CN116300763A - Mixed flow shop mathematical heuristic scheduling method and system considering machine configuration - Google Patents
Mixed flow shop mathematical heuristic scheduling method and system considering machine configuration Download PDFInfo
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Abstract
The invention belongs to the technical field of workshop scheduling, and discloses a mathematical heuristic scheduling method and system for a mixed flow workshop taking machine configuration into consideration, wherein the method comprises the following steps: (1) Constructing a mixed integer linear programming model for a mixed flow shop considering machine configuration; (2) Determining a coding structure of a mathematical heuristic algorithm based on decision variables of the model, and decoding to obtain an optimal scheduling solution of the current round; (3) Updating the solutions in each iteration elite population to replace the last suboptimal solution; (4) Determining a transmission rule of an elite population to a mixed integer linear programming model transmission variable based on an example scale, and determining a sub-model corresponding to the transmission rule; (5) Solving the sub-model, wherein each solved value is used as the fitness function value of the current transfer chromosome and enters the population to perform superior and inferior elimination, so as to obtain the final dispatching optimal solution. The invention improves the searching quality of the algorithm and realizes a scheduling scheme for efficiently acquiring the optimal target.
Description
Technical Field
The invention belongs to the technical field related to workshop scheduling, and particularly relates to a mathematical heuristic scheduling method and system for a mixed flow workshop taking machine configuration into consideration.
Background
In modern manufacturing, order scheduling in a production management process is closely related to the operating conditions of the entire plant. Scheduling is a scheduling scheme meeting actual requirements under limited production resources and workshop resources. At present, due to the small-batch and customized production mode of modern factories, orders often have the characteristics of scattered and large fluctuation along with time, and enterprises generally preferentially meet the production requirement of the largest order in order to ensure the maximization of benefits, so that workshop resources are redundant for the order resources. Meanwhile, a Hybrid Flow Shop (HFS) type is taken as one of typical workshop types of a modern automatic factory, and is widely applied to industries such as food, electronic manufacturing and chemical industry, so that the scheduling problem (Hybrid Flow Shop Scheduling with Machine Configurations, HFSP-MC) of the Hybrid Flow Shop of machine configuration is considered, the energy is saved by optimizing the use quantity of machines, the purpose of solving the fluctuation of orders and the difference of the saturation degree of workshops is achieved, the number of machines per stage, the workpiece sequence and the machine selection are optimized in the Hybrid Flow Shop, and the purpose of optimizing the delivery period and the number of machines of an overall order is achieved.
In the conventional mixed flow shop scheduling problem and its variant, the conventional algorithm is often designed around the same coding and decoding mode, and in the decoding stage, whether mixed rule decoding or positive and negative mixed decoding is adopted, a part of solution space cannot be searched. The algorithm makes the solution space complex by adding a complex domain searching mechanism and preferential performance, and the stability of algorithm solution is challenged.
The current algorithm and the model are separately solved, and constraint properties of the modulation model are not analyzed and solved.
Disclosure of Invention
In order to meet the above defects or improvement demands of the prior art, the invention provides a mathematical heuristic scheduling method and a mathematical heuristic scheduling system for a mixed flow shop taking into consideration machine configuration.
To achieve the above object, according to one aspect of the present invention, there is provided a mathematical heuristic scheduling method of a hybrid flow shop considering machine configuration, the method comprising the steps of:
(1) Constructing a mixed integer linear programming model for a mixed flow shop taking into account machine configuration, the optimization objective of the mixed integer linear programming model being to determine the number of machines per stage and the order of processing of the workpiece processes on the machines such that the weighted sum of lead time offset time and number of machines used f=log a ∑∑M j,k +log b ∑(W i E ·E i +W i T ·T i ) Minimum, where M j,k If the kth machine in the jth stage participates in machining, 1 represents that the machine participates in machining, otherwise, the machine does not participate in machining; a, b are logarithmic parameters, and are obtained through parameter adjustment experiments; w (W) i E A weight value for advancing the finishing time; e (E) i To advance the finishing time; w (W) i T Weight value for delaying finishing time; t (T) i To delay the completion time;
(2) Determining a coding structure of a mathematical heuristic algorithm based on decision variables of a mixed integer linear programming model, adding a coding sequence into a population as a chromosome, and decoding to obtain an optimal scheduling solution of a current round;
(3) Adding the optimal scheduling solution in the chromosome population of each iteration to the elite population, namely updating the solution in the elite population of each iteration to replace the last suboptimal solution so as to ensure that the solution in the elite population is a historical optimal solution;
(4) Determining a transmission rule of an elite population to a mixed integer linear programming model transmission variable based on an example scale, and determining a sub-model corresponding to the transmission rule, namely parameterizing the mixed integer linear programming model selected by the machine number of each stage and the machine of each stage of the workpiece;
(5) And solving the obtained submodel, wherein each solved value is used as the fitness function value of the current transfer chromosome and enters the population to perform superior and inferior elimination search, so as to obtain the final dispatching optimal solution.
Further, the coding structure is a double-layer coding structure, the first layer is a workpiece sequence, and the first layer represents a processing machine which can be used in each stage of workpiece procedure; the second layer is a workpiece sequence representing the priority relationship of a workpiece process at a certain stage.
Further, the double-layer coding sequence is added into the population as a chromosome, and the sequence of the coding structure is as follows:
[M 1 M 2 M 3 ... M j-1 M j ]
[S 1 S 2 ... S i-2 S i-1 S i ]。
further, during decoding, the chromosome coding sequence is used as a workpiece sequence at the first stage of the workpiece, and the earliest idle machine is sequentially arranged for processing according to the machine number of each stage represented by the machine number coding sequence, so as to obtain a scheduling solution G after forward decoding Positive direction The method comprises the steps of carrying out a first treatment on the surface of the Then, the chromosome coding sequence is used as a workpiece sequence of the end stage of the workpiece, and the processing is sequentially carried out according to the latest idle machine according to the machine number of each stage represented by the machine number coding sequence, so as to obtain a scheduling solution G after reverse decoding Reverse-rotation The method comprises the steps of carrying out a first treatment on the surface of the Comparing forward decoded scheduling solutions G Positive direction And scheduling solution G for reverse decoding Reverse-rotation Better solution is selected as the scheduling solution G of decoding 0 The method comprises the steps of carrying out a first treatment on the surface of the Processing the decoded scheduling solution by using the idle time block movement rule with the delivery date deviation of each workpiece reduced as a target to obtain a better scheduling solution after processing, and using the better scheduling solution as a final scheduling solution G of the round Terminal (A) 。
Further, the forward decoding is to process the workpiece sequence provided by the chromosome of the workpiece sequence as a first stage workpiece sequence according to the rule of idle machine first processing; the reverse decoding is to process the workpiece sequence of the chromosome from right to left by taking the workpiece sequence of the chromosome as a processing sequence from right to left in the last stage, and also process the workpiece sequence by adopting a rule of idle machine processing first, and select a better solution in the two decoding processes as a decoding result.
Further, for the continuous time block on each machine at the end stage of the decoded feasible solution, judging whether the continuous time block is an independent time block or not sequentially from right to left, judging whether the independent continuous time block meets the condition of left shift or right shift, carrying out shifting by one unit each time, if the integral objective function value is reduced after shifting, shifting effectively, otherwise, not shifting.
Further, in the iterative process of elite population generation, firstly, performing crossover operation on the chromosome according to the randomly generated probability p, namely selecting two chromosome sequences, randomly selecting two crossover positions for a machine number layer and a workpiece process layer respectively, exchanging genes between crossover points, removing genes exchanged from another chromosome in an original chromosome, then sequentially filling residual genes to vacant positions, then, performing mutation operation on the chromosome according to the randomly generated probability p, namely randomly selecting one gene position in the sequences for the machine number layer and the workpiece process layer, randomly generating a value to replace the value of the original gene position by a standard machine number, and keeping the integrity of the sequence.
Further, the transmission rule comprises a rule A, and the machine number of each stage and the machine selection of each stage workpiece are transmitted to the MILP model, namely, the sub-model to be solved corresponding to the rule A is the MILP model parameterized by the machine number of each stage and the machine selection of each stage workpiece.
Further, decision variables include number of machines per stage, work piece sequence, and machine selection; solving the sub-model, taking the value obtained by each solving as the fitness function value of the transfer chromosome, entering the population to perform superior and inferior elimination search, continuing to perform rule judgment, sub-model determination and model solving on the chromosomes in the elite population in the generation until the elite population in the generation is completely optimized, judging whether the iteration time threshold of the algorithm is met, outputting the optimal solution if the iteration time threshold is met, and if the iteration time threshold is not met, continuing to generate part of elite population of the genetic algorithm, and circulating.
The invention provides a mathematical heuristic scheduling system of a mixed flow shop taking machine configuration into consideration, which comprises a memory and a processor, wherein the memory stores a computer program, and the processor executes the mathematical heuristic scheduling method of the mixed flow shop taking machine configuration into consideration when executing the computer program.
In general, compared with the prior art, the mixed flow shop mathematical heuristic scheduling method and system taking the machine configuration into consideration mainly have the following beneficial effects:
1. compared with the existing hybrid algorithm, the hybrid meta-heuristic algorithm provided by the invention acquires elite population information by adopting the meta-heuristic algorithm, designs a transmission rule for a subsequence thereof, determines a specified corresponding submodel, and accurately solves the submodel, so that an optimal solution in the current field range can be obtained, the searching quality of the algorithm is improved, and a scheduling scheme for efficiently acquiring an optimal target is realized.
2. According to the invention, through model refinement of the feasible solution subsequence of the elite population, the elite population can acquire the current optimal solution, and on the basis, the model can search the optimal solution in the field range of the feasible solution.
3. The invention ensures the optimality of the decoding process by mixing the decoding method and the idle time block movement rule, and can obtain a better solution of the corresponding scheduling result in the coding space by adopting the mode because the objective function comprises the minimum advance/delay time weighted sum, thereby improving the searching efficiency.
4. For the mixed flow shop scheduling problem considering the machine configuration, when the scale of an example is increased, the searching efficiency of using other mixed algorithms is reduced, and the local optimization is possibly involved, and when the solving method is used, more feasible domain solutions can be searched, so that the global optimality is ensured.
Drawings
FIG. 1 is a flow chart of a mathematical heuristic scheduling method for a hybrid flow shop that takes into account machine configuration provided by the present invention;
FIG. 2 (a), (b), (c) and (d) are diagrams of chromosome encoding and decoding, respectively;
fig. 3 (a) and (b) are schematic diagrams of idle time block movement, respectively;
FIG. 4 is a schematic representation of elite population subsequence variable transfer.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
The invention provides a mathematical heuristic scheduling method of a mixed flow shop considering machine configuration, which mixes a mathematical solving method and a (meta) heuristic solving method by the mathematical heuristic method to realize graded solving of decision variables and is used for solving the technical problem that the algorithm is difficult to solve due to multiple decision variables and large solution space in the scheduling problem. The method comprises the steps of firstly modeling a mixed flow shop scheduling considering machine configuration, establishing a Mixed Integer Linear Programming (MILP) model, and carrying out fusion solution on the established MILP model by adopting a mathematical heuristic algorithm based on a genetic algorithm so as to solve the problems of regular decoding and solution space explosion in the traditional scheduling problem and improve the scheduling solution quality in the limit solution time.
Referring to fig. 1, the scheduling method mainly includes the following steps:
step one, constructing a mixed integer linear programming model for a mixed flow shop considering machine configuration, wherein the optimization goal of the mixed integer linear programming model is to determine the number of machines in each stage and the processing sequence of workpiece procedures on the machines, so that the weighted sum f=log of the delivery date deviation time and the number of machines used a ∑∑M j,k +log b Σ(W i E ·E i +W i T ·T i ) Minimum, where M j,k If the kth machine in the jth stage participates in machining, 1 represents that the machine participates in machining, otherwise, the machine does not participate in machining; a, b are logarithmic parameters, and are obtained through parameter adjustment experiments; w (W) i E A weight value for advancing the finishing time;E i to advance the finishing time; w (W) i T Weight value for delaying finishing time; t (T) i To delay the completion time.
Linearizing a traditional mixed flow shop scheduling model, realizing linearization of the model by introducing 0-1 variable and a large M method, taking machine configuration of each stage into consideration, and introducing machine number decision of each stage as model constraint to obtain an MILP model taking the mixed flow shop scheduling problem of the machine configuration into consideration, wherein the optimization goal of the model is to determine the number of machines of each stage and the processing sequence of workpiece procedures on the machines, so that the weighted sum of delivery period deviation time and the number of used machines is achieved:
f＝log a ∑∑M j,k +log b Σ(W i E ·E i +W i T ·T i ) Minimum.
The constraint formula of the workpiece priority relation on each stage of machine is as follows:
wherein the variable x i,j,j' Representing a priority relationship between the j-th stage workpiece i and the workpiece i'; i is the work set, i= {1, 2., i..n }, n is the number of work pieces; j is a set of phases, j= {1, 2., j..m, m being the number of stages.
The corresponding constraints on the number of machines used per stage of the work-piece process are:
wherein the variable M j,k 1, the number of the kth machines in the jth stage is smaller than the standard number of machines;
standard machine number per stage; j is a set of phases, j= {1, 2., j..m, m being the number of stages.
The constraint formula corresponding to the machining machine number selected by the workpiece at each stage is as follows:
wherein the variable y i,j,k A kth machine which indicates whether the workpiece i is selected for processing in the jth stage, wherein the total number of the kth machine is smaller than the number of usable machines; k is the machine label; k is a set of machines, k= {1,2,..k, M j -a }; n is the number of work pieces; i is the workpiece set, i= {1,2, i., n }; j is the stage index, J is the stage set, j= {1,2,..j,..m }.
The constraint formula of the workpiece processing time of the same processing machine without conflict is as follows:
in the processing machine selected per stage, where the variable y i,j,k A kth machine which indicates whether the workpiece i is selected for processing in the jth stage, wherein the total number of the kth machine is smaller than the number of usable machines; c (C) i,j The finishing time of the workpiece i in the j-th stage is set; m is the number of stages; c (C) i,0 The finishing time of the workpiece i in the first stage is set; t is t i',0 For work i' atFinishing time of the first stage; y is i,0,k For whether the workpiece i is machined on the machine k in the first stage, if so, it is 1, otherwise it is 0; y is i',0,k For the work piece i' whether it is machined on machine k in the first stage, 1 if it is machined, or 0 if it is not; x is x i,i',0 A priority relation between the workpiece i and the workpiece i' in the first stage; a is a maximum positive number; t is t i',j The processing time of the workpiece i' at the stage j; y is i',j,k For workpiece i' whether it is being machined on machine k at stage j, if so, it is 1, otherwise it is 0; x is x i,i',j Is the priority relationship between the j-th stage workpiece i and the workpiece i'.
The formula for determining the lead time variable and the lead delay time variable is:
in the formula, the variables
And->
Respectively representing the lower limit and the upper limit of the delivery period of the workpiece i; e (E) i The advanced finishing time of the workpiece i; c (C) i,m For finishing work piece i in the final stage; t (T) i Delay finishing time for workpiece i;
and secondly, encoding and decoding of a mathematical heuristic algorithm based on a mixed integer linear programming model.
And determining a coding structure of a mathematical heuristic algorithm based on decision variables of the mixed integer linear programming model, adding the coding sequence into the population as a chromosome, and decoding to obtain an optimal scheduling solution of the current round.
Encoding: designing a coding structure based on a genetic algorithm according to decision variables of a mixed integer linear programming model (a main model), wherein the main model comprises three decision variables of the number of machines in each stage, a workpiece sequence and machine selection, and the coding structure is designed into a double-layer coding structure, wherein a first layer is a workpiece sequence and represents a processing machine which can be used by a workpiece procedure in each stage; the second layer is a workpiece sequence and represents the priority relation of a workpiece process at a certain stage; adding the double-layer coding sequence as chromosome into population, and the coding structure sequence is as follows:
[M 1 M 2 M 3 ... M j-1 M j ]
[S 1 S 2 ... S i-2 S i-1 S i ]
decoding: firstly, a chromosome coding sequence is used as a workpiece sequence of a first stage of a workpiece, and the earliest idle machine is orderly arranged for processing according to the machine number of each stage represented by the machine number coding sequence to obtain a scheduling solution G after forward decoding Positive direction The method comprises the steps of carrying out a first treatment on the surface of the Then, the chromosome coding sequence is used as a workpiece sequence of the end stage of the workpiece, and the processing is sequentially carried out according to the latest idle machine according to the machine number of each stage represented by the machine number coding sequence, so as to obtain a scheduling solution G after reverse decoding Reverse-rotation The method comprises the steps of carrying out a first treatment on the surface of the Comparing forward decoded scheduling solutions G Positive direction And scheduling solution G for reverse decoding Reverse-rotation Better solution is selected as the scheduling solution G of decoding 0 The method comprises the steps of carrying out a first treatment on the surface of the Processing the decoded scheduling solution by using the idle time block movement rule with the delivery date deviation of each workpiece reduced as a target to obtain a better scheduling solution after processing, and using the better scheduling solution as a final scheduling solution G of the round Terminal (A) 。
The decoding process of the 6×3 example shown in fig. 2, forward decoding, is to process according to the rule of idle machine first processing by taking the workpiece sequence provided by the workpiece sequence chromosome as the first stage workpiece sequence; the reverse decoding is to process the workpiece sequence of the chromosome from right to left by taking the workpiece sequence of the chromosome as a processing sequence from right to left in the last stage, and also process the workpiece sequence by adopting a rule of idle machine processing first, and select a better solution in the two decoding processes as a decoding result.
Judging whether the continuous time blocks on each machine at the end stage of the decoded feasible solution are independent time blocks from right to left in sequence, judging whether the independent continuous time blocks meet the condition of left shift or right shift, carrying out shifting by one unit each time, if the integral objective function value is reduced after shifting, shifting effectively, otherwise, not shifting;
as shown in the 6 x 3 example of fig. 3, assuming the workpiece time block distribution on the current last stage machine is as shown, then at M 3,1 In the process, the workpiece 3 does not meet the moving condition, namely the starting processing time cannot exceed the finishing time of the stage on the workpiece, so the workpiece cannot move; and M is 3,2 In the time block consisting of the workpiece 6 and the workpiece 1, after shifting to the right by one unit, the total weighted advance/retard time can be optimally minimized by one unit, so the shifting is effective.
And thirdly, adding the optimal scheduling solution in the chromosome population of each iteration round into the elite population, namely updating the solution in the elite population of each iteration round to replace the last suboptimal solution so as to ensure that the solution in the elite population is the historical optimal solution.
Specifically, adding the optimal scheduling solution in the chromosome population of each iteration round into the elite population, and keeping the elite population size to be 10, namely updating the solution in the elite population of each iteration round, and exchanging the last suboptimal solution to ensure that the solution in the elite population is the historical optimal solution.
Iterative process of elite population generation: firstly, performing crossover operation on chromosomes according to randomly generated probability p, namely selecting two chromosome sequences, randomly selecting two crossover positions for a machine number layer and a workpiece process layer respectively, exchanging genes between crossover points, removing genes exchanged from another chromosome in an original chromosome, sequentially filling residual genes to vacant positions, then performing mutation operation on the chromosomes according to randomly generated probability p, namely randomly selecting one gene position in the sequence for the machine number layer and the workpiece process layer, randomly generating a value to replace the value of the original gene position by a standard machine number, and maintaining the integrity of the sequence.
And step four, determining a transmission rule of an elite population to a mixed integer linear programming model based on an example scale, and determining a sub-model corresponding to the transmission rule, namely, parameterizing the mixed integer linear programming model selected by the machine number of each stage and the machine of each stage of workpiece.
Determining the transmission rule of elite population to main model transmission variable according to the scale, wherein the larger the scale, the algorithm tends to select transmission of more variable, and the smaller the determined decision variable type of sub-model optimization. According to the problem characteristics, the number of machines at each stage in the model, the priority relation among work procedures of the work pieces and the machine selection three decision variables of the work pieces at each stage, three transmission rules and corresponding submodel representations to be solved are designed A, B, C.
Wherein, rule A: and transmitting the number of machines per stage and the machine selection of the workpieces per stage to the MILP model, namely, parameterizing the MILP model of the machine selection of the machines per stage and the workpieces per stage according to the submodel to be solved corresponding to the rule A, wherein the constraint of the submodel is as follows:
constraining workpiece priority relationships on each machine per stage, where variables
Representing the process XY on the kth machine at the jth stage j,k,i And XY j,k,i' Priority relation of (c) is provided.
Constraining the work-piece processing time on the same machine from conflict, wherein the variables XY j,k,i Representing the elite population selecting machine k machined workpiece number at stage j.
In the method, in the process of the invention,
for work XY j,k,i Processing completion time at the j-th stage; />
For work XY j,k,i' Processing time at the j-th stage; />
For the workpiece XY on the kth machine of the jth stage j,k,i And workpiece XY j,k,i' Priority relationships between; />
For work XY j,k,i' Processing completion time at stage j; i 1 Distributing the completed workpiece set for the machine; i' is the workpiece label.
Rule B: and transmitting the number of machines per stage, the machine selection of the workpieces per stage and the workpiece priority relation on each machine of the non-end stage to the MILP model, namely, parameterizing the sub-model to be solved corresponding to the rule B, namely, the MILP model with the number of machines per stage, the machine selection of the workpieces per stage and the workpiece priority relation on each machine of the non-end stage, wherein the constraint of the sub-model refers to the model after the parameterization of A.
Rule C: rule C, the number of machines per stage, the machine selection of the workpieces per stage and the workpiece processing sequence on the non-end stage and non-end stage machine are transferred to the MILP model, namely the sub-model to be solved corresponding to the rule C is the MILP model parameterized by the number of machines per stage, the machine selection of the workpieces per stage and the workpiece processing sequence on the non-end stage and non-end stage machine, and the constraint of the sub-model refers to the model parameterized by A.
After the decoding rule and the idle time block movement rule are determined, a better elite population can be ensured, but the solution represented by the elite population at the moment is not necessarily the optimal solution, and when the solution space is increased, the quality of the solution is more difficult to ensure, so that the implementation mode continuously optimizes the elite population, specifically:
elite population, the transmitted elite population subsequence rule is determined according to the size of the solution space corresponding to the scale of the example and the dimension of the variable, and when the solution space is too large, the model receives more transmitted variables.
As shown in FIG. 4, in a 10X 3 embodiment, among the feasible solutions in elite populations of the current genetic algorithm, a 3X 1 size machine quantity sequence [2 3 2], a work piece sequence [6 1 9 4 8 10 7 2 5 3] and a machine selection sequence [1 2 2 1 2 2 1 2 1 1] are included by rational evaluation of the selection rules.
After the rule of the transmitted subsequence is obtained, on the basis of the main model, the parameterization of the variables is set, the obtained decision variables are fixed as model parameters, the variable range can be reduced, the variable dimension is reduced, and the MILP submodel with smaller corresponding solution space is obtained through a relaxation model.
And fifthly, solving the obtained submodel, wherein each solved value is used as an fitness function value of the current transfer chromosome and enters a population to perform superior and inferior elimination search, so that a final dispatching optimal solution is obtained.
In this embodiment, the fifth step includes the following sub-steps:
1. for the machine quantity variable and machine selection variable of the embodiment of FIG. 4, it is used to parameterize the master model, convert the sequence variable to a binary 0-1 variable in the model, determine the variable y i,j,k The decision variables represented by the parameterized MILP sub-model are converted into the priority relation of the workpieces on each machine, the dimension of the variables is reduced, and the specific constraint of the MILP sub-model is as follows:
(1) The priority relation constraint of the workpieces on each machine at each stage is used for constraining the workpiece priority on each machine:
(2) The work pieces on each machine occupy time constraint, and only one work piece can be processed on each machine at the same time:
2. model solving, as a function f=log b Σ(W i E ·E i +W i T ·T i ) And (3) solving the submodel by calling a linear solving module in the IBM CPLEX as an objective function, wherein each solved value is used as an fitness function value of the transfer chromosome, and entering a population to perform superior and inferior elimination search.
3. And continuing to perform rule judgment, sub-model determination and model solving on the subsequences in the elite population in the generation until the elite population in the generation is completely optimized, judging whether the iteration time threshold of the algorithm is met, outputting an optimal solution if the iteration time threshold is met, and if the iteration time threshold is not met, continuing to generate part of elite population of the genetic algorithm, and circulating.
Based on the model and the solving algorithm, in order to verify the practical application effect of the invention, the invention carries out repeated tests on a self-generated random computing example and compares the repeated tests with other common algorithms for solving the mixed flow shop scheduling, wherein GMHA is the result of the invention.
As the MILP result shown in table 1 is the result of directly solving the problem by the main model, it can be seen that the mixed integer linear programming submodel established by the invention has good solving effect, and the solving example has larger scale and smaller time; the GMHA algorithm results shown in table 1 are mathematical heuristic algorithm results of the present invention, and the solution quality is significantly superior compared to pure GA and hybrid algorithms employing full encoding; table 2 shows the results of solving the problem by several common scheduling algorithms, and the average solution of the optimal solution for multiple repeated experiments is not as good as the mathematical heuristic algorithm proposed by the invention. Therefore, the method provided by the invention has obvious advantages in solving the scheduling problem of the mixed flow shop considering the machine configuration, has high calculation result and has guiding effect in actual production.
Table 1 smaller scale example test results
TABLE 2 larger Scale example test results
As shown in tables 1 and 2, the numerical values in the tables represent the optimal solution for solving the corresponding algorithm and the average solution for ten repeated experiments, and it can be seen that the method provided by the invention can solve the optimal solution better than the MILP, is better than other meta-heuristic algorithms and mixing algorithms, achieves advantages in the scheduling problem of the mixed flow shop considering the machine configuration, and can be used for guiding actual production.
The invention also provides a mathematical heuristic scheduling system of the mixed flow shop considering the machine configuration, which comprises a memory and a processor, wherein the memory stores a computer program, and the processor executes the mathematical heuristic scheduling method of the mixed flow shop considering the machine configuration when executing the computer program.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (10)
1. A mathematical heuristic scheduling method for a hybrid flow shop taking machine configuration into account, the method comprising the steps of:
(1) Constructing a mixed integer linear programming model for a mixed flow shop taking into account machine configuration, the optimization objective of the mixed integer linear programming model being to determine the number of machines per stage and the order of processing of the workpiece processes on the machines such that the weighted sum of lead time offset time and number of machines used f=log a ΣΣM j,k +log b Σ(W i E ·E i +W i T ·T i ) Minimum, where M j,k If the kth machine in the jth stage participates in processing, 1 represents that the kth machine participates in processing, otherwise, the kth machine does not participate in processing; a, b are logarithmic parameters, and are obtained through parameter adjustment experiments; w (W) i E A weight value for advancing the finishing time; e (E) i To advance the finishing time; w (W) i T Weight value for delaying finishing time; t (T) i To delay the completion time;
(2) Determining a coding structure of a mathematical heuristic algorithm based on decision variables of a mixed integer linear programming model, adding a coding sequence into a population as a chromosome, and decoding to obtain an optimal scheduling solution of a current round;
(3) Adding the optimal scheduling solution in the chromosome population of each iteration to the elite population, namely updating the solution in the elite population of each iteration to replace the last suboptimal solution so as to ensure that the solution in the elite population is a historical optimal solution;
(4) Determining a transmission rule of an elite population to a mixed integer linear programming model transmission variable based on an example scale, and determining a sub-model corresponding to the transmission rule, namely parameterizing the mixed integer linear programming model selected by the machine number of each stage and the machine of each stage of the workpiece;
(5) And solving the obtained submodel, wherein each solved value is used as the fitness function value of the current transfer chromosome and enters the population to perform superior and inferior elimination search, so as to obtain the final dispatching optimal solution.
2. The hybrid flow shop mathematical heuristic scheduling method considering machine configuration as claimed in claim 1, wherein: the coding structure is a double-layer coding structure, the first layer is a workpiece sequence, and represents a processing machine which can be used in each stage of workpiece procedure; the second layer is a workpiece sequence representing the priority relationship of a workpiece process at a certain stage.
3. The hybrid flow shop mathematical heuristic scheduling method taking into account machine configuration as set forth in claim 2, wherein: adding the double-layer coding sequence as chromosome into population, and the coding structure sequence is as follows:
[M 1 M 2 M 3 ...M j-1 M j ]
[S 1 S 2 ...S i-2 S i-1 S i ]。
4. the hybrid flow shop mathematical heuristic scheduling method considering machine configuration as claimed in claim 1, wherein: when decoding, the chromosome coding sequence is used as a workpiece sequence at the first stage of the workpiece, and the earliest idle machine is orderly arranged for processing according to the machine number of each stage represented by the machine number coding sequence to obtain a scheduling solution G after forward decoding Positive direction The method comprises the steps of carrying out a first treatment on the surface of the Then, the chromosome coding sequence is used as a workpiece sequence of the end stage of the workpiece, and the processing is sequentially carried out according to the latest idle machine according to the machine number of each stage represented by the machine number coding sequence, so as to obtain a scheduling solution G after reverse decoding Reverse-rotation The method comprises the steps of carrying out a first treatment on the surface of the Comparing forward decoded scheduling solutions G Positive direction And scheduling solution G for reverse decoding Reverse-rotation Better solution is selected as the scheduling solution G of decoding 0 The method comprises the steps of carrying out a first treatment on the surface of the Processing the decoded scheduling solution by using the idle time block movement rule with the aim of reducing the delivery date deviation of each workpiece to obtain a better scheduling solution after processing as the final of the roundScheduling solution G Terminal (A) 。
5. The hybrid flow shop mathematical heuristic scheduling method considering machine configuration as claimed in claim 1, wherein: the forward decoding is to process the workpiece sequence provided by the chromosome of the workpiece sequence as a first stage workpiece sequence according to the rule of idle machine first processing; the reverse decoding is to process the workpiece sequence of the chromosome from right to left by taking the workpiece sequence of the chromosome as a processing sequence from right to left in the last stage, and also process the workpiece sequence by adopting a rule of idle machine processing first, and select a better solution in the two decoding processes as a decoding result.
6. A machine configuration-aware hybrid flow shop mathematical heuristic scheduling method according to any of claims 1-5, wherein: and judging whether the continuous time blocks on each machine at the end stage of the decoded feasible solution are independent time blocks from right to left, judging whether the independent continuous time blocks meet the condition of left shift or right shift, carrying out shifting by one unit each time, and if the integral objective function value is reduced after shifting, enabling shifting, otherwise, not shifting.
7. A machine configuration-aware hybrid flow shop mathematical heuristic scheduling method according to any of claims 1-5, wherein: in the iteration process of elite population generation, firstly, carrying out crossover operation on chromosomes according to randomly generated probability p, namely selecting two chromosome sequences, randomly selecting two crossover positions for a machine number layer and a workpiece process layer respectively, exchanging genes between crossover points, removing genes exchanged from another chromosome in an original chromosome, then sequentially filling residual genes to vacant positions, then carrying out mutation operation on the chromosomes according to randomly generated probability p, namely randomly selecting one gene position in the sequences for the machine number layer and the workpiece process layer, randomly generating a value for replacing the value of the original gene position by a standard machine number, and maintaining the integrity of the sequences.
8. A machine configuration-aware hybrid flow shop mathematical heuristic scheduling method according to any of claims 1-5, wherein: the transmission rule comprises a rule A, and the number of machines in each stage and the machine selection of the workpieces in each stage are transmitted to the MILP model, namely, the sub-model to be solved corresponding to the rule A is the MILP model parameterized by the number of machines in each stage and the machine selection of the workpieces in each stage.
9. A machine configuration-aware hybrid flow shop mathematical heuristic scheduling method according to any of claims 1-5, wherein: decision variables include number of machines per stage, work piece sequence, and machine selection; solving the sub-model, taking the value obtained by each solving as the fitness function value of the transfer chromosome, entering the population to perform superior and inferior elimination search, continuing to perform rule judgment, sub-model determination and model solving on the chromosomes in the elite population in the generation until the elite population in the generation is completely optimized, judging whether the iteration time threshold of the algorithm is met, outputting the optimal solution if the iteration time threshold is met, and if the iteration time threshold is not met, continuing to generate part of elite population of the genetic algorithm, and circulating.
10. A mathematical heuristic scheduling system for a hybrid flow shop taking machine configuration into account, characterized by: the system comprising a memory storing a computer program and a processor executing the computer program to perform the hybrid flow shop mathematical heuristic scheduling method taking into account machine configuration of any of claims 1-9.
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