CN117035364A - Distributed heterogeneous flow shop scheduling method based on improved mixed cause algorithm - Google Patents
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Abstract
The invention discloses a distributed heterogeneous flow shop scheduling method based on an improved mixed cause algorithm, belongs to the field of shop scheduling, and aims to solve the problem that the scheduling method of the existing heterogeneous factory is low in efficiency. The invention comprises the following steps: step S1: constructing a distributed heterogeneous flow shop scheduling model; step S2: determining a value of basic parameters of a given algorithm, and generating an initial population by adopting a random strategy according to a coding rule; step S3: evaluating the initial population, and performing pareto non-dominant ranking according to the fitness value; step S4: performing two-layer coding EOX crossing operation on the population; step S5: multiple operators jointly search the solution space; step S6: adopting elite retention strategy, combining parent population and offspring population, and selecting half of individuals as the evolution target of the next stage; step S7: performing an evolutionary operation of local search on the selected individuals; step S8: updating the population; step S9: if the algorithm reaches the stop condition, ending the algorithm and outputting a result, otherwise, jumping to the step S4 to continue execution.
Description
Technical Field
The invention relates to a scheduling method for a flow shop problem, and belongs to the field of shop scheduling.
Background
With the continued development of economic technology, manufacturing enterprises are facing unprecedented survival challenges. For enterprises, only the improvement of the competitiveness can survive in the strong competition. The excellent yield can not only reduce the production cost of factories, but also ensure the product quality and promote the customer satisfaction, thus having good influence on the economic benefit and reputation of enterprises. However, the existing research on optimizing the yield of products is very lack.
With the continuous advancement of economic globalization, the conventional single production plant is no longer suitable for the current manufacturing scenario, and distributed manufacturing is a trend. Compared with the traditional production mode, the distributed manufacturing is more flexible, can reasonably distribute production resources and improve production efficiency, so that a great deal of research on distributed scheduling is emerging. The global environmental problem is increasingly serious due to population expansion and excessive consumption, and the "energy crisis" is increasingly strong. While manufacturing can consume 25% -50% of the total energy consumption, so researching green scheduling has its important value. Existing research on distributed scheduling is mostly about isomorphic factories, and obviously, heterogeneous factories are more in line with actual production scenes than isomorphic factories. At present, the scheduling technology of the isomorphic factory is relatively mature, but the scheduling method of the heterogeneous factory is only in the primary stage, and the efficiency is low.
Disclosure of Invention
Aiming at the problem of low efficiency of the scheduling method of the existing heterogeneous factory, the invention provides a distributed heterogeneous flow shop scheduling method based on an improved mixed cause algorithm.
The invention discloses a distributed heterogeneous flow shop scheduling method based on an improved mixed cause algorithm, which comprises the following steps:
step S1: constructing a distributed heterogeneous flow shop scheduling model;
step S2: determining a value of basic parameters of a given algorithm, and generating an initial population by adopting a random strategy according to a coding rule;
step S3: evaluating the initial population, and performing pareto non-dominant ranking according to the fitness value;
step S4: performing two-layer coding EOX crossing operation on the population;
step S5: multiple operators jointly search the solution space;
step S6: adopting elite retention strategy, combining parent population and offspring population, and selecting half of individuals as the evolution target of the next stage;
step S7: performing an evolutionary operation of local search on the selected individuals;
step S8: updating the population;
step S9: if the algorithm reaches the stop condition, ending the algorithm and outputting a result, otherwise, jumping to the step S4 to continue execution.
Preferably, the distributed heterogeneous flow shop 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 working procedure of the workpieces is required to be completed, and the processing sequence of the working procedures has constraint conditions; 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 objective function comprises 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):
min f 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.
Preferably, the basic parameters of the algorithm in step S2 include population size PS, 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, in step S3, the fitness value of each individual in the initial population is calculated according to the fitness value formula, and the rapid non-dominant ranking is performed, so that the individuals in the population are divided into different dominant classes, and the crowding distances of the individuals in the same dominant class are calculated.
Preferably, the two-layer coded EOX crossover operation is performed on the population in step S4, with a probability of P for each individual in the population Cr The method comprises the steps of carrying out a first treatment on the surface of the The specific process is as follows:
S4A-1: converting the factory-arranged part chromosome and the workpiece-ordered part chromosome of the chromosome into a two-layer coding mode with consistent dimensions, wherein genes at the same position of the factory-arranged part chromosome and the workpiece-ordered part chromosome are related to the same workpiece;
S4A-2: randomly selecting an individual from the non-dominant solution set as a parent individual 1, wherein the parent individual 2 is a current individual;
S4A-3: randomly selecting a gene segment of the chromosome of the work piece sequencing part of the parent individual 1; then deleting the genes which are the same as segments in the chromosomes of the work sorting part of the parent individual 2, and carrying out the same operation on the genes at the same positions of the chromosomes of the factory arrangement part;
S4A-4: inserting segments into the first deleted gene position of the chromosome of the work-piece ordering part of the parent individual 2 to obtain the chromosome of the work-piece ordering part of the offspring, and arranging the genes at the same position of the chromosome of the part of the factory to perform the same operation.
Preferably, in step S5, the principle of searching the solution space by adopting multiple operators in a joint way is as follows:
applying TAYR optimization operator MU to all individuals 3 Performing a search;
then randomly selecting C for each individual max Optimization operator MU 1 Or TEC optimization operator MU 2 Performing a search;
finally, each individual randomly selects SA 1 Or SA 2 Performing a search;
the C is max Optimization operator MU 1 Comprises FJ sc 、FJ sr 、FJ ic And FJ ir Searching operators; TEC optimization operator MU 2 Comprises FJ se 、FJ ie 、FJ sr And FJ ir 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 : exchanging a randomly selected workpiece and F of any non-critical factory c A randomly selected position of the workpiece;
FJ sr : randomly selecting any two workpiece exchange positions in two different factories;
FJ ic : random selection of F c Is inserted into F e1 Is selected at random;
FJ ir : factory F r1 ,F r2 Is two different factories selected randomly, will F r1 Is inserted into F r2 Any position in the (3);
FJ se : to randomly select any one of the workpieces in the non-critical factory and F e Any one of the workpiece exchange positions;
FJ ie : random selection of F e Is inserted into F e2 Is selected at random;
FJ sy : random selection of F y One workpiece and F of e3 A randomly selected workpiece exchange;
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 : at F c Randomly selecting a workpiece, and improving the processing speed of each procedure by one grade;
SA 2 : at F e1 Randomly selecting a workpiece, and reducing the processing speed of each 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 evolution targets in the next stage in the 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 local search in step S7 refers to FJ for each individual in the population ic And (3) operating.
Preferably, the updating population process of step S8 is: and (3) merging the PS individuals subjected to the local search operation and the PS individuals not subjected to the local search operation selected in the step (S6), and selecting the PS individuals to replace the original parent population to become the parent population of the new generation.
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 distributed heterogeneous flow shop scheduling model, takes maximum finishing time, total energy consumption and total yield as optimization targets, and is a multi-target optimization problem. Due to the significance of the product yield on production scheduling, the invention also designs a search operator for optimizing the yield. In order to find a reliable and feasible scheduling scheme for the problem, an improved hybrid cause algorithm is proposed. Firstly, generating an initial population by adopting a random strategy to ensure the diversity of the initial population; then, performing EOX crossing operation of two layers of codes, and then adopting a plurality of operators to perform joint search so as to ensure that the algorithm searches a solution space towards different directions; and selecting PS individuals to perform local search according to elite strategies, and finally selecting PS individuals from the individuals subjected to the local search and 2PS individuals not subjected to the local search to participate in the next generation evolution. The method is used for scheduling the heterogeneous factory, and the efficiency is obviously improved.
Drawings
FIG. 1 is a block diagram of an algorithm flow of the present invention;
FIG. 2 is a graph of a scheduled Gantt chart of an example of a problem according to the present invention;
FIG. 3 is a schematic representation of individual codes;
FIG. 4 is a schematic diagram of individual two-layer coding;
FIG. 5 is a schematic diagram of a two-layer encoded EOX crossover process;
FIG. 6 is a schematic view of HV values;
fig. 7 is a schematic diagram of GD values.
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 the present embodiment with reference to fig. 1 to 7, and the method for scheduling a distributed heterogeneous flow shop based on an improved mixed cause algorithm according to the present embodiment, in which a distributed heterogeneous flow shop scheduling model is built, and maximum finishing time, total energy consumption and total yield are used as optimization targets, which is a multi-target optimization problem. The improved mixed cause algorithm firstly adopts a random strategy to generate an initial population so as to ensure the diversity of the initial population; then, performing EOX crossing operation of two layers of codes, and then adopting a plurality of operators to perform joint search so as to ensure that the algorithm searches a solution space towards different directions; and selecting PS individuals to perform local search according to elite strategies, and finally selecting PS individuals from the individuals subjected to the local search and 2PS individuals not subjected to the local search to participate in the next generation evolution. The invention can provide a reliable and feasible scheduling scheme for the problems.
Specifically, the method comprises the following steps:
step S1: constructing a distributed heterogeneous flow shop scheduling model;
step S2: determining a value of basic parameters of a given algorithm, and generating an initial population by adopting a random strategy according to a coding rule;
step S3: evaluating the initial population, and performing pareto non-dominant ranking according to the fitness value;
step S4: performing two-layer coding EOX crossing operation on the population;
step S5: multiple operators jointly search the solution space;
step S6: adopting elite retention strategy, combining parent population and offspring population, and selecting half of individuals as the evolution target of the next stage;
step S7: performing an evolutionary operation of local search on the selected individuals;
step S8: updating the population;
step S9: if the algorithm reaches the stop condition, ending the algorithm and outputting a result, otherwise, jumping to the step S4 to continue execution.
The distributed heterogeneous flow shop 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 plants (Permutation flow shop, PFS) and F having different processing capacities h A mixed flow shop (HFS) with different processing capacities; 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 working procedure of the workpieces is required to be completed, and the processing sequence of the working procedures has constraint conditions; 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 objective function comprises 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):
min f 1 ＝C max ＝max{ Cj,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.
The constraint conditions of the scheduling problem of the distributed heterogeneous flow shop are as follows:
indicating that each work piece must be assigned to a factory process;
indicating that the workpiece must go through all processing stages;
indicating that the completion time of a process is greater than or equal to the processing time of the process;
indicating that the next process can be started when the current process is completed;
indicating that only one workpiece can be processed at a time by the same machine;
the range of values of the binary variable is constrained.
Wherein F represents the total number of factories, S represents the total number of processes, N represents the total number of workpieces, j ' represents the workpiece index, j+.j ', j=1,..n, j ' =1,., N, k is the process index, k=1,..s, F is the factory index, f=1,., F, p j,k Indicating procedure O j,k Actual processing time of C j,k Indicating procedure O j,k Is the finishing time of S j’,k Indicating procedure O j’,k Is a start processing time of (1); if the workpiece j is assigned to factory f, x j,f =1, otherwise x j,f =0; if procedure O j,k Processing on machine m of the kth process in factory f, then y j,m,k,f =1, otherwise y j,m,k,f =0; if the workpiece j is located before the workpiece j' in the factory f, z j,j’,k,f =1, otherwise z j,j’,k,f = 0,U represents a sufficiently large integer.
In order to clearly explain the method for calculating the machine fitness function of the problem according to the present invention, an example of the problem is given below, and fig. 2 is a gand diagram of a scheduling scheme of the example.
Tables 1 and 2 show processing information of examples.
TABLE 1
TABLE 2
As can be seen from tables 1 and 2, there are a total of 3 factories and 10 workpieces. The two working procedures of the workpiece 1 are respectively 2 and 3 in the processing time of the factory 1, 4 and 3 in the processing time of the factory 2 and 1 and 2 in the processing time of the factory 3; the unit energy consumption of two working procedures of the workpiece 1 in the processing of the factory 1 is 5 and 7, the factory 2 is 9 and 5, and the factory 3 is 6 and 7; the yield of the work 1 at the factory 1 was 0.98, the yield at the factory 2 was 0.99, and the yield at the factory 3 was 0.89. And other workpieces are similar. In addition, the above table shows that plant 1 and plant 2 are replacement flow plants, plant 3 is a mixed flow plant, process 1 has two machines, and process 2 has 1 machine; the unit idle energy consumption of the machine in the first process of the factory 1 is 1, the unit idle energy consumption of the machine in the second process is 2, and other factories are the same.
The solution to the scheduling problem can be represented graphically by a Gantt chart, which can be obtained as shown in FIG. 2.
As can be seen from the Gantt chart of FIG. 2, the maximum finishing time is equal to the finishing time f of the plant 2 1 =15, total energy consumption f 2 = (2×8+2×7+1×6) +2×2+ (2× 9+4 ×8+3×10) +173+137=430, total non-good yield f 3 ＝(1-0.98)+(1-1)+(0.99-0.91)+0.02+0.16＝0.28。
In the step S2, the invention adopts a random strategy to initialize the population, so that the initial population with rich diversity can be obtained. The basic parameters of the algorithm in the step S2 comprise 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;
the dimension of a factory-arranged chromosome is 1 xF, the position of a factory-arranged chromosome gene is equal to the factory index, the gene number represents the number of workpieces, and the first gene 2 of the factory-arranged chromosome in FIG. 3 represents that 2 workpieces need to be processed by the factory 1; a workpiece ordering chromosome dimension of 1 xn, the gene positions representing the order of processing of the workpiece at the first stage, the gene numbers representing the workpiece serial numbers, e.g., the first gene "5" of fig. 3 represents the first processing of the workpiece 5 at the first stage; one speed selection chromosome dimension is n×s, the row index of the genes is equal to the workpiece index, the column index is equal to the process index, the gene numbers represent the speed level, and the gene "1" of the first row and first column of the speed selection chromosome in fig. 3 represents the lowest speed level one selected in the first process of the workpiece 1.
It is noted that the process machines of each stage of the hybrid flow shop are also selected for simplicity of coding, and the process machines of each stage of the hybrid flow shop are determined by the "first come first process (First Come First Processed, FCFP)" principle and the "first available machine (First Available Machine, FAM)" principle at decoding.
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 algorithm adopts a random strategy to obtain the initial population, so that the obtained initial population is rich in diversity.
In step S3, according to the fitness value formulas (1) - (4), the fitness value of the obtained initial population is evaluated, the pareto non-dominant ranking is performed, and the crowding distance between individuals at the same level is calculated.
The fast non-dominant ordering mainly comprises the following steps:
step S3A-1: each individual in the population is scanned, and two variables for each individual p are initialized: number n of solutions governing individual p p Solution set S for individuals subject to individual p p ；
Step S3A-2: let front=1, n p Individual dominance rank of =0 equal front, n p Individuals with=0 fall into set f_i;
step S3A-3: for each individual in F_i, traversing each individual' S solution set S p Will solve S p N of each individual in (a) p Subtracting one;
step S3A-4: front=front+1, n will be p Individuals with=0 fall into set f_i;
step S3A-5: steps S3A-3, S3A-4 are repeated until each individual in the population is assigned to a certain set f_i.
The congestion distance calculation formula is as follows:
wherein n represents 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 the step S4, two-layer coding EOX crossing operation is carried out on the population, and the species is bredThe probability of each individual in the population performing an EOX crossover operation is P Cr The method comprises the steps of carrying out a first treatment on the surface of the Each individual of the population has a probability P Cr Is a two-layer encoded EOX crossover operation. Randomly generating a random number rand, if rand<P Cr An EOX crossover operation is performed, otherwise the individual remains unchanged. The specific process is as follows:
S4A-1: converting the factory-arranged part chromosome and the workpiece-ordered part chromosome of the chromosome into a two-layer coding mode with consistent dimensions, wherein genes at the same position of the factory-arranged part chromosome and the workpiece-ordered part chromosome are related to the same workpiece;
S4A-2: randomly selecting an individual from the non-dominant solution set as a parent individual 1, wherein the parent individual 2 is a current individual;
S4A-3: randomly selecting a gene segment of the chromosome of the work piece sequencing part of the parent individual 1; then deleting the genes which are the same as segments in the chromosomes of the work sorting part of the parent individual 2, and carrying out the same operation on the genes at the same positions of the chromosomes of the factory arrangement part;
S4A-4: inserting segments into the first deleted gene position of the chromosome of the work-piece ordering part of the parent individual 2 to obtain the chromosome of the work-piece ordering part of the offspring, and arranging the genes at the same position of the chromosome of the part of the factory to perform the same operation.
FIG. 4 is a schematic diagram of two layers of individual codes:
it can be seen that the dimensions of the work piece ordering chromosome and the factory scheduling chromosome are identical, where the genes of the factory scheduling chromosome refer to the processing factory, which can be seen as the "identity number" of each work piece. Genes at the same location describe information about the same workpiece. For example, work piece ordering chromosome first gene "5" and factory scheduling chromosome first gene "1" refer to work piece 5 being assigned to factory 1 processing. The coding mode can make two parts of chromosomes perform the same crossing operation.
FIG. 5 is a schematic diagram of an EOX crossover process for two layer encoding:
one individual 5718236411112222 is randomly selected from the population non-dominant solution set as parent individual 1 and the current individual 7458621311122222 as parent individual 2.
A segment is randomly selected 182 in the work piece ordered chromosome of parent individual 1, the factory arranged chromosome segment 112. The genes identical to segments in the parent individual 2 work-ordered chromosome are deleted, genes at the same positions of the factory-ordered chromosome are deleted, the deletion positions are 4, 6 and 7, and the remaining genes are 7456311122.
Segment182 is inserted from position 4 of the work-ordered chromosome of the deleted parent individual 2, while segment 112 is inserted from position 4 of the factory-ordered chromosome of the deleted parent individual 2, resulting in offspring individual 7451826311111222.
In the step S5, the principle of searching the solution space by adopting multiple operators in a combined way is as follows:
applying TAYR optimization operator MU to all individuals 3 Performing a search;
then randomly selecting C for each individual max Optimization operator MU 1 Or TEC optimization operator MU 2 Performing a search;
finally, each individual randomly selects SA 1 Or SA 2 Performing a search;
the C is max Optimization operator MU 1 Comprises FJ sc 、FJ sr 、FJ ic And FJ ir Searching operators; TEC optimization operator MU 2 Comprises FJ se 、FJ ie 、FJ sr And FJ ir 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 : exchanging a randomly selected workpiece and F of any non-critical factory c A randomly selected position of the workpiece;
FJ sr : randomly selecting any two workpiece exchange positions in two different factories;
FJ ic : random selection of F c Is inserted into F e1 Is selected at random;
FJ ir : worker's workFactory F r1 ,F r2 Is two different factories selected randomly, will F r1 Is inserted into F r2 Any position in the (3);
FJ se : to randomly select any one of the workpieces in the non-critical factory and F e Any one of the workpiece exchange positions;
FJ ie : random selection of F e Is inserted into F e2 Is selected at random;
FJ sy : random selection of F y One workpiece and F of e3 A randomly selected workpiece exchange;
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 : at F c Randomly selecting a workpiece, and improving the processing speed of each procedure by one grade;
SA 2 : at F e1 Randomly selecting a workpiece, and reducing the processing speed of each 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 。
Step S6: adopting elite retention strategy, combining parent population and offspring population, selecting half of individuals to enter the evolution of the next stage; in the step S6, the process of selecting half individuals as the evolution targets in the next stage 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 pseudocode for the global search is shown as Algorithm 1.
The local search in step S7 refers to FJ for each individual in the population ic And (3) operating.
The population updating process in the step S8 is as follows: and (3) merging the PS individuals subjected to the local search operation and the PS individuals not subjected to the local search selected in the step (S6), and selecting the PS individuals to replace the original parent population to become the parent population of the new generation.
The algorithm stop condition in step S9 is that the CPU running time does not exceed τxnxsxf seconds.
In order to verify the effectiveness and reliability of the distributed heterogeneous flow shop scheduling method based on the improved hybrid cause algorithm, the invention is implemented on a computational scale (F p ,F h ,N,S)＝(1,2,50,5)，(F p ,F h ,N,S)＝(2,1,50,8)，(F p ,F h ,N,S)＝(1,2,100,5)，(F p ,F h Comparative experiments were performed on the examples of N, S) = (2,1,100,8).
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.
Since there is no example concerning the problem to which the present invention belongs, the example is generated according to the following numerical ranges: the standard working time of the working procedure of the workpiece is a random, discrete and uniform integer of 10-100 in different factories. The energy consumption per unit time of the machine is a random discrete even integer of 15-40 when the machine is running, and the energy consumption per unit time of the machine in an idle state is a random discrete even integer of 5-10. The yield of each workpiece in different factories is a fraction of 0.85-1. The number of parallel machines in each stage of the mixed flow shop is 1-5. There are 5 alternative speed classes, speed set u= {1,1.3,1.55,1.75,2.1}.
The problem is a multi-objective optimization problem, and the result of the algorithm comparison test is measured by using HV (Hyper volume) values, GD (Generate distance, generation distance) values and CM (C metric, solution coverage) values.
The HV value is calculated as the volume of the hypercube enclosed by the non-dominant solution set of the population pareto and the reference point. Taking a two-dimensional target as an example, as shown in fig. 6, the HV value is the area enclosed between the pareto front individual and the reference point. (1, 1) is chosen herein as the normalized reference point for pareto frontier individuals. Clearly, the larger the HV value, the more diverse and better the convergence of the non-dominated solution set of the population pareto.
The average minimum distance from each individual in solution set E to the reference set E is represented.
Where dis denotes the Euclidean distance between x and y, and x and y denote two individuals in space. The pareto solution set obtained by a single algorithm is selected as a solution set E, and the pareto solution set formed by the pareto fronts obtained by all algorithms is used as a reference set E. FIG. 7 is a diagram of GD values. The smaller the GD value, the better the convergence of the solution set.
The CM value computes two solution sets E 1 And E is 2 Is the dominant relationship between individuals.
Wherein E is 1 、E 2 Two different solutions are provided.
C(E 1 ,E 2 ) The larger the value, the description solution set E 1 Can dominate solution set E 2 The more individuals.
If C (E) 1 ,E 2 ) =0, then explain solution set E 2 None of which can be deconcentrated E 1 The subject in dominance, in contrast, if C (E 1 ,E 2 ) =1, then describe solution set E 2 All individuals in (3)Can be disaggregated E 1 Dominating.
To demonstrate the effectiveness of the algorithm (HMOMA) of the present invention, the HMOMA algorithm, the decomposition-based multi-objective algorithm (MOEA/D), and the non-dominant order genetic algorithm (NSGA-II) were run independently 10 times on each example, and the average HV value, GD value, CM value of each algorithm on different examples were compared.
The parameters of the MOMA were set as follows: population size ps=200, crossover probability P Cr =0.4, the cross-segment ratio α=0.05, and the stop condition coefficient τ=0.05.
The experimental results are shown in table 3 and table 4.
TABLE 3 Table 3
TABLE 4 Table 4
Wherein A is 1 HMOAM, A 2 Is MOEA/D, A 3 Is NSGA-II.
As can be seen from Table 3, table 4, the average HV value of HMOMA is much greater than the average HV values of MOEA/D and NSGA-II; the average GD value of HMOMA is much smaller than that of MOEA/D and NSGA-II; c (HMOAM, MOEA/D) and C (HMOAM, NSGA-II) are both greater than C (MOEA/D, HMOAM) and C (NSGA-II, HMOAM). It is explained that the comprehensive performance of the population obtained by the HMOMA is superior to that of two algorithms except two algorithms, and the non-dominant solution set of the HMOMA can be used for controlling the individual proportion of the comparison algorithm to be higher than that of the individual proportion controlled by the comparison algorithm in the dominant relation, which means that the HMOMA can obtain the individuals with shorter maximum finishing time, lower total energy consumption and higher total yield than the comparison algorithm. In summary, the distributed heterogeneous flow shop scheduling method based on the improved mixed cause algorithm can provide an efficient scheduling scheme.
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 improved mixed cause algorithm is characterized by comprising the following steps of:
step S1: constructing a distributed heterogeneous flow shop scheduling model;
step S2: determining a value of basic parameters of a given algorithm, and generating an initial population by adopting a random strategy according to a coding rule;
step S3: evaluating the initial population, and performing pareto non-dominant ranking according to the fitness value;
step S4: performing two-layer coding EOX crossing operation on the population;
step S5: multiple operators jointly search the solution space;
step S6: adopting elite retention strategy, combining parent population and offspring population, and selecting half of individuals as the evolution target of the next stage;
step S7: performing an evolutionary operation of local search on the selected individuals;
step S8: updating the population;
step S9: if the algorithm reaches the stop condition, ending the algorithm and outputting a result, otherwise, jumping to the step S4 to continue execution.
2. The method for scheduling distributed heterogeneous flow workshops based on the improved hybrid cause algorithm according to claim 1, wherein the distributed heterogeneous flow workshops scheduling model in step S1 is described as:
the whole manufacturing system is distributed in the non-uniform wayF factories in the same region, wherein F is 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 working procedure of the workpieces is required to be completed, and the processing sequence of the working procedures has constraint conditions; 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 objective function comprises 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 At the mostFitness function of large 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 method for scheduling distributed heterogeneous flow workshops based on the improved hybrid cause algorithm according to claim 1, wherein the algorithm basic parameters in step S2 include population size PS, 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 method for scheduling distributed heterogeneous flow workshops based on the improved mixed cause algorithm according to claim 1, wherein in step S3, the fitness value of each individual in the initial population is calculated according to the fitness value formula, and rapid non-dominant ranking is performed, the population individuals are divided into different dominant classes, and the crowding distances of individuals among the same dominant class are calculated.
5. The method of claim 1, wherein the probability of performing EOX crossover operations on each individual in the population in step S4 is P Cr The method comprises the steps of carrying out a first treatment on the surface of the The specific process is as follows:
S4A-1: converting the factory-arranged part chromosome and the workpiece-ordered part chromosome of the chromosome into a two-layer coding mode with consistent dimensions, wherein genes at the same position of the factory-arranged part chromosome and the workpiece-ordered part chromosome are related to the same workpiece;
S4A-2: randomly selecting an individual from the non-dominant solution set as a parent individual 1, wherein the parent individual 2 is a current individual;
S4A-3: randomly selecting a gene segment of the chromosome of the work piece sequencing part of the parent individual 1; then deleting the genes which are the same as segments in the chromosomes of the work sorting part of the parent individual 2, and carrying out the same operation on the genes at the same positions of the chromosomes of the factory arrangement part;
S4A-4: inserting segments into the first deleted gene position of the chromosome of the work-piece ordering part of the parent individual 2 to obtain the chromosome of the work-piece ordering part of the offspring, and arranging the genes at the same position of the chromosome of the part of the factory to perform the same operation.
6. The distributed heterogeneous flow shop scheduling method based on the improved mixed cause algorithm as claimed in claim 1, wherein the principle of adopting multiple operators to search solution space jointly in the step S5 is as follows:
applying TAYR optimization operator MU to all individuals 3 Performing a search;
then randomly selecting C for each individual max Optimization operator MU 1 Or TEC optimization operator MU 2 Performing a search;
finally, each individual randomly selects SA 1 Or SA 2 Performing a search;
the C is max Optimization operator MU 1 Comprises FJ sc 、FJ sr 、FJ ic And FJ ir Searching operators; TEC optimization operator MU 2 Comprises FJ se 、FJ ie 、FJ sr And FJ ir 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 : exchanging a randomly selected workpiece and F of any non-critical factory c A randomly selected position of the workpiece;
FJ sr : randomly selecting any two workpiece exchange positions in two different factories;
FJ ic : random selection of F c Is inserted into F e1 Is selected at random;
FJ ir : factory F r1 ,F r2 Is two different factories selected randomly, will F r1 Is inserted into F r2 Any position in the (3);
FJ se : to randomly select any one of the workpieces in the non-critical factory and F e Any one of the workpiece exchange positions;
FJ ie : random selection of F e Is inserted into F e2 Is selected at random;
FJ sy : random selection of F y One workpiece and F of e3 A randomly selected workpiece exchange;
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 : at F c Randomly selecting a workpiece, and improving the processing speed of each procedure by one grade;
SA 2 : at F e1 Randomly selecting a workpiece, and reducing the processing speed of each 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 method for scheduling distributed heterogeneous flow workshops based on the improved hybrid cause algorithm according to claim 1, wherein the process of selecting half of the individuals as the evolution targets in the next stage in the 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 method of claim 1, wherein the local search in step S7 is performed by FJ for each individual in the population ic And (3) operating.
9. The distributed heterogeneous flow shop scheduling method based on the improved hybrid cause algorithm according to claim 1, wherein the updating population process of step S8 is: and (3) merging the PS individuals subjected to the local search operation and the PS individuals not subjected to the local search selected in the step (S6), and selecting the PS individuals to replace the original parent population to become the parent population of the new generation.
10. The method of claim 1, wherein the algorithm stopping condition in step S9 is that the CPU running time does not exceed τxnxsxf seconds.
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| CN117829550A (en) * | 2024-03-04 | 2024-04-05 | 聊城大学 | Solving method for batch scheduling of distributed reentrant heterogeneous mixed flow shop |
| CN117829550B (en) * | 2024-03-04 | 2024-05-24 | 聊城大学 | Solving method for batch scheduling of distributed reentrant heterogeneous mixed flow shop |
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| CN117745152A (en) * | 2024-02-04 | 2024-03-22 | 工业云制造(四川)创新中心有限公司 | Industrial automatic modeling method and system based on AIGC |
| CN117745152B (en) * | 2024-02-04 | 2024-04-19 | 工业云制造(四川)创新中心有限公司 | AIGC-based industrial automatic modeling method and AIGC-based industrial automatic modeling system |
| CN117829550A (en) * | 2024-03-04 | 2024-04-05 | 聊城大学 | Solving method for batch scheduling of distributed reentrant heterogeneous mixed flow shop |
| CN117829550B (en) * | 2024-03-04 | 2024-05-24 | 聊城大学 | Solving method for batch scheduling of distributed reentrant heterogeneous mixed flow shop |
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