a trend graph of experimental results of an orthogonal experiment provided by an embodiment of the present application;
FIG. 8 is a graph illustrating experimental objective function value changes provided in accordance with an embodiment of the present application;
FIG. 9 is a gray gantt chart based on IMK01 provided by one embodiment of the present application;
FIG. 10 is a schematic structural diagram of a flexible job shop scheduling device with interval gray processing time according to an embodiment of the present application.
Reference numerals: a processor-21; a memory-22.
Detailed Description
Reference will now be made in detail to the exemplary embodiments, examples of which are illustrated in the accompanying drawings. When the following description refers to the accompanying drawings, like numbers in different drawings represent the same or similar elements unless otherwise indicated. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present application. Rather, they are merely examples of apparatus and methods consistent with certain aspects of the present application, as detailed in the appended claims.
A flexible job shop scheduling method with interval gray processing time, referring to fig. 1, includes:
s11: acquiring data to be processed, wherein the data to be processed comprises: data of workpieces to be processed, processing time ranges of the workpieces and candidate machine data;
s12: according to the data to be processed, a processing scheduling scheme is obtained based on a flexible job shop scheduling model trained in advance; the flexible job shop scheduling model is loaded with a step-size self-adaptive discrete particle swarm algorithm with load balancing.
The flexible job shop scheduling model in the embodiment is provided with the load balancing step-size self-adaptive discrete particle swarm algorithm, the algorithm sets the particle updating step size as the self-adaptive parameter, the fast convergence in the early stage and the local search capability in the later stage of the algorithm are ensured, the local search capability of the particles is further increased by introducing the load balancing strategy, and the solving efficiency and the solving quality of the algorithm are ensured.
In some embodiments, in the flexible job shop scheduling method with interval gray processing time, a flexible job shop scheduling model is trained with the maximum value of the minimum interval gray completion time as a target;
the flexible job shop scheduling model comprises:
optimizing the target:
Figure BDA0003344143920000071
constraint conditions are as follows:
Figure BDA0003344143920000072
wherein J ═ { J ═ JiN represents a set of n workpieces to be machined;
M＝{Mkm denotes a set of m candidate machines;
Oi，h，h∈{1，2，...qidenotes a workpiece JiThe step (2);
M(Oi，h)＝{Me}，e＝1，2，...，li，hrepresents a step Oi，hThe available set of processing machines;
Figure BDA0003344143920000073
represents a step Oi，hAt MkUpper interval gray processing time;
and is
Figure BDA0003344143920000074
Figure BDA0003344143920000075
Figure BDA0003344143920000076
Represents a step Oi，hInterval gray start time;
Figure BDA0003344143920000081
represents a step Oi,hThe interval gray completion time of (1);
Figure BDA0003344143920000082
the maximum value of gray completion time of all the process sections is represented;
Figure BDA0003344143920000083
Figure BDA0003344143920000084
due to the characteristic of interval gray number, the flexible job shop scheduling method with interval gray processing time is different from the traditional flexible job shop scheduling method, and the problems of interval gray number comparison, calculation, time gap insertion and the like are considered in the algorithm design process. The flexible job shop scheduling model in this embodiment is a flexible job shop scheduling model having an interval gray processing time.
The flexible job shop scheduling problem with interval gray processing time can be described as n workpieces (J)1,J2,J3,...,Jn) Needs to be on M machines (M)1,M2,...,Mm) Processing is carried out; each workpiece comprises at least one process; the working procedures are divided into the following steps; each process can be processed on one or more machines; the interval gray processing time required for the process is determined by the selected processing machine. The dispatching aim is to select a proper processing machine for each procedure and reasonably arrange the processing sequence of different workpiece procedures, so as to determine the interval gray processing starting time of each procedure on each machine and optimize one or more indexes of the whole system. Similar to the traditional flexible job shop scheduling model, the flexible job shop scheduling model with interval gray processing time makes the following assumptions:
1. all processing machines in the scheduling system can start processing at the time when t is 0.
2. Different workpieces and different procedures in the dispatching system are required to be processed in order according to the fixed processing sequence.
3. Any one of the processes in process cannot be stopped halfway.
4. The priority levels of all different types of workpieces within the scheduling system must be consistent.
5. The interval gray processing time of the workpiece includes the transport and adjustment time of the workpiece.
Based on this, the flexible job shop scheduling model with the interval gray processing time is proposed. In the constraint conditions of the flexible job shop scheduling model with the interval gray processing time:
equation 1-1: limiting the machining end time not to be earlier than the start time;
equations 1-2: limiting the processing start time of the next procedure of the same workpiece to be not earlier than the processing end time of the previous procedure;
formulas 1 to 3: limiting the processing machine to execute only one processing task at a certain time;
equations 1-4: limiting a process to be finished by only one machine;
equations 1-5: the limited processing time must be after zero
Figure BDA0003344143920000091
The flexible job shop scheduling method with interval gray processing time in some embodiments further includes: and solving the time parameter of the flexible job shop scheduling model based on an addition operator, a number multiplication operator, a comparison operator, a combination operator and an interpolation operator.
Further, the operation rule of the addition operator is defined as:
Figure BDA0003344143920000092
the operation rule of the number multiplication operator is defined as:
Figure BDA0003344143920000093
the operation rule of the compare operator is defined as:
Figure BDA0003344143920000094
Figure BDA0003344143920000101
Figure BDA0003344143920000102
or
Figure BDA0003344143920000103
And a is+-a-＞b+-b-；
Figure BDA0003344143920000104
And a + -a- ═ b + -b-;
the operation rule of the merge operator is defined as:
Figure BDA0003344143920000105
the operation rule of the merge operator is defined as:
definition of
Figure BDA0003344143920000106
Figure BDA0003344143920000107
So that y is less than or equal to x and
Figure BDA0003344143920000108
so that x is more than or equal to y;
define the g-th idle time on machine k as
Figure BDA0003344143920000109
If and only if
Figure BDA00033441439200001010
And is
Figure BDA00033441439200001011
The process may be inserted into a free slot of a candidate machine.
In this embodiment, when the flexible job shop scheduling model with the interval gray processing time is solved, all time parameters are the interval gray numbers, so the basic mathematical operation rule of the interval gray numbers must be specified. The basic mathematical operation rule of interval gray number comprises: addition operator, number multiplication operator, comparison operator, combination operator and interpolation operator. The comparison operator is used for comparing the fitness of the particles and determining the particles with the optimal fitness; the merging operator is used for calculating the maximum completion time of the gray section; the insert operator is used to determine whether the work process can be inserted into the free space of the candidate machine. The method improves on operators in the prior art, and the specific operation rule is defined as above.
In the flexible job shop scheduling method with interval gray processing time in some embodiments, a step-size adaptive discrete particle swarm algorithm for load balancing divides a code of each particle into a machine selection part and a process sequencing part by using segmented integer coding;
the machine selection part is arranged from small to large in sequence according to the process numbers of the candidate machines, and the numbers of the corresponding positions are the numbers of the candidate machines in the process selectable machine set; the process sequencing part represents the workpiece number by a number, and the number of times of occurrence of the number represents the number of process steps of the workpiece corresponding to the number.
The flexible job shop scheduling problem with interval gray processing time is similar to the flexible job shop scheduling problem, and comprises two strongly coupled subproblems of machine selection and process sequencing. The algorithm efficiency can be greatly improved by selecting a reasonable coding and decoding mode.
In this embodiment, a segmented integer code is adopted, and the code of each particle is divided into two parts: a machine selection part (MS) and an operation sequencing part (OS). The total length of the particles is twice of the total length of all the procedures in the scheduling system, and the lengths of the machine selection part MS and the procedure sorting part OS are the total length of the procedures.
To illustrate the encoding rules more intuitively, FIG. 2 shows an example of a flexible job shop scheduling problem with interval gray processing time. The corresponding particle encoding scheme is shown in figure 3. Number of available processing machines in the scheduling system: m is 6, the number of workpieces: n is 3, total process number: to 9, and the total length of the particle is 2 To.
The machine selection part MS is arranged from small to large according to the process numbers, and the numbers of the corresponding positions are the numbers of the processing machines in the process selectable machine set, but not the machine numbers. In FIG. 3, the MS sections represent the process O from left to right11、O12、O13、O21、O22、O23、O31、O32、O33The location of the selected processing machine in the selectable set of machines is numbered. As shown in the left half of FIG. 3, process O12Numeral 2 stored in the corresponding position indicates a process O12In its optional machine set { M2，M3，M5Middle selector M3Procedure O33Numeral 3 stored in the corresponding position indicates a process O12In its optional machine set { M1，M2，M6Middle selector M6。
Each number in the process sequencing part represents a workpiece number, and the k-th occurrence of the number represents the k-th process of the workpiece. As shown in the right half of fig. 3, the to-be-processed processes represented by the values 2, 3, 1, 3, 2 of the OS segment in turn are: o is21、O31、O11、O12、O13、O32、O22、O33、O23。
In the flexible job shop scheduling method with interval gray processing time in some embodiments, a load balancing step-size adaptive discrete particle swarm algorithm performs machine selection on all the procedures based on a global random selection initialization method, and sequences all the procedures to complete initialization of a machine selection part and a procedure sequencing part.
Population initialization is a key problem in an evolutionary algorithm, and the quality of an initial solution has great influence on the speed and convergence of the discrete particle swarm algorithm. Therefore, in this embodiment, a global random selection initialization method is adopted to perform machine selection on all processes, and a random method is used to sequence all processes, thereby completing initialization of the MS segment and the OS segment.
(1) Firstly, based on the idea of stacking, n arrays (representing n workpieces) are generated, and each array is divided into two cell arrays: j-only and J-muti. And putting the process of only one optional machine in the optional machine set into the J-only array, and putting the process of a plurality of optional machines in the optional machine set into the J-muti array. Both are stored in sequence from small to large according to the number of processes.
(2) And selecting a first element in the J-only array in the corresponding array as a current operation procedure by using a certain number randomly generated from 1 to n as a workpiece number, and deleting the element from the J-only array. And because the optional machine of the process in the J-only is unique, the corresponding position of the process in the MS section is directly assigned as 1. And calculating the current machine load value, wherein the machine load array MT is not cleared. And (5) circulating the step (2) until all J-only array elements are selected.
(3) And selecting a first element in the J-muti array as a current operation procedure by using a certain number randomly generated from 1 to n as a workpiece number, and deleting the element from the J-muti array. And according to the current machine load condition, selecting the machine with the minimum machine load in the selectable machine set as the processing machine in the process, and placing the serial number of the machine into the corresponding position of the MS section. And meanwhile, calculating the machine load value at the moment, and not clearing the machine load array MT. And (5) circulating the step (3) until all the J-muti array elements are selected.
In some embodiments, in the flexible job shop scheduling method with interval gray processing time, a step-size adaptive discrete particle swarm algorithm for load balancing sets an update step size as an adaptive parameter, and introduces a load balancing strategy, and a particle position update formula of the step-size adaptive discrete particle swarm algorithm for load balancing includes:
Figure BDA0003344143920000121
wherein, c1、c2Respectively expressed as a particle confidence coefficient and a particle social confidence coefficient; ω represents an inertial weight factor; i represents the ith particle in the particle group, t and t +1 represent the number of iterations,
Figure BDA0003344143920000131
representing that the historical position of the ith particle in the t generation is optimal; gBtRepresenting t generation of global optimal particles; f, p and g all represent operation operators.
In this embodiment, a step-size adaptive discrete particle swarm algorithm for load balancing is provided based on updating of a discrete particle swarm algorithm in the prior art. c. C1、c2Respectively representing the probability that the particle updates itself along with the optimal particle at the historical position or the globally optimal particle; omega is an inertia weight factor and represents the possibility of self-renewal of the particles; the value ranges of the three are (0, 1). i represents the ith particle in the particle group, t and t +1 represent the number of iterations,
Figure BDA0003344143920000132
representing the best historical position of the ith particle in the t generation, gBtRepresenting t generation of globally optimal particles. f, p, g are operators. Considering the characteristic that the particle swarm algorithm has optimal learning towards the global optimal particles and the historical positions compared with other algorithms, the fast convergence of the particle swarm is ensured, and the particle position adjusting mode in the embodiment keeps the position information of the better particles as much as possible. And aiming at the problem that the particles are easy to fall into local optimum, the space exploration capacity of the particles is enhanced by carrying out load balancing on the processing machine with the maximum load.
Specifically, the formula for updating the particle position of the load-balanced step-size adaptive discrete particle swarm algorithm comprises:
Figure BDA0003344143920000133
Figure BDA0003344143920000134
Figure BDA0003344143920000135
wherein, formula 2-2 represents the updating operation of the particle self, r is a random number in the interval (0, 1), and f operator acts like the mutation operation of the genetic algorithm: selecting the machine M with the greatest load of the processing machineskAt MkRandomly selecting a to-be-processed procedure O from the processing listi，hIf in the process Oi，hIs not the only alternative processing machine, then in this process step Oi，hThe corresponding MS section deletes the element and performs the procedure Oi，hSelecting other processing machines in the alternative machine set, and filling in the procedure Oi，hCorresponding MS segment. The particle self-updating mode not only can balance the load of the processing machine, but also can further improve the space exploration capability of the algorithm, and avoids the particles from falling into local optimum.
Equations 2-3 and 2-4 represent the update operations of the particle following the historical position optimal particle and the global optimal particle respectively, and the p and g operators act like the crossover operation of the genetic algorithm. Taking a p operator as an example, giving a specific operation step:
for the MS section, first according to the particle
Figure BDA0003344143920000141
Particles optimized to historical locations
Figure BDA0003344143920000142
The Euclidean distance is calculated to obtain an updating step length, and the step length calculation formula is as follows:
Figure BDA0003344143920000143
step size calculation formula of MS sectionTo represents the total process number, distance (i) represents granules
Figure BDA0003344143920000144
Particles optimized to historical locations
Figure BDA0003344143920000145
MAX represents the particle in the particle swarm and the optimal particle
Figure BDA0003344143920000146
The maximum value of the euclidean distance ceil represents rounding down. Then randomly optimize particles at historical positions
Figure BDA0003344143920000147
Selecting the element fragment with the length of MSL from the MS section, and separating the particles
Figure BDA0003344143920000148
The elements of the corresponding positions are replaced. For ease of understanding, fig. 4 illustrates a specific operational procedure.
For the OS segment, the step update formula is as follows:
Figure BDA0003344143920000149
step size updating formula of OS section, wherein n represents total number of workpieces, distance (i) represents particles
Figure BDA00033441439200001410
With globally optimal particles
Figure BDA00033441439200001411
MAX represents the particle in the particle swarm and the optimal particle
Figure BDA00033441439200001412
The maximum value of the euclidean distance ceil represents rounding down. Unlike the MS segment, the OS segment is liable to cause generation of illegal particles if the segment copy is directly taken. Therefore this embodiment designsBased on the crossing mode of the workpieces: randomly taking out the numbers from 1 to n of OSL as a set g1, and forming a set g2 by the elements in the rest 1 to n; first of all, the historical position is optimally granulated
Figure BDA00033441439200001413
The element of the middle OS segment belonging to the set g1 is set to zero; then the particles are mixed
Figure BDA00033441439200001414
The element of the middle OS segment belonging to g2 is set to zero; finally will be
Figure BDA00033441439200001415
Sequentially filling non-zero elements of the middle OS segment into particles according to sequence
Figure BDA00033441439200001416
At zero element of the mid OS segment, fig. 5 shows a specific operation procedure.
The action of the g operator is similar to that of the p operator, the updating reference object is replaced by the global optimal particle from the optimal particle at the historical position, and the specific operation process is not described in detail.
Unlike the conventional flexible job shop scheduling problem, the flexible job shop scheduling problem with section gray processing time uses section gray processing time (section gray number) instead of specific time (natural number), so the gantt chart with section gray processing time is also different from the conventional gantt chart in representation, this embodiment refers to the definition of gray gantt degree given in the prior art, and the gray gantt chart obtained by combining the operation result of the data in fig. 2 is shown in fig. 6, where the left side indicates the processing machine number, the upper half arc indicates the section gray start time of the process, and the lower half arc indicates the process section gray completion time. As the 3 rd process of the workpiece 2: the starting point of the upper half arc represents the earliest possible machining starting time of the process on the alternative machine, the end point of the upper half arc represents the latest possible machining starting time of the process on the alternative machine, and the same applies to the lower half arc. As can be seen from FIG. 6, the maximum completion time for gray color between the minimum zones is [16, 20 ].
In order to verify the effectiveness of the step-size adaptive discrete particle swarm algorithm with load balancing in solving the flexible job shop scheduling problem with interval gray processing time, the embodiment performs improved generation on a benchmark example of the branch design, and the improvement mode of the interval gray processing time is shown in formulas (5-1 and 5-2):
Figure BDA0003344143920000151
Figure BDA0003344143920000152
where tl is the process processing time in the reference data set, and r is a random number within (0, 1).
In order to prove the effectiveness of the step-size adaptive discrete particle swarm algorithm parameter with load balancing and the superiority of the algorithm in processing the scheduling problem of the flexible job shop with interval gray processing time, the embodiment designs two types of experiments: firstly, in order to efficiently and quickly select proper algorithm parameter variables, a three-factor three-level L is designed through an orthogonal experiment method9(34) And (4) an orthogonal table. And secondly, the superiority of the step-size self-adaptive discrete particle swarm algorithm is proved by comparing with the algorithm proposed in recent years.
In the step-size adaptive discrete particle swarm optimization algorithm with load balancing, an inertia weight factor (omega) and a particle confidence coefficient (c)1) Particle social trust coefficient (c)2) The three parameters greatly influence the searching efficiency and the convergence speed of the algorithm, and the correctness of the parameter selection has obvious influence on the performance of the algorithm. The embodiment adopts an orthogonal experiment method to select appropriate parameter variables: omega, c1And c2The value ranges are respectively as follows: 0.3-0.5, 0.7-0.9 and 0.3-0.5, and the data collection adopts improved IMK 02. Because the interval gray processing time is the interval gray number, the interval gray processing time is obtained in the orthogonal experiment, and the interval gray number is replaced by the median in the interval to express in consideration of the inconvenience of calculation in comparison of subsequent experimentsThe algorithm operation result; meanwhile, in order to eliminate the influence of random errors on the experiment, the orthogonal experiment averages the results after the orthogonal experiment is independently operated for 20 times. The results of the specific experiments are shown in table 1. Where observations were averaged over the median of the interval gray processing time run 20 times independently.
Table 1:
Figure BDA0003344143920000161
by range (visual) analysis, we can find that c is 0.5 ═ ω1＝0.8、c2When the value is 0.4, the performance of the algorithm is optimal. In order to more intuitively show the experimental result of the orthogonal experiment, a trend graph is drawn as shown in fig. 7, wherein the left line segment on the left side in fig. 7 is an inertia factor, the middle line segment is a particle confidence coefficient, and the right line segment is a social confidence coefficient.
In order to verify the effectiveness of the improved method provided by the embodiment in solving, the embodiment solves the example IMK01 by using a discrete particle swarm algorithm without GRS initialization and a step-size adaptive discrete particle swarm algorithm with load balancing; meanwhile, in order to verify the improvement of GRS initialization on the performance of the algorithm, GRS initialization is introduced, and the example IMK01 is solved through a step-size self-adaptive discrete particle swarm algorithm with load balance. And respectively displaying the results through the experimental results and the change curve of the target function value in the experimental process. The experimental parameters of the discrete particle swarm algorithm and the step-size self-adaptive discrete particle swarm algorithm with load balance are set to be omega-0.5, c1＝0.8、c20.4. In order to eliminate random errors of the experiment, the three examples are independently performed for ten times of experiments, and the optimal value, the average value and the single algorithm running time are taken out. Specific numerical values are shown in table 2, and a curve of changes in the values of the objective function is shown in fig. 8.
Table 2:
Figure BDA0003344143920000171
the data in the table show that the improved step-size self-adaptive discrete particle swarm algorithm with load balance is superior to the original discrete particle swarm algorithm in three aspects, and the minimum value and the average value of the obtained scheduling time are respectively improved by 9.1% and 9.7% if the median of the interval is taken for comparison. The time is shortened by 2.9% in terms of the time consumption of the algorithm. After GRS initialization is introduced, the step size adaptive discrete particle swarm algorithm with load balance is improved in the aspects of the minimum value and the average value, but the time consumption of the algorithm is increased by 3.2%. Comparing (1) and (2) in fig. 8, it can be known that the step-size adaptive discrete particle swarm algorithm with load balancing has better space search capability than the discrete particle swarm algorithm, thereby avoiding premature algorithm, and comparing (2) and (3) in fig. 8 can find that the particle quality of the initial solution space is greatly improved and the convergence speed of the algorithm is greatly accelerated after introducing GRS initialization. In summary, the load balancing and step size adaptive parameter strategy and the GRS initialization method introduced in this embodiment both greatly improve the performance of the algorithm.
In order to verify the superiority of the step-size adaptive discrete particle swarm algorithm with load balancing, five examples of IMK01 to IMK05 in the improved data set are selected for simulation experiments. Based on the selected parameters, the present embodiment further compares the step-size adaptive discrete particle swarm algorithm with load balancing with two excellent algorithms in the prior art, including the modified harmonic search algorithm (G-HM) with interval gray processing time, the modified genetic algorithm (G-GA) with interval gray processing time. The programming language of the simulation experiment is MatlabR2017a, and the computer hardware parameters are as follows: intel (R) core (TM) i7-8750H CPU @2.20GHz, memory 16 GB.
Setting algorithm parameters: for the step-size adaptive discrete particle swarm algorithm LS-DPSO with load balancing: the number of cycles was set to 300, the population size was 200, ω 0.5, c1＝0.8，c20.4; for G-GA: the size of the genetic population is 100, the maximum iteration number is 300, the cross probability is 0.8, and the variation probability is 0.01; for G-HM: the harmony memory bank is 40 in size, the probability of values in the harmony memory bank is 0.95, the probability of harmony tone is adjusted to be 0.05, and the intelligent variation probability0.8, and 25000 iterations.
In order to avoid the interference of random errors on experimental results, when five calculation examples are solved, three algorithms independently perform twenty experiments, and the optimal value, the average value and the single algorithm running time are taken out. Specific values are shown in table 3, wherein the bold-faced bold part is the optimal value after comparison by the comparison operator.
Table 3:
Figure BDA0003344143920000181
as can be seen from Table 3, the step-size adaptive discrete particle swarm algorithm with load balancing has better operation results in different examples. In the aspect of the minimum value of the interval gray maximum completion time, the results of the step-size self-adaptive discrete particle swarm algorithm with load balance in five calculation examples are better than those of the other two algorithms. In the aspect of time consumption of algorithm operation, compared with the time consumption of algorithms of IMK01 and IMK03, it can be found that the operation time of algorithms of G-GA and G-HM is increased by 273% and 349% respectively, while the operation time of the step-size adaptive discrete particle swarm algorithm with load balancing is only increased by 176%, and along with the increase of the calculation scale, the time consumption of the step-size adaptive discrete particle swarm algorithm with load balancing is far lower than that of the other two algorithms, which shows that the step-size adaptive discrete particle swarm algorithm with load balancing has a greater advantage in large-scale scheduling. In the aspect of the average value of the maximum completion time of gray intervals, the step self-adaptive discrete particle swarm algorithm with load balance is also superior to other two algorithms in IMK01, IMK02 and IMK 05; the difference between IMK03 and IMK04 is slightly less than that of G-GA, and is within 0.2-0.4, and the difference is small.
Through the experimental analysis, the step-size self-adaptive discrete particle swarm algorithm with load balance has excellent performance in processing the scheduling problem of the flexible job shop with interval gray processing time. To further show how the algorithm results guide the actual scheduled production, a grey gantt chart based on IMK01 is presented here. As shown in FIG. 9, the minimum inter-cell gray maximum completion time for example IMK01 is: [40,53].
In the production scheduling process, after a workpiece processing time range is given, a gray gantt chart shown in fig. 9 can be obtained through a step-size adaptive discrete particle swarm algorithm with load balancing. Since the machining end time is not an accurate time point due to factors such as different proficiency of workers in actual production, the gray gantt chart represents the machining start and end time of the workpiece in a real production scene by using a time interval. The method comprises the steps of arranging and processing the work procedures in sequence according to a gray Gantt chart, and simultaneously processing the work procedures of other tasks in the interval time of waiting for subsequent work pieces on a machine, so that the time is utilized more reasonably; subsequent workpiece processing only needs to be carried out within the time interval specified in the gray Gantt chart, the whole processing progress is not influenced, the processing task can be completed on time, and the processing process is more flexible.
A flexible job shop scheduling apparatus having an interval gray processing time, referring to fig. 10, comprising:
a processor 21 and a memory 22;
the processor 21 is connected to the memory 22 by a communication bus:
the processor 21 is configured to call and execute a program stored in the memory 22;
a memory 22 for storing a program for performing at least one of the flexible job shop scheduling methods with interval gray processing time of any of the above embodiments.
It is understood that the same or similar parts in the above embodiments may be mutually referred to, and the same or similar parts in other embodiments may be referred to for the content which is not described in detail in some embodiments.
It should be noted that, in the description of the present application, the terms "first", "second", etc. are used for descriptive purposes only and are not to be construed as indicating or implying relative importance. Further, in the description of the present application, the meaning of "a plurality" means at least two unless otherwise specified.
Any process or method descriptions in flow charts or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing specific logical functions or steps of the process, and the scope of the preferred embodiments of the present application includes other implementations in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the present application.
It should be understood that portions of the present application may be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, the various steps or methods may be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, any one or combination of the following techniques, which are known in the art, may be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application specific integrated circuit having an appropriate combinational logic gate circuit, a Programmable Gate Array (PGA), a Field Programmable Gate Array (FPGA), or the like.
It will be understood by those skilled in the art that all or part of the steps carried by the method for implementing the above embodiments may be implemented by hardware related to instructions of a program, which may be stored in a computer readable storage medium, and when the program is executed, the program includes one or a combination of the steps of the method embodiments.
In addition, functional units in the embodiments of the present application may be integrated into one processing module, or each unit may exist alone physically, or two or more units are integrated into one module. The integrated module can be realized in a hardware mode, and can also be realized in a software functional module mode. The integrated module, if implemented in the form of a software functional module and sold or used as a stand-alone product, may also be stored in a computer readable storage medium.
The storage medium mentioned above may be a read-only memory, a magnetic or optical disk, etc.
In the description herein, reference to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the application. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
Although embodiments of the present application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present application, and that variations, modifications, substitutions and alterations may be made to the above embodiments by those of ordinary skill in the art within the scope of the present application.

Claims (9)

1. A flexible job shop scheduling method with interval gray processing time is characterized by comprising the following steps:
acquiring data to be processed, wherein the data to be processed comprises: data of workpieces to be processed, processing time ranges of the workpieces and candidate machine data;
obtaining a processing scheduling scheme based on a flexible job shop scheduling model trained in advance according to the data to be processed; the flexible job shop scheduling model is loaded with a step-size self-adaptive discrete particle swarm algorithm with load balancing.
2. The method of claim 1, wherein the flexible job shop scheduling model is trained with the goal of minimizing a maximum value of interval gray completion times;
the flexible job shop scheduling model comprises:
optimizing the target:
Figure FDA0003344143910000011
constraint conditions are as follows:
Figure FDA0003344143910000012
wherein J ═ { J ═ JiN represents a set of n workpieces to be machined;
M＝{Mkm denotes a set of m candidate machines;
Oi，h，h∈{1，2，...qidenotes a workpiece JiThe step (2);
M(Oi，h)＝{Me}，e＝1，2，...，li，hrepresents a step Oi，hThe available set of processing machines;
Figure FDA0003344143910000013
represents a step Oi，hAt MkUpper interval gray processing time;
and is
Figure FDA0003344143910000014
h＝1，2，...qi；k∈M(Oi，h)；
Figure FDA0003344143910000015
Figure FDA0003344143910000021
Represents a step Oi，hInterval gray start time;
Figure FDA0003344143910000022
represents a step Oi，hThe interval gray completion time of (1);
Figure FDA0003344143910000023
the maximum value of gray completion time of all the process sections is represented;
Figure FDA0003344143910000024
Figure FDA0003344143910000025
3. the method of claim 2, further comprising: and solving the time parameter of the flexible job shop scheduling model based on an addition operator, a number multiplication operator, a comparison operator, a combination operator and an interpolation operator.
4. The method of claim 3, wherein the operation rule of the addition operator is defined as:
Figure FDA0003344143910000026
the operation rule of the number multiplication operator is defined as:
Figure FDA0003344143910000027
the operation rule of the comparison operator is defined as:
Figure FDA0003344143910000028
Figure FDA0003344143910000029
Figure FDA00033441439100000210
or
Figure FDA00033441439100000211
And a is+-a-＞b+-b-；
Figure FDA00033441439100000212
And a is+-a-＝b+-b-；
The operation rule of the merge operator is defined as:
Figure FDA0003344143910000031
the operation rule of the merge operator is defined as:
definition of
Figure FDA0003344143910000032
Figure FDA0003344143910000033
So that y is less than or equal to x and
Figure FDA0003344143910000034
so that x is more than or equal to y;
define the g-th idle time on machine k as
Figure FDA0003344143910000035
If and only if
Figure FDA0003344143910000036
And is
Figure FDA0003344143910000037
The process may be inserted into a free slot of a candidate machine.
5. The method of claim 1, wherein the load-balanced step-size adaptive discrete particle swarm algorithm employs segmented integer coding to divide the code of each particle into a machine selection part and a process ordering part;
the machine selection part is arranged from small to large in sequence according to the process numbers of the candidate machines, and the numbers of the corresponding positions are the numbers of the candidate machines in the process selectable machine set; the process sequencing part represents the workpiece number by a number, and the occurrence frequency of the number represents the process channel number of the workpiece corresponding to the number.
6. The method according to claim 5, wherein the load balancing step-size adaptive discrete particle swarm algorithm is based on a global random selection initialization method, performs machine selection on all processes, sorts all processes, and completes initialization of the machine selection part and the process sorting part.
7. The method according to claim 1, wherein the load balancing step-size adaptive discrete particle swarm algorithm sets an update step size as an adaptive parameter and introduces a load balancing strategy, and the particle position update formula of the load balancing step-size adaptive discrete particle swarm algorithm comprises:
Figure FDA0003344143910000038
wherein, c1、c2Respectively expressed as a particle confidence coefficient and a particle social confidence coefficient; ω represents an inertial weight factor; i represents the ith particle in the particle group, t and t +1 represent the number of iterations,
Figure FDA0003344143910000039
representing that the historical position of the ith particle in the t generation is optimal; gBtRepresenting t generation of global optimal particles; f, p and g all represent operation operators.
8. The method of claim 7, wherein the formula for updating the particle positions of the load balancing step-size adaptive discrete particle swarm algorithm further comprises:
Figure FDA0003344143910000041
Figure FDA0003344143910000042
Figure FDA0003344143910000043
9. a flexible job shop scheduling apparatus having an interval gray processing time, comprising:
a processor and a memory;
the processor and the memory are connected through a communication bus:
the processor is used for calling and executing the program stored in the memory;
the memory for storing a program for performing at least a method of flexible job shop scheduling with interval gray processing time according to any of claims 1-8.
CN202111317709.0A 2021-11-09 2021-11-09 Flexible job shop scheduling method and device with interval gray processing time Pending CN114254721A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202111317709.0A CN114254721A (en) 2021-11-09 2021-11-09 Flexible job shop scheduling method and device with interval gray processing time

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202111317709.0A CN114254721A (en) 2021-11-09 2021-11-09 Flexible job shop scheduling method and device with interval gray processing time

Publications (1)

Publication Number Publication Date
CN114254721A true CN114254721A (en) 2022-03-29

Family

ID=80790661

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202111317709.0A Pending CN114254721A (en) 2021-11-09 2021-11-09 Flexible job shop scheduling method and device with interval gray processing time

Country Status (1)

Country Link
CN (1) CN114254721A (en)

Similar Documents

Publication Publication Date Title
CN107590603B (en) Based on the dispatching method and system for improving change neighborhood search and differential evolution algorithm
US20210373888A1 (en) Multi-objective optimization method and system for master production plan of casting parallel workshops
CN107392402B (en) Production and transport coordinated dispatching method based on modified Tabu search algorithm and system
Lo et al. A genetic algorithm with new local operators for multiple traveling salesman problems
CN105629927A (en) Hybrid genetic algorithm-based MES (Manufacturing Execution System) production planning and scheduling method
CN112561225B (en) Flexible job shop scheduling method based on marker post co-evolution algorithm
CN112580922A (en) Flexible job shop scheduling method based on multilevel neighborhood structure and hybrid genetic algorithm
CN115471133A (en) Workshop comprehensive scheduling system based on order management and rolling optimization scheduling
CN110458326B (en) Mixed group intelligent optimization method for distributed blocking type pipeline scheduling
CN116933939A (en) Flexible workshop collaborative production method and system based on improved raccoon optimization algorithm
CN115933568A (en) Multi-target distributed hybrid flow shop scheduling method
CN109074348A (en) For being iterated the equipment and alternative manner of cluster to input data set
CN117521788A (en) Multi-mode and multi-target evolution method with double reference vector guidance
CN112651488A (en) Method for improving training efficiency of large-scale graph convolution neural network
CN113139720A (en) Casting shop production scheduling optimization method with learning effect
CN114254721A (en) Flexible job shop scheduling method and device with interval gray processing time
CN112801361A (en) UAVs and UGVs long-term multi-target path planning problem and solving algorithm
CN116774657A (en) Dynamic scheduling method for remanufacturing workshop based on robust optimization
CN110991917A (en) Multi-mode resource-limited project scheduling optimization method adopting two-stage genetic algorithm
CN115619200A (en) Production scheduling and multi-functional scheduling combined optimization method and device for split type Seru
CN116090773A (en) Flexible job shop scheduling method based on improved wolf algorithm
CN114936739A (en) Multi-target flexible job shop scheduling method based on improved cross entropy algorithm
CN110400073B (en) FSP method and system based on multi-direction convergence particle swarm optimization algorithm
CN115249113A (en) Distributed zero-waiting flow shop scheduling method and system with preparation time
CN110989542B (en) Production scheduling method and system for tobacco threshing and redrying production

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination