CN115034615A

CN115034615A - Method for improving feature selection efficiency in genetic programming scheduling rule for job shop scheduling

Info

Publication number: CN115034615A
Application number: CN202210656998.5A
Authority: CN
Inventors: 曾亮; 李燕燕; 张豪; 王珊珊; 常雨芳; 全睿; 黄文聪
Original assignee: Hubei University of Technology
Current assignee: Hubei University of Technology
Priority date: 2022-06-10
Filing date: 2022-06-10
Publication date: 2022-09-09

Abstract

The invention belongs to the field of workshop scheduling problems in the manufacturing industry, and particularly relates to a method for improving feature selection efficiency in a genetic programming scheduling rule for job workshop scheduling, which specifically comprises the following steps: selecting a training example, and running for N times by adopting a hyper-heuristic genetic programming method (GP) to generate N scheduling rules; for each rule and each feature corresponding to the rule, respectively applying an original model and a proxy model to calculate the contribution value of each feature to each rule; set to the median of all contribution values. The invention can greatly improve the efficiency of feature selection, thereby improving the production efficiency of workshops and further improving the working efficiency of enterprises.

Description

Method for improving feature selection efficiency in genetic programming scheduling rule for job shop scheduling

Technical Field

The invention belongs to the field of workshop scheduling problems in the manufacturing industry, and particularly relates to a method for improving the characteristic selection efficiency in an agent-assisted genetic programming scheduling rule based on a simplified model, so that the workshop production efficiency is further improved.

Background

Job Shop Scheduling (JSS) has been a popular research topic in the fields of intelligent manufacturing and artificial intelligence, and has many applications in different industries such as manufacturing industry and project Scheduling. With the rapid development of the information technology and the increased competition of global market, the enterprise benefits are closely related to the diversified demands of customers. Accordingly, enterprises are increasingly concerned about how to formulate a shop floor production schedule (e.g., assigning workpieces to machines and determining the order in which the assigned workpieces are processed on each machine) to optimize process time, on-time delivery, or customer satisfaction, among other criteria, to benefit companies and thereby increase their profits or reputations.

Currently, for solving the job shop scheduling problem, a method of fusing a neural network and Q learning in a patent (publication number "CN 112598309A", name "job shop scheduling method based on Keras") has been disclosed to optimize the job shop scheduling problem. A scheduling method based on an advanced novel evolutionary algorithm is proposed in a patent (publication number "CN 110458478A", name "job shop scheduling method based on discrete invasive weed algorithm"), and the scheduling method is made to solve the job shop scheduling problem in the manufacturing industry more intelligently. Although all the methods can solve the job shop scheduling problem to a certain extent, when the shop scheduling faces the challenges of dynamics and uncertainty of the shop environment (such as machine failure and task cancellation), the calculation difficulty is brought to the traditional meta-heuristic optimization technology (such as the method). Instead, the scheduling rules may cope with complex dynamic plant environment changes while reacting to unpredictable events that are about to arrive at the plant. Therefore, the Scheduling rules are widely adopted in solving the Dynamic Job Shop Scheduling Problem (DJSSP).

When a scheduling rule is generated by evolution through a heuristic Genetic Programming (GP) method, the selection of a feature terminal set is crucial, and the results show that the test performance is obviously improved by using an effective feature subset compared with all feature sets. However, existing feature selection algorithms applied to generate job shop scheduling rules models have yet to be improved and enhanced. Aiming at the problem of dynamic workshop scheduling by taking minimum average process time as a scheduling target, the invention provides a method for carrying out feature selection based on simplified-model-Assisted Genetic Programming (SGP) to intelligently design and generate scheduling rules, and the agent model is utilized to reduce the complexity of fitness evaluation to reduce the time of a Genetic Programming training process and improve the efficiency of a feature selection algorithm. The method has important significance for the problem of workshop production scheduling efficiency.

Disclosure of Invention

In order to improve the efficiency of genetic programming for feature selection in job shop scheduling problems, the invention utilizes an original training set and an agent training set to respectively evolve and generate scheduling rules, and then performs feature selection on a shop terminal set. On the premise of ensuring that the evaluation precision is not lost, the agent model can obtain a workshop characteristic terminal set similar to the original model, and meanwhile, the time for training rules can be greatly reduced.

In order to achieve the purpose, the invention adopts the following technical scheme.

A method for improving feature selection efficiency in genetic programming scheduling rules for job shop scheduling, characterized by defining: m machines and n workpieces to be processed are arranged in the workshop; the workpiece i (i is 1, 2.. n) has J working procedures J _i ＝(J _i1 ,...J _ij ) J th step of working the workpiece i _ij According to a certain process sequence in a designated machine m _ij In the upper processing, the required processing time is t _ij (ii) a The time that the workpiece i dynamically and randomly arrives at the workshop in a certain distribution form is a _i Delivery date of workpiece i is d _i ；

Selecting a training example, and running for N times by adopting a hyper-heuristic genetic programming method (GP) to generate N scheduling rules;

for each rule and each feature corresponding to the rule, respectively applying an original model and a proxy model to calculate the contribution value of each feature to each rule;

set to the median of all contribution values.

In the above method, the original model fitness

And proxy model fitness

The average normalized target value is:

in the above-described method of the present invention,

is the best reference target value, but the best value is usually unknown, the present invention sets it as the target value of the reference rule "2 PT + WINQ + NPT", which is the best efficient scheduling rule for the target value.

Secondly, the feature selection algorithm is described as follows, and the features x in the original model and the proxy model are respectively defined _i To priority function

Contribution of (1)

And

the two contributions are in two models, from

Delete in x _i The difference between the preceding and following fitness values.

In the above method, the contribution value of each feature to each rule is calculated using the original model and the proxy model according to

equations

3 and 4, respectively.

In the above method, the median of all the contribution values is based on the contribution of the GP to the best rule.

In the above method, the GP generating the scheduling rule includes:

step 1: the method for generating Ramped-half-and-half is adopted to randomly initialize the population, the depth of the GP tree is given to be (2, 6), so that the GP tree has various sizes and shapes, and the population diversity can be kept. The population is randomly initialized from the set of functions { +, -, -/, min, max } and the set of terminals shown in the attached table, as shown in figure 2.

Step 2: setting iteration times, namely a maximum generation number 51;

and step 3: carrying out fitness evaluation on each initialized rule;

and 4, step 4: if the generated best rule has better training performance than the current best rule, the current best rule is updated. If the stop condition (i.e., the maximum genetic algebra in the SGP) is met, the SGP will stop;

and 5: if the stop condition is not met, the intermediate population is created by the genetic operations of copying, crossing and mutation and the like and the elite reservation strategy through the tournament selection method, and the size parameter of the tournament selection method is set to be 7. Compared with the original population, the larger intermediate population scale increases the diversity of the population, and provides the opportunity of obtaining better rules, and the fitness of all rules in the intermediate population is evaluated through a proxy model;

step 6: and (3) carrying out fitness evaluation on the generated intermediate population by using the agent model, then selecting 1024 individuals to enter the next generation according to the sequence of the fitness from good to bad, and returning to the step 3 until the stopping condition is met.

In the above method, step 5 specifically includes:

step 501: the replication operation is carried out, all individuals of the 0 th generation are selected by a championship selection method, the probability that the individuals with smaller fitness are inherited to the next generation group is higher, and the replication rate is 5%;

step 502: performing a crossover operation, as shown in fig. 3, randomly selecting two parent GP trees, randomly selecting child nodes therein, and performing crossover to form children, wherein the crossover rate is 85%, and the maximum depth of the crossover sub-tree is 8;

step 503: mutation operation, as shown in fig. 4, randomly selecting a child node as a mutation point in the parent, and randomly generating a subtree to replace the subtree in the parent, wherein the mutation point is used as a root node, the mutation rate is 10%, and the maximum depth of the mutation subtree is 8%; meanwhile, the elite retention strategy can ensure that the optimal individuals in the population are inherited to the next generation;

504: the original population size is set to 1024 and the intermediate population size is set to 256 × 7 — 1792.

The invention has the advantages that:

(1) the rules were analyzed experimentally by calculating the length of the best rule, the mean of the leaves (number of terminals). FIG. 12 shows the length of the best rule, the mean of the leaves, obtained by 30 independent runs of the original and proxy models in a dynamic job shop scenario minimizing the average flow time. As expected, the proxy model achieves a simpler rule than the original model, with lower values on the length of the best rule, on the mean of the leaves.

(2) Figure 5 also shows that the proxy model is smaller than the original model for each generation of the average of the rule length obtained in 30 independent runs over the original and proxy models.

(3) One of the main objectives of the invention is to improve the efficiency of feature selection, so that the calculation time is analyzed, fig. 6 shows the calculation time of 30 independent operations of GP on the original model training set and the proxy model training set, and the efficiency of feature selection is greatly improved, thereby improving the production efficiency of a workshop and further improving the working efficiency of an enterprise.

Drawings

Fig. 1 is a flow chart of the SGP algorithm for proxy model evaluation.

Fig. 2 is an example of a randomly initialized population.

Fig. 3 is a cross operation of GP tree.

FIG. 4 shows mutation operations of GP trees.

FIG. 5 is an average of the lengths of the rules in 30 independent runs in two training sets in a specific embodiment.

FIG. 6 is a run-time of 30 independent training rules in two training sets in a particular embodiment.

FIG. 7 is a diagram illustrating the meaning of symbolic expressions in feature selection in a particular embodiment.

FIG. 8 is a terminal set notation of plant characteristics in a particular embodiment.

Fig. 9 is a characteristic correlation of 30 independent runs of ET-GP on the original training set in a specific embodiment.

FIG. 10 is a graph of the feature correlation of 30 independent runs of ET-SGPs on the agent training set in a particular embodiment.

FIG. 11 is a set of key terminals for a shop scenario in two training sets in a particular embodiment.

FIG. 12 is the length, mean of leaves, of the best rule obtained in 30 independent runs of the two training sets in a specific embodiment.

FIG. 13 is a test performance of different plant scenarios in a particular embodiment.

Detailed Description

In order to make the purpose and technical solution of the present invention more apparent, the present invention is further described in detail with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

First, the principle of the method of the present invention will be described.

Firstly, establishing a mathematical model, wherein m machines and n workpieces to be processed are arranged in a workshop in DJSSP; the workpiece i (i is 1, 2.. n) has J working procedures J _i ＝(J _i1 ,...J _ij ) J th step of working the workpiece i _ij According to a certain process sequence in a designated machine m _ij In the upper processing, the required processing time is t _ij (ii) a The time that the workpiece i dynamically and randomly arrives at the workshop in a certain distribution form is a _i Delivery date of workpiece i is d _i 。

Defining original model fitness simultaneously

And proxy model fitness

Average normalized target value over example set I:

in the ideal situation, the temperature of the air conditioner,

is the best reference target value, but the best value is usually unknown, which the present invention sets as the target value of the reference rule "2 PT + WINQ + NPT", which is the best efficient scheduling rule for the target value.

Secondly, the feature selection algorithm is described as follows, and the features x in the original model and the proxy model are respectively defined _i To a priority function

Contribution of (2)

And

the two contributions are in two models, from

Deletion of x in _i The difference between the preceding and following fitness values. A positive difference indicates deletion x _i Later, new scheduling rules will result in worse performance; conversely, negative values indicate x _i For is to

Negative contributions are generated, and their deletion results in better performance; if it is not

And

x is then _i No contribution and no influence on performance. According to equations (1) and (2), the feature x is defined _i Correlation of (2) × _ω (x _i ) So as to optimize the scheduling rules generated under different job shop scenes omega. If a feature x _i With better correlation, it will contribute more in the plant scenario. Therefore, χ _ω (x _i ) Is based on the contribution of the GP to the optimal rule, the following calculation steps are taken.

Step 1: selecting a set of training instances

Step 2: using all workshop characteristics

As a terminal set, applying GP to evolve and generate a scheduling rule;

and step 3: 30 independent GP runs were performed and 30 optimal rules were obtained

And 4, step 4: for each rule

And each feature

The two models calculate x by equations (3) and (4), respectively _i To

Contribution of (1)

And 5: will be x _ω (x _i ) Is set as all

The median of the values (k ═ 1.. 30).

The Genetic Programming for Feature Selection of the original model is denoted as FS-GP (Feature Selection-Genetic Programming), and the Genetic Programming for Feature Selection of the Surrogate model is denoted as FS-SGP (Feature Selection-surface Genetic Programming). The framework of FS-GP and FS-SGP consists of three phases. In the first stage, the GP of all feature terminal sets is run independently 30 times to obtain 30 best rules. In the second stage, each feature x is calculated based on 30 optimal rules _i Correlation of (2) × _ω (x _i ) And selecting the characteristic with the correlation larger than 0 to form a new key terminal set

The correlation results of feature selection are shown in the attached tables 3, 4 and 5. In the third phase, the new terminal set is operated again

The GP to obtain new rules.

Finally, the method for improving the feature selection efficiency in the proxy-assisted genetic programming based on the simplified model aims to reduce the complexity of the original model fitness evaluation and keep the precision level within an acceptable range. The design strategy of the proxy model reduces the complexity of the original model by reducing the number of machines and the number of warm-up jobs. The agent model sets the number of jobs and the number of warm-up jobs to 500 and 100, respectively. The proxy model cannot provide the absolute performance of the original plant (e.g., minimize mean flow time) because the simplification of the model makes it statistically inaccurate (caused by small amounts of duplication and bias). Therefore, we should demonstrate that rule a is superior to rule b based on the absolute performance of the original model, and the proxy model should also demonstrate that a is superior to b, i.e., relative performance. The algorithm uses three types of fitness functions at different stages, and the original model fitness

And proxy model fitness

Degree of adaptability

Is the true fitness (absolute performance) obtained using the original model,

is the estimated fitness obtained by the agent model, and the optimal fitness

Is a rule

Performance in a particular generation. Because simulation is expensive, it is impractical to use a large number of copies to obtain fitness; thus, only one replication per generation is used to evolve rule gains

Based on the best fitness

And after the intermediate population is generated, evaluating the fitness of the newly generated rule by using the agent model. Although the three fitness function evaluation algorithms are complex, the three fitness function evaluation algorithms are more effective, the time for training rules can be integrally reduced, and the efficiency of the feature selection algorithm is improved, so that the production efficiency of the whole workshop is improved. The algorithm flow chart is shown in figure 1.

The invention takes job shop scheduling as a background problem, generates a corresponding model according to the number of workpieces and the number of machines, and sets related parameters of the dynamic job shop scheduling problem, as shown in an attached table. The whole algorithm solving steps are as follows:

step 1: the method for generating Ramped-half-and-half is adopted to randomly initialize the population, the depth of the GP tree is given to be (2, 6), so that the GP tree has various sizes and shapes, and the population diversity can be kept. The population is randomly initialized from the set of functions { +, -,/, min, max } and the set of terminals shown in the attached table, as shown in figure 2.

And 2, step: setting iteration times, namely a maximum generation number 51;

and step 3: carrying out fitness evaluation on each initialized rule;

step 502: performing intersection operation, as shown in fig. 3, randomly selecting two parent GP trees, randomly selecting child nodes therein, and performing intersection to form children, wherein the intersection rate is 85%, and the maximum depth of the intersected subtrees is 8;

step 503: mutation operation, as shown in fig. 4, randomly selecting a child node as a mutation point in the parent, and randomly generating a subtree to replace the subtree in the parent with the mutation point as a root node, wherein the mutation rate is 10%, and the maximum depth of the mutation subtree is 8%; meanwhile, the elite retention strategy can ensure that the optimal individuals in the population are inherited to the next generation;

504: the original population size was set to 1024, and the intermediate population size was set to 256 × 7 — 1792;

and 6: and (3) carrying out fitness evaluation on the generated intermediate population by using the agent model, then selecting 1024 individuals to enter the next generation according to the sequence of the fitness from good to bad, and returning to the step 3 until the stopping condition is met.

Second, the following is a specific case of using the above-described principle of the method.

According to the method, workshop simulation experiment parameters are set according to the established model, 10 machines are arranged in a workshop, the number of workpieces is 4000, and 1000 workpieces are used for preheating at the beginning of each simulation experiment in consideration of stability of a workshop state and effectiveness of the simulation experiment. The process of the workpiece arriving at the workshop complies with Poisson distribution, namely, the workpiece arrives at the workshop dynamically according to the exponential distribution interval time. The number of processes of each workpiece is randomly generated from discrete uniform distribution DU [2,10], the processing time of each process is subject to discrete uniform distribution DU [1,49], and the candidate processing machine of each process is randomly generated from 10 machines in a non-return sampling mode. Meanwhile, the utilization rate of the machine is 0.8, 0.85, 0.9 and 0.95 for testing; missing means that the number of steps of each operation is randomly drawn between 2 and 10, subject to U (2, 10); full represents the number of steps of all operations as 10; the lead time margin factor of the workpiece is set to 4. Meanwhile, the dynamic job shop scheduling problem should satisfy the following assumptions:

assume that 1: from time zero, all machines are operational.

Assume 2: when one process of the workpiece is finished, the workpiece is immediately sent to the next machine to process the next process (the transmission time is ignored).

Assume that 3: each machine can only process one process at the same time.

Assume 4: scheduling is non-preemptive, and once a process begins on the machine, it cannot be interrupted by other operations.

Assume that 5: different processes of a workpiece cannot be processed together at any given time.

And then, making a decision according to the workshop information by using a scheduling rule generated by GP evolution. In the workshop decision queue, when one machine is in an idle state, a plurality of workpieces to be processed waiting on the machine are subjected to the application of a scheduling rule to calculate the priorities of the workpieces, and the workpiece with the highest priority is selected for processing. For example, in the Shortest Processing Time (SPT) rule, the workpiece having the Shortest Processing Time has the highest priority. And after all workpieces in the workshop are processed, calculating the target value of the workpieces and evaluating the fitness of the rule.

After the first operation is finished, the best rule in 51 generations is selected, 30 independent operations are simultaneously carried out, and 30 best rules are selected for feature selection. The feature contributions of the two training sets are calculated according to the formulas (3) and (4), the correlation size of each feature is calculated, the key terminal set with the correlation larger than 0 is selected, the GP is operated again, the same process as the operation process of using all the feature terminal sets is performed, and the process is not repeated here.

Finally, a 51-generation rule after feature selection is used for performance testing on the test set, the average value of the performance of 30 independent operation tests is calculated, Wilcoxon symbol rank test with alpha being 0.05 is respectively carried out between results before and after feature selection, and statistically significant and better rules are marked in bold as shown in figure 13.

The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.

Claims

1. A method for improving feature selection efficiency in genetic programming scheduling rules for job shop scheduling, characterized by defining: m machines and n workpieces to be processed are arranged in the workshop; the workpiece i (i is 1, 2.. n) has J working procedures J _i ＝(J _i1 ,...J _ij ) J th step of working the workpiece i _ij According to a certain process sequence in a specified machine m _ij In the upper processing, the required processing time is t _ij (ii) a The time that the workpiece i dynamically and randomly arrives at the workshop in a certain distribution form is a _i Delivery date of workpiece i is d _i ；

for each rule and each feature corresponding to the rule, respectively applying an original model and an agent model to calculate the contribution value of each feature to each rule;

set to the median of all contribution values.

2. The method for improving feature selection efficiency in genetic programming scheduling rules for job shop scheduling according to claim 1, wherein the original model fitness is

And proxy model fitness

The average normalized target value is:

3. the method for improving the efficiency of feature selection in genetic programming rules for job shop scheduling as recited in claim 1, wherein,

is the best reference target value, but the best value is usually unknown, the present invention sets it as the target value of the reference rule "2 PT + WINQ + NPT", which is the best effective scheduling rule for the target value;

Contribution of (1)

And

the two contributions are in two models, from

Deletion of x in _i The difference between the preceding and following fitness values.

4. The method of claim 1, wherein the applying the original model and the proxy model to calculate the contribution of each feature to each rule is according to equations 3 and 4, respectively.

5. The method for improving feature selection efficiency in genetic programming scheduling rules for job shop scheduling according to claim 1, wherein the median of all contribution values is based on the contribution of GP to the best rule.

6. The method for improving the efficiency of feature selection in genetic programming scheduling rules for job shop scheduling according to claim 1, wherein the GP generating the scheduling rules comprises:

step 1: randomly initializing a population by adopting a Ramped-half-and-half generation method, and giving the GP tree depth of (2, 6) so that the GP trees have various sizes and shapes and can keep the population diversity; randomly initializing the population from the set of functions { +, -, +,/, min, max } and the set of terminals shown in the attached table, as shown in FIG. 2;

step 2: setting iteration times, namely a maximum generation number 51;

and step 3: carrying out fitness evaluation on each initialized rule;

and 4, step 4: if the generated optimal rule has better training performance than the current optimal rule, updating the current optimal rule; if the stop condition (i.e., the maximum genetic algebra in the SGP) is met, the SGP will stop;

and 5: if the stop condition is not met, performing copy, cross and variation genetic operations and elite retention strategies by a tournament selection method to create an intermediate population, wherein the size parameter of the tournament selection method is set to be 7; compared with the original population, the larger intermediate population scale increases the diversity of the population, and provides the opportunity of obtaining better rules, and the fitness of all rules in the intermediate population is evaluated through a proxy model;

7. The method for improving the efficiency of feature selection in genetic programming scheduling rules for job shop scheduling according to claim 1, wherein step 5 specifically comprises:

504: the original population size was set to 1024 and the intermediate population size was set to 256 x 7-1792.