CN116596293B - Distributed full-flow job shop scheduling method and terminal based on genetic algorithm - Google Patents
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Abstract
The invention discloses a distributed whole-flow job shop scheduling method and a terminal based on a genetic algorithm, which relate to the technical field of shop scheduling. The method solves the NP problem in the distributed whole-process workshop scheduling problem of comprehensively considering three-stage scheduling production in the prior art.
Description
Technical Field
The invention belongs to the technical field of workshop scheduling, and particularly relates to a distributed full-flow job workshop scheduling method and terminal based on a genetic algorithm.
Background
With the continuous advancement of economic globalization, manufacturing enterprises have begun to shift from traditional centralized production modes to emerging distributed multi-factory collaborative production modes to relieve production pressure and optimize supply chain system efficiency. Therefore, the traditional shop scheduling problem of scheduling multiple machines within a single shop to produce multiple workpieces cannot meet the distributed manufacturing requirements of modern enterprises, and new scheduling schemes are needed.
The current production process of modern enterprises can be divided into the following three stages: (1) distributed manufacturing of product operations; the problem at this stage is how to distribute the multiple jobs for processing the product to different factories and how to reasonably coordinate the processing sequences of the jobs between the different factories to minimize the maximum completion time of the jobs; (2) work to assembly of the product; when all operations of a product have been produced, the operations can be assembled to produce the complete product, the goal of this stage being to minimize the maximum assembly time of the product; (3) differentiation treatment of the products; in order to meet the personalized demands of customers, the assembled products often need to be subjected to differentiation treatment, and the aim of the stage is to minimize the maximum differentiation treatment time of the products.
The production process of modern enterprise products is shown in FIG. 1, assuming that each product Pi contains two jobs J i,1 And J i,2 And all products can be classified together into t categories; all products which execute the same specific operation in the differentiation processing stage are the same type of products, for example, some products need to be cleaned at last, and some products need to be colored at last; the machine that handles the d-th stage of the production process is called M d The method comprises the steps of carrying out a first treatment on the surface of the In stage 1, a total of f identical distributed plants can produce all jobs, each job J i,p Machine M to be at kth distributed plant k,1,1 , M k,1,2 , M k,1,3 Sequentially processing to finish production; when J i,1 And J i,2 Can be after the production is finished 2 Upper completion P i Is then P i To different differentiation processing machines M according to the category to which they belong 3,h And finally carrying out differentiation treatment to obtain a final product.
In recent years, researchers have begun to focus on the multi-stage modern product production scheduling problem, wherein the problem of considering only stage 1 to minimize the maximum completion time of a job is called the distributed replacement flow shop scheduling problem, and as disclosed in patent publication No. CN114066120a, a distributed replacement flow shop scheduling method based on a differential evolution algorithm is provided; meanwhile, considering the problem of minimizing the maximum assembly time of the product in the stage 1 and the stage 2 is called as the scheduling problem of the distributed assembly replacement flow shop, for example, the patent with the publication number of CN110632907B provides a scheduling optimization method and system of the distributed assembly replacement flow shop; the problem of considering both stage 2 and stage 3 to minimize the maximum differentiated processing time of the product is referred to as the differentiated flow shop scheduling problem, and the relationship between these three types of problems and the product production stage is shown in fig. 1. While existing methods that only consider one or two stages of the overall product flow can reduce the complexity of the overall problem and reduce the amount of computation, such methods yield results that are only one scheduling scheme at a single stage or at two stages and cannot be applied to the complete production schedule for the entire product. Compared with the scheduling problem considering only part of production stages, the constraint of the distributed full-flow workshop scheduling problem comprehensively considering three stages of scheduling production is more complex, the arrangement scheduling difficulty of the jobs is NP-level, and as the solving scale is increased, an accurate algorithm for calculating the optimal solution by solving a mathematical model can not obtain an answer in a certain time. Furthermore, existing methods typically only consider the completion time factor and ignore the cost factor of machine operation, but it should be the ultimate goal how to trade off between the two to make the maximum profit for the plant.
Therefore, a method and a terminal for scheduling a distributed full-flow job shop based on a genetic algorithm are needed to solve the above problems.
Disclosure of Invention
Aiming at the problems existing in the prior art, the invention provides a distributed full-flow job shop scheduling method and a terminal based on a genetic algorithm, which utilize two populations to respectively optimize the completion time of products and the running cost of machines, and finally obtain a plurality of optimal scheduling schemes comprehensively considering the two targets of the completion time of the products and the running cost of the machines.
The technical scheme of the invention is realized as follows:
the distributed full-flow job shop scheduling method based on the genetic algorithm comprises the following steps:
step S1, initializing parameters and a population, and calculating the adaptation value of individuals in the population: setting the current evolution algebra gen=1, the maximum evolution algebra MaxGen, the population scale NP and the crossover probability P c Probability of variation P m The method comprises the steps of carrying out a first treatment on the surface of the Randomly initializing population pop 1 And pop 2 And calculating all individuals in both populationsIs adapted to the value of (a); wherein the individual refers to a sequence in which a plurality of operations are produced and processed at a plurality of factories;
step S2, calculating non-dominant solutions in all individuals by using a rapid non-dominant sorting method, and putting the non-dominant solutions into an external archive A; fast non-dominant ordering is one way to determine non-dominant solutions. In dealing with multi-objective optimization problems, if and only if an individual x 1 The fitness value on all targets is greater than that of another individual x 2 Can only consider x 1 Dominant x 2 I.e. x 1 Is better than x 2 The method comprises the steps of carrying out a first treatment on the surface of the Otherwise they are considered to be incomparable. The rapid non-dominant ranking method is a method for ranking individuals in a population, by which the non-dominant rank of each individual can be determined, and finally all individuals with the non-dominant rank of 1 are the optimal solutions in the current population, namely non-dominant solutions;
step S3, the pop 1 And the pop 2 Selecting NP individuals to be crossed from the population itself and the external archive a using a binary tournament method, respectively; wherein the pop 1 Selecting an individual with the completion time as an index, the pop 2 Selecting an individual by taking the cost as an index;
s4, respectively executing cross operation on the two populations;
s5, respectively executing mutation operation on the two populations;
step S6, updating the individuals in the external archive A;
step S7, the gen is increased by 1; if the gen is smaller than the MaxGen, executing a step S3; otherwise, the procedure terminates.
As a further optimization of the above solution, in step S1, the initialized parameters include n products and f distributed factories; the job scheduling stage of the product comprises a production stage, an assembly stage and a differentiation stage;
wherein the number of categories of the products is t, and the number of operations of each product is w; p (P) i Represents the ith product, J i,p A p-th job representing an i-th product; the J is i,p Mapped as J j The J is j Represents the j-th job, where j=i×w+p and j∈ [1, n×w ]]；
Wherein each of the distributed factories is provided with m machines; m is M k,1,z Representing a z-th machine of a kth one of said distributed plants during said production phase;
wherein M is 2 Representing the machine at the assembly stage; m is M 3,h Representing a machine for processing a class h product in the differentiation stage;
the initialization steps of the individuals in the population are as follows:
step S1-1, representing the individual by a double-layer coding mode, namely x s ={π(1), π(2), …, π(f)}，π(k)={π(k,1), π(k,2), …, π(k,n k ) -a }; wherein x is s Denoted as the s-th individual in the population, pi (k) is denoted as the scheduling sequence of the k-th of the individuals in the distributed plant, and k.epsilon.1, f]The method comprises the steps of carrying out a first treatment on the surface of the Pi (k, q) represents the q-th job of pi (k) processing, and q ε [1, n ] k ], n k Representing the total number of jobs processed by the kth plant; individual x s The storage structure of (2) is a two-dimensional structure;
step S1-2, randomly generating a sequence { J } of job production 1 ，J 2 ，…，J j Sequentially assigning the first f jobs in the sequence to individuals x s Is assigned to the same individual x s Pi (k);
step S1-3, calculating individual x s And adapt individual x s Distribution population pop 1 Or population pop 2 ；
Step S1-4, repeating steps S1-1 to S1-3 until both populations contain NP individuals.
Each distributed factory can process all jobs, each job can only be distributed to one distributed factory for processing, each machine can only process one job or one product at a time, the product assembly stage and the differentiated processing stage can process the products according to the first come first serve principle, and the buffer size between adjacent production stages is infinite.
As a further optimization of the above scheme, the adaptation value of the individual includes a completion time T max And cost C total The method comprises the steps of carrying out a first treatment on the surface of the The full-flow job scheduling problem modeling is realized in order to solve the problem of double-objective optimization, and two objectives of optimization are the maximum completion time of a product and the working cost of a machine scheduled at the time respectively;
the completion time T max The calculation steps are as follows:
in the production phase, the q-th job in the sequence pi (k) is in machine M k,1,z The production completion time is CTP π(k,q),z The calculation method is as follows:
（1）；
（2）；
（3）；
（4）；
wherein TP π(k,q),z Represents that the q-th job in pi (k) is in machine M k,1,z Production time, TP π(k,q),m Representing the completion time of the q-th job in pi (k); the latest end time of all jobs in the product is CTP i The method comprises the following steps:
（5）；
determining the assembly sequence of products in the assembly phase as a = { a (1), a (2), …, a (n) } based on the start assembly time of each product and the first come first serve principle, wherein the first product in the sequence a is in the machine M 2 The calculation method of the assembly completion time comprises the following steps:
（6）；
（7）；
wherein TA α(l) Representing the assembly time of the first job in sequence α on machine M2;
in the differentiation stage, in machine M 3，h The sequence on which the differentiation was performed was λ (h) = { λ (h, 1), λ (h, 2), …, λ (h, n) h ) N is }, where n h Indicating the number of class h products; the nth product in the sequence lambda (h) is in machine M 3，h The calculation method of the differentiation processing completion time comprises the following steps:
（8）；
（9）；
wherein TD λ(h,r) Representing the nth product in the sequence lambda (h) in machine M 3,h At a differentiated processing time, CTD λ(h,nh) Representing machine M 3,h End time of finishing last product, ET h The method comprises the steps of carrying out a first treatment on the surface of the The final time for all kinds of products to finish is:
（10）；
the cost C total The calculation method of (1) is as follows:
（11）；
（12）；
（13）；
wherein T is work Representing the total operating time of the machine, T rest Representing the total rest period of the machine c 1 C is the working cost of the machine in unit time 2 Is the resting cost of the machine in unit time. For each machine, its working time is the processing time of all jobs or products scheduled thereon, and the rest time is the completion time of the last job scheduled on that machine minus the working time.
The two objectives of the optimization of the present invention are the maximum completion time of the product and the working cost of the machine, respectively, wherein the working cost of the machine is related to the working time and rest time of the machine. For each machine, the working and rest time of each machine can be obtained by only knowing the working time of the beginning and the end of each machine and subtracting the time consumed for processing the work or the product. In particular, the start and end working times of the machine are the start and end processing times of the work or product being processed thereon.
As a further optimization of the above scheme, in the step S3, the individuals selected for crossing are P1 and P2, respectively; in the step S4, the specific steps of crossing are as follows:
step S4-1, generating random number R c ，R c A decimal fraction between 0 and 1; if R is c Greater than P c Step S4-2 is continuously executed, otherwise, step S5 is directly executed;
step S4-2 according to P 1 、P 2 Respectively generating S by dimension and size of (2) 1 And S is 2 The method comprises the steps of carrying out a first treatment on the surface of the At P 1 、P 2 Respectively randomly selecting a sequence pi (u) and pi (v), wherein u, v E [1, f]The method comprises the steps of carrying out a first treatment on the surface of the The sequences pi (u) and pi (v) are assigned to S, respectively 1 And S is 2 And pi (u) and pi (v) are in the individual S 1 、S 2 The sequence order in (a) is equivalent to that in P 1 、P 2 In (2) a sequence order of (2);
step S4-3, P 2 The operations except pi (u) are sequentially filled into S 1 The method comprises the steps of carrying out a first treatment on the surface of the Will P 1 The operations except pi (v) are sequentially filled into S 2 ；
Step S4-4, S 1 And S is 2 Respectively replace P 1 、P 2 The interleaving operation is completed, and step S5 is performed.
The crossover operation is used to create new individuals to enhance diversity of the population, and in the present invention, the crossover operation only changes the scheduling order of the processing jobs in each plant, not the number of jobs processed per plant.
As a further optimization of the above scheme, in the step S5, the operation steps of mutation are as follows:
step S5-1, generating random number R m ，R m A decimal fraction between 0 and 1; if R is m Greater than P m Step S5-2 is continuously executed, otherwise, step S6 is directly executed;
step S5-2, for selected individual x s Two sequences pi (w) and pi (y) are randomly selected, where w, y.epsilon.1, f]And w is not equal to y, and the number of operations of the sequence pi (w) and the sequence pi (y) is greater than 1;
step S5-3, deleting any one of the two sequences, and inserting the operation into a random position in the other sequence;
and step S5-4, finishing the mutation operation, and executing step S6.
The mutation operation can increase the searching capability of the genetic algorithm, avoid the algorithm to fall into a local optimal solution, and aim to adjust the number of the operations processed by part of factories and adjust the scheduling sequence of the operations.
As a further optimization of the above scheme, the updating operation in the step S6 is as follows:
step S6-1, performing local search operation on all non-dominant solutions in the external archive A to obtain a disturbed external archive A'; wherein, the disturbance method is exchange and insertion;
step S6-2, calculating pop by using a rapid non-dominant sorting method 1 ，pop 2 The non-dominant solution in A, A' is calculated, and the result obtained by calculation is stored in a temporary archive S;
step S6-3, if the number of non-dominant solutions in S is smaller than NP, directly replacing A with S; otherwise, calculating the congestion degree of the non-dominant solution in S, and then selecting the NP individuals with the highest congestion degree in S to replace the individuals in A.
The method has the advantages that the precision of the solution is improved, more non-dominant solutions are obtained by slightly perturbing the current non-dominant solutions, in addition, the update of individuals in A in each generation of evolution process can ensure that the individuals stored in A are non-dominant solutions, and the method is favorable for guiding the evolution of the individuals in the next generation of evolution process and improving the quality of the solutions. The setting of the crowding degree can reserve NP non-dominant solutions with better diversity.
As a further optimization of the above scheme, the method for calculating the congestion degree is as follows:
in the temporary archiving S, sorting all individuals according to the fitness value of all individuals under the current target to obtain the maximum fitness value f max And a minimum fitness value f min The method comprises the steps of carrying out a first treatment on the surface of the For the ordered rs-th individual, the fitness value of the individual is f rs The crowding degree of an individual is the result of normalization of the difference between the fitness values of adjacent individuals, i.e., (f) rs+1 -f rs-1 ）/（f max -f min ) The method comprises the steps of carrying out a first treatment on the surface of the The adaptive value of each individual is two, and the two calculated crowding degrees are added to obtain the final crowding degree of the individual.
As a further optimization of the above scheme, the exchanges include co-sequence exchanges and cross-sequence exchanges; the same sequence exchange is that two job exchange positions are randomly selected in the same scheduling sequence in an individual; and the cross-sequence exchange is to randomly select two scheduling sequences from an individual, and randomly select two job exchange positions from the two scheduling sequences respectively. The exchange operation can improve the speed of local search, and search and optimize local areas more quickly, thereby finding better solutions; meanwhile, since the exchange operation involves the exchange of two elements, it has a large moving distance, and it is possible to jump out of the locally optimal solution and explore the globally optimal solution.
As a further optimization of the above scheme, the insertion is: for the inserted individuals, randomly selecting the scheduling sequence pi stored therein r ，π r The number of operations is greater than 1; pi in random deletion r Is pi of one operation of (2) qr The method comprises the steps of carrying out a first treatment on the surface of the Calculating the completion time and cost of all scheduling sequences in an individual and operating pi qr Random insertion is performed in any position of the sequence with the lowest completion time or cost. The insertion operation is advantageous for enhancing the diversity of solutions, while locally improving the quality of solutions.
The invention also discloses a terminal, which comprises a storage device for storing a plurality of instructions and a processor for executing each instruction in the storage device, wherein the instructions are suitable for loading and executing the distributed full-flow job shop scheduling method based on the genetic algorithm by the processor.
The beneficial effects are as follows:
the invention provides a distributed whole-flow job shop scheduling method based on a genetic algorithm aiming at the product production process of modern enterprises, which simultaneously considers distributed manufacturing of product jobs, assembly of jobs to products and differentiated treatment of products, converts the scheduling flow of the whole-flow jobs in the workshops into a mathematical model, optimizes the maximum completion time of the products and the total running cost of a machine simultaneously by solving genetic algorithms of multi-objective problems based on multiple groups, optimizes one objective for each individual in each group respectively, guides the evolution of the individual by utilizing non-dominant solutions stored in an external archive, and simultaneously perturbs the existing non-dominant solutions by utilizing a local search strategy to improve the precision of the solutions and the convergence of the algorithms, and finally obtains an optimal scheduling scheme of comprehensively considering the two objectives of the completion time of the products and the running cost of the machine. Compared with the scheduling problem in the prior art, which only considers part of production stages, the technical scheme provided by the invention solves the NP problem in the distributed whole-process workshop scheduling problem of comprehensively considering three-stage scheduling production, and is more in line with the production process of the products of modern manufacturing enterprises compared with the existing workshop scheduling problem, and has important practical significance.
Drawings
FIG. 1 is a flow diagram of a product manufacturing process for a modern enterprise;
FIG. 2 is a schematic flow diagram of a distributed full-flow job shop scheduling method based on a genetic algorithm according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a crossover operation provided by an embodiment of the present invention;
fig. 4 is a schematic diagram of a mutation operation according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are only some embodiments of the present invention, but not all embodiments of the present invention. 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.
As shown in fig. 1 and 2, the present embodiment discloses a distributed full-flow job shop scheduling method based on a genetic algorithm, which includes the following steps:
step S1, initializing parameters and a population, and calculating the adaptation value of individuals in the population: setting the current evolution algebra gen=1, the maximum evolution algebra MaxGen, the population scale NP and the crossover probability P c Probability of variation P m The method comprises the steps of carrying out a first treatment on the surface of the Randomly initializing population pop 1 And pop 2 Calculating the adaptation values of all individuals in the two populations; wherein the individual refers to a sequence in which a plurality of operations are produced and processed at a plurality of factories;
in this embodiment, the parameters initialized in step S1 include n products and f distributed factories; the job scheduling stage of the product comprises a production stage, an assembly stage and a differentiation stage;
wherein the number of categories of the products is t, and the number of operations of each product is w; p (P) i Represents the ith product, J i,p A p-th job representing an i-th product; the J is i,p Mapped as J j The J is j Represents the j-th job, where j=i×w+p and j∈ [1, n×w ]]；
Wherein each of the distributed factories is provided with m machines; m is M k,1,z Representing a z-th machine of a kth one of said distributed plants during said production phase;
wherein M is 2 Representing the machine at the assembly stage; m is M 3,h Representing a machine for processing a class h product in the differentiation stage;
the initialization steps of the individuals in the population are as follows:
step S1-1, representing the individual by a double-layer coding mode, namely x s ={π(1), π(2), …, π(f)}，π(k)={π(k,1), π(k,2), …, π(k,n k ) -a }; wherein x is s Denoted as the s-th individual in the population, pi (k) is denoted as the scheduling sequence of the k-th of the individuals in the distributed plant, and k.epsilon.1, f]The method comprises the steps of carrying out a first treatment on the surface of the Pi (k, q) represents the q-th job of pi (k) processing, and q ε [1, n ] k ], n k Representing the total number of jobs processed by the kth plant; individual x s The storage structure of (2) is a two-dimensional structure;
step S1-2, randomly generating a sequence { J } of job production 1 ，J 2 ，…，J j Sequentially assigning the first f jobs in the sequence to individuals x s Is assigned to the same individual x s Pi (k);
step S1-3, calculating individual x s And adapt individual x s Distribution population pop 1 Or population pop 2 ；
Step S1-4, repeating steps S1-1 to S1-3 until both populations contain NP individuals.
Each distributed factory can process all jobs, each job can only be distributed to one distributed factory for processing, each machine can only process one job or one product at a time, the product assembly stage and the differentiated processing stage can process the products according to the first come first serve principle, and the buffer size between adjacent production stages is infinite.
In this embodiment, the adaptation value of the individual includes a completion time T max And cost C total ；
The completion time T max The calculation steps are as follows:
in the production phase, the q-th job in the sequence pi (k) is in machine M k,1,z The production completion time is CTP π(k,q),z The calculation method is as follows:
（1）；
（2）；
（3）；
（4）；
wherein TP π(k,q),z Represents that the q-th job in pi (k) is in machine M k,1,z Production time, TP π(k,q),m Representing the completion time of the q-th job in pi (k); the latest end time of all jobs in the product is CTP i The method comprises the following steps:
（5）；
determining the assembly sequence of products in the assembly phase as a = { a (1), a (2), …, a (n) } based on the start assembly time of each product and the first come first serve principle, wherein the first product in the sequence a is in the machine M 2 The calculation method of the assembly completion time comprises the following steps:
（6）；
（7）；
wherein TA α(l) Representing the assembly time of the first job in sequence α on machine M2;
in the differentiation stage, in machine M 3，h The sequence on which the differentiation was performed was λ (h) = { λ (h, 1), λ (h, 2), …, λ (h, n) h ) N is }, where n h Indicating the number of class h products; the nth product in the sequence lambda (h) is in machine M 3，h The calculation method of the differentiation processing completion time comprises the following steps:
（8）；
（9）；
wherein TD λ(h,r) Representing the nth product in the sequence lambda (h) in machine M 3,h At a differentiated processing time, CTD λ(h,nh) Representing machine M 3,h End time of finishing last product, ET h The method comprises the steps of carrying out a first treatment on the surface of the The final time for all kinds of products to finish is:
（10）；
the cost C total The calculation method of (1) is as follows:
（11）；
（12）；
（13）；
wherein T is work Representing the total operating time of the machine, T rest Representing the total rest period of the machine c 1 C is the working cost of the machine in unit time 2 Is the resting cost of the machine in unit time. The two objectives of the optimization of the present invention are the maximum completion time of the product and the working cost of the machine, respectively, wherein the working cost of the machine is related to the working time and rest time of the machine. For each machine, the working and rest time of each machine can be obtained by only knowing the working time of the beginning and the end of each machine and subtracting the time consumed for processing the work or the product. In particular, the start and end working times of the machine are the start and end processing times of the work or product being processed thereon.
Step S2, calculating non-dominant solutions in all individuals by using a rapid non-dominant sorting method, and putting the non-dominant solutions into an external archive A; fast non-dominant ordering is one way to determine non-dominant solutions. In dealing with multi-objective optimization problems, if and only if an individual x 1 The fitness value on all targets is greater than that of another individual x 2 Can only consider x 1 Dominant x 2 I.e. x 1 Is better than x 2 The method comprises the steps of carrying out a first treatment on the surface of the Otherwise they are considered to be incomparable. A fast non-dominant ranking method is a method of ranking individuals in a population, by which the non-dominant rank of each individual can be determined, and finally all individuals with a non-dominant rank of 1 are the optimal solutions, i.e. non-dominant solutions, in the current population.
Step S3, the pop 1 And the pop 2 Selecting NP individuals to be crossed from the population itself and the external archive a using a binary tournament method, respectively; wherein the pop 1 Selecting an individual with the completion time as an index, the pop 2 Selecting an individual by taking the cost as an index;
s4, respectively executing cross operation on the two populations; as shown in FIG. 3, assume that two parent individuals are P 1 And P 2 Wherein P is 1 ={{5, 2, 8}, {7, 4, 1}, {3, 9, 6, 10}}，P 2 ={{2, 5}, {7, 8,1,3,4}, {10, 9,6}, in this embodiment, the specific steps of crossing are as follows:
step S4-1, generating random number R c ，R c A decimal fraction between 0 and 1; if R is c Greater than P c Step S4-2 is continuously executed, otherwise, step S5 is directly executed;
step S4-2 according to P 1 、P 2 Respectively generating S by dimension and size of (2) 1 And S is 2 The method comprises the steps of carrying out a first treatment on the surface of the At P 1 、P 2 Respectively randomly selecting a sequence pi (u) and pi (v), wherein u, v E [1, f]The method comprises the steps of carrying out a first treatment on the surface of the The sequences pi (u) and pi (v) are assigned S respectively 1 And S is 2 And pi (u) and pi (v) are in the individual S 1 、S 2 The sequence order in (a) is equivalent to that in P 1 、P 2 In (2) a sequence order of (2); thus, according to P 1 、P 2 The three dimensions of S1 and S2 generated are 3,4 and 2,5,3, respectively; at this time, S1 inherits the information of the first dimension of P1, i.e., {5,2,8}; s2 inherits the information of the second dimension of P2, i.e., {7,8,1,3,4}.
Step S4-3, P 2 The operations except pi (u) are sequentially filled into S 1 The method comprises the steps of carrying out a first treatment on the surface of the Will P 1 The operations except pi (v) are sequentially filled into S 2 The method comprises the steps of carrying out a first treatment on the surface of the At this time, the scheduling order of the jobs other than the job 5,2,8 (i.e., {7,1,3,4, 10,9,6 }) is acquired from P2 and the remaining gene positions of S1 are filled, so that the crossed individual S1 is obtained; similarly, the scheduling sequence of the jobs except the job 7,8,1,3,4 can be obtained from the P1, and the remaining gene positions of the S2 are filled to obtain the complete S2;
step S4-4, S 1 And S is 2 Respectively replace P 1 、P 2 The interleaving operation is completed, and step S5 is performed.
The crossover operation is used to create new individuals to enhance diversity of the population, and in the present invention, the crossover operation only changes the scheduling order of the processing jobs in each plant, not the number of jobs processed per plant.
S5, respectively executing mutation operation on the two populations; as shown in FIG. 4, variant individual x s ={{5, 2, 8}, {7, 4, 1}, {3, 9,6, 10}, in this embodiment, the operation steps of the mutation are:
step S5-1, generating random number R m ，R m A decimal fraction between 0 and 1; if R is m Greater than P m Step S5-2 is continuously executed, otherwise, step S6 is directly executed;
step S5-2, for selected individual x s Two sequences pi (w) and pi (y) are randomly selected, where w, y.epsilon.1, f]And w is not equal to y, and the number of operations of the sequence pi (w) and the sequence pi (y) is greater than 1; individual x s Selected sequences pi (1) and pi (2);
step S5-3, deleting any one of the two sequences, and inserting the operation into a random position in the other sequence; deleting the operation 8 in the sequence pi (1), and inserting the operation 8 into a random position of the sequence pi (2);
and step S5-4, finishing the mutation operation, and executing step S6.
The mutation operation can increase the searching capability of the genetic algorithm, avoid the algorithm to fall into a local optimal solution, and aim to adjust the number of the operations processed by part of factories and adjust the scheduling sequence of the operations.
Step S6, updating the individuals in the external archive A; in this embodiment, the update operation steps are as follows:
step S6-1, performing local search operation on all non-dominant solutions in the external archive A to obtain a disturbed external archive A'; wherein, the disturbance method is exchange and insertion; wherein the exchange includes a co-sequence exchange and a cross-sequence exchange; the same sequence exchange is that two job exchange positions are randomly selected in the same scheduling sequence in an individual; and the cross-sequence exchange is to randomly select two scheduling sequences from an individual, and randomly select two job exchange positions from the two scheduling sequences respectively.
The insertion is as follows: for the inserted individuals, randomly selecting the scheduling sequence pi stored therein r ，π r The number of operations is greater than 1; pi in random deletion r Is pi of one operation of (2) qr The method comprises the steps of carrying out a first treatment on the surface of the Computing all schedules in an individualCompletion time and cost of the sequence, and will operate pi qr Random insertion is performed in any position of the sequence with the lowest completion time or cost. The insertion operation is advantageous for enhancing the diversity of solutions, while locally improving the quality of solutions.
Step S6-2, calculating pop by using a rapid non-dominant sorting method 1 ，pop 2 The non-dominant solution in A, A' is calculated, and the result obtained by calculation is stored in a temporary archive S;
step S6-3, if the number of non-dominant solutions in S is smaller than NP, directly replacing A with S; otherwise, calculating the congestion degree of the non-dominant solution in S, and then selecting the NP individuals with the highest congestion degree in S to replace the individuals in A.
The method for calculating the crowding degree comprises the following steps:
in the temporary archiving S, sorting all individuals according to the fitness value of all individuals under the current target to obtain the maximum fitness value f max And a minimum fitness value f min The method comprises the steps of carrying out a first treatment on the surface of the For the ordered rs-th individual, the fitness value of the individual is f rs The crowding degree of an individual is the result of normalization of the difference between the fitness values of adjacent individuals, i.e., (f) rs+1 -f rs-1 ）/（f max -f min ) The method comprises the steps of carrying out a first treatment on the surface of the The adaptive value of each individual is two, and the two calculated crowding degrees are added to obtain the final crowding degree of the individual.
Step S7, the gen is increased by 1; if the gen is smaller than the MaxGen, executing a step S3; otherwise, the procedure terminates.
The embodiment also discloses a terminal, which comprises a storage device for storing a plurality of instructions and a processor for executing each instruction in the storage device, wherein the instructions are suitable for the processor to load and execute the distributed full-flow job shop scheduling method based on the genetic algorithm.
Variations and modifications to the above would be obvious to persons skilled in the art to which the invention pertains from the foregoing description and teachings. Therefore, the invention is not limited to the specific embodiments disclosed and described above, but some modifications and changes of the invention should be also included in the scope of the claims of the invention. In addition, although specific terms are used in the present specification, these terms are for convenience of description only and do not limit the present invention in any way.
Claims (8)
1. The distributed full-flow job shop scheduling method based on the genetic algorithm is characterized by comprising the following steps of:
step S1, initializing parameters and a population, and calculating the adaptation value of individuals in the population: setting the current evolution algebra gen=1, the maximum evolution algebra MaxGen, the population scale NP and the crossover probability P c Probability of variation P m The method comprises the steps of carrying out a first treatment on the surface of the Randomly initializing population pop 1 And pop 2 Calculating the adaptation values of all individuals in the two populations; wherein the individual refers to a sequence in which a plurality of operations are produced and processed at a plurality of factories;
the initialized parameters include n products and f distributed factories; the job scheduling stage of the product comprises a production stage, an assembly stage and a differentiation stage;
wherein the number of categories of the products is t, and the number of operations of each product is w; p (P) i Represents the ith product, J i,p A p-th job representing an i-th product; the J is i,p Mapped as J j The J is j Represents the j-th job, where j=i×w+p and j∈ [1, n×w ]]；
Wherein each of the distributed factories is provided with m machines; m is M k,1,z Representing a z-th machine of a kth one of said distributed plants during said production phase;
wherein M is 2 Representing the machine at the assembly stage; m is M 3,h Representing a machine for processing a class h product in the differentiation stage;
the initialization steps of the individuals in the population are as follows:
step S1-1, representing the individual by a double-layer coding mode, namely x s ={π(1), π(2), …, π(f)}，π(k)={π(k,1), π(k,2), …, π(k,n k ) -a }; wherein x is s Expressed as the s-th individual in the population, pi (k) expressed as the k-th said distribution in the individualScheduling sequence of jobs in factory, and k E [1, f]The method comprises the steps of carrying out a first treatment on the surface of the Pi (k, q) represents the q-th job of pi (k) processing, and q ε [1, n ] k ], n k Representing the total number of jobs processed by the kth plant; individual x s The storage structure of (2) is a two-dimensional structure;
step S1-2, randomly generating a sequence { J } of job production 1 ，J 2 ，…，J j Sequentially assigning the first f jobs in the sequence to individuals x s Is assigned to the same individual x s Pi (k);
step S1-3, calculating individual x s And adapt individual x s Distribution population pop 1 Or population pop 2 ；
Step S1-4, repeating steps S1-1 to S1-3 until both populations contain NP individuals;
the adaptation value of the individual includes a completion time T max And cost C total ；
The completion time T max The calculation steps of (a) are as follows:
in the production phase, the q-th job in the sequence pi (k) is in machine M k,1,z The production completion time is CTP π(k,q),z The calculation method is as follows:
（1）；
（2）；
（3）；
（4）；
wherein TP π(k,q),z Represents the q-th job in pi (k)In machine M k,1,z Production time, TP π(k,q),m Representing the completion time of the q-th job in pi (k); the latest end time of all jobs in the product is CTP i The method comprises the following steps:
（5）；
determining the assembly sequence of products in the assembly phase as a = { a (1), a (2), …, a (n) } based on the start assembly time of each product and the first come first serve principle, wherein the first product in the sequence a is in the machine M 2 The calculation method of the assembly completion time comprises the following steps:
（6）；
（7）；
wherein TA α(l) Representing the assembly time of the first job in sequence α on machine M2;
in the differentiation stage, in machine M 3，h The sequence on which the differentiation was performed was λ (h) = { λ (h, 1), λ (h, 2), …, λ (h, n) h ) N is }, where n h Indicating the number of class h products; the nth product in the sequence lambda (h) is in machine M 3，h The calculation method of the differentiation processing completion time comprises the following steps:
（8）；
（9）；
wherein TD λ(h,r) Representing the nth product in the sequence lambda (h) in machine M 3,h At a differentiated processing time, CTD λ(h,nh) Representing machine M 3,h End time of finishing last product, ET h The method comprises the steps of carrying out a first treatment on the surface of the The final time for all kinds of products to finish is:
（10）；
the cost C total The calculation method of (1) is as follows:
（11）；
（12）；
（13）；
wherein T is work Representing the total operating time of the machine, T rest Representing the total rest period of the machine c 1 C is the working cost of the machine in unit time 2 The rest cost of the machine in unit time is set;
step S2, calculating non-dominant solutions in all individuals by using a rapid non-dominant sorting method, and putting the non-dominant solutions into an external archive A;
step S3, the pop 1 And the pop 2 Selecting NP individuals to be crossed from the population itself and the external archive a using a binary tournament method, respectively; wherein the pop 1 Selecting an individual with the completion time as an index, the pop 2 Selecting an individual by taking the cost as an index;
s4, respectively executing cross operation on the two populations;
s5, respectively executing mutation operation on the two populations;
step S6, updating the individuals in the external archive A;
step S7, the gen is increased by 1; if the gen is smaller than the MaxGen, executing a step S3; otherwise, the procedure terminates.
2. The method according to claim 1, wherein in step S3, the individuals selected for crossing are P1 and P2, respectively; in the step S4, the specific steps of crossing are as follows:
step S4-1, generating random number R c ，R c A decimal fraction between 0 and 1; if R is c Greater than P c Step S4-2 is continuously executed, otherwise, step S5 is directly executed;
step S4-2 according to P 1 、P 2 Respectively generating S by dimension and size of (2) 1 And S is 2 The method comprises the steps of carrying out a first treatment on the surface of the At P 1 、P 2 Respectively randomly selecting a sequence pi (u) and pi (v), wherein u, v E [1, f]The method comprises the steps of carrying out a first treatment on the surface of the The sequences pi (u) and pi (v) are assigned to S, respectively 1 And S is 2 And pi (u) and pi (v) are in the individual S 1 、S 2 The sequence order in (a) is equivalent to that in P 1 、P 2 In (2) a sequence order of (2);
step S4-3, P 2 The operations except pi (u) are sequentially filled into S 1 The method comprises the steps of carrying out a first treatment on the surface of the Will P 1 The operations except pi (v) are sequentially filled into S 2 ；
Step S4-4, S 1 And S is 2 Respectively replace P 1 、P 2 The interleaving operation is completed, and step S5 is performed.
3. The genetic algorithm-based distributed full-flow job shop scheduling method according to claim 1, wherein in the step S5, the operation steps of mutation are:
step S5-1, generating random number R m ，R m A decimal fraction between 0 and 1; if R is m Greater than P m Step S5-2 is continuously executed, otherwise, step S6 is directly executed;
step S5-2, for selected individual x s Two sequences pi (w) and pi (y) are randomly selected, where w, y.epsilon.1, f]And w is not equal to y, sequence pi (w) and sequence pi (y)The number of operations is greater than 1;
step S5-3, deleting any one of the two sequences, and inserting the operation into a random position in the other sequence;
and step S5-4, finishing the mutation operation, and executing step S6.
4. The genetic algorithm-based distributed full-flow job shop scheduling method according to claim 1, wherein the updating operation in step S6 is as follows:
step S6-1, performing local search operation on all non-dominant solutions in the external archive A to obtain a disturbed external archive A'; wherein, the disturbance method is exchange and insertion;
step S6-2, calculating pop by using a rapid non-dominant sorting method 1 ，pop 2 The non-dominant solution in A, A' is calculated, and the result obtained by calculation is stored in a temporary archive S;
step S6-3, if the number of non-dominant solutions in S is smaller than NP, directly replacing A with S; otherwise, calculating the congestion degree of the non-dominant solution in S, and then selecting the NP individuals with the highest congestion degree in S to replace the individuals in A.
5. The genetic algorithm-based distributed full-flow job shop scheduling method according to claim 4, wherein the congestion degree calculating method is as follows:
in the temporary archiving S, sorting all individuals according to the fitness value of all individuals under the current target to obtain the maximum fitness value f max And a minimum fitness value f min The method comprises the steps of carrying out a first treatment on the surface of the For the ordered rs-th individual, the fitness value of the individual is f rs The crowding degree of an individual is the result of normalization of the difference between the fitness values of adjacent individuals, i.e., (f) rs+1 -f rs-1 ）/（f max -f min ) The method comprises the steps of carrying out a first treatment on the surface of the The adaptive value of each individual is two, and the two calculated crowding degrees are added to obtain the final crowding degree of the individual.
6. The genetic algorithm-based distributed full flow job shop scheduling method according to claim 4, wherein the exchange includes a co-sequence exchange and a cross-sequence exchange; the same sequence exchange is that two job exchange positions are randomly selected in the same scheduling sequence in an individual; and the cross-sequence exchange is to randomly select two scheduling sequences from an individual, and randomly select two job exchange positions from the two scheduling sequences respectively.
7. The genetic algorithm-based distributed full flow job shop scheduling method according to claim 4, wherein the inserting is: for the inserted individuals, randomly selecting the scheduling sequence pi stored therein r ，π r The number of operations is greater than 1; randomly delete pi r Is pi of one operation of (2) qr The method comprises the steps of carrying out a first treatment on the surface of the Calculating the completion time and cost of all scheduling sequences in an individual and operating pi qr Random insertion is performed in any position of the sequence with the lowest completion time or cost.
8. A terminal comprising a memory means storing a plurality of instructions and a processor for executing the instructions in the memory means, wherein the instructions are adapted to load and execute the genetic algorithm-based distributed full flow job shop scheduling method according to any one of claims 1 to 7 by the processor.
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