CN117077975A - Distributed heterogeneous flow shop scheduling method based on mixed initialization modular factor algorithm - Google Patents
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Abstract
The invention discloses a distributed heterogeneous flow shop scheduling method based on a mixed initialization model algorithm, belongs to the field of shop scheduling, and aims to solve the problem that the existing production scheduling method is only suitable for isomorphic factory models. The method comprises the following steps: step S1: establishing a distributed heterogeneous flow shop scheduling model; step S2: initializing basic parameters of a model factor algorithm, and generating an initial population according to a mixed initialization strategy; step S3: evaluating fitness values of population individuals, and performing pareto non-dominant ranking; step S4: performing certain probability cross operation on individuals in the population; step S5: collaborative searching is carried out on the population by adopting a searching operator; step S6: combining the offspring population with the father population, and selecting half of individuals as local search targets; step S7: performing local search on the selected target individual; step S8: updating the population; step S9: if the algorithm meets the stopping condition, ending the algorithm process and outputting a non-dominant solution set; otherwise, the algorithm goes to S4 to continue the iteration.
Description
Technical Field
The invention relates to a scheduling method for a flow shop problem, and belongs to the field of shop scheduling.
Background
Production scheduling problems have been a great concern. In recent years, due to the continuous development of society and the daily and monthly variation of technology, conventional manufacturing enterprises are facing unprecedented risks, and how to efficiently allocate existing resources and complete target production tasks becomes a concern. With the continuous advancement of economic globalization, distributed manufacturing is becoming a common scenario in manufacturing industry; with the increasing prominence of global energy problems, energy conservation and emission reduction become a common knowledge, so green scheduling is generated. As a common manufacturing scenario in production systems, many different types of flow shops have been extended through years of research and development, and hybrid flow shops can be considered as a combination of replacement flow shops and parallel machines. As a problem of the current hot spot, there have been a lot of researches on optimizing the indexes such as the maximum finishing time, but most of research ranges are isomorphic factories, and few researches on distributed heterogeneous factories are performed, and obviously, the production model of the heterogeneous factories is closer to the actual production situation. Therefore, research into distributed isomerism production is necessary.
Disclosure of Invention
Aiming at the problem that the existing production scheduling method is only suitable for isomorphic factory models, the invention provides a distributed heterogeneous flow shop scheduling method based on a mixed initialization model algorithm.
The invention discloses a distributed heterogeneous flow shop scheduling method based on a mixed initialization modular factor algorithm, which comprises the following steps:
step S1: establishing a distributed heterogeneous flow shop scheduling model;
step S2: initializing basic parameters of a model factor algorithm, and generating an initial population according to a mixed initialization strategy;
step S3: evaluating fitness values of population individuals, and performing pareto non-dominant ranking;
step S4: performing certain probability cross operation on individuals in the population;
step S5: collaborative searching is carried out on the population by adopting a searching operator;
step S6: combining the offspring population with the father population, and selecting half of individuals as local search targets;
step S7: performing local search on the selected target individual;
step S8: updating the population;
step S9: if the algorithm meets the stopping condition, ending the algorithm process and outputting a non-dominant solution set; otherwise, the algorithm goes to S4 to continue the iteration.
Preferably, the distributed heterogeneous flow shop scheduling model in step S1 may be specifically described as:
The whole manufacturing system consists of F factories distributed in different areas, wherein F is arranged in the F factories p Replacement flow shop and F with different processing capacities h The mixed flow workshops with different processing capacities are formed; m identical parallel machines are arranged at each stage of the mixed flow shop, and M is more than or equal to 1; all workpieces can be processed by any factory and can only be processed by one factory, each workpiece needs to undergo all working procedures, and a sequence constraint condition exists among the working procedures; each machine has 5 gears of selectable speeds, and the actual processing time of the workpiece is related to the standard processing time of the workpiece and the machine speed; the greater the machining speed, the shorter the actual machining time of the workpiece, but the more energy is consumed; the standard processing time and the yield of the same workpiece in different factories are different under the influence of factors such as the production environment and the process technology of each factory; the setting time of the working procedure and the transportation time of the workpiece are included in the standard processing time, and the buffer area between machines is set to be infinite; the optimization targets comprise maximum finishing time, total energy consumption and total yield, and the fitness value is calculated according to the following formula:
the adaptation of the maximum finishing time is obtained according to (1):
minf 1 ＝C max ＝max{C j,k } (1)
The fitness of the total energy consumption is obtained according to formula (2):
the adaptability of the total yield is obtained according to the step (4), and the total non-yield is taken as the adaptability value:
wherein the function f 1 As a fitness function of maximum finishing time, function f 2 Fitness function as total energy consumption, function f 3 C is the fitness function of the total yield max TEC, TAYR as fitness value, C max The maximum finishing time is represented, TEC is the total energy consumption, and TAYR represents the total non-good product rate; j is the work index, j=1,.. F is the factory index, f=1,..f, F is the total number of factories, M is the index of the machine and, m=1..m f,k ，M f,k The number of machines in the kth process of the factory f; c (C) j,k Is the procedure O j,k Is equal to the finishing time of O j,k A kth step of expressing a workpiece j; EC (EC) f For energy consumption of plant f, P j,f,k Is the procedure O j,k Standard processing time in factory f, v j,k Is the procedure O j,k Is a processing speed of (a);is the procedure O j,k Energy consumption per unit time of processing at factory f, < >>Idle time of the machine m for the k-th process of the factory f, +.>For adding the k-th procedure of the factory fThe unit time energy consumption of the working machine m in the idle mode; YR (Yttrium barium titanate) j,f For the yield of the workpiece j in the factory f, if the workpiece j is distributed to the factory f, x is j,f =1, otherwise 0.
Preferably, basic parameters of the modular factor algorithm are initialized, specifically including population size PS and crossover probability P Cr The cross segment ratio alpha, the stop condition coefficient tau;
the algorithm chromosome comprises a factory arrangement part, a workpiece sorting part and a speed selection part;
wherein, the dimension of the chromosome of the factory arrangement part is 1 xF, the gene position represents the serial number of the factory, and the gene represents the number of workpieces; the chromosome dimension of the workpiece sorting part is 1 XN, the genes represent workpiece serial numbers, and the gene positions represent processing sequences; the chromosome dimension of the speed selection part is N×S, the row index represents the workpiece number, and the column index represents the process number.
Preferably, the mixed initialization strategy in step S2 includes a random strategy, an SPT strategy (Similarities between processing times, an initialization strategy based on processing time similarity) and an SAS strategy (the slowest allowable speed, the lowest speed strategy allowed by the previous process), wherein the individual is generated using the random strategy, the chromosome factory arrangement part and the workpiece sorting part are initialized using the SPT strategy, and the chromosome speed selection part is initialized using the SAS strategy;
the process of generating individuals by adopting a random strategy is as follows: randomly selecting processing factories for workpieces, randomly generating a processing sequence of the workpieces in each factory, and randomly selecting the processing speed of each procedure;
Wherein, the process of initializing the chromosome factory arrangement part and the workpiece ordering part by adopting the SPT strategy is as follows:
S2A-1: the first workpiece of the factory f is placed in a mode of randomly selecting from a workpiece sequence JS;
S2A-2: sequentially calculating the similarity of the working procedure processing time vector of the workpiece j and the workpiece j' put into the factory in the rest workpiece sequence seq,
the Euclidean distance is used for measuring the similarity of time vectors, and the similarity is divided into two cases that a workpiece j is inserted into the workpiece j':
calculating a processing time vector when the workpiece j is inserted before the workpiece jAnd a processing time vector->Euclidean distance between, where p j,2,f ,...,p j,S,f The actual processing time, p, of the workpiece j in the 2 nd to S th steps of the factory f j',1,f ,...,p j',S-1,f The actual processing time of the workpiece j' in the 1 st to S-1 th working procedures of the factory f; after inserting the workpiece j into the workpiece j', calculating the processing time vector +.>And a processing time vector->Euclidean distance between, where p j,1,f ,...,p j,S-1,f The actual processing time, p, of the workpiece j in the 1 st to S-1 st steps of the factory f j',2,f ,...,p j',S,f The actual processing time of the workpiece j' in the 2 nd to S th working procedures of the factory f;
S2A-3: selecting an insertion mode with highest vector similarity to insert a workpiece j, and updating a residual workpiece sequence seq;
S2A-4: if the workpiece sequence is leftOutputting an initialization result; otherwise, turning to the step S2A-2;
the process of initializing the chromosome speed selection part chromosome by adopting the SAS strategy comprises the following steps:
S2B-1: randomly selecting the processing speed of the first procedure of all the workpieces in the workpiece sequence JS;
S2B-2: determining a processing speed according to the standard processing time of the working procedure and the ending time of the last working procedure of the subsequent workpiece, and acquiring a processing speed reference value u according to a formula (5):
wherein C is j+1,k-1 Representing the processing time of the (j+1) th workpiece in the workpiece sequence JS (k-1) th procedure, C j-1,k Representing the processing time of the kth process of j-1 workpieces in the workpiece sequence JS, C j,k-1 Representing the processing time, P, of the kth-1 process of the jth workpiece in the workpiece sequence JS j,k,f The value of the selected speed v is equal to or greater than the machining speed reference u, which represents the standard machining time of the jth workpiece in the workpiece sequence JS in the kth process of the factory f.
Preferably, the step S4 of performing a probabilistic crossover operation on individuals in the population means that each individual in the population is given a probability P Cr EOX crossover operation of (a); generating a random number rand, if rand>P Cr Keep the current individual motionless, if rand<P Cr The following operations are performed:
S4A-1: randomly selecting one individual in the non-dominant solution set as a parent individual 1, and taking the current individual as a parent individual 2;
S4A-2: randomly selecting a gene segment of the parent individual 1; then, deleting the same gene as segment in parent individual 2;
S4A-3, inserting segment into the first deleted gene position of the parent individual 2 to obtain offspring individual.
Preferably, in step S5, the principle of collaborative searching for the population by using the search operator is as follows:
adopting TAYR optimization operator MU for the population completing the cross operation 3 Searching;
will complete the MU according to the fitness value 3 The population of the search operation is divided into two equal sub-populations, C for each individual a max Normalizing the value and TEC value, calculating the theta value of each individual a,sorting individuals of the population according to non-descending order of theta values, wherein the first half of individuals of the population become population Pop 2 Selecting TEC optimization operator MU 2 The second half of individuals become population Pop 1 Select C max Optimization operator MU 1 ；
The C is max Optimization operator MU 1 Comprises FJ sc 、FJ sr 、FJ ic 、FJ ir Sum SA 1 Searching operators; TEC optimization operator MU 2 Comprises FJ se 、FJ ie 、FJ sr 、FJ ir Sum SA 2 Searching operators; TAYR optimization operator MU 3 Comprises FJ sy And FJ iy Search operators, wherein the operation mode of each search operator is as follows:
FJ sc : randomly selecting any one of the workpieces and F in a non-critical factory c A workpiece exchange position randomly selected from the plurality;
FJ sr : randomly selecting two workpiece exchange positions in two different factories;
FJ ic : random selection of F c Is inserted into F e1 Any position in the above;
FJ ir : randomly selecting two different factories F r1 ,F r2 Randomly select F r1 Is inserted into F r2 Any position in the (3);
FJ se : randomly selecting any one of the workpieces and F in a non-critical factory e A workpiece exchange position randomly selected from the plurality;
FJ ie : random selection of F e Is inserted into F e2 Any position in the above;
FJ sy : random selection of F y One workpiece and F of e3 Is exchanged for one of the workpieces;
FJ iy : random selection of F y One of the workpieces j is inserted into YR j,f Any position of the largest plant;
SA 1 : random selection of F c Processing one workpiece in each working procedureThe speed is increased by one grade;
SA 2 : random selection of F e1 Reducing the processing speed of each working procedure by one grade;
wherein the plant with the largest finishing time is the key plant F c The plant with the smallest finishing time is the easiest plant F e1 The plant with the largest energy consumption is the key plant F e The plant with the least energy consumption is the easiest plant F e2 The method comprises the steps of carrying out a first treatment on the surface of the The total non-yield of the factories F divided by the number of workpieces is the average non-yield of the factories F, and the factory with the largest average non-yield is the key factory F y The factory with the minimum average non-good product rate is F e3 。
Preferably, the process of selecting half of the individuals as the local search targets in step S6 is as follows: combining the parent population and the offspring population into a population with the size of 2PS, calculating the fitness value of each individual of the population, performing non-dominant ranking, preferentially selecting individuals with low non-dominant ranking, and selecting individuals with large crowding distance at the same dominant ranking until PS individuals are selected for local searching.
Preferably, the process of performing the local search on the selected target individual in step S7 is:
local search is divided into LS 1 、LS 2 Two phases, LS 1 Stage FJ for each individual in the population ic Operation, LS 2 The specific operation is as follows: random selection of F c One of the non-critical processes located on the critical path increases a speed level while randomly selecting one of the non-critical processes in each of the non-critical plants decreases a speed level. Critical process speed increases can reduce maximum finishing time and non-critical process speed decreases can reduce energy consumption.
Preferably, the process of updating the population in step S8: and combining the population subjected to the local search with the population not subjected to the local search, and selecting PS excellent individuals to enter the next generation to participate in evolution through non-dominant sorting.
Preferably, the algorithm stop condition in step S9 is that the CPU running time does not exceed τxnxsxf seconds.
The invention has the beneficial effects that: the invention establishes a production scheduling model consisting of different replacement flow workshops and different mixed flow workshops, takes maximum finishing time, total energy consumption and total yield as optimization targets, and is a multi-target optimization problem. To solve this problem efficiently, a hybrid initialization modular factor algorithm is employed to solve the problem. The algorithm firstly adopts a mixed initialization strategy to generate an initial population, then carries out EOX (Extended order crossover, extended sequence crossover method) crossover operation on the population, then uses different types of operators to enable individuals of the population to evolve towards different directions, and finally carries out local search to enhance the individuals and update the population. The invention not only provides the production scheduling model for the first time, but also designs a mixed initialization model algorithm to solve the problem aiming at the problem characteristics, and provides a reliable and feasible solution to the problem.
Drawings
FIG. 1 is a flow chart of an algorithm of the present invention;
FIG. 2 is a schematic representation of individual codes of the present invention;
FIG. 3 is a schematic illustration of SPT initialization strategy workpiece insertion according to the present invention;
FIG. 4 is a Gantt chart of an SAS initialization strategy according to the present invention;
FIG. 5 is a schematic illustration of an EOX crossover process according to the present invention;
FIG. 6 shows LS of the present invention 1 An operation process schematic diagram;
FIG. 7 is a schematic diagram of a critical path of the present invention;
FIG. 8 shows LS of the present invention 2 A key process accelerating schematic diagram.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It should be noted that, without conflict, the embodiments of the present invention and features of the embodiments may be combined with each other.
The invention is further described below with reference to the drawings and specific examples, which are not intended to be limiting.
The first embodiment is as follows: the following describes a distributed heterogeneous flow shop scheduling method based on a hybrid initialization modular factor algorithm according to the present embodiment with reference to fig. 1 to 8, and the method includes the following steps:
step S1: establishing a distributed heterogeneous flow shop scheduling model;
Step S2: initializing basic parameters of a model factor algorithm, and generating an initial population according to a mixed initialization strategy;
step S3: evaluating fitness values of population individuals, and performing pareto non-dominant ranking; and calculates the crowding distance between individuals of the same class.
Step S4: performing certain probability cross operation on individuals in the population;
step S5: collaborative searching is carried out on the population by adopting a searching operator;
step S6: combining the offspring population with the father population, and selecting half of individuals as local search targets;
step S7: performing local search on the selected target individual;
step S8: updating the population;
step S9: if the algorithm meets the stopping condition, ending the algorithm process and outputting a non-dominant solution set; otherwise, the algorithm goes to S4 to continue the iteration.
The distributed heterogeneous flow shop scheduling model in step S1 may be specifically described as:
the whole manufacturing system consists of F factories distributed in different areas, wherein F is arranged in the F factories p Replacement flow shop and F with different processing capacities h The mixed flow workshops with different processing capacities are formed; m identical parallel machines are arranged at each stage of the mixed flow shop, and M is more than or equal to 1; all workpieces can be processed by any one factory and can only be processed by one factory, each workpiece is subjected to all A procedure, wherein a sequence constraint condition exists among the procedures; each machine has 5 gears of selectable speeds, and the actual processing time of the workpiece is related to the standard processing time of the workpiece and the machine speed; the greater the machining speed, the shorter the actual machining time of the workpiece, but the more energy is consumed; the standard processing time and the yield of the same workpiece in different factories are different under the influence of factors such as the production environment and the process technology of each factory; the setting time of the working procedure and the transportation time of the workpiece are included in the standard processing time, and the buffer area between machines is set to be infinite; the optimization targets comprise maximum finishing time, total energy consumption and total yield, and the fitness value is calculated according to the following formula:
the adaptation of the maximum finishing time is obtained according to (1):
minf 1 ＝C max ＝max{C j,k } (6)
the fitness of the total energy consumption is obtained according to formula (2):
the adaptability of the total yield is obtained according to the step (4), and the total non-yield is taken as the adaptability value:
wherein the function f 1 As a fitness function of maximum finishing time, function f 2 Fitness function as total energy consumption, function f 3 C is the fitness function of the total yield max TEC, TAYR as fitness value, C max The maximum finishing time is represented, TEC is the total energy consumption, and TAYR represents the total non-good product rate; j is the work index, j=1,.. Let f=1..f, F is the total number of factories, M is the machine index, m=1..m f,k ，M f,k The number of machines in the kth process of the factory f; c (C) j,k Is the procedure O j,k Is equal to the finishing time of O j,k A kth step of expressing a workpiece j; EC (EC) f For energy consumption of plant f, P j,f,k Is the procedure O j,k Standard processing time in factory f, v j,k Is the procedure O j,k Is a processing speed of (a);is the procedure O j,k Energy consumption per unit time of processing at factory f, < >>Idle time of the machine m for the k-th process of the factory f, +.>The energy consumption per unit time of the processing machine m in the idle mode for the kth procedure of the factory f; YR (Yttrium barium titanate) j,f For the yield of the workpiece j in the factory f, if the workpiece j is distributed to the factory f, x is j,f =1, otherwise 0.
Basic parameters of an initialization modular factor algorithm specifically comprise population size PS and crossover probability P Cr The cross segment ratio alpha, the stop condition coefficient tau;
the individual code diagram of the invention is shown in figure 2. The algorithm chromosome comprises a factory arrangement part, a workpiece sorting part and a speed selection part;
wherein, the dimension of the chromosome of the factory arrangement part is 1 xF, the gene position represents the serial number of the factory, and the gene represents the number of workpieces; the chromosome dimension of the workpiece sorting part is 1 XN, the genes represent workpiece serial numbers, and the gene positions represent processing sequences; the chromosome dimension of the speed selection part is N×S, the row index represents the workpiece number, and the column index represents the process number. Wherein F is the total number of factories, N is the total number of workpieces, and S is the total number of working procedures.
The factory layout chromosome gene position represents the factory number, the number represents the number of workpieces, and the first gene "2" of chromosome 1 in FIG. 2 represents that factory 1 has two workpieces. The number of the work piece ordering chromosome represents the work piece number, the gene position represents the processing order, e.g., the first gene "9" of chromosome 1 represents the first processing of work piece 9. One speed selection chromosome has dimensions n×s, a row number indicates a workpiece number, and a column number indicates a process number. For example, the gene "2" in the first row and first column of chromosome 1 indicates that the first-pass processing speed of workpiece 1 is 2.
It should be noted that for mixed flow shop scheduling, the work piece also requires machine selection at each stage, and for simplicity of encoding, the machines are typically selected on a "first come first process (First Come First Processed, FCFP)" basis and a "first available machine (First Available Machine, FAM)" basis when decoding the partial chromosome containing mixed flow shop scheduling information.
The principle of 'first to first processing' refers to that a work piece with a kth procedure finished first starts a kth+1th procedure first; the "earliest machine availability" principle refers to the selection of the earliest machine work piece available from a plurality of parallel machines.
The mixed initialization strategy in the step S2 comprises a random strategy, an SPT strategy and an SAS strategy, wherein the random strategy is adopted to generate individuals, the SPT strategy is adopted to initialize a chromosome factory arrangement part and a workpiece ordering part, and the SAS strategy is adopted to initialize a chromosome speed selection part chromosome; the processing speeds of ten individuals are all selected to be the lowest speed, the speeds of ten individuals are all selected to be the highest speed, and 45% of individuals in the population initialize the speeds by adopting an SAS strategy.
The process of generating individuals by adopting a random strategy is as follows: randomly selecting processing factories for workpieces, randomly generating a processing sequence of the workpieces in each factory, and randomly selecting the processing speed of each procedure;
wherein, the process of initializing the chromosome factory arrangement part and the workpiece ordering part by adopting the SPT strategy is as follows:
S2A-1: the first workpiece of the factory f is placed in a mode of randomly selecting from a workpiece sequence JS;
S2A-2: sequentially calculating the similarity of the working procedure processing time vector of the workpiece j and the workpiece j' put into the factory in the rest workpiece sequence seq,
the Euclidean distance is used for measuring the similarity of time vectors, and the similarity is divided into two cases that a workpiece j is inserted into the workpiece j':
Calculating a processing time vector when the workpiece j is inserted before the workpiece jAnd a processing time vector->Euclidean distance between, where p j,2,f ,...,p j,S,f The actual processing time, p, of the workpiece j in the 2 nd to S th steps of the factory f j',1,f ,...,p j',S-1,f The actual processing time of the workpiece j' in the 1 st to S-1 th working procedures of the factory f; after inserting the workpiece j into the workpiece j', calculating the processing time vector +.>And a processing time vector->Euclidean distance between, where p j,1,f ,...,p j,S-1,f The actual processing time, p, of the workpiece j in the 1 st to S-1 st steps of the factory f j',2,f ,...,p j',S,f The actual processing time of the workpiece j' in the 2 nd to S th working procedures of the factory f;
S2A-3: selecting an insertion mode with highest vector similarity to insert a workpiece j, and updating a residual workpiece sequence seq;
S2A-4: if the workpiece sequence is leftOutputting an initialization result; otherwise, turning to the step S2A-2;
taking the data of table 1 as an example, the work piece sequence JS initially includes n=3 work pieces, j=1, 2,3, each work piece includes s=3 work pieces, k=1, 2,3. The sequence seq of the initial remaining workpieces is identical to the workpiece sequence JS, seq= {1,2,3}. All process speeds v were 1.
TABLE 1
A workpiece is randomly selected to be placed in the first position, where workpiece 1 is selected, where j' =1, and the remaining workpiece sequence seq= {2,3}, where j=2, 3. The second workpiece may be optionally inserted before workpiece 1 or after workpiece 1, for a total of four cases: after the workpiece 2 is placed on the workpiece 1, after the workpiece 3 is placed on the workpiece 1, the workpiece 2 is inserted into the workpiece 1, and the workpiece 3 is inserted into the workpiece 1.
According to the problem characteristics, the first case requires calculation of a processing time vector composed of the steps 2 and 3 of the workpiece 1Processing time vector comprising step 1 and step 2 of workpiece 2->A Euclidean distance between them; second case calculation vector +.>Processing time vector with workpiece 3>A Euclidean distance between them; in the third case, the processing time vector of the work 1 consisting of the step 1 and the step 2 is calculated>Processing time vector formed by step 2 and step 3 of workpiece 2->A Euclidean distance between them; finally, the vector is calculated for the case->Sum vector->The Euclidean distance between the two workpieces is compared to determine the insertion mode of the second workpiece.
The smaller the Euclidean distance is, the higher the vector similarity is, and the insertion mode with the smallest Euclidean distance is selected. Definition of the Euclidean distance: after the work piece 2 is selected to be inserted into the work piece 1.
A gante diagram of the four insertion cases is shown in fig. 3.
The remaining workpiece sequence seq= {3}. J' =1, 2, j=3.
At this time, the workpiece 3 has four insert options. Before inserting the work piece 1, before inserting the work piece 2, after inserting the work piece 1, after inserting the work piece 2. The first option requires calculation of a vectorSum vector->Euclidean distance between The second option requires calculation of the vector +.>Sum vector->Euclidean distance between->The third option requires calculation of the vector +.>Sum vector->Euclidean distance between->The fourth option requires calculation of vectorsSum vector->Euclidean distance between->Thus, the workpiece 3 is placed behind the workpiece 2. Remaining work sequence->
SPT policy pseudocode is shown as Algorithm 1.
The process of initializing the chromosome speed selection part chromosome by adopting the SAS strategy comprises the following steps:
S2B-1: randomly selecting the processing speed of the first procedure of all the workpieces in the workpiece sequence JS;
S2B-2: determining a processing speed according to the standard processing time of the working procedure and the ending time of the last working procedure of the subsequent workpiece, and acquiring a processing speed reference value u according to a formula (5):
wherein C is j+1,k-1 Representing the processing time of the (j+1) th workpiece in the workpiece sequence JS (k-1) th procedure, C j-1,k Representing the processing time of the kth process of j-1 workpieces in the workpiece sequence JS, C j,k-1 Representing the processing time, P, of the kth-1 process of the jth workpiece in the workpiece sequence JS j,k,f The value of the selected speed v is equal to or greater than the machining speed reference u, which represents the standard machining time of the jth workpiece in the workpiece sequence JS in the kth process of the factory f.
Taking the data of table 1 as an example, assume that the workpiece ordering pi= {2,1,3}, the speed set is u= {1,1.1,1.3}. The speeds of the first pass of all the workpieces are randomly selected, here 1. With such an arrangement, O 1,1 End time of 7, and O 2,2 Starting time of 3, O 2,2 Standard processing time of 5, so O 2,2 1.3 is selected because if 1.1 or 1,O is selected 2,2 Will exceed 7; o of the same kind 2,2 The speed is chosen to be 1 because of O 1,2 Is 7 and the standard processing time is 3, and does not exceed O 1,3 End time of (2); o (O) 3,1 The processing time is not limited and the speed is randomly selected because of the last procedure on the machine.
A gater diagram as shown in fig. 4 may be obtained according to SAS policy.
The minimum speed policy pseudo code allowed based on the previous procedure is shown as Algorithm 2.
The specific operation of step S3 is: and (3) evaluating the fitness value of the obtained initial population according to the fitness value formulas (1) - (4), performing pareto non-dominant ranking, and calculating the crowding distance between individuals of the same grade. The congestion distance formula is calculated as follows:
wherein n is an optimization target index, i is a serial number index of individuals at the same level and ordered according to a certain fitness value, and f n min Is the minimum value of the nth objective function, f n max Maximum value for the nth optimization objective.
Individuals with low dominant ranks are preferentially selected to participate in subsequent evolutions, and individuals with large crowding distances are preferentially selected to participate in subsequent evolutions at the same dominant rank.
In step S4, the cross operation with a certain probability on the individuals in the population means that the probability on each individual in the population is P Cr EOX crossover operation of (a); generating a random number rand, if rand>P Cr Keep the current individual motionless, if rand<P Cr The following operations are performed:
S4A-1: randomly selecting one individual in the non-dominant solution set as a parent individual 1, and taking the current individual as a parent individual 2;
S4A-2: randomly selecting a gene segment of the parent individual 1; then, deleting the same gene as segment in parent individual 2;
S4A-3, inserting segment into the first deleted gene position of the parent individual 2 to obtain offspring individual.
Fig. 5 is a schematic diagram of EOX crossover process, and taking fig. 5 as an example for illustration:
randomly selecting an individual 5 7 182 3 6 4 in the non-dominant solution set as a parent individual 1, and taking a current individual 745 8 6 2 1 3 as a parent individual 2;
randomly selecting one gene segment 182 of the parent individual 1, deleting the gene segment 182 in the parent individual 2 to obtain a residual gene segment 74563, wherein the deleted gene positions are 4, 6 and 7;
the gene fragment 182 is inserted into the parent individual 2 from the position 4 after deletion of the gene fragment, to obtain the offspring individual 74518263.
In the step S5, the principle of collaborative searching of the population by adopting a searching operator is as follows:
Adopting TAYR optimization operator MU for the population completing the cross operation 3 Searching;
will complete the MU according to the fitness value 3 The population of the search operation is divided into two equal sub-populations, C for each individual a max Normalizing the value and TEC value, calculating the theta value of each individual a,sorting individuals of the population according to non-descending order of theta values, wherein the first half of individuals of the population become population Pop 2 Selecting TEC optimization operator MU 2 The second half of individuals become population Pop 1 Select C max Optimization operator MU 1 ；
The C is max Optimization operator MU 1 Comprises FJ sc 、FJ sr 、FJ ic 、FJ ir Sum SA 1 Searching operators; TEC optimization operator MU 2 Comprises FJ se 、FJ ie 、FJ sr 、FJ ir Sum SA 2 Searching operators; TAYR optimization operator MU 3 Comprises FJ sy And FJ iy Search operators, wherein the operation mode of each search operator is as follows:
FJ sc : randomly selecting any one of the workpieces and F in a non-critical factory c A workpiece exchange position randomly selected from the plurality;
FJ sr : randomly selecting two workpiece exchange positions in two different factories;
FJ ic : random selection of F c Is inserted into F e1 Any position in the above;
FJ ir : randomly selecting two different factories F r1 ,F r2 Randomly select F r1 Is inserted into F r2 Any position in the (3);
FJ se : randomly selecting any one of the workpieces and F in a non-critical factory e A workpiece exchange position randomly selected from the plurality;
FJ ie : random selection of F e Is inserted into F e2 Any position in the above;
FJ sy : random selection of F y One workpiece and F of e3 Is exchanged for one of the workpieces;
FJ iy : random selection of F y One of the workpieces j is inserted into YR j,f Any position of the largest plant;
SA 1 : random selection of F c The processing speed of each working procedure is increased by one grade;
SA 2 : random selection of F e1 Reducing the processing speed of each working procedure by one grade;
wherein the plant with the largest finishing time is the key plant F c The plant with the smallest finishing time is the easiest plant F e1 The plant with the largest energy consumption is the key plant F e The plant with the least energy consumption is the easiest plant F e2 The method comprises the steps of carrying out a first treatment on the surface of the The total non-yield of the factories F divided by the number of workpieces is the average non-yield of the factories F, and the factory with the largest average non-yield is the key factory F y The factory with the minimum average non-good product rate is F e3 。
Global search pseudocode is shown as Algorithm 3.
In the step S6, the process of selecting half individuals as local search targets is as follows: combining the parent population and the offspring population into a population with the size of 2PS, calculating the fitness value of each individual of the population, performing non-dominant ranking, preferentially selecting individuals with low non-dominant ranking, and selecting individuals with large crowding distance at the same dominant ranking until PS individuals are selected for local searching.
The process of performing local search on the selected target individual in step S7 is as follows:
local search is divided into LS 1 、LS 2 Two phases, LS 1 Stage FJ for each individual in the population ic Operation, FIG. 6 is LS 1 An operation process schematic diagram; LS (least squares) 2 The specific operation is as follows: random selection of F c One of the non-critical processes located on the critical path increases a speed level while randomly selecting one of the non-critical processes in each of the non-critical plants decreases a speed level. Critical process speed increases can reduce maximum finishing time and non-critical process speed decreases can reduce energy consumption.
A schematic diagram of the critical path is shown in fig. 7. The key process schematic accelerating schematic is shown in fig. 8.
The process of updating the population in step S8: and combining the population subjected to the local search with the population not subjected to the local search, and selecting PS excellent individuals to enter the next generation to participate in evolution through non-dominant sorting.
The algorithm stop condition in step S9 is that the CPU running time does not exceed τxnxsxf seconds.
In order to verify the feasibility of the distributed heterogeneous flow shop scheduling method based on the mixed initialization modular factor algorithm, the method is implemented in the scale of (F p ,F h ,N,S)＝(1,2,20,2)，(F p ,F h ,N,S)＝(2,1,20,5)，(F p ,F h ,N,S)＝(1,2,50,2)，(F p ,F h Comparison experiments were performed on N, S) = (2,1,50,5).
Wherein F is p Representing the number of replacement flow workshops, F h The number of the mixing flow shops is represented by N, the number of the workpieces is represented by N, and the total number of the processes is represented by S.
The data set for each example is as follows: the standard machining time of each working procedure of the workpiece in different factories is a random uniform and discrete integer in the interval [10,100 ]. The running energy consumption of the machine in unit time is a random uniform discrete integer in the interval [15,40], and the idle energy consumption of the machine in unit time is a random uniform discrete integer in the interval [5,10 ]. The yield of each workpiece at different factories is a fraction between [0.85,1 ]. The number of processing machines per stage of the mixing flow shop ranges from [1,5]. The machine selectable machining speeds have 5 grades, speed set u= {1,1.3,1.55,1.75,2.1}.
The problem described in the present invention is a multi-objective optimization problem, using HV (Hyper volume) values, GD (Generation distance ) values, and CM (C metric, solution coverage) values.
The performance of the resulting population is measured.
The larger the HV value, the more diverse the population, and the better the convergence.
The smaller the GD value, the better the population convergence.
The CM value calculation formula is shown as (7):
wherein E is 1 、E 2 Two different solutions are provided.
C(E 1 ,E 2 ) The larger the representation solution set E 2 Individual disaggregated E 1 The more individual the ratio of the population.
C(E 1 ,E 2 ) =0, then explain solution set E 1 None of them can dominate solution set E 2 The solution of any one of the individuals, whereas if C (E 1 ,E 2 ) =1, then specify E 2 All solutions in (a) can be E 1 Is subject to a solution.
In the comparative experiment, the algorithm (IMA) of the present invention was independently run 10 times on each example separately from the decomposition-based multi-objective algorithm (MOEA/D) and the non-dominant order genetic algorithm (NSGA-II), and finally the average HV value, average GD value and average CM value of the population obtained from the 10 experiments were compared.
The relevant parameters for IMA settings are as follows: population size ps=140, crossover probability P Cr =0.7, the cross-segment ratio α=0.05, and the stop condition coefficient τ=0.05.
The experimental comparison results are shown in tables 2 and 3.
TABLE 2
TABLE 3 Table 3
Wherein A is 1 Is IMA, A 2 Is MOEA/D, A 3 Is NSGA-II.
As can be seen from tables 2 and 3, the average HV value obtained for IMA is greater than the average HV values for MOEA/D and NSGA-II and the average GD value for IMA is much less than the GD value for the comparison algorithm. Both C (IMA, MOEA/D) and C (IMA, NSGA-II) are greater than C (MOEA/D, IMA) and C (NSGA-II, IMA), which suggests that IMA is easier to solve the problem of the present invention for more highly convergent, diverse populations than MOEA/D and NSGA-II algorithms, and that the non-dominant solution set of IMA is superior in dominant relationship to the non-dominant solution set of the comparative algorithm.
In conclusion, the distributed heterogeneous flow shop scheduling method based on the mixed initialization modular factor algorithm can effectively solve the problem.
Although the invention herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the different dependent claims and the features described herein may be combined in ways other than as described in the original claims. It is also to be understood that features described in connection with separate embodiments may be used in other described embodiments.
Claims (10)
1. The distributed heterogeneous flow shop scheduling method based on the mixed initialization modular factor algorithm is characterized by comprising the following steps of:
step S1: establishing a distributed heterogeneous flow shop scheduling model;
step S2: initializing basic parameters of a model factor algorithm, and generating an initial population according to a mixed initialization strategy;
Step S3: evaluating fitness values of population individuals, and performing pareto non-dominant ranking;
step S4: performing certain probability cross operation on individuals in the population;
step S5: collaborative searching is carried out on the population by adopting a searching operator;
step S6: combining the offspring population with the father population, and selecting half of individuals as local search targets;
step S7: performing local search on the selected target individual;
step S8: updating the population;
step S9: if the algorithm meets the stopping condition, ending the algorithm process and outputting a non-dominant solution set; otherwise, the algorithm goes to S4 to continue the iteration.
2. The method for scheduling distributed heterogeneous flow workshops based on the mixed initialization modular factor algorithm according to claim 1, wherein the distributed heterogeneous flow workshops scheduling model in step S1 is described as:
the whole manufacturing system consists of F factories distributed in different areas, wherein F is arranged in the F factories p Replacement flow shop and F with different processing capacities h The mixed flow workshops with different processing capacities are formed; m identical parallel machines are arranged at each stage of the mixed flow shop, and M is more than or equal to 1; all workpieces can be processed by any factory and can only be processed by one factory, each workpiece needs to undergo all working procedures, and a sequence constraint condition exists among the working procedures; each machine has 5 gears of selectable speeds, and the actual processing time of the workpiece is related to the standard processing time of the workpiece and the machine speed; the greater the machining speed, the shorter the actual machining time of the workpiece, but the more energy is consumed; the standard processing time and the yield of the same workpiece in different factories are different under the influence of factors such as the production environment and the process technology of each factory; the setting time of the working procedure and the transportation time of the workpiece are included in the standard processing time, and the buffer area between machines is set to be infinite; optimization objectives include maximum completion time, total energy consumption And the total yield, the fitness value is calculated according to the following formula:
the adaptation of the maximum finishing time is obtained according to (1):
minf 1 ＝C max ＝max{C j,k } (1)
the fitness of the total energy consumption is obtained according to formula (2):
the adaptability of the total yield is obtained according to the step (4), and the total non-yield is taken as the adaptability value:
wherein the function f 1 As a fitness function of maximum finishing time, function f 2 Fitness function as total energy consumption, function f 3 C is the fitness function of the total yield max TEC, TAYR as fitness value, C max The maximum finishing time is represented, TEC is the total energy consumption, and TAYR represents the total non-good product rate; j is the work index, j=1,.. F is the factory index, f=1,..f, F is the total number of factories, M is the index of the machine and, m=1..m f,k ，M f,k The number of machines in the kth process of the factory f; c (C) j,k Is the procedure O j,k Is equal to the finishing time of O j,k A kth step of expressing a workpiece j; EC (EC) f For energy consumption of plant f, P j,f,k Is the procedure O j,k Standard processing time in factory f, v j,k Is the procedure O j,k Is a processing speed of (a);is the procedure O j,k Energy consumption per unit time of processing at factory f, < >>Idle time of the machine m for the k-th process of the factory f, +.>The energy consumption per unit time of the processing machine m in the idle mode for the kth procedure of the factory f; YR (Yttrium barium titanate) j,f For the yield of the workpiece j in the factory f, if the workpiece j is distributed to the factory f, x is j,f =1, otherwise 0.
3. The distributed heterogeneous flow shop scheduling method based on the mixed initialization modular factor algorithm according to claim 2, wherein the basic parameters of the initialization modular factor algorithm include population size PS and crossover probability P Cr The cross segment ratio alpha, the stop condition coefficient tau;
the algorithm chromosome comprises a factory arrangement part, a workpiece sorting part and a speed selection part;
wherein, the dimension of the chromosome of the factory arrangement part is 1 xF, the gene position represents the serial number of the factory, and the gene represents the number of workpieces; the chromosome dimension of the workpiece sorting part is 1 XN, the genes represent workpiece serial numbers, and the gene positions represent processing sequences; the chromosome dimension of the speed selection part is N×S, the row index represents the workpiece number, and the column index represents the process number.
4. The distributed heterogeneous flow shop scheduling method based on the mixed initialization modular factor algorithm according to claim 3, wherein the mixed initialization strategy in the step S2 includes a random strategy, an SPT strategy and an SAS strategy, wherein individuals are generated by using the random strategy, a chromosome factory arrangement part and a workpiece ordering part are initialized by using the SPT strategy, and a chromosome speed selection part is initialized by using the SAS strategy;
The process of generating individuals by adopting a random strategy is as follows: randomly selecting processing factories for workpieces, randomly generating a processing sequence of the workpieces in each factory, and randomly selecting the processing speed of each procedure;
wherein, the process of initializing the chromosome factory arrangement part and the workpiece ordering part by adopting the SPT strategy is as follows:
S2A-1: the first workpiece of the factory f is placed in a mode of randomly selecting from a workpiece sequence JS;
S2A-2: sequentially calculating the similarity of the working procedure processing time vector of the workpiece j and the workpiece j' put into the factory in the rest workpiece sequence seq,
the Euclidean distance is used for measuring the similarity of time vectors, and the similarity is divided into two cases that a workpiece j is inserted into the workpiece j':
calculating a processing time vector when the workpiece j is inserted before the workpiece jAnd a processing time vectorEuclidean distance between, where p j,2,f ,...,p j,S,f The actual processing time, p, of the workpiece j in the 2 nd to S th steps of the factory f j',1,f ,...,p j',S-1,f The actual processing time of the workpiece j' in the 1 st to S-1 th working procedures of the factory f; after inserting the workpiece j into the workpiece j', calculating the processing time vector +.>And a processing time vectorEuclidean distance between, where p j,1,f ,...,p j,S-1,f The actual processing time, p, of the workpiece j in the 1 st to S-1 st steps of the factory f j',2,f ,...,p j',S,f The actual processing time of the workpiece j' in the 2 nd to S th working procedures of the factory f;
S2A-3: selecting an insertion mode with highest vector similarity to insert a workpiece j, and updating a residual workpiece sequence seq;
S2A-4: if the workpiece sequence is leftOutputting an initialization result; otherwise, turning to the step S2A-2;
the process of initializing the chromosome speed selection part chromosome by adopting the SAS strategy comprises the following steps:
S2B-1: randomly selecting the processing speed of the first procedure of all the workpieces in the workpiece sequence JS;
S2B-2: determining a processing speed according to the standard processing time of the working procedure and the ending time of the last working procedure of the subsequent workpiece, and acquiring a processing speed reference value u according to a formula (5):
wherein C is j+1,k-1 Representing the processing time of the (j+1) th workpiece in the workpiece sequence JS (k-1) th procedure, C j-1,k Representing the processing time of the kth process of j-1 workpieces in the workpiece sequence JS, C j,k-1 Representing the processing time, P, of the kth-1 process of the jth workpiece in the workpiece sequence JS j,k,f The value of the selected speed v is equal to or greater than the machining speed reference u, which represents the standard machining time of the jth workpiece in the workpiece sequence JS in the kth process of the factory f.
5. The method for scheduling distributed heterogeneous flow workshops based on the mixed initialization modular factor algorithm of claim 4, wherein the step S4 of performing a probabilistic cross operation on individuals in the population means performing a probabilistic cross operation on each individual in the population as P Cr EOX crossover operation of (a); generating a random number rand, if rand>P Cr Keep the current individual motionless, if rand<P Cr The following operations are performed:
S4A-1: randomly selecting one individual in the non-dominant solution set as a parent individual 1, and taking the current individual as a parent individual 2;
S4A-2: randomly selecting a gene segment of the parent individual 1; then, deleting the same gene as segment in parent individual 2;
S4A-3, inserting segment into the first deleted gene position of the parent individual 2 to obtain offspring individual.
6. The distributed heterogeneous flow shop scheduling method based on the mixed initialization modular factor algorithm according to claim 5, wherein the principle of collaborative searching for the population by adopting the search operator in step S5 is as follows:
adopting TAYR optimization operator MU for the population completing the cross operation 3 Searching;
will complete the MU according to the fitness value 3 The population of the search operation is divided into two equal sub-populations, C for each individual a max Normalizing the value and TEC value, calculating the theta value of each individual a,sorting individuals of the population according to non-descending order of theta values, wherein the first half of individuals of the population become population Pop 2 Selecting TEC optimization operator MU 2 The second half of individuals become population Pop 1 Select C max Optimization operator MU 1 ；
The C is max Optimization operator MU 1 Comprises FJ sc 、FJ sr 、FJ ic 、FJ ir Sum SA 1 Searching operators; TEC optimization operator MU 2 Comprises FJ se 、FJ ie 、FJ sr 、FJ ir Sum SA 2 Searching operators; TAYR optimization operator MU 3 Comprises FJ sy And FJ iy Search operators, wherein the operation mode of each search operator is as follows:
FJ sc : randomly selecting any one of the workpieces and F in a non-critical factory c A workpiece exchange position randomly selected from the plurality;
FJ sr : randomly selecting two workpiece exchange positions in two different factories;
FJ ic : random selection of F c Is inserted into F e1 Any position in the above;
FJ ir : randomly selecting two different factories F r1 ,F r2 Randomly select F r1 Is inserted into F r2 Any position in the (3);
FJ se : randomly selecting any one of the workpieces and F in a non-critical factory e A workpiece exchange position randomly selected from the plurality;
FJ ie : random selection of F e Is inserted into F e2 Any position in the above;
FJ sy : random selection of F y One workpiece and F of e3 Is exchanged for one of the workpieces;
FJ iy : random selection of F y One of the workpieces j is inserted into YR j,f Any position of the largest plant;
SA 1 : random selection of F c The processing speed of each working procedure is increased by one grade;
SA 2 : random selection of F e1 Reducing the processing speed of each working procedure by one grade;
Wherein the plant with the largest finishing time is the key plant F c The plant with the smallest finishing time is the easiest plant F e1 The plant with the largest energy consumption is the key plant F e The plant with the least energy consumption is the easiest plant F e2 The method comprises the steps of carrying out a first treatment on the surface of the The total non-yield of the factories F divided by the number of workpieces is the average non-yield of the factories F, and the factory with the largest average non-yield is the key factory F y The factory with the minimum average non-good product rate is F e3 。
7. The distributed heterogeneous flow shop scheduling method based on the hybrid initialization modular factor algorithm according to claim 1, wherein the process of selecting half of individuals as local search targets in step S6 is as follows: combining the parent population and the offspring population into a population with the size of 2PS, calculating the fitness value of each individual of the population, performing non-dominant ranking, preferentially selecting individuals with low non-dominant ranking, and selecting individuals with large crowding distance at the same dominant ranking until PS individuals are selected for local searching.
8. The distributed heterogeneous flow shop scheduling method based on the hybrid initialization modular factor algorithm according to claim 1, wherein the process of performing the local search on the selected target individual in step S7 is as follows:
Local search is divided into LS 1 、LS 2 Two phases, LS 1 Stage FJ for each individual in the population ic Operation, LS 2 The specific operation is as follows: random selection of F c One of the non-critical processes located on the critical path increases a speed level while randomly selecting one of the non-critical processes in each of the non-critical plants decreases a speed level. Critical process speed increases can reduce maximum finishing time and non-critical process speed decreases can reduce energy consumption.
9. The distributed heterogeneous flow shop scheduling method based on the hybrid initialization modular factor algorithm according to claim 1, wherein the process of updating the population in step S8: and combining the population subjected to the local search with the population not subjected to the local search, and selecting PS excellent individuals to enter the next generation to participate in evolution through non-dominant sorting.
10. The method for scheduling distributed heterogeneous flow workshops based on the mixed initialization modular factor algorithm according to claim 1, wherein the algorithm stopping condition in the step S9 is that the CPU running time does not exceed τxnxs x F seconds.
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