CN106125684A - Based on the multiple target Flow Shop under uncertain environment against dispatching method - Google Patents
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Abstract
A kind of based on the multiple target Flow Shop under uncertain environment against dispatching method, the invention belongs to Job-Shop field, mainly solve the uncertain noises situation that traditional dispatching method is difficult to effectively process, it is ensured that Workshop Production even running.The present invention comprises the following steps: 1) for the inverse scheduling of the multiple target Flow Shop under uncertain environment, respectively from client and maker angle, establishes and considers plant efficiency and the problem model of workshop system fluctuation situation；2) hybrid multi-objective genetic algorithm improved is used to solve described problem；3) the non-dominated ranking method of mixed strategy is this method proposed, meanwhile, use two species diversities to keep strategy and the elite retention strategy of mixing, introduce based on NEH local searching strategy in outside archive set, carry out its scope of conservative control by iteration function, reduce the calculating time.The present invention can improve workshop system state effectively, it is ensured that its stability, may be used for the optimization of Workshop Production system with perfect.
Description
Technical Field
The invention belongs to the field of workshop scheduling, and particularly relates to a multi-target flow shop inverse scheduling method in an uncertain environment.
Technical Field
The deep integration of new-generation informatization and industrialization enables industrial enterprises to enter a new development stage of intelligent manufacturing, and a workshop scheduling system is taken as a key link for realizing intelligent manufacturing, so that the development of a novel workshop scheduling theory and method is urgently needed to solve the challenge of intelligent workshops under an industrial background. Conventional scheduling problems often assume that production is performed in an ideally defined environment, that process information and plant conditions for each workpiece are ideal and not freely modifiable, and that allocation among multiple production tasks is performed according to these given process parameters or existing resources on a cost-effective or cost-effective basis.
However, in a market economy environment, part of the resource constraints owned in the shop floor system are elastic, the shop floor conditions are actually dynamically uncertain, there are a series of incident disturbances such as random arrival of workpieces, machine trouble shooting, etc., which makes the initially optimized scheduling scheme often lose optimality due to changes in the shop floor conditions, and sometimes even become infeasible. In the past, the solution is to perform rescheduling or dynamic scheduling, and the methods solve the problem by continuously adjusting a scheduling scheme. However, this may result in: 1) the adjusted scheduling scheme is not in accordance with the actual processing process route, and the process route constraint is violated; 2) the system adjustment causes the delivery date to change, and even can influence the upstream and downstream production scheduling; 3) the stability of the system is also influenced by adjusting the scheduling sequence for many times, which is contrary to certain characteristics constrained in actual production, and the traditional scheduling method is difficult to be effectively applied to workshop production practice under the dynamic uncertain environment.
Therefore, some researchers discuss the problem that some non-feasible solutions based on the plant scheduling model become optimal solutions according to the complementary optimality conditions of inverse optimization, which is called "plant inverse scheduling", and is a new idea appearing in the field of plant scheduling in recent years. The method comprises the following steps: how to adjust the estimated values of given process parameters as "small" as possible, on the basis of which the changed values of these parameters are obtained, so that a feasible previous schedule becomes the optimal one in this case. For example, for some production workshops (e.g., numerical control processing workshops in industries such as automobiles, airplanes, and shipbuilding), the existing production cannot be completed due to changes in actual market requirements or delivery date, raw materials, and design schemes, and it is often necessary to adjust relevant parameters of production states of workshops such as devices and tools to ensure stable and efficient production. How to adjust the relevant parameters to ensure that the scheme meets the expectation and the relevant cost is minimized or the scheme change is minimized becomes an urgent problem to be solved, which makes the research of inverse scheduling practical.
However, the research of the inverse scheduling method of the workshop based on the uncertain environment has the following problems, and currently, the research of the inverse scheduling problem is still in a starting stage, and the research of a corresponding scheduling model, strategy and method is lacked. The method is only limited to the research of the inverse scheduling problem of the single-machine workshop, and the problem is solved by adopting a simple and accurate algorithm, and the problem solved by adopting an intelligent algorithm is still blank. This is not due to lack of practical application of inverse scheduling, but due to the current lack of research efforts on the problem, which itself has its own characteristics and complexity; moreover, the background of research on the inverse scheduling problem is insufficient, and the research on the inverse scheduling problem is limited. According to statistics, uncertain interference factors often exist in the actual production process to influence the operation of a workshop scheduling system, the research result of inverse scheduling is applied to actual production, the performance of the original scheduling system is improved, the production efficiency is improved, and the method is better suitable for variable production environments.
Disclosure of Invention
The invention provides a multi-target flow shop inverse scheduling method based on an uncertain environment, which mainly solves the problem that the traditional scheduling method is difficult to effectively process the interference condition existing in some actual production, ensures stable operation of workshop production, and simultaneously improves scheduling efficiency and scheduling stability.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a multi-target flow shop inverse scheduling method based on an uncertain environment is used for responding to dynamic variable conditions existing in a shop scheduling system in time and achieving effective operation of the shop system. The method comprises the following steps:
1) establishing multi-target flow shop inverse scheduling problem model based on uncertain environment
The main consideration in this problem is the workshop efficiency and the fluctuation condition of the workshop system, including three goals:
(1) the machining parameters are adjusted as little as possible, namely:
（1）
wherein,
(2) the finishing time sum is as close as possible to the original index, namely:
（2）
wherein,
(3) minimizing the scheduling system adjustment amount, namely:
（3）
wherein H represents Hamming distance, i.e., direct individual difference between two chromosomes
2) Solving the problem model by adopting an improved hybrid multi-target genetic algorithm, wherein the specific process is as follows:
(1) the number of the groups is set asNAccording to the coding scheme, producing an initialization population by adopting a hybrid initialization mode;
(2) evaluating the initialized population, and enabling the iteration number Gen = 1;
(3) updating the current population by adopting genetic operation based on improved mutation operation and cross operation;
(4) forming sub-population, and combining with parent population to form population number of 2N(ii) a new population of (c); to 2NThe individuals are sorted by adopting a rapid non-dominance sorting method in NSGAII to perform non-dominance solution sorting to obtain a non-inferior solution set;
(5) comparing the non-inferior solution set with the solutions in the external file set in sequence by adopting a comparison mode, replacing the old solution with the new non-dominant solution, and updating the external file set;
(6) selecting part of individuals in the external archive set, performing local search by adopting a local search strategy based on NEH to obtain new individuals, and updating the external archive set again;
(7) through cross and variation operation, new population is formed by recombinationN；
(8) And (4) judging whether the iteration number Gen reaches a specified threshold maxGen, if so, ending the algorithm, outputting the final non-dominated solution set, otherwise, letting Gen = Gen +1, and skipping to the step (3) to continue the operation.
As a further improvement of the invention, the multi-target flow shop inverse scheduling problem model under the uncertain environment changes the original scheduling sequence into the optimal core by changing the processing parameters at the minimum, and establishes a problem model considering the minimum processing parameter fluctuation, system fluctuation and completion time and fluctuation in view of customers and manufacturers.
As a further improvement of the present invention, the coding scheme is a coding scheme based on real number expression. The information such as arrangement of processing procedures, fluctuation of processing parameters and the like is needed in coding design, and a traditional procedure-based coding scheme or a workpiece-based coding scheme is adopted, so that an infeasible solution is easy to appear in crossing and mutation operations aiming at the problem. Therefore, this problem is avoided by using a coding scheme based on real number expression, specifically: each element in the coding scheme is composed ofI.D) The two parts are as follows:Iis an integer value, representing the order of the workpieces,Dis a decimal value, consisting ofThree-digit decimal compositionABC]WhereinABShowing the machining process of the workpiece,Cthe fluctuation amount of the corresponding processing parameters of different procedures.
As a further improvement of the invention, the population initialization mode adopts an initialization method of mixing two non-optimal schedules to generate a reverse scheduling excitation mechanism. The method specifically comprises the following steps: the first way is by random generationABPart of the population is initialized, i.e. the part of the random generation procedure, and then, in a second way, by random generationCThe other populations are initialized in part, i.e., the randomly generated process parameters.
As a further improvement of the present invention, the fitness value evaluation method is based on a fast non-dominated sorting method in NSGAII, and a crowding distance and a distribution function are respectively introduced to increase population diversity, and simultaneously, non-dominated solution sets are uniformly dispersed. The method specifically comprises the following steps:
and (3) introducing a crowding distance to cut off the external archive set, so that solutions in the external archive are uniformly distributed, and on the basis of a fast non-dominated sorting method in NSGAII, adopting a distribution function: whereinn i Is as followsiLayer curved surfaceFiUpper selected individual number ofF i | （iNot less than 1) representsiThe number of non-dominant solutions on the layer non-dominant surface,r∈（0，1）。
as a further improvement of the present invention, the external archive set update mode adopts a hybrid mode, specifically: establishing an external archive set independent of the evolutionary population, and updating the external archive set by adopting two strategies, namely, enabling the individuals in the memory to participate in the generation of a new population and performing updating by excellently replacing the old individuals, and adopting a NEH-based local search method to perform updating on part of the individuals in the external archive set.
As a further improvement of the present invention, the external archive set update method adopts a partial search method based on NEH insertion method for updating, specifically: adopting NEH insertion idea, mainlyPerforming interpolation conversion for decimal fund, performing local search, and adopting formula to control number of neighbor search individuals and reduce calculation timen GB=max{N M× (1-t/TG), 1}, adjusting evolution algebra and number of artifacts for performing insert operations, constraining the number of individuals performing a domain search, wherein,N M represents the maximum number of workpieces performing an insertion operation;tmeans the current evolution algebra;TGrefers to the maximum number of evolutions. Two other variables need to be noted: distribution as starting and ending positions of the insertion of the workpiece:iandm=i+n GB-1。
as a further improvement of the invention, the production mode of the final new population is specifically as follows: and selecting two individuals from the external archive set and the new mixed population, performing cross operation and mutation operation, and repeating the operation until the number of the populations reaches N.
The invention has the following beneficial effects: (1) aiming at a dynamically variable flow shop scheduling system, based on the inverse optimization thought, the preset non-optimal scheduling sequence is optimized and adjusted by fine tuning the workpiece processing parameters. Aiming at the problem of inverse scheduling of the multi-target flow shop, the problem model considering the minimum processing parameter fluctuation, the system fluctuation and the completion time and fluctuation is established by considering the customer and the manufacturer.
(2) A coding scheme based on real number expression is provided, processing parameter information is expressed in a blocking mode, and information such as different procedures and processing parameters is optimized in a coordinated mode. And an initialization method of mixing two non-optimal schedules is adopted to generate a reverse scheduling excitation mechanism, so that the initial population diversity and the individual quality are improved.
(3) Aiming at the problem characteristics, based on the insertion operation in NEH, four different neighborhood structures are designed, and local search is executed through switching of the neighborhood structures. Meanwhile, a mathematical formula is introduced to control the number of the individual neighbor searching units, so that the purpose of reducing the calculation time is achieved, the operation can ensure that large-scale neighbor searching is executed at the initial stage of population evolution, and the range of the neighbor searching is reduced at the final stage of the population evolution, so that the local searching performance of the algorithm is improved, and the calculation time is reduced.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic flow diagram of an improved hybrid multi-objective genetic algorithm of the present invention;
FIG. 3 is a diagram illustrating a real number based coding scheme according to the present invention;
FIG. 4 is a schematic diagram of a partial process initialization scheme of the present invention;
FIG. 5 is a schematic diagram of a partial initialization scheme for process parameters in accordance with the present invention;
FIG. 6 is a schematic cross-over operation of the present invention;
FIG. 7 is a schematic diagram of the variant operation of the present invention;
FIG. 8 is a diagram illustrating a NEH-based local search method according to the present invention.
Detailed description of the invention
The invention is further described with reference to the following figures and specific embodiments.
Referring to fig. 1, a multi-target flow shop inverse scheduling method based on an uncertain environment includes the following steps:
1. establishing multi-target flow shop inverse scheduling problem model based on uncertain environment
The main consideration in this problem is the workshop efficiency and the fluctuation condition of the workshop system, including three goals:
(1) the machining parameters are adjusted as little as possible, namely:
（1）
wherein,
(2) the finishing time sum is as close as possible to the original index, namely:
（2）
wherein,
(3) minimizing the scheduling system adjustment amount, namely:
（3）
wherein H represents Hamming distance, i.e., direct individual difference between two chromosomes
The improved hybrid multi-target genetic algorithm flow is shown in the attached figure 2, and the specific operation is as follows:
(1) parameter setting
Setting algorithm parameters, mainly including maximum iteration timesTg. Number of groupsNCross probabilityP cProbability of variationP mProbability of duplicationP rChampionship selection parametersr、NEH maximum number of individuals to perform local searchN m And the like.
(2) Encoding
Coding scheme using real number basedCoding scheme for the expression. In the coding design, information such as arrangement of processing procedures and fluctuation of processing parameters needs to be considered, and a traditional procedure-based coding scheme or a workpiece-based coding scheme is adopted, so that an infeasible solution is easy to occur in crossing and mutation operations aiming at the problem. Therefore, this problem is avoided by using a coding scheme based on real number expression, specifically: each element in the coding scheme is composed ofI.D) The two parts are as follows:Iis an integer value, representing the order of the workpieces,Dis a decimal value consisting of three decimal placesABC]WhereinABShowing the machining process of the workpiece,Cthe fluctuation amount of the corresponding processing parameters of different procedures. Take the scheduling problem of 4 workpieces as an example, the coding scheme is shown in fig. 3, and the codes = [ +1.032, -3.014, +4.021, +2.042]The coding scheme consists of 4 real numbers, where the first part is an integer, which are decoded sequentially as [1, 3, 4, 2 ]]It means that the workpiece 1 is machined first and the other work rates are machined sequentially. The decimal part consists of three decimal places, the first two decimal places are the processing sequence of the workpiece and are decoded into [03, 01, 02, 04 ]]Sequentially represents the third process of the first workpieceO 13 And the others are in turn:O 31 ，O 42 ，O 24 . The last decimal is the amount of processing time fluctuation, decoded as [2, 4, 1, 2 ] in this chromosome]A positive sign "+" represents an increase and a negative sign "-" represents a decrease. For example, +1.032 represents an increase of 2 in the processing time of the third processing operation of the first workpiece.
(3) Initializing a population
The population initialization method has obvious influence on the evolutionary algorithm, the good initial solution can improve the solving quality and speed of the algorithm, and an inverse scheduling excitation mechanism is generated by adopting an initialization method of mixing two non-optimal schedules. The method specifically comprises the following steps: the first way is by random generationABPart, i.e. the random generation process part, initializes part of the population. The specific operation is as shown in fig. 4, the integer part is not changed, the last bit of the decimal part is not changed, and the other two bits are randomly generated. Produced in this wayMAnd (4) individuals.
The second way is by random generationCPart, i.e. part of randomly generated process parameters, is initialized in this wayN-MThe specific operation of the individual is shown in figure 5.
(4) Genetic manipulation
Selecting partial individuals in the population, and executing genetic operations, mainly comprising cross operations and mutation operations. The usual crossover strategy: linear interleaving operation and block interleaving operation. The linear crossover operation, as shown in FIG. 6, takes the chromosomes of 7 workpieces as an example. Randomly selecting 3 and 5 as cross positions and combining the parentsP1、P2 to progenyC1、C2; the work pieces 4 and 5 have been used and will therefore beP2 removing the workpieces 4 and 5 to obtainP2 the rest elements are filled in sequenceC1, forming a new chromosome, and generating the same wayC2 chromosome.
Mutation operations in the genetic algorithm mainly adopt single-point mutation operations and insertion mutation operations, and are improved on the basis of the single-point mutation operations and the insertion mutation operations, as shown in fig. 7. The single point mutation operation specifically comprises: randomly selecting a gene position, and carrying out mutation operation on the first two genes of the decimal part in the element.
(5) Adaptive value evaluation method
The multi-objective optimization problem has a plurality of sub-objectives to be optimized, the target adaptive value allocation is a key part in the multi-objective problem solving, the NSGA-II adopts a win-based fast non-dominated sorting method to carry out fitness assignment, and the method has wide application in the field of multi-objective optimization. The fitness value evaluation method adopts a fast non-dominant sorting method in NSGAII, but the algorithm has the defects of weak global search capability, uneven distribution, easy convergence and the like. In order to overcome the problems, a crowding distance and a distribution function are respectively introduced into a fitness value evaluation mode to increase population diversity and uniformly disperse a non-dominated solution set. The method specifically comprises the following steps:
and (3) introducing a crowding distance to cut off the external archive set, so that solutions in the external archive are uniformly distributed, and on the basis of a fast non-dominated sorting method in NSGAII, adopting a distribution function:n i=|Fi| ×riwhereinn i Is as followsiLayer curved surfaceFiUpper selected individual number ofF i | （iNot less than 1) representsiThe number of non-dominant solutions on the layer non-dominant surface,r∈（0，1）。
(6) external archive set update
The updating mode of the external archive set adopts a mixed mode, and specifically comprises the following steps: establishing an external archive set independent of the evolutionary population, and updating the external archive set by adopting two strategies, namely, enabling the individuals in the memory to participate in the generation of a new population and performing updating by excellently replacing the old individuals, and adopting a NEH-based local search method to perform updating on part of the individuals in the external archive set. In addition, the newly formed external archive is intensively updated by adopting a local search method based on an NEH insertion method, specifically: adopting NEH insertion idea, performing insertion transformation mainly aiming at decimal fund, performing local search, and adopting formula for controlling individual number of neighborhood search and reducing calculation timen GB=max{N M× (1-t/TG), 1}, adjusting evolution algebra and number of artifacts for performing insert operations, constraining the number of individuals performing a domain search, wherein,N M represents the maximum number of workpieces performing an insertion operation;tmeans the current evolution algebra;TGrefers to the maximum number of evolutions. Two other variables need to be noted: distribution as starting and ending positions of the insertion of the workpiece:iandm=i+n GB-1. Which is based on the NEH local search method shown in fig. 8.
(7) Forming a new population
According to cross probabilityP c The following procedure is followed until the population number of the individuals produced is reached, randomly selecting one from the external archive setTaking the individual as a parent 1, selecting one individual from the combined new population as a parent 2, and performing improved cross operation; repeating the operation until the number of individuals reachesN(ii) a According to the variation probabilityP m And performing mutation operation to replace the current individual with the obtained new individual.
(8) Algorithm end condition
And judging whether an algorithm termination condition is met (the termination condition is that the iteration number reaches the maximum iteration number). If yes, stopping iteration and returning to the optimal solution; otherwise, let Gen = Gen +1, and jump to step (4) to continue the operation. .
The effect of the invention can be further illustrated by the following simulation experiment:
(1) test examples
The method adopts a commonly used problem example in the flow shop scheduling problem, and mainly comprises the following steps: the Taillard benchmark test set, the Car problem test set and the Rec problem test set.
(2) Simulation experiment parameter setting
To verify the excellent performance of the improved hybrid multi-objective genetic algorithm, the NSGAII algorithm was used for comparison. Both algorithms were run independently 30 times in the same environment and the results were compared. The algorithm-related parameter settings are shown in table 1.
TABLE 1 Algorithm parameter set
(3) Comparison of results
In order to compare two algorithms, three performance evaluation indexes are adopted to show the non-dominant solution condition, wherein the three performance evaluation indexes are respectively as follows: distance of inverse generationI IGD Number of solutions without dominanceN NDS Non-dominant solution ratio (R NDS ). Table 2 shows the indices obtained after the two algorithms were run independently 30 times for each exampleI IGD And (6) comparing results.
TABLE 2 modified hybrid Multi-target genetic Algorithm H1 and NSGAII AlgorithmI IGD Comparison of results
Table 2 shows the comparison of the anti-generation distances of 119 problem cases obtained by the two algorithms. The inverse generation distance reflects the distance between the solution obtained by the algorithm and the real solution of the problem, so that the smaller the inverse generation distance is, the better the inverse generation distance is, and if the value is 0, the solution obtained by the algorithm is completely close to the real solution of Pareto. For each problem instance, the mean obtained by the modified mixed multiobjective genetic algorithm is much smaller than that obtained by the NSGAII algorithm. Particularly for medium-scale and small-scale problem examples, the obtained anti-generation distance value is close to 0, and the result shows that almost all Pareto optimal solutions can be found by the improved hybrid multi-objective genetic algorithm.
In conclusion, aiming at the problem of inverse scheduling of the multi-target flow shop in the uncertain environment, the method is obviously superior to the NSGAII algorithm in the aspects of solution quality and stability.
Claims (6)
1. The multi-target flow shop inverse scheduling method based on the uncertain environment is used for optimizing and perfecting a shop production system and is characterized by comprising the following steps of:
1) establishing a multi-target flow shop inverse scheduling problem model based on the uncertain environment
The main consideration in this problem is the workshop efficiency and the fluctuation condition of the workshop system, including three goals:
(1) the machining parameters are adjusted as little as possible, namely:
（1）
wherein,
(2) the finishing time sum is as close as possible to the original index, namely:
（2）
wherein,
(3) minimizing the scheduling system adjustment amount, namely:
（3）
wherein H represents Hamming distance, i.e., direct individual difference between two chromosomes
2) Solving the problem model by adopting an improved hybrid multi-target genetic algorithm, wherein the specific process is as follows:
(1) the number of the groups is set asNAccording to the coding scheme, producing an initialization population by adopting a hybrid initialization mode;
(2) evaluating the initialized population, and enabling the iteration number Gen = 1;
(3) updating the current population by adopting genetic operation based on improved mutation operation and cross operation;
(4) forming sub-population, and combining with parent population to form population number of 2N(ii) a new population of (c); to 2NThe individuals are sorted by adopting a rapid non-dominance sorting method in NSGAII to perform non-dominance solution sorting to obtain a non-inferior solution set;
(5) comparing the non-inferior solution set with the solutions in the external file set in sequence by adopting a comparison mode, replacing the old solution with the new non-dominant solution, and updating the external file set;
(6) selecting part of individuals in the external archive set, performing local search by adopting a local search strategy based on NEH to obtain new individuals, and updating the external archive set again;
(7) through cross and variation operation, new population is formed by recombinationN；
(8) And (4) judging whether the iteration number Gen reaches a specified threshold maxGen, if so, ending the algorithm, outputting the final non-dominated solution set, otherwise, letting Gen = Gen +1, and skipping to the step (3) to continue the operation.
2. The multi-target flow shop inverse scheduling method based on the uncertain environment as claimed in claim 1, wherein: the modified hybrid multi-target genetic algorithm in the step 2) adopts a coding scheme expressed by real numbers, and specifically comprises the following steps: each element in the coding scheme is composed ofI.D) The two parts are as follows:Iis an integer value, representing the order of the workpieces,Dis a decimal value consisting of three decimal placesABC]WhereinABShowing the machining process of the workpiece,Cthe fluctuation amount of the corresponding processing parameters of different procedures.
3. The multi-objective flow shop inverse scheduling method based on uncertain environments according to one of claims 1-2, characterized by: the population initialization mode adopts an initialization method of mixing two non-optimal schedules to generate a reverse scheduling excitation mechanism.
4. The multi-objective flow shop inverse scheduling method based on uncertain environments according to one of claims 1 to 3, characterized by: the fitness value evaluation mode respectively introduces crowding distance and distribution function to increase population diversity and simultaneously enable non-dominated solution sets to be uniformly dispersed on the basis of a fast non-dominated sorting method in NSGAII.
5. The multi-target flow shop inverse scheduling method based on the uncertain environment as claimed in claims 1-4, wherein: for the external archive set, updating by adopting a local search method based on NEH, specifically: adopting the insertion idea of NEH algorithm, designing four neighborhood structures, executing local search by switching the neighborhood structures, and simultaneously, executing local search by formulan GB = max {N M .（1 -t/TG) 1 to control the number of individuals performing neighborhood search, reducing the computation time。
6. The multi-objective flow shop inverse scheduling method based on uncertain environments of claims 1-5, characterized by: the production mode of the last new population is as follows: the distribution picks two individuals from the external archive set and the new mixed population, and performs crossover operation and mutation operation, thereby generating N individuals.
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