CN116090773A - Flexible job shop scheduling method based on improved wolf algorithm - Google Patents

Flexible job shop scheduling method based on improved wolf algorithm Download PDF

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CN116090773A
CN116090773A CN202310058666.1A CN202310058666A CN116090773A CN 116090773 A CN116090773 A CN 116090773A CN 202310058666 A CN202310058666 A CN 202310058666A CN 116090773 A CN116090773 A CN 116090773A
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沈国强
顾惠
吴欣
范浩然
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Abstract

The invention discloses a flexible job shop scheduling method based on an improved wolf algorithm. And secondly, generating an initial population by combining chaotic mapping and opposite learning expansion GLR methods, evaluating all individuals in the population, determining decision layer individuals, and updating an external file. And finally judging whether an algorithm termination condition is met, if yes, ending the algorithm to obtain flexible job shop equipment codes and corresponding procedure code sequences, otherwise, judging whether the absolute value of the coefficient vector A calculated by the convergence factor is greater than or equal to 1, and updating the position until the algorithm is ended. The invention improves the performance on a flexible job shop, and solves the problems of slow convergence speed and easy sinking into local optimum of the traditional group intelligent optimization algorithm.

Description

Flexible job shop scheduling method based on improved wolf algorithm
Technical Field
The invention relates to the technical field of flexible job shop scheduling, in particular to a flexible job shop scheduling method based on an improved gray wolf algorithm.
Background
The Flexible Job shop scheduling problem (FJSP) is a development of Job shop scheduling problem (Job-shop Scheduling Problem, JSP). Job shop scheduling problems need to consider the sequence of the procedures; the flexible job shop scheduling problem not only considers the sequence of the processes, but also selects the processing machines for different processes. In recent years, a crowd optimization algorithm has been widely developed and applied in solving the FJSP problem. However, the traditional group intelligent optimization algorithm has the problems of low convergence speed, easy sinking to local optimum and the like.
As with most intelligent optimization algorithms, the gray wolf algorithm is easy to fall into local optimum in the later iteration stage, and at the moment, how to coordinate local search of the algorithm is particularly critical, although the gray wolf optimization algorithm is already applied to some fields and has good performance at present, the gray wolf algorithm is applied to less fields of workshop scheduling, and some problems still exist in practical application: the iterative optimization process of the gray wolf algorithm is closely related to the positions of the first three optimal individuals of each iteration, so as the iteration is continuously carried out, the probability of sinking into the local optimal is gradually increased, and a proper and excellent method for jumping out of the local optimal is required to be found.
Moreover, the gray wolf algorithm is the same as other intelligent optimization algorithms, and has a self convergence factor a, and the gray wolf algorithm is controlled to perform local search or global search when solving the optimal value according to the convergence factor a. However, since the convergence factor of the wolf algorithm is linearly decreasing, although the complexity of the algorithm is somewhat simplified, the performance of the algorithm is not affected as much.
Disclosure of Invention
Aiming at the problems of the technology, the invention provides a flexible job shop scheduling method based on an improved gray wolf algorithm, which solves the problems of low algorithm convergence speed and easy sinking into local optimum, and improves the precision of scheduling results.
A flexible job shop scheduling method based on an improved wolf algorithm is implemented according to the following steps:
step one: constructing a flexible job shop scheduling problem model: including flexible job shop scheduling problem description and model assumptions.
Step two: coding workshop equipment and working procedures required to be processed, and adopting natural number two-section coding based on the working procedure coding and the equipment coding; creating an empty external archive A0 to save the current population situation, with a scale of N'; setting parameters of a gray wolf algorithm: initial population scale N, current iteration number t, maximum iteration number t max 。
Step three: an initial population of size N is generated by an extended GLR (global, local, random) method combining chaotic mapping and opponent learning.
Step four: combining the current population with the external file, calculating the fitness value of the individuals in the combined population to evaluate all the individuals in the population, determining the individuals alpha, beta and gamma of the decision layer, and updating the external file.
Step five: judging whether the terminating condition of the gray wolf algorithm is satisfied or not: t=t max If yes, go to step eight, otherwise execute step six.
Step six: and judging whether the absolute value of the coefficient vector A calculated by the convergence factor is greater than or equal to 1, if so, performing global search, and updating the position by adopting Levy flight. If not, the position is updated according to the position updating method of the gray wolf algorithm.
Step seven: in the optimizing stage of the gray wolf algorithm, the population individuals update the positions of the population individuals by taking the current optimal individuals as the reference, and the local search of the optimal individuals can greatly improve the solving precision and convergence speed of the algorithm. So that the local search is performed by combining three kinds of domain search algorithms. And generating a new generation of gray wolf population, and then turning to the fourth step for the next iteration.
Step eight: and (3) ending the gray wolf algorithm, outputting an optimal solution meeting the conditions, and decoding through the optimal solution to obtain the flexible job shop equipment codes and the corresponding procedure code sequences.
Compared with the prior art, the technical scheme provided by the invention has the following technical effects:
the invention improves the gray wolf algorithm and applies the gray wolf algorithm to the solution of the scheduling problem of the flexible job shop, and the population is initialized by the method of combining chaotic mapping and the extended GLR of opposite learning, thereby ensuring the diversity and the quality of the population; the Levy strategy is adopted, so that the capability of the algorithm for jumping out of local optimum is enhanced, and the capability of global searching is improved; and finally, designing a domain searching algorithm to improve the local searching capability of the algorithm. The gray wolf algorithm is improved, the performance of the gray wolf algorithm on a flexible job shop is improved, and the problem that the traditional intelligent group optimization algorithm is slow in convergence speed and easy to sink into local optimum is solved.
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FIG. 1 is a coding scheme;
FIG. 2 is a flow chart of an algorithm in the present invention;
FIG. 3 is a graph of convergence of a traditional gray wolf algorithm solving FJSP at MK 02;
FIG. 4 is a graph of convergence of the improved gray wolf algorithm solution FJSP at MK 02;
FIG. 5 is a Gantt chart obtained by solving FJSP at MK02 with an improved wolf algorithm.
Detailed Description
The invention will now be described in detail with reference to the accompanying drawings and detailed description.
The invention discloses a flexible job shop scheduling method based on an improved wolf algorithm, which is implemented according to the following steps:
1. constructing a flexible job shop scheduling problem model: including flexible job shop scheduling problem description and model assumptions.
The flexible job shop scheduling problem is described as follows:
the flexible job shop problem (hereinafter abbreviated FJSP) is essentially an extension of the conventional job shop problem, and can be expressed in particular as: on m pieces of equipment, n pieces of work are needed to be processed, each piece is formed by J i The process is composed of different steps, each step can be processed on different equipment, and the processing time is different, so that the complexity is greatly improved. The need for optimal solutions therein is urgent.
The model assumption is that the model satisfies the following conditions:
(1) The same equipment can only process one process at the same time.
(2) The same workpiece can only be processed on one device at the same time.
(3) All workpieces can be machined at time 0.
(4) The working procedures of different workpieces are mutually independent, and the same working procedure is constrained in sequence.
(5) Each workpiece cannot be interrupted during processing.
(6) Neglecting equipment preparation time and workpiece transfer time.
The objective function is constructed as follows:
the invention uses the maximum finishing time C max Minimum as optimization target, set C i For the ith workpiece J i The objective function is as follows, n represents the total number of workpieces,
minC max ＝min{max(C i )}(1≤i≤n)
2. coding workshop equipment and required machining procedures, and adopting natural number two-section coding based on procedure coding and equipment coding; creating an empty external archive A0, of scale N'; setting algorithm parameters: initial population scale N, current iteration number t, maximum iteration number t max 。
The method adopts an equal-length two-section coding method, namely each scheduling solution comprises a front section and a rear section which are equal in length and respectively correspond to a device selection scheme and a procedure coding ordering scheme, and the coding mode is shown as a figure 1 by taking 3 work pieces and 8 procedures as examples, wherein the total number of the procedures is represented by the coding length, J1, J2 and J3 are three work pieces, a bracket encloses the procedure of each work piece, the number of the work piece is represented by each part element of an OS, oh and k are the kth procedure of the h work piece, and the device number correspondingly selected by each procedure is represented by an MS.
3. An initial population of size N is generated using extended GLR (global, random) by combining chaotic mapping and opposite learning.
The initialized population is very important for the evolutionary algorithm, and is generated by using a Gaussian map and a strategy of standard opponent learning with the proportion of 25% on the basis of generating individuals by a GLR method. The specific process is as follows: the GLR method is to generate 20% of individuals by using a global selection method in consideration of working time and load balance on the basis of randomly generating 50% of individuals. In the method, a procedure is randomly selected, the working time of all machinable machines is added with the working time of the procedure, and then the machine with the smallest current working time is selected as the working machine of the procedure and the working time is updated. The local selection method generates 30% of individuals, in which a workpiece is selected at random, a machine is selected for all the working procedures of the workpiece, the machine is selected according to the global selection method, and the difference is that when all the working procedures of one workpiece are selected corresponding machines, the running time of all the machines is set to zero. On the basis of generating individuals through a GLR method, generating an initialized population by adopting a strategy of Gaussian mapping and standard opposite learning with the proportion of 25%, wherein the Gaussian mapping and standard opposite learning expression is shown as the following specific expression:
Figure BDA0004060896790000041
Figure BDA0004060896790000042
wherein: x is X d Represents an individual generated by the GLR method,
Figure BDA0004060896790000043
representing the size after being gaussian mapped; []Representing rounding; x's' d Representing the size after opponent learning; />
Figure BDA0004060896790000044
And->
Figure BDA0004060896790000045
Respectively indicate->
Figure BDA0004060896790000046
Upper and lower limits of the value.
4. Combining the current population with an external file, calculating the fitness value of individuals in the combined population to evaluate all the individuals in the population, determining the individuals alpha, beta and gamma of a decision layer, and updating the external file; the specific process is as follows:
step 4.1, merging the current population with an external file, and calculating individual fitness values in the population according to an objective function of the energy-saving scheduling problem model of the flexible job shop, wherein the individual fitness values are expressed as follows:
sorting according to the fitness value from small to large, selecting individuals ranked in the first 3 positions, and respectively taking the individuals as alpha, beta and gamma individuals to form a decision layer of the population;
and 4.2, sequencing according to the fitness value, sequentially adding the individuals ranked in the front N' into the external file, and updating the external file.
5. Judging whether an algorithm termination condition is reached: t=t max If yes, go to step 8, otherwise go to step 6.
6. Judging whether the absolute value of the coefficient vector A is greater than or equal to 1, if so, performing global search, and performing Levy flight updating. If not, updating according to the position updating method of the gray wolf algorithm. The specific process is as follows:
the expression for setting the coefficient vector a, a is as follows:
A＝2*a*r-a
wherein r is a random variable on [0,1], a is a convergence factor, the population position is updated according to the judgment condition that whether the absolute value of A is more than or equal to 1, if true, global search is carried out, and Levy flight updating is carried out. If false, the position updating method of the gray wolf algorithm is normally used for updating, and the specific updating formula is as follows:
Figure BDA0004060896790000053
wherein X is i (t) represents the ith solution of the t generation; and represents a point-to-point multiplication; l represents the weight of the control step, l=0.01×s (X i (t)-X b )，X b Is the current optimal solution; levy (λ) represents a path following the Levy distribution, and the specific expression required for Levy flight is as follows:
Figure BDA0004060896790000051
u～N(0,σ 2 )，ν～N(0，1)
Figure BDA0004060896790000052
in the formula: u, v are normal distributions, Γ represents a standard gamma function: delta is typically 1.5, and thresholding is a common practice to prevent trapping in local optimum. The detailed method comprises the following steps: in the initial state of the algorithm, setting a global optimal algebra g for keeping the global optimal algebra g to be 0, keeping the current optimal algebra by using the global optimal algebra g in the process of continuously iterating the algorithm, when the global optimal algebra g reaches a threshold value l, discarding half of inferior individuals, randomly generating equal individuals to replace the inferior individuals, wherein the algorithm is greatly influenced by the quality of the threshold value, if the set threshold value is higher, the algorithm can not complete convergence of the block, and if the set threshold value is lower, the effect of the algorithm convergence is poor, and the complexity of the algorithm is also increased.
If the absolute value of a is smaller than 1, the position updating method of the gray wolf algorithm is normally used for updating, but as the convergence factor of the gray wolf algorithm is linearly decreased, the complexity of the algorithm is simplified to a certain extent, but the performance of the algorithm is not affected little, so that the following convergence factors are used:
a＝2-2*(t/t max ) 2
wherein t represents the current iteration number, t max Representing the maximum number of iterations.
7. In the development stage, the population individuals update their own positions by taking the current optimal individuals as the reference, and the local search of the optimal individuals can greatly improve the algorithm solving precision and convergence speed. So that the local search is performed by combining three kinds of domain search algorithms. Generating a new generation of gray wolf population, and then turning to the fourth step for the next iteration; the specific process is as follows:
the individual values are checked and updated, and then local search is performed, so that the search space is wider and deeper through progressive investigation of different neighborhoods, and the method has stronger local search capability. The probability of performing a variable domain search for individuals in which the population fitness value is the first three is greatly increased compared to performing a variable domain search for only the optimal individual therein, or for the optimal solution. The variable domain searching algorithm achieves the purpose of searching by changing domain structures, and three variable domain structures are described as follows:
domain structure N1: in the coding of the working procedures required by the workpiece processing, a random selection method is adopted, and the two positions are selected and interchanged on the premise of ensuring that the working procedures of different workpieces are selected.
Domain structure N2: in the encoding of the process required for the machining of the workpiece, a randomly selected method is used to select two positions and to insert the latter position before the former position.
Domain structure N3: in the encoding of equipment usable in a process corresponding to the machining of a workpiece, a random selection method is used, and machining is performed by a plurality of equipment in a process corresponding to a position to be selected, and one of the selectable equipment is selected at random to replace the position.
Based on the three domain structures, the variable domain searching algorithm for the procedures and the equipment comprises the following steps:
7.1, setting initial parameters, and setting an individual to be subjected to variable domain search as an initial individual X; setting the maximum number of search iterations of the variable domain to n max 5, the current iteration number n is 1, the domain structure p to which the current iteration is performed is set to be 1, p max Set to 3.
7.2, judging whether n is not less than n max If true, the current individual X is output at this time, and if false, the following step 7.3 is performed.
7.3, randomly selecting a domain structure to be applied to the initial individual X to generate a disturbance individual X'.
7.4, carrying out variable neighborhood search again on the basis of disturbance of the individual X', wherein the specific steps are as follows:
(1) Judging whether the termination condition p is more than or equal to p max If satisfied, the current solution X' is output.
(2) Selecting a neighborhood structure corresponding to the number and p on the basis of X ', obtaining a new individual X', and setting X 'as X' and p as 1 if the fitness value f (X ') is less than or equal to f (X') at the moment; if f (X ') =f (X'), then updating the individual with a probability of 0.5, p being set to 1; otherwise, the individual is unchanged, p is set to p+1, and the process is changed to (1).
7.5, let X set to X', n set to n+1, go to step 7.2
8. And (3) outputting an optimal solution meeting the conditions after the algorithm is finished, and decoding through the optimal solution to obtain the flexible job shop equipment codes and the corresponding procedure code sequences. The specific process is as follows:
and (3) outputting an optimal solution meeting the conditions after the algorithm is finished, and obtaining the flexible job shop equipment codes and the corresponding procedure code sequences through the optimal solution. And decoding the process code and the equipment code, respectively decoding the process code and the equipment code, searching the equipment serial number selected by the corresponding process from left to right when decoding the equipment code, generating an equipment selection scheme, sequentially reading the process code from left to right, combining the allocation scheme in the equipment code according to the process sequence information in the process code, and finally generating a feasible scheduling scheme. The final algorithm flow is shown in fig. 2.
Examples:
the three improved wolf algorithm of the invention is adopted, the traditional wolf algorithm carries out simulation solution on 10 standard examples, and the simulation environment is as follows: with python3.10 programming, the win10 operating system is run on a computer configured as memory 16G.
The improved gray wolf algorithm is obtained by calculation, wherein the parameter setting of the improved gray wolf algorithm is 500, the iteration number is 300, the crossover probability is 0.9, the mutation probability is 0.1, and the improved gray wolf algorithm obtains the optimal values of 10 examples of MK01, MK02, MK03, MK04, MK05, MK06, MK07, MK08, MK09 and MK10, and the traditional gray wolf algorithm obtains the optimal values of 0 examples and the average value of 0 examples. In each calculation example, the optimal value and the average value obtained by the improved wolf algorithm are better than those of the traditional wolf algorithm, so that the improved wolf algorithm has better comprehensive performance in solving the scheduling problem of the flexible job shop compared with the traditional wolf algorithm.
Fig. 3 and fig. 4 show a convergence curve obtained when the FJSP is solved by the improved wolf algorithm in MK02 single operation, and compared with a convergence curve obtained when the FJSP is solved by the traditional wolf algorithm in MK02 single operation, it can be seen that the improved wolf algorithm has better solving effect under the same population scale and the same iteration number.
FIG. 5 is a Gantt chart obtained by improving the Grey wolf algorithm to solve FJSP in MK02 (6 pieces, 10 machines) single run, wherein the numbers in the chart frame represent the number of pieces being processed by the machine corresponding to the vertical axis, the numbers are arranged in time sequence along the horizontal axis, and the number of times the piece number appears represents the number of working procedures of the piece being processed, so that the method can be obtained.
In summary, the invention aims at the characteristics of the flexible job shop scheduling problem, improves the gray wolf algorithm in three aspects, provides a flexible job shop scheduling method based on the improved gray wolf algorithm, solves the problems of low algorithm convergence speed and easy sinking into local optimum, and improves the precision of scheduling results.

Claims (8)

1. The flexible job shop scheduling method based on the improved wolf algorithm is characterized by comprising the following steps of:
step one: constructing a flexible job shop scheduling problem model, including flexible job shop scheduling problem description and model assumption;
step two: encoding the workshop equipment and the required processing procedures;
creating an empty external archive A0 to store the current population condition in the wolf algorithm, wherein the scale is N';
setting parameters of a gray wolf algorithm;
step three: generating an initial population with a scale of N by adopting an extended GLR method combining chaotic mapping and opposite learning;
step four: combining the current population with an external file A0, calculating the fitness value of individuals in the combined population to evaluate all the individuals in the population, determining decision layer individuals alpha, beta and gamma, and updating the external file;
step five: judging whether the terminating condition of the gray wolf algorithm is satisfied or not: if the termination condition is that the maximum iteration number is reached, the step is switched to the step eight, otherwise, the step six is executed;
step six: judging whether the absolute value of the coefficient vector A obtained by calculation of the convergence factor is greater than or equal to 1, if so, performing global search, and updating the position by adopting Levy flight; if not, updating the position according to the position updating method of the gray wolf algorithm;
step seven: in the optimizing stage of the wolf algorithm, the population individuals update their own positions based on the current optimal individuals, local search is performed by combining three field search algorithms, a new generation of wolf population is generated, and then the next iteration is performed by turning to the fourth step;
step eight: and (3) ending the gray wolf algorithm, outputting an optimal solution meeting the conditions, and decoding through the optimal solution to obtain the flexible job shop equipment codes and the corresponding procedure code sequences.
2. The flexible job shop scheduling method according to claim 1, wherein in step one, the flexible job shop scheduling problem description and model assumption are described in detail as follows:
flexible job shop scheduling problem description: on m-station equipment, there are n workpieces processed, each workpiece being formed by J i The process comprises processing each process on different equipment and processing time is different, and optimal equipment and process arrangement are required, so that finishing time is minimum;
the model assumption is specifically: the model meets the following conditions: the same equipment can only process one procedure at the same time; the same workpiece can be processed on only one piece of equipment at the same time, and all the workpieces can be processed at the time 0; the working procedures of different workpieces are mutually independent, and the same working procedure is sequentially constrained; each workpiece cannot be interrupted during processing; neglecting equipment preparation time and workpiece transfer time.
3. The flexible job shop scheduling method according to claim 2, wherein in step one, further comprising constructing an objective function, in particular as follows:
with maximum finishing time C max Minimum is set C as the optimization target i For the ith workpiece J i The objective function is as follows:
minC max ＝min{max(C i )}(1≤i≤n)
where n represents the total number of workpieces.
4. A flexible job shop scheduling method based on an improved wolf algorithm according to claim 3, wherein in step two, a natural number two-stage code based on process code and equipment code is used for coding;
the parameters of the gray wolf algorithm comprise an initial population scale N, a current iteration number t and a maximum iteration number t max 。
5. The flexible job shop scheduling method based on the modified wolf algorithm according to claim 4, wherein the extended GLR method in the third step has the specific procedures that: on the basis of individual generation by the GLR method, an initialized population is generated by using a Gaussian map and a strategy of standard oppositional learning with a proportion of 25%.
6. A flexible job shop scheduling method based on an improved wolf algorithm according to claim 5 or 3, wherein the step four specific process is:
step 4.1, merging the current population with an external file A0, and calculating individual fitness values in the population according to an objective function;
sorting according to the fitness value from small to large, selecting individuals ranked in the first 3 positions, and respectively taking the individuals as alpha, beta and gamma individuals to form a decision layer of the population;
and 4.2, sequencing according to the fitness value, sequentially adding the individuals ranked in the first N' into the external file, and updating the external file A0.
7. The flexible job shop scheduling method based on the modified wolf algorithm according to claim 6, wherein in the seventh step, the three variable domain searching algorithms achieve the purpose of searching by changing domain structures, and the changing domain structures specifically include the following three types:
domain structure N1: in the coding of working procedures required by workpiece processing, a random selection method is adopted, and the two positions are selected and interchanged on the premise of ensuring that the working procedures of different workpieces are selected;
domain structure N2: in the coding of the working procedure required by the workpiece processing, adopting a random selection method, selecting two positions and inserting the rear position before the front position;
domain structure N3: in the process of processing the workpiece, a random selection method is adopted in the coding of the usable equipment, and the processing is performed by a plurality of equipment in the process of ensuring the correspondence of the selected position, and one of the selectable equipment is randomly selected to replace the position.
8. The flexible job shop scheduling method according to claim 7, wherein in step eight, the decoding is performed as follows: respectively decoding the process code and the equipment code, and searching the equipment serial number selected by the corresponding process from left to right when decoding the equipment code to generate an equipment selection scheme; the process codes are also sequentially read from left to right, the process codes are combined with the allocation scheme in the equipment codes according to the process sequence information in the process codes, the processes are arranged in a 'blank' manner, and finally a feasible scheduling scheme is generated.
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CN116646568A (en) * 2023-06-02 2023-08-25 陕西旭氢时代科技有限公司 Fuel cell stack parameter optimizing method based on meta heuristic
CN116646568B (en) * 2023-06-02 2024-02-02 陕西旭氢时代科技有限公司 Fuel cell stack parameter optimizing method based on meta heuristic

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