CN114707294B - Multi-target scheduling method for job shop with limited transportation capacity constraint - Google Patents

Multi-target scheduling method for job shop with limited transportation capacity constraint Download PDF

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CN114707294B
CN114707294B CN202210108708.3A CN202210108708A CN114707294B CN 114707294 B CN114707294 B CN 114707294B CN 202210108708 A CN202210108708 A CN 202210108708A CN 114707294 B CN114707294 B CN 114707294B
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CN114707294A (en
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彭乘风
廖勇
李翔
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Xiangnan University
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    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06Q10/063—Operations research, analysis or management
    • G06Q10/0631—Resource planning, allocation, distributing or scheduling for enterprises or organisations
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    • G06Q50/04—Manufacturing
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    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
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    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
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Abstract

The application relates to the technical field of job shop scheduling, in particular to a job shop multi-target scheduling method with limited transportation capacity constraint, which comprises the following steps: constructing a multi-target scheduling scene of a job shop with limited transportation capacity constraint according to an actual production shop; determining scheduling parameters and prerequisites of a multi-target scheduling scene of a job shop; constructing a multi-target workshop scheduling model with dual constraints of transportation resources and processing equipment resources; analyzing a multi-target workshop scheduling model based on a multi-target morein algorithm; acquiring optimal minimum maximum completion time and minimum AGV total transportation time according to the analysis result, and outputting a multi-target scheduling scheme of the job shop according to the optimal minimum maximum completion time and the minimum AGV total transportation time; the invention makes a reasonable combined scheduling scheme under the limited transportation capacity constraint scene, so that the manufacturing system has better processing efficiency and the transportation consumption of the AGV can be reduced.

Description

Multi-target scheduling method for job shop with limited transportation capacity constraint
Technical Field
The invention relates to the technical field of job shop scheduling, in particular to a job shop multi-target scheduling method with limited transportation capacity constraint.
Background
Aiming at the traditional job shop scheduling problem research, the flow transfer process of workpieces/materials between devices is not considered in the solving process, or the transfer time is assumed to be the transportation time of a certain fixed value. However, in an actual manufacturing system, the material handling cost generated by the handling activities associated with the workpieces/materials in the product manufacturing process usually accounts for 15% -70% of the product manufacturing cost, and usually requires 25% of human resources, 55% of factory space and 87% of production time, so it is important to consider the influence of the circulation of the materials/workpieces among the devices when making the workshop production scheduling plan.
When an Automatic Guided Vehicle (AGV) is used as an intelligent manufacturing workshop of a main Automatic material storage and transportation device to make a scheduling plan, not only the processing process of a workpiece on the processing device but also the circulation process of the workpiece among network transportation nodes (including processing devices, loading/unloading ports, material center warehouses and other non-additional device auxiliary nodes) of the workshop need to be considered. In an actual production manufacturing system, due to the influences of factors such as equipment purchasing cost, workshop layout design and actual operation of a workshop, a material storage and transportation system constructed by transport equipment such as an AGV has limited transportation capacity, and it cannot be guaranteed that all transport tasks can obtain responses from the AGV at a generation time (completing a processing task waiting sequence). Therefore, how to formulate a reasonable joint scheduling scheme under the limited transportation capability constraint scene to enable the manufacturing system to obtain better processing efficiency and reduce the transportation consumption of the AGVs (improve the long-term service capability of the AGVs) becomes a key problem to be solved urgently.
Disclosure of Invention
Aiming at the defects, the invention aims to provide a job shop multi-target scheduling method with limited transport capacity constraint, and a reasonable combined scheduling scheme is formulated under the limited transport capacity constraint scene, so that the manufacturing system has better processing efficiency, and the transport consumption of an AGV is reduced.
In order to achieve the purpose, the invention adopts the following technical scheme:
the multi-target scheduling method for the job shop with limited transportation capacity constraint comprises the following steps:
step A1: constructing a multi-target scheduling scene of a job shop with limited transportation capacity constraint according to an actual production shop;
step A2: determining scheduling parameters and prerequisites of a multi-target scheduling scene of a job shop;
step A: constructing a multi-target workshop scheduling model with dual constraints of transportation resources and processing equipment resources based on the steps A1 and A2;
and B: analyzing a multi-target workshop scheduling model based on a multi-target modular factorial algorithm;
and C: and acquiring the optimal minimum maximum completion time and the minimum AGV total transportation time according to the analysis result, and outputting a multi-target scheduling scheme of the job shop according to the optimal minimum maximum completion time and the minimum AGV total transportation time.
The step B comprises the step of analyzing the multi-target workshop scheduling model by solving the MO-JSPMH problem, and comprises the following steps: and designing a coding and decoding scheme aiming at the MO-JSPMH problem characteristics, executing crossover and mutation operator operations, and acquiring an initial solution to generate a strategy.
Preferably, in the step a, a scheduling model is constructed based on formula (1) and formula (2):
f 1 ＝minC max (1)
Figure GDA0003936991160000021
wherein f is 1 To minimize the objective function of the maximum completion time, f 2 An objective function that minimizes the total transport time of the AGV;
in the step a, constructing the scheduling model further includes setting constraints, where the constraints include formula (3) to formula (20):
C max ≥f i(n+1) (3)
f ij ≥d ij +p ij (4)
p i0 ＝0，p i(m+1) ＝0 (5)
d i(j+1) ≥f′ ij (6)
Figure GDA0003936991160000022
d′ ij ≥f ij (8)
Figure GDA0003936991160000023
Figure GDA0003936991160000024
Figure GDA0003936991160000025
Figure GDA0003936991160000026
Figure GDA0003936991160000031
Figure GDA0003936991160000032
Figure GDA0003936991160000033
Figure GDA0003936991160000034
Figure GDA0003936991160000035
Figure GDA0003936991160000036
δ ij，lq +δ lq，ij ＝1 (19)
C pl ＝V pl (20)。
preferably, the analyzing by using the multi-objective modular factorial optimization algorithm in the step B includes the following steps:
b1. setting parameters in the multi-target modular factorial algorithm, including setting population scale, iteration times, crossover operators, mutation operators and neighborhood search operators;
b2. coding in a mode of combining procedures and processing equipment, and performing population initialization: setting up the inter -no =0, generated by a combination of a random generation method of the code and a heuristic rule method
Figure GDA0003936991160000037
Individuals, which together form an initial population P (inter _ no);
b3. performing cross operation on the population based on a cross operator to generate a cross product
Figure GDA0003936991160000038
New population P of individuals cross (inter_no)；
b4. Performing mutation operation on the crossed population based on mutation operator to generate a mutation vector
Figure GDA0003936991160000039
New population P of individuals mut (inter_no)；
b5. Combining the new population generated after the cross mutation operation with the parent population to generate a new population P child (inter _ no) with an individual number of
Figure GDA00039369911600000310
b6. Carrying out duplication elimination treatment on repeated individuals in the combined population, and carrying out population filling on individuals removed by the duplication elimination treatment by newly generating equal number of individuals in a mode of combining a random generation method and heuristic rules to obtain a new population
Figure GDA00039369911600000311
b7. Randomly selecting a certain number of individuals from the population, and performing neighborhood search on the individuals of the certain number of individuals to obtain a new individualPopulation
Figure GDA00039369911600000312
b8. Performing non-dominated sorting and crowded distance calculation on the population, and updating the iterated times through inter _ no = inter _ no + 1;
b9. selecting from the population by a tournament selection strategy according to the results of the non-dominated sorting and the congestion degree calculation
Figure GDA0003936991160000041
Individuals, forming a parent population P (inter _ no) entering the next iteration;
b10. judging the iteration times: and when the inter _ no is larger than the inter _ max, outputting the population P (inter _ no), otherwise, returning to the step b3.
Preferably, the setting of the crossover operator in step b1 includes the following steps:
b11: randomly selecting two parent individuals P from parent population 1 And P 2 As a starting point for performing the crossover operation;
b12: based on the mapping relation, the workpiece sequencing layer and the AGV transportation layer are subjected to associated position matching, and the parent chromosome P is obtained through retrieval 1 And P 2 The same index position of the same position and the same gene segment, the adjacent positions are reserved, the gene point positions with the same positions as the gene segment are also met, and the adjacent positions are respectively reserved to the filial generation C 1 And C 2 Performing the following steps;
b13: randomly generating a numerical value between 1 and N as a cross gene locus N by taking the length of the chromosome as a base number N g The parent chromosome P 1 And P 2 In N g The genes before the position are respectively inherited to the offspring chromosome C 1 And C 2 At the corresponding position of (2);
b14: respectively to parent chromosome P 1 And C 2 、P 2 And C 1 Sequentially deleting the inherited genes in the sequencing layer of the middle workpiece, extracting to obtain a deleted gene sequence, and then performing deletion gene non-repeated insertion operation on the genes in the deleted gene sequence by taking left and right directions as guidance;
b15: and extracting chromosomes of the filial generation I and the filial generation II as filial generation results of the current cross operation.
Preferably, the setting of mutation operator in step b1 includes the following steps: acquiring a population needing to participate in mutation operation judgment; judging whether the individual population is subjected to variation operation one by one based on variation probability, and selecting to perform workpiece sequencing level variation or AGV transportation level variation according to 1/2 probability when the probability variation requirement is met; combining the new individuals after mutation operation and the individuals without mutation to form a new population.
Preferably, the setting of the neighborhood search operator in step b1 includes the following steps:
step 1: randomly selecting one procedure O in the critical path procedure set ij ；
And 2, step: the AGV transport is reselected for a process, and in order to avoid an invalid selection, the newly selected transport may not be the original transport.
Preferably, the step b2 includes obtaining an extended double-chain coding scheme based on the workpiece, where the extended double-chain coding scheme includes two parts: a workpiece sorting layer and an AGV transportation layer.
Preferably, the step b2 generates an initial solution by applying a heuristic rule method, specifically including 5 initial solution generation methods, which are 4 heuristic rule initial solution generation strategies and one heuristic rule based on an MNEH algorithm, respectively; the 4 heuristic rule initial solution generation strategies are as follows: rule1: combining an earliest transport completion strategy of the AGV and an earliest process starting strategy; rule2: combining the AGV minimum invalid transportation time strategy with the procedure earliest start strategy; rule3: combining the AGV minimum invalid transportation time strategy with the process earliest completion time strategy; rule4: and combining the AGV earliest transportation completion strategy with the process earliest completion time strategy.
Preferably, the heuristic rule is randomly used, and the specific using steps are as follows:
c1. generating a workpiece procedure according to the initial population decoding;
c2. according to the process, from left to right, determining whether the process needs AGV transportation, if so, continuing, otherwise, turning to the step c3;
c21. determining the number and the positions of the current idle AGV, selecting a scheduling rule, and designating the transported AGV;
c22. moving the selected AGV from the current position to a workpiece point to take a workpiece and then to a processing point;
c23. after the AGV reaches the processing point, the workpiece is put down and stops at the processing point, and the operation of other AGVs is not hindered;
c3. and d, judging whether the process is the last process, if so, finishing the AGV distribution, and otherwise, returning to the step c2.
The technical scheme comprises the following beneficial effects:
in the embodiment, firstly, a multi-target workshop scheduling model with dual constraints of transportation resources and processing equipment resources is constructed, secondly, a multi-target modular optimization algorithm is provided for the multi-target workshop scheduling model with dual constraints of transportation resources and processing equipment resources, corresponding coding and decoding methods are designed based on the characteristics of the researched scheduling problem, and crossover, mutation operator action and selection strategy are designed to obtain the optimal minimum maximum completion time (C) max ) And adjusting the workshop scheduling scheme according to the two conditions to realize optimization of the AGV scheduling strategy, so that the manufacturing system can obtain better processing efficiency, and the effect of reducing the transport consumption of the AGV can be achieved.
Drawings
FIG. 1 is a schematic diagram of a job shop of the present invention that takes into account limited transport capacity constraints;
FIG. 2 is a flow chart of the multi-objective modulo factor optimization algorithm of the present invention;
FIG. 3 is a schematic diagram of the SBOX crossover process of the present invention: the method comprises the following steps of (a) marking the same gene of a parent chromosome, (b) identifying the position of a tangent point and inheritance of the gene, and (c) filling of a deleted gene;
FIG. 4 is a schematic diagram of the SWAP mutation process of the present invention: (a) A process sequencing layer (JS) mutation operation, (b) an AGV transportation layer (TS) mutation operation;
FIG. 5 is a schematic diagram of the double-chain chromosome coding scheme of the present invention;
fig. 6 is an exemplary diagram of a decoding result of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
In the description of the present invention, it is to be understood that the terms "longitudinal", "lateral", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. indicate orientations or positional relationships based on those shown in the drawings, and are merely for convenience of description and simplicity of description, but do not indicate or imply that the device or element referred to must have a particular orientation, be constructed in a particular orientation, and be operated, and thus, are not to be construed as limiting the present invention. Furthermore, features defined as "first" and "second" may explicitly or implicitly include one or more of the features for distinguishing between descriptive features, non-sequential, non-trivial and non-trivial.
In the description of the present invention, "a plurality" means two or more unless otherwise specified.
In the description of the present invention, it should be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly and may be, for example, fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
The multi-objective job shop scheduling method with limited transportation capacity constraint according to the embodiment of the present invention is described below with reference to fig. 1 to 6 and tables 1 and 2, and includes the following steps:
step A1: constructing a multi-target scheduling scene of a job shop with limited transportation capacity constraint according to an actual production shop;
step A2: determining scheduling parameters and prerequisites of a multi-target scheduling scene of a job shop;
step A: constructing a multi-target workshop scheduling model with dual constraints of transportation resources and processing equipment resources based on the steps A1 and A2;
and B: analyzing a multi-target workshop scheduling model based on a multi-target modulo factor algorithm;
and C: and acquiring the optimal minimum maximum completion time and the minimum AGV total transportation time according to the analysis result, and outputting a multi-target scheduling scheme of the job shop according to the optimal minimum maximum completion time and the minimum AGV total transportation time.
The step B comprises the step of analyzing the multi-target workshop scheduling model by solving the MO-JSPMH problem, and comprises the following steps: and designing a coding and decoding scheme aiming at the MO-JSPMH problem characteristics, executing crossover and mutation operator operations, and acquiring an initial solution to generate a strategy.
Specifically, aiming at the problem of Multi-Objective scheduling of a job shop with limited transport capacity constraint, the invention provides a Multi-Objective Memetic Algorithm (MOMA) for solving the problem. Firstly, a multi-target workshop scheduling model with dual constraints of transportation resources and processing equipment resources is constructed. Secondly, a multi-objective modular optimization algorithm is provided for a multi-objective workshop scheduling model with dual constraints of transportation resources and processing equipment resources, corresponding coding and decoding methods are designed based on the characteristics of the researched scheduling problem, and crossover and mutation operator actions and selection strategies are designed to obtain the optimal minimum maximum completion time (C) max ) And the total transport time of the AGV is adjusted according to the workshop scheduling scheme under the two conditions, so that the optimization of the AGV scheduling strategy is realized, the manufacturing system can obtain better processing efficiency, and the effect of reducing the transport consumption of the AGV can be achieved.
Specifically, the scheme is that a multi-objective scheduling scene of the job shop with limited transportation capacity constraint is constructed based on an actual production shop. Fig. 1 is a schematic diagram of a job shop considering a limited transportation capacity constraint, which is composed of three areas, namely a processing area, a transfer warehouse and a trolley parking lot, wherein the processing area is used for processing raw materials/parts and consists of a plurality of processing units with different functions (each processing unit comprises processing equipment and a front/rear material buffer area) and a transportation track with a known guiding path; the transfer warehouse is used as a storage area for raw materials, parts, semi-finished products and other materials and is responsible for the distributed work of workshop materials; car parks are storage locations where transport equipment is idle (the need for capacity in the plant is less than the capacity available from the transport system). The work process of the workpiece in the work shop can be described as follows: based on the process constraint of the workpiece, the trolley is used for carrying the workpiece to an appointed processing unit of a processing area for processing operation, the trolley is still used for carrying out transfer work (transferring to appointed equipment/transfer warehouse of the next procedure) after the processing operation is finished, and the workpiece is transferred to the transfer warehouse for storage operation after all procedures of processing tasks of the workpiece in the workshop are finished.
Further, the scheduling parameters of the multi-objective scheduling scenario of the job shop with limited transportation capacity constraint may be specifically described as follows: there is a set of workpieces J = {1, 2.., n } each workpiece having n j The method comprises the steps that processing is to be carried out on each process, each process is processed by uniquely-assigned processing equipment M, M belongs to M = {1,.., M }, and a conveying equipment set R = {1,2,..., R } formed by R AGVs is responsible for transferring operation of workpieces among nodes (a processing equipment set and a transfer warehouse), and the scheduling optimization target is to minimize the maximum completion time (C) max ) And minimizing total transit time.
Further, the multi-objective scheduling problem of the job shop is optimized under the following preconditions: (1) At an initial moment (which can be regarded as a decision moment), all the processing equipment and the AGV are in an idle state; (2) The carrying routes of the AGVs among the nodes are planned based on the shortest path principle, and the AGVs do not interfere with each other in the carrying task executing process; (3) The AGV is responsible for accepting from the cache area of the processing equipment in the previous processCorresponding workpieces are conveyed to a buffer area of the next process; (4) Neglecting the time consumption of loading the workpieces from the buffer area to the AGV and the time consumption of unloading the workpieces from the AGV to the buffer area; (5) The transport time consumption of the AGV between any transport nodes is only related to the distance between the nodes and the transport speed of the AGV, and special conditions such as faults and the like in the transport process are not considered; (6) The carrying distance between any two nodes of the AGV meets the principle of triangle inequality, namely T ij ＜T ik +T kj The method also means that the transfer transportation needs to generate larger consumption than the direct transportation; (7) Each AGV can only provide the carrying service for one workpiece at the same time, and the carrying service has non-interruptability and does not consider the condition that the AGV has faults; (8) Each processing device can only process one workpiece at the same time, the processing of the workpiece on the device is non-interruptible, and the condition that the processing device breaks down is not considered; (9) Different workpieces have no association constraint, but for the same workpiece, the processing of the previous procedure is completed firstly, and the processing operation of the next procedure can be carried out; (10) The criterion of processing the workpieces by the processing equipment is first come first serve, namely, sequencing processing is carried out according to the sequence of the workpieces reaching the processing equipment; (11) All workpieces to be processed are initially located in the transfer warehouse.
Preferably, in the step a, a scheduling model is constructed based on formula (1) and formula (2):
f 1 ＝minC max (1)
Figure GDA0003936991160000081
wherein f is 1 To minimize the objective function of the maximum completion time, f 2 An objective function that minimizes total transport time of the AGV;
in the step a, constructing the scheduling model further includes setting constraints, where the constraints include formula (3) to formula (20):
C max ≥f i(n+1) (3)
f ij ≥d ij +p ij (4)
p i0 ＝0，p i(m+1) ＝0 (5)
d i(j+1) ≥f′ ij (6)
Figure GDA0003936991160000091
d′ ij ≥f ij (8)
Figure GDA0003936991160000092
Figure GDA0003936991160000093
Figure GDA0003936991160000094
Figure GDA0003936991160000095
Figure GDA0003936991160000096
Figure GDA0003936991160000097
Figure GDA0003936991160000098
Figure GDA0003936991160000099
Figure GDA00039369911600000910
Figure GDA00039369911600000911
δ ij，lq +δ lq，ij ＝1 (19)
C pl ＝V pl (20)。
specifically, the parameters in the formulas (1) to (20) are as follows: workpiece numbering: i, l; numbering processing equipment: m l (ii) a P/D port number: m 0 (ii) a Carrying equipment number: r is s ，r k (ii) a And task procedure numbering: o is ij ，O lq (ii) a Release task of workpiece i: o is i0 (ii) a Recovery task of workpiece i: o is i(n+1) (ii) a Process O ij The processing time of (2): p is a radical of ij (ii) a The loading of the AGV to transport material from equipment p to equipment l takes time: c pl (ii) a Empty elapsed time for AGV to transfer from device p to device l: v pl (ii) a One maximum value: h; set of task workpieces, J = { J = { (J) 1 ，J 2 ，...，J n }; set of processing equipment, M = { M = } 1 ，M 2 ，...，M m }; set of handling equipment, R = { R = 1 ，r 2 ，..，r k }; set of machining tasks for workpiece i, J i ＝{O i1 ，O i2 ，...，O in }；T ij : the workpiece i is processed by the procedure O ij Transporting to procedure O on the processing equipment i(j+1) Transporting tasks of processing equipment; d is a radical of ij : process task O ij Start of process time on the machine; f. of ij : procedure task O ij Task completion time on the machine; d' ij : transport task T ij The start of conveyance time of (2); f' ij : transport task T ij The transport completion time of (2);
Figure GDA0003936991160000101
Figure GDA0003936991160000102
Figure GDA0003936991160000103
Figure GDA0003936991160000104
Figure GDA0003936991160000105
specifically, the formula (1) and the formula (2) respectively represent that the optimization target of the scheduling problem is to minimize C max And minimizing total transit time; formula (3) represents C max The value is the maximum value of the time for returning all the workpieces to the P/D port after processing; equations (4) and (5) show that the task can not be interrupted during the machining process, wherein (4) shows the updating of the completion time of the workpiece, and equation (5) shows that the workpiece does not need to spend extra time when going out of the P/D port or entering the station; the expressions (6) to (8) are used for ensuring that the task workpiece can enter a conveying and processing state as soon as possible after finishing the processing and conveying operation, and the expression (6) represents that the workpiece processing starting time is limited by the conveying arrival time; the expressions (7) and (8) indicate that the workpiece can be transported to the processing side when waiting for the completion of the processing; equations (9) to (11) indicate that the processing device has uniqueness in processing the processing task: only one workpiece can be processed by one device at the same time, and only one workpiece can be processed by one device at the same time; wherein formula (12) indicates that a transport job can only be serviced by one AGV; equations (13) - (19) represent the uniqueness of performing the handling task: one AGV can only process one transfer task at the same time, and one transfer task can only be served by one AGV. Equation (20) indicates that the problem does not take into account the transit time offset between load and no load.
Preferably, the analyzing by using the multi-objective modular factorial optimization algorithm in the step B includes the following steps:
b1. setting parameters in the multi-target modular factorial algorithm, including setting population scale, iteration times, crossover operators, mutation operators and neighborhood search operators;
b2. coding in a mode of combining procedures and processing equipment, and performing population initialization: setting up the inter -no =0, generated by combining a random generation method of coding with a heuristic rule method
Figure GDA0003936991160000111
Individuals, which together form an initial population P (inter _ no);
b3. performing cross operation on the population based on a cross operator to generate a cross product
Figure GDA0003936991160000112
New population P of individuals cross (inter_no)；
b4. Performing mutation operation on the crossed population based on mutation operator to generate a mutation vector
Figure GDA0003936991160000113
New population P of individuals mut (inter_no)；
b5. Combining the new population generated after the cross mutation operation with the parent population to generate a new population P child (inter _ no) with an individual number of
Figure GDA0003936991160000114
b6. Carrying out duplication elimination treatment on repeated individuals in the combined population, and carrying out population filling on individuals removed by the duplication elimination treatment by newly generating equal number of individuals in a mode of combining a random generation method and heuristic rules to obtain a new population
Figure GDA0003936991160000115
b7. Randomly selecting a certain number of individuals from the population, and performing neighborhood search on the individuals of the certain number of individuals to obtain a new population
Figure GDA0003936991160000116
b8. Performing non-dominated sorting and crowded distance calculation on the population, and updating the iterated times through inter _ no = inter _ no + 1;
b9. selecting from the population by a tournament selection strategy according to the results of the non-dominated sorting and the congestion degree calculation
Figure GDA0003936991160000117
Individuals, forming a parent population P (inter _ no) entering the next iteration;
b10. judging the iteration times: and when the inter _ no is larger than the inter _ max, outputting the population P (inter _ no), otherwise, returning to the step b3.
Specifically, as shown in fig. 2, the MO-MA Algorithm is a general flow framework of the MO-MA Algorithm, and the MO-MA Algorithm is a neighborhood search method that combines an Evolutionary Algorithm (FA) framework with a specific problem, so as to implement global search and local mining for the problem: a plurality of initial populations are randomly generated through coding, and heuristic rules are embedded in the algorithm to generate an initial solution scheme with higher quality, so that high-quality gene segments are provided for the algorithm at the initial stage of searching, and the initial populations with high quality are formed together; after the parent population is generated, new child populations are generated through crossing and mutation operations respectively, then the child populations and the parent populations are subjected to de-coincidence, and a part of individuals are randomly selected from the combined population to perform neighborhood search.
In this embodiment, the binary tournament selection policy is used in b9 to randomly equally divide the population having the number of individuals N into the number of individuals
Figure GDA0003936991160000121
Then randomly selecting an individual from the two groups to "compete": preferentially selecting individuals with low dominance solution level, and if the two levels are at the same level, selecting the individuals with large crowding values; finally, one can be generated based on this individual selection policy
Figure GDA0003936991160000122
Population of individual population. Because of the limitation of equipment computing power and the difficulty of the problem, the number of individuals in the population cannot be increased without limit, and simultaneously, the diversity of population individuals is easily reduced due to the overhigh population scale, so that the reasonable strategy can be selected to ensure the balance of the population searching capability and the mining capability in the searching process.
Preferably, the setting of the crossover operator in step b1 includes the following steps:
b11: randomly selecting two parent individuals P from parent population 1 And P 2 As a starting point for performing the crossover operation;
b12: based on the mapping relation, the workpiece sequencing layer and the AGV transportation layer are subjected to associated position matching, and the parent chromosome P is obtained through retrieval 1 And P 2 The same index position of the same position and the same gene segment, the adjacent positions are reserved, the gene point positions with the same positions and the same gene segments are also satisfied, and the adjacent positions are respectively reserved to offspring C 1 And C 2 Performing the following steps;
b13: randomly generating a numerical value between 1 and N as a cross gene locus N by taking the length of a chromosome as a base number N g The parent chromosome P 1 And P 2 In N g The genes in the front position are respectively inherited to offspring chromosome C 1 And C 2 At the corresponding position of (2);
b14: respectively to parent chromosome P 1 And C 2 、P 2 And C 1 Sequentially deleting the inherited genes in the sequencing layer of the middle workpiece, extracting to obtain a deleted gene sequence, and then performing deletion gene non-repeated insertion operation on the genes in the deleted gene sequence by taking left and right directions as guidance;
b15: and extracting chromosomes of the first filial generation and the second filial generation as filial generation results of the current crossover operation.
Specifically, step b12 is shown in fig. 3 (a), step b13 is shown in fig. 3 (b), and step b14 is shown in fig. 3 (c); the essence of the crossover operation is to simulate the process of gene exchange of the parent chromosome, so that the offspring inherits part of the excellent gene from the parent chromosome. In order to promote the inheritance of high-quality gene segments in parent population to offspring population and consider that the intermediate process task of double-chain chromosome coding has certain relevance with the handling task, the handling task needs to be considered when chromosome crossing is carried out. In the embodiment, the SBOX crossover with better comprehensive performance is selected as the final crossover operator of the research algorithm.
Preferably, the setting of mutation operator in step b1 includes the following steps: acquiring a population needing to participate in variation operation judgment; judging whether individual population is subjected to variation operation one by one based on variation probability, and selecting workpiece sequencing level variation or AGV transportation level variation according to 1/2 probability when the probability variation requirement is met; and combining the new individuals subjected to the mutation operation and the individuals without the mutation operation to form a new population.
Specifically, the design process of the workpiece sequencing layer (JS) mutation operator is as shown in fig. 4 (a), and first, two workpiece sequencing layer gene segments with different workpiece numbers in an individual to be subjected to mutation operation are randomly selected; then, the selected gene segments are subjected to interchange operation; and finally, obtaining the variant updated filial generation individuals.
The design process of the AGV transport layer (TS) mutation operator is shown in FIG. 4 (b), firstly, randomly selecting an AGV transport layer gene segment in an individual needing mutation operation; then, randomly selecting an AGV device which is not the current AGV from the available AGV carrying device set to replace the original AGV; and finally, obtaining the variant updated filial generation individuals.
Preferably, the setting of the neighborhood search operator in step b1 includes the following steps:
step 1: randomly selecting one procedure O in the critical path procedure set ij ；
And 2, step: the AGV transport is reselected for a process, and in order to avoid an invalid selection, the newly selected transport may not be the original transport.
Specifically, the critical path of the scheduling scheme is retrieved in the following manner: in a working process O ij For reference, the process O is determined by the equations (21) to (23) ij Earliest start-up time S Earliest (O ij ) Latest start time S Latest (O ij ) When S is Earliest (O ij )＝S Latest (O ij ) Time procedure O ij Is one of the processes in the key process chain.
Figure GDA0003936991160000131
Figure GDA0003936991160000132
Figure GDA0003936991160000133
Wherein, C Earliest (PO ij ) In the workpiece i prior to O ij The working procedures of the operation are as follows,
Figure GDA0003936991160000134
to precede O in machine k ij Procedure of operation S Latest (SO ij ) For the workpiece i later than O ij The working procedures of the operation are as follows,
Figure GDA0003936991160000135
to be later than O in machine k ij And (4) operating.
Preferably, the step b2 includes obtaining an extended double-chain coding scheme based on the workpiece, where the extended double-chain coding scheme includes two parts: a workpiece sorting layer and an AGV transportation layer.
Specifically, as shown in fig. 5, the gene value of the workpiece sorting layer (JS) represents the corresponding workpiece number, and the cumulative frequency of occurrence of the workpieces from left to right represents the workpiece number corresponding to the workpiece; the code of the AGV transport layer (TS) corresponds one-to-one to the process information indicated by the work code, and the gene value represents an AGV equipment number assigned to perform a corresponding process transport task. Production resources needing to participate in scheduling decision making in consideration of scheduling problems comprise processing equipment and AGV transportation equipmentTwo types of operation can be realized through the action description of AGV 'firstly carrying the workpiece to the processing equipment', and the implicit expression of the sequencing of the workpiece on the processing equipment is realized: the workpiece which is first carried out the carrying operation has the priority of occupation to the target processing equipment. Therefore, the present study employs an extended dual chain coding scheme based on workpieces. As shown in FIG. 5, the numerical information of the gene segment of the workpiece sorting layer indicates the workpiece number, and the first process O of the workpiece 1 is indicated by the appearance frequency of the current workpiece number, such as the first 1 11 The second 1 represents a second step O of the workpiece 1 12 And so on. The value of the gene layer in the AGV transport layer indicates the AGV number assigned to transport the workpiece to the process facility, and if the AGV cart with the number 2 at the second position transports the workpiece 3 to the processing facility M3 (the associated information is retrieved from table 2), and so on.
As shown in tables 1 and 2, the transportation time matrix information table and the workpiece processing process path information table of each node of one of the test case sets proposed by bill ge are respectively, wherein the numbers in table 1 represent the transportation time required between two nodes, the number 12 in the first row in table 1 represents the transportation time of the M4 device transported from L/U, and the rest of the numbers in the tables are similar. Reference is made to Bilge U.S.A. time window approach to synergistic and cyclic scheduling of technologies and systems in FMS [ J ]. Operations Research,199543 (6): 1058-1070.
Figure GDA0003936991160000141
TABLE 1
Figure GDA0003936991160000151
TABLE 2
Preferably, the step b2 generates an initial solution by applying a heuristic rule method, specifically including 5 initial solution generation methods, which are 4 heuristic rule initial solution generation strategies and one heuristic rule based on an MNEH algorithm, respectively; the 4 heuristic rule initial solution generation strategies are as follows: rule1: combining an AGV earliest transportation completion strategy with a process earliest start strategy; rule2: combining the AGV minimum invalid transportation time strategy with the procedure earliest start strategy; rule3: combining the AGV minimum invalid transportation time strategy with the process earliest completion time strategy; rule4: and combining the AGV earliest transportation completion strategy with the process earliest completion time strategy.
Specifically, a heuristic dynamic decision algorithm framework is shown in the following table, in order to use a processing task (task start time and task completion time) and a transport task (transport task completion time and invalid transport time) as auxiliary decision variables to perform dynamic decision algorithm flow pseudo codes, different selection strategies are respectively embedded into an AGV selection strategy on the 10 th row and a task selection strategy on the 13 th row of the algorithm flow pseudo codes, so as to form 4 different heuristic rules:
Figure GDA0003936991160000152
Figure GDA0003936991160000161
the MNEH algorithm flow is shown in the following table, and the adaptive improvement of the algorithm based on the problem is realized by embedding the AGV earliest release preference strategy in the traditional NEH scheduling decision process, and meanwhile, C is used max The value is a sorting scheme selection index, and the final sorting scheme is selected.
Figure GDA0003936991160000162
Figure GDA0003936991160000171
By embedding an initial solution generation strategy with a higher solution quality effect, the search efficiency of an MO-MA algorithm on an effective solution space can be improved, the search time of the MO-MA algorithm is reduced, and the solution quality of the algorithm in a limited time is ensured; especially in large-scale problem scenes, compared with searching without preposed high-quality genes, the optimization algorithm with high-quality scheme gene inheritance has higher utilization rate for limited searching time.
Preferably, the heuristic rule is randomly used, and the specific using steps are as follows:
c1. decoding according to the initial population to generate a workpiece procedure;
c2. according to the process, from left to right, determining whether the process needs AGV transportation, if so, continuing, otherwise, turning to the step c3;
c21. determining the number and the position of the current idle AGV, selecting a scheduling rule, and appointing the AGV to be transported;
c22. moving the selected AGV from the current position to a workpiece point to take a workpiece and then to a processing point;
c23. after the AGV reaches the processing point, the workpiece is put down and stops at the processing point, and the operation of other AGVs is not hindered;
c3. and judging whether the process is the last process, if so, finishing the AGV distribution, and otherwise, returning to the step c2.
Specifically, after the encoding is completed, the target value needs to be decoded, and in the decoding process, the process constraint of the workpiece, the non-interruptibility and exclusivity of the process, the processing equipment and the AGV need to be considered. In the process O in FIG. 5 11 And a step O 21 For example, the process is the first process corresponding to the workpiece, but the AGV and the processing equipment assigned to service the process are both the same equipment, and the process O is based on the encoded information 21 Need to be placed in the working procedure O 11 Then carrying and processing are carried out.
The decoding steps are as follows:
step 1: extracting gene segments from the left side of the workpiece sorting layer (JS), and converting the gene segments into a corresponding procedure O ip ；
Step 2: acquiring a procedure O from the workpiece processing path information table through the mapping relation ip Processing apparatus M ip And the preceding step O i(p-1) Processing apparatus M i(p-1) And a step O ip Processing time of
Figure GDA0003936991160000172
Mapping the AGV transportation layer gene segments to obtain a carrying AGV;
and 3, step 3: obtaining the release time of the current AGV through forward retrieval
Figure GDA0003936991160000181
And a release location node D for carrying the AGV a And a processing apparatus M i(p-1) Position node of (2)
Figure GDA0003936991160000182
Calculating empty transport time of AGV
Figure GDA0003936991160000183
The AGV reaching the processing equipment M is obtained through a formula (24) i(p-1) Time of
Figure GDA0003936991160000184
Figure GDA0003936991160000185
And 4, step 4: obtaining the release time of the workpiece completing process according to the workpiece processing information
Figure GDA0003936991160000186
And judges the starting time of the work according to the formula (25)
Figure GDA0003936991160000187
And passing through the current location node
Figure GDA0003936991160000188
And a target node
Figure GDA0003936991160000189
Calculating load transport time for AGV
Figure GDA00039369911600001810
The AGV reaching the processing equipment M is calculated by a formula (26) ip Time of
Figure GDA00039369911600001811
And synchronously updating the release time of the current AGV
Figure GDA00039369911600001812
Figure GDA00039369911600001813
Figure GDA00039369911600001814
And 5: obtaining the finished processing equipment arrangement procedure O by carrying out forward retrieval on the processing equipment ip Release time of pre-processing tasks
Figure GDA00039369911600001815
And judging the earliest start-up time of the process according to the formula (27)
Figure GDA00039369911600001816
And based on process time
Figure GDA00039369911600001817
Updating the completion time of a workpiece i
Figure GDA00039369911600001818
Figure GDA00039369911600001819
Step 6: if all the genes in the workpiece sorting layer (JS) are decoded, ending the decoding program; otherwise, returning to the step 1.
As shown in fig. 6, which is the decoding result in the case of the encoding of fig. 5.
Other configurations and operations of the limited transportability constrained job-shop multi-objective scheduling method according to embodiments of the present invention are known to those of ordinary skill in the art and will not be described in detail herein.
In the description herein, references to the description of the terms "embodiment," "example," etc., mean 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 invention. 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.
While embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims (7)

1. The multi-target scheduling method of the job shop with limited transport capacity constraint is characterized in that: the method comprises the following steps:
step A1: constructing a multi-target scheduling scene of a job shop with limited transportation capacity constraint according to an actual production shop;
step A2: determining scheduling parameters and prerequisites of a multi-target scheduling scene of a job shop;
step A: constructing a multi-target workshop scheduling model with dual constraints of transportation resources and processing equipment resources based on the steps A1 and A2;
and B, step B: analyzing a multi-target workshop scheduling model based on a multi-target modulo factor algorithm;
and C: acquiring optimal minimum maximum completion time and minimum AGV total transportation time according to the analysis result, and outputting a multi-target scheduling scheme of the job shop according to the optimal minimum maximum completion time and the minimum AGV total transportation time;
the step B comprises the step of analyzing the multi-target workshop scheduling model by solving an M0-JSPMH problem, and comprises the following steps: designing a coding and decoding scheme aiming at MO-JSPMH problem features, executing crossover and mutation operator operations, and acquiring an initial solution to generate a strategy;
in the step a, a scheduling model is constructed based on formula (1) and formula (2):
f 1 ＝minC max (1)
Figure FDA0003936991150000011
wherein f is 1 To minimize the objective function of the maximum completion time, f 2 An objective function that minimizes the total transport time of the AGV;
in the step a, constructing the scheduling model further includes setting constraints, where the constraints include formula (3) to formula (20):
C max ≥f i(n+1) (3)
f ij ≥d ij +p ij (4)
p i0 ＝0，p i(m+1) ＝0 (5)
d i(j+1) ≥f′ ij (6)
Figure FDA0003936991150000012
d′ ij ≥f ij (8)
Figure FDA0003936991150000013
Figure FDA0003936991150000014
Figure FDA0003936991150000015
Figure FDA0003936991150000021
Figure FDA0003936991150000022
Figure FDA0003936991150000023
Figure FDA0003936991150000024
Figure FDA0003936991150000025
Figure FDA0003936991150000026
Figure FDA0003936991150000027
δ ij，lq +δ lq，ij ＝1 (19)
C pl ＝V pl (20)
wherein, the workpiece number is: i, l; numbering processing equipment: m is a group of l (ii) a P/D port number: m is a group of 0 (ii) a The number of the conveying equipment: r is s ，r k (ii) a And task procedure numbering: o is ij ，O lq (ii) a Release task of workpiece i: o is i0 (ii) a Recovery task of workpiece i: o is i(n+1) (ii) a Process O ij The processing time of (2): p is a radical of ij (ii) a The loading of the AGV to transport material from equipment p to equipment l takes time: c pl (ii) a Empty elapsed time for AGV to transfer from device p to device l: v pl (ii) a One maximum value: h; set of task workpieces, J = { J = { (J) 1 ，J 2 ，...，J n }; set of processing equipment, M = { M = } 1 ，M 2 ，...，M m }; set of handling equipment, R = { R = 1 ，r 2 ，...，r k }; set of machining tasks for workpiece i, J i ＝{O i1 ，O i2 ，...，O in }；T ij : the workpiece i is processed by the procedure O ij Transporting to procedure O on the processing equipment i(j+1) Transporting tasks of the processing equipment; d ij : process task O ij Start of process time on the machine; f. of ij : process task O ij Task completion time on the machine; d' ij : transport task T ij The start transport time of (2); f' ij : transport task T ij The transport completion time of (2);
Figure FDA0003936991150000028
Figure FDA0003936991150000029
Figure FDA0003936991150000031
Figure FDA0003936991150000032
Figure FDA0003936991150000033
wherein, the formula (1) and the formula (2) respectively represent that the optimization target of the scheduling problem is to minimize and minimize the total transportation time; the expression (3) is the maximum value of the time for all the workpieces to return to the P/D port after processing; equations (4) and (5) show that the task can not be interrupted during the machining process, wherein (4) shows the updating of the completion time of the workpiece, and equation (5) shows that the workpiece does not need to spend extra time when going out of the P/D port or entering the station; the formulas (6) - (8) are used for ensuring that the task workpiece can enter a conveying and processing state as soon as possible after finishing the processing and conveying operation, and the formula (6) shows that the workpiece processing starting time is limited by the transportation arrival time; the formulas (7) and (8) show that the workpiece can be transported to the processing party when waiting for finishing; equations (9) to (11) indicate that the processing device has uniqueness in processing the processing task: only one workpiece can be processed by one device at the same time, and only one workpiece can be processed by one device at the same time; wherein formula (12) indicates that a transport job can only be serviced by one AGV; equations (13) - (19) represent the uniqueness of performing the handling task: one AGV can only process one carrying task at the same time, and one carrying task can be only served by one AGV; equation (20) indicates that the problem does not take into account the transit time offset between loading and unloading;
the analysis by using the multi-objective modular factor optimization algorithm in the step B comprises the following steps:
b1. setting parameters in the multi-target modular factorial algorithm, including setting population scale, iteration times, crossover operators, mutation operators and neighborhood search operators;
b2. coding in a mode of combining procedures and processing equipment, and performing population initialization: setting inter -no =0, generated by a combination of a random generation method of the code and a heuristic rule method
Figure FDA0003936991150000034
Individuals, which together form an initial population P (inter _ no);
b3. performing cross operation on the population based on a cross operator to generate a cross product
Figure FDA0003936991150000035
New population P of individuals cross (inter_no)；
b4. Performing mutation operation on the crossed population based on mutation operator to generate a mutation vector
Figure FDA0003936991150000036
New population P of individuals mut (inter_no)；
b5. Combining the new population generated after the cross mutation operation with the parent population to generate a new population P child (inter _ no) with an individual number of
Figure FDA0003936991150000041
b6. Carrying out duplication elimination treatment on repeated individuals in the combined population, and carrying out population filling on individuals removed by the duplication elimination treatment by newly generating equal number of individuals in a mode of combining a random generation method and heuristic rules to obtain a new population
Figure FDA0003936991150000042
b7. Randomly selecting a certain number of individuals from the population, and performing neighborhood search on the individuals to obtain a new population
Figure FDA0003936991150000043
b8. Performing non-dominated sorting and crowded distance calculation on the population, and updating the iterated times through inter _ no = inter _ no + 1;
b9. selecting from the population by adopting a tournament selection strategy according to the results of non-dominated sorting and crowding calculation
Figure FDA0003936991150000044
Individuals, forming a parent population P (inter _ no) entering next iteration;
b10. judging the iteration times: and when the inter _ no is larger than the inter _ max, outputting the population P (inter _ no), otherwise, returning to the step b3.
2. The limited transportability constrained job shop multi-objective scheduling method according to claim 1, characterized in that: the setting of the crossover operator in the step b1 comprises the following steps:
b11: randomly selecting two parent individuals P from parent population 1 And P 2 As a starting point for performing the crossover operation;
b12: based on the mapping relation, the workpiece sequencing layer and the AGV transportation layer are subjected to associated position matching, and the parent chromosome P is obtained through retrieval 1 And P 2 The same index position of the same position and the same gene segment, the adjacent positions are reserved, the gene point positions with the same positions and the same gene segments are also satisfied, and the adjacent positions are respectively reserved to offspring C 1 And C 2 The preparation method comprises the following steps of (1) performing;
b13: randomly generating a numerical value between 1 and N as a cross gene locus N by taking the length of a chromosome as a base number N g The parent chromosome P 1 And P 2 In N g The genes in the front position are respectively inherited to offspring chromosome C 1 And C 2 At the corresponding position of (2);
b14: respectively to parent chromosome P 1 And C 2 、P 2 And C 1 Sequentially deleting the genes which are not inherited in the middle workpiece sequencing layer, extracting to obtain a deleted gene sequence, and then carrying out non-repeated insertion operation on the deleted genes in the deleted gene sequence by taking left and right directions as a guide;
b15: and extracting chromosomes of the first filial generation and the second filial generation as filial generation results of the current crossover operation.
3. The limited-transportability-constrained job shop multi-objective scheduling method according to claim 1, characterized in that: the setting of the mutation operator in the step b1 comprises the following steps: acquiring a population needing to participate in mutation operation judgment; judging whether the individual population is subjected to variation operation one by one based on variation probability, and selecting to perform workpiece sequencing level variation or AGV transportation level variation according to 1/2 probability when the probability variation requirement is met; and combining the new individuals subjected to the mutation operation and the individuals without the mutation operation to form a new population.
4. The limited-transportability-constrained job shop multi-objective scheduling method according to claim 1, characterized in that: the setting of the neighborhood search operator in the step b1 comprises the following steps:
step 1: randomly selecting one procedure O in the critical path procedure set ij ；
Step 2: the AGV transport is reselected for the process, and in order to avoid invalid selection, the newly selected transport may not be the original transport.
5. The limited transportability constrained job shop multi-objective scheduling method according to claim 1, characterized in that: in the step b2, an extended double-chain coding scheme based on the workpiece is obtained, wherein the extended double-chain coding scheme comprises two parts: a workpiece sequencing layer and an AGV transportation layer.
6. The limited-transportability-constrained job shop multi-objective scheduling method according to claim 1, characterized in that: in the step b2, a heuristic rule method is used for generating an initial solution, specifically, the method comprises 5 initial solution generation methods, namely 4 heuristic rule initial solution generation strategies and a heuristic rule based on an MNEH algorithm; the 4 heuristic rule initial solution generation strategies are as follows: rule1: combining an AGV earliest transportation completion strategy with a process earliest start strategy; rule2: combining an AGV minimum invalid transportation time strategy with a procedure earliest starting strategy; rule3: combining the AGV minimum invalid transportation time strategy with the process earliest completion time strategy; rule4: and combining the AGV earliest transportation completion strategy with the process earliest completion time strategy.
7. The limited transportability constrained job shop multi-objective scheduling method according to claim 6, characterized in that: the heuristic rule is randomly used, and the specific using steps are as follows:
c1. generating a workpiece procedure according to the initial population decoding;
c2. according to the process, from left to right, determining whether the process needs AGV transportation, if so, continuing, otherwise, turning to the step c3;
c21. determining the number and the position of the current idle AGV, selecting a scheduling rule, and appointing the AGV to be transported;
c22. moving the selected AGV from the current position to a workpiece point to take a workpiece and then to a processing point;
c23. after the AGV reaches the processing point, the workpiece is put down and stops at the processing point, and the operation of other AGVs is not hindered;
c3. and judging whether the process is the last process, if so, finishing the AGV distribution, and otherwise, returning to the step c2.
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