CN114841581A - Feature selection method in dynamic job shop scheduling rule based on GEP-VNS evolution - Google Patents

Abstract

The invention provides a GEP-VNS evolution-based feature selection method in dynamic job shop scheduling rules, which comprises the following steps: setting basic parameters of a GEP-VNS algorithm; step two: initializing a population; step three: evaluating the fitness of population individuals according to the performance indexes of the workshop scene; step four: dividing the initial population into a series of sub-populations, performing global optimization on each sub-population by using GEP genetic operation, and forming an elite library by an optimization result; step five: constructing four different neighborhood structures, and performing local search in an elite library by using a self-adaptive variable neighborhood search method to obtain an optimized population; step six: sequencing the individuals in the optimized population according to the fitness, and selecting the first K excellent individuals as an optimal scheduling rule set; step seven: and comprehensively considering the fitness of the rule in the optimal scheduling rule set and the contribution of the characteristic to the rule to select the characteristic. The invention solves the problems of large search space and low algorithm efficiency caused by redundant and irrelevant characteristics in the intelligent design of the dynamic job shop scheduling rule based on GEP.

Description

Feature selection method in dynamic job shop scheduling rule based on GEP-VNS evolution

Technical Field

The invention relates to a GEP-VNS evolution-based feature selection method in dynamic job shop scheduling rules.

Background

With the continuous personalized development of product requirements, manufacturing processes are more diversified, and competition among manufacturing enterprises is more and more intense. In order to improve the competitiveness of the manufacturing enterprises, the manufacturing enterprises pay more and more attention to how to efficiently schedule the variability of production nodes under complex working conditions of a workshop and the randomness of production disturbance under a network environment so as to meet diversified customer requirements. The traditional workshop scheduling optimization method is difficult to immediately respond to various disturbances caused by working condition changes in a complex manufacturing system. The scheduling rule has lower time complexity in algorithm solving and has the capability of timely responding to dynamic changes and disturbances of the workshop, so that the method is suitable for solving the highly complex dynamic job workshop scheduling problem in actual production.

The scheduling rules are composed of priority functions considering the current job shop state and the characteristics of the to-be-processed process, so the performance of the scheduling rules is related to the scheduling environment, and the scheduling rules need to be correspondingly designed and selected according to different shop scenes. Many documents summarize the dynamic design and selection methods of the scheduling rules, and the design methods of the scheduling rules can be divided into manual methods and intelligent methods. Due to the complex interactions involving different waiting procedures and job shop states, it is very difficult to manually acquire all potential interactions to design a good-performing scheduling rule, which can be solved by using machine learning, especially Gene Expression Programming (GEP), to create a shop-scenario specific scheduling algorithm. The advantages of GA and GP are successfully integrated by Gene Expression Programming (GEP), the defects of the GA and the GP are overcome, and a rule for solving a scheduling problem is provided.

Zhong et al propose a GEP algorithm with self-learning ability, in which the expression of an individual is determined by the subfunctions constituting it, and the subfunctions have a self-learning function and can be repeated and varied continuously during the evolution process; for the scheduling problem of integration of a single AGV and a processing workshop, Tang and autumn and the like provide a workshop scheduling rule generation method based on GEP, and the high efficiency and robustness of the mined rule are demonstrated through comparison experiments and cases; li and the like provide a new coding and decoding scheme for reasonably scheduling dynamically arrived workpieces in real time and applying GEP to the problem of workshop scheduling, and an efficient scheduling rule is automatically constructed; ozturk et al propose two methods for extracting composite priority rules by using simulation and gene expression programming methods, and can evolve specific priority rules according to the characteristics of all dynamic scheduling problems. Zhang et al, in a traditional flexible job shop, consider the objective of minimizing the sum of energy consumption and weighted delay cost, and propose a Parallel Gene Expression Programming (PGEP) method with a migration scheme to solve the problem by evolving heuristic rules.

The research results show that the GEP is used as a hyper-heuristic algorithm to generate effective scheduling rules for various job shop environment designs. But the challenge of GEP algorithms in designing efficient scheduling rules comes from the search space, which is dependent on the tree, function set, and termination set. Candidate terminals include global bay level features (such as current time), workpiece related features (such as processing time and delivery date), and machine related features (such as machine set-up time and pre-machine queuing). Obviously, not all features are relevant to the performance of the scheduling rules, and the contribution of features also varies from plant scenario to plant scenario. In order to reduce the space of algorithmic searches without losing a promising search area, it is important to select a suitable set of relevant features as the terminal set of GEPs. On the other hand, while the GEP inherits the strong global search capability of the GA, it also has the disadvantage of poor local search capability of the GA.

Disclosure of Invention

Aiming at the problems, the invention aims to provide a GEP-VNS evolution-based characteristic selection method in a dynamic job shop scheduling rule, which can effectively solve the problems of large search space and low algorithm efficiency when a gene expression programming evolution dynamic job shop scheduling rule is adopted, and can obviously improve the quality of generated scheduling rules.

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

a feature selection method in a GEP-VNS evolution-based dynamic job shop scheduling rule comprises the following steps:

s1, setting basic parameters of the GEP-VNS algorithm: total iteration number ITER, population size popsize, gene number n, head length head, tail length tail, variation probability p _m Recombination probability p _r Sum and shift probability p _s The number z of neighborhoods, a function set FS { +, -, ×, +/-min, max, if }, and a terminal set TS, namely a dynamic job shop original feature set, comprise shop related, workpiece related and machine related features;

the set ITER parameter is an end condition of the algorithm, when ITER is larger than ITER, the algorithm is ended and an excellent scheduling rule set of a dynamic job shop scene is given, and one scheduling rule corresponds to one multi-gene chromosome in the GEP-VNS algorithm; the popsize parameter is the total number of chromosomes to be generated, the popsize chromosomes making up a population; the gene consists of a head part and a tail part, and the length of the head part and the tail part satisfies tail ═ head × (n-1) + 1; the function nodes of the algorithm use FS { +, -, ×, ÷, min, max }, where +, -, ×, ÷ is the basic arithmetic operator and "÷" is the protective division, i.e., returns 1 when the divisor is zero; "min" and "max" are the acceptance of two parameters and the return of a smaller or larger value, respectively; the terminal set TS, i.e. the set of raw features of the dynamic job shop, is shown in the following table:

s2, carrying out random initialization operation on the population according to the function set FS, the terminal set TS and the algorithm parameters in the S1 to obtain an initial population Pop with the size of the population being popsize, namely a candidate scheduling rule set R, wherein each individual in the population represents a workshop scheduling rule R, and R belongs to the R;

s21, coding multigene chromosomes, wherein each chromosome is composed of 3 genes, each gene is divided into a head part and a tail part, elements of the head part are from a function set FS and a terminal set TS, elements of the tail part are only from the terminal set TS, the head part length of each gene is 8, the tail part length of each gene is 9, and sub-expression trees formed by mapping the genes respectively are connected in an 'adding' mode to form a multi-sub-tree expression tree;

s22, carrying out random initialization operation on the population to obtain an initial population Pop with the population size of popsize, namely a candidate scheduling rule set R, wherein each chromosome in the population represents a workshop scheduling rule R, and R belongs to R;

s23, performing a decoding operation on the multigene chromosome, specifically as follows:

converting each gene of the chromosome in the initial population into a sub-expression tree respectively according to the inverse process of depth-first traversal;

connecting the sub-expression trees in an 'adding' mode to form a multi-subtree expression tree with a complex structure;

s3, evaluating the fitness of population individuals: transmitting the initial population Pop obtained in the step S2 to a dynamic operation workshop scene, evaluating the fitness of population individuals according to the performance index of the scene, taking out 10% of excellent individuals, storing the excellent individuals into an elite library, and setting the cycle number iter to be 0;

s31, setting basic structure parameters of the job shop, and recording the equipment number m and the product type x; consider 4 key variables in the plant uncertainty: the total number N of workpieces, the urgent delivery date factor C, the equipment fault level F and the workshop utilization rate Ug, J (J is more than or equal to 3) parameter levels can be set for all the key variables, and J is combined ⁴ Planting production scenes so as to construct a job shop dynamic multi-scene set S;

s32, the initial population Pop obtained in S2, namely the candidate dispatching rule set R is applied to the dynamic job workshop scene S _i ,s _i Scheduling by belonging to S, and using a candidate scheduling rule R belonging to R to wait for a processing workpiece queue on the machine when the machine is idle, and selecting a workpiece with the highest priority to be processed on the machine;

s33, according to the dynamic workshop scene S _i (i＝1，…J ⁴ ) The scheduling target of (2) calculates the fitness value of each scheduling rule R, R belongs to R, and a fitness function is defined as

Wherein, f (r, s) _i (I) Means that the scheduling rule r is applied to the dynamic plant scenario s _i The performance index value f of the scheduling scheme obtained in (1) _ref (s _i (I) Means that the reference scheduling rule is applied to the plant scene s _i The performance index value of the scheduling scheme obtained in (1),

representing a scene s _i I denotes an example, the scheduling goal of the scenario is to minimize the maximum completion time, or minimize the average flow-through time or minimize the average delay time;

s34, taking 10% of excellent individuals from the initial population Pop and storing the excellent individuals into an elite library according to the calculation result of the fitness value, and enabling the cycle number iter to be 0;

s4, averagely dividing the initial population Pop into L sub-populations, performing genetic operation in each sub-population according to a gene expression programming GEP, wherein the genetic operation comprises variation, item shifting and recombination, evaluating the fitness value of each individual in each sub-population, storing the optimal individual in each sub-population into an elite library, and replacing L poor solutions in the elite library;

s41, dividing the whole population into L sub-populations, and dividing each sub-population into groups according to variation probability p _m Probability of item shift p _s Recombination probability p _r Carrying out genetic manipulation;

s42, mutation;

first, several positions are randomly selected in the chromosome and then replaced with another element: any symbol in the head of a gene can be changed into another symbol representing a function or a terminal, and a terminal symbol in the tail of the gene can only be changed into another terminal symbol;

s43, item shifting;

the transposition operation IS to activate a certain gene segment in the chromosome, the activated gene segment IS called a transposition factor, and the transposition factor IS jumped to another position of the chromosome to form a new chromosome, and the transposition operation comprises three transposition items, namely IS transposition item, RIS transposition item and gene transposition item;

s431, IS term shift: randomly selecting any gene segment, namely IS factor, from the gene of the chromosome, inserting the copy of the IS factor into any position of the head of the gene except the head position, and simultaneously deleting the same number of symbols as the transposition factors from the tail end of the head of the gene so as to ensure that the head and tail division lines are not damaged;

s432, RIS shift item: randomly selecting any gene segment, namely RIS factor, starting with a function from the gene of the chromosome, inserting the copy of the RIS factor into the head position of the head of the gene, and simultaneously deleting the same number of symbols as the transposition factors from the tail end of the head of the gene so as to ensure that the head and tail division lines are not damaged;

s433, gene transposition: firstly, randomly selecting genes to be moved, then inserting the whole selected genes into the initial position of a chromosome, and deleting the whole genes on the original position;

s44, recombining;

the recombination operation is to make two chromosomes into a pair and exchange partial substances to form two new chromosomes, and comprises three kinds of recombination operation, namely single-point recombination, two-point recombination and gene recombination;

s441, single-point recombination: two ancestral chromosomes form a pair and then the same position is cut, and the substances behind the cut position are exchanged;

s442, two-point recombination: randomly selecting two cross points after the two parent chromosomes are paired, and then interchanging materials between the cross points between the two parent chromosomes to generate two new child chromosomes;

s443, gene recombination: the interchange part of the paired chromosomes is the whole gene, and the genes involved in interchange are randomly selected and exchanged at the designated positions;

s45, according to the dynamic workshop scene S _i (i＝1，…J ⁴ ) To minimize the average delay time

By a fitness function

Calculating the fitness value of each individual in each sub-population, storing the optimal individual in each sub-population into the elite library, and replacing L poor solutions in the original elite library;

s5, constructing four different neighborhood structures, performing neighborhood-variable search on the optimal individuals in the elite library obtained in the above steps, and searching a better solution near the local optimal solution to further optimize the population;

s6, updating individuals, generating a new population, making ITER be ITER +1, judging whether the algorithm meets the termination condition ITER > ITER, if so, outputting an optimized population

Otherwise, go to step S3 to execute until the termination condition is satisfied;

s7, optimizing the population obtained by the step S6

The individuals in the method are sorted according to the fitness, and the first K excellent individuals are selected to be put into an optimal scheduling rule set

S71, according to the dynamic workshop scene S _i (i＝1，…J ⁴ ) Through a fitness function

Optimized population of final output of calculation algorithm

Selecting the first K excellent individuals to put into an optimal scheduling rule set

Performing the following steps;

s8, comprehensively considering the optimal scheduling rule set

The fitness of the medium rule and the contribution of the characteristics to the rule are subjected to characteristic selection to obtain a dynamic job shop scene s _i The set of key features TS:

s81, in dynamic workshop scenario S _i (i-1, … J4), calculating the optimal scheduling rule set for each feature t, te TS in the feature set TS

Each scheduling rule in

The contribution degree of (A) is shown in the following formula;

wherein

Representing scheduling rules in a dynamic job shop scenario s

A fitness value of;

scheduling rules for fixing the characteristic t to a constant 1

The feature is fixed to a constant of 1, meaning that the scheduling rule does not select the feature, then

Representing a scene s in a dynamic job shop _i Scheduling rules without selection feature t

A fitness value of;

s82, dynamic Job shop scenario S _i (i＝1，…J ⁴ ) The target of the scheduling is the non-decreasing function of the completion time, the voting weight of each rule is defined as the monotone decreasing function of the fitness, and each scheduling rule is calculated

For each feature t, t ∈ TS, the voting weight is given by the following formula:

s83, judging the characteristic contribution value calculated in the step S81

If the threshold value theta is larger than the threshold value theta, the threshold value theta is set to be 0.001, and if the threshold value theta is larger than the threshold value theta

Scheduling rule

The support ticket is thrown to t, otherwise, a negative ticket is thrown;

s84, if the weight of the support ticket obtained by each feature t in the original feature set TS is larger than the weight of the negative ticket, selecting the feature t and putting the feature t into the key feature set TS;

s85, repeating the steps S81 to S84 for each feature t in the original feature set TS, and finally selecting a dynamic workshop scene S _i (i＝1，…J ⁴ ) The set of key features.

Preferably, in step S33, the dynamic job shop scenario S is used _i (i＝1，…J ⁴ ) With the aim of minimizing the mean delay time

Wherein N is the total number of the processed workpieces, c _j For finishing time of the work, d _j Is the delivery date of the workpiece.

As another preferable scheme, the step S5 specifically includes the following contents:

s51, initialization parameters: initial solution x, iteration number P, determining neighborhood structure Nz (z is 1,2,3,4), loop variable i is 1, neighborhood search success and failure number are respectively expressed as N _s ＝0，N _f ＝0；

S511, four different neighborhood structures Nz are designed (z ═ 1,2,3, 4):

neighborhood structure N ₁ -an insertion neighborhood, randomly selecting two points in the gene tail of the chromosome, the points of the gene tail being from the set of raw features TS of the workshop, inserting the gene of the latter position before the gene of the former position;

neighborhood structure N ₂ -a two-point crossover neighborhood, randomly selecting two points in the gene tail, to crossover the genes at the two positions with each other;

neighborhood structure N ₃ Randomly shuffling the neighborhood, randomly selecting four positions in the gene tail, shuffling the order of the four elements, and then shuffling;

neighborhood structure N ₄ -a reverse-order neighborhood, randomly selecting two positions in the gene tail, and then arranging the elements between the two positions in reverse order to obtain a new gene;

s52, judging whether the termination criterion (i > P) is met, if so, outputting a local optimal solution X, otherwise, turning to the step S53;

s53, if i is less than P/3, randomly selecting neighborhood Nz to search neighborhood to obtain new solution X', otherwise, according to

And

calculating the selection probability eta value to select a neighborhood Nz, performing neighborhood search to obtain a new solution X', wherein a parameter xi is used for measuring the improvement degree of the chromosome,

represents a relative fitness value, f (X) ^* ) Representing the global optimal solution obtained in the current elite library, wherein f (q) is the fitness value of the chromosome in the current neighborhood search, and the selection probability eta value of each neighborhood is calculated according to the zeta value in the search process;

s54, if f (X') < f (X) ^* ) Then X ^* ＝X′，N _s ＝N _s +1，N _f ＝N _f +1；

And S55, updating the selection probability eta values of each field, and turning to S52.

As a preferable scheme, the step S5 specifically includes the following contents:

s51, initialization parameters: initially solving X, iterating for a time P, determining a neighborhood structure Nz (z is 1,2,3 and 4), and a loop variable i is 1;

s511, four different neighborhood structures Nz are designed (z ═ 1,2,3, 4):

neighborhood structure N ₁ -an insertion neighborhood, randomly selecting two points in the gene tail of the chromosome, the points of the gene tail being from the set of raw features TS of the workshop, inserting the gene of the latter position before the gene of the former position;

neighborhood structure N ₂ -a two-point crossover neighborhood, randomly selecting two points in the gene tail, to crossover the genes at the two positions with each other;

neighborhood structure N ₃ Random scrambling of the rearranged neighbourhood, random in the gene tailSelecting four positions, disordering the sequence of the four elements, and then rearranging;

neighborhood structure N ₄ -a reverse-order neighborhood, randomly selecting two positions in the gene tail, and then arranging the elements between the two positions in reverse order to obtain a new gene;

s52, judging whether the termination criterion (i > P) is met, if so, outputting a local optimal solution X, otherwise, turning to the step S53;

s53, randomly selecting a neighborhood structure Nz to generate a new solution X ', and comparing the fitness value of the new solution X' with the fitness value of the initial solution X;

s54, if f (X') < f (X) ^* ) If so, outputting z, where X is X', replacing the initial solution with a new solution with a larger fitness value, and continuing to search in the neighborhood structure Nz; otherwise, z is z + 1;

s55, if z > 4, returning to step S52; otherwise, returning to step S53, entering the next neighborhood structure for searching.

Preferably, the value of K in step S71 is set to 30.

Due to the adoption of the technical scheme, the invention has the following advantages:

the invention provides a GEP-VNS evolution-based feature selection method in a dynamic job shop scheduling rule, which is used for feature selection in a dynamic job shop scene based on GEP mining of the scheduling rule.

The method aims at various common uncertain factors of a workshop, a large number of dynamic operation workshop scenes considering the uncertain factors are generated through an object-oriented simulation model, a feature selection method in a dynamic operation workshop scheduling rule based on GEP-VNS evolution is provided, a whole initial population is divided into a series of sub-populations, each sub-population is globally optimized by using a GEP algorithm, an elite library is formed by the optimization results of each sub-population, and fine local search is performed in the elite library by using a variable neighborhood search algorithm. The method has the advantages that the method fully utilizes the characteristics of strong global search capability and strong local search capability of variable neighborhood search of the GEP algorithm while improving the quality of population solutions, prevents the loss of optimal solutions, and can remarkably improve the accuracy and efficiency of the production scheduling rule mining algorithm.

By comprehensively considering the fitness of the optimal scheduling rule and the contribution of the characteristics to the scheduling rule, the important characteristic subset in a workshop scene is further selected, the number of the characteristics after the characteristics are selected is obviously reduced, the scheduling rule is formed after irrelevant characteristics are removed, the scheduling performance is better, and the rule structure is simpler and easier to understand.

The method further improves the local searching capability of the algorithm on the premise of original strong searching capability of the GEP, ensures the diversity of the population, and solves the defects of large searching space and slow convergence speed when the GEP directly generates the scheduling rule.

Drawings

FIG. 1 is a flow diagram of feature selection in dynamic job shop scheduling rules based on GEP-VNS evolution

FIG. 2 is a flow chart of adaptive variable neighborhood search

FIG. 3 is a dynamic job shop scenario s ₅₈ Contribution graph generated by medium candidate characteristics to optimal scheduling rule

FIG. 4 is a dynamic job shop scenario s ₅₈ Medium candidate feature voting weight graph

FIG. 5 is a graph comparing performance of the GEP-VNS algorithm before and after feature selection scheduling rules

Detailed Description

The invention is described in detail below with reference to the figures and examples.

The GEP-VNS evolution-based feature selection method in the dynamic job shop scheduling rule comprises the following steps:

s1, setting basic parameters of the GEP-VNS algorithm: total iteration number ITER, population size popsize, gene number n, head length head, tail length tail, variation probability p _m Recombination probability p _r Sum and shift probability p _s The number z of neighborhoods, a function set FS { +, -, ×, +/-min, max, if }, and a terminal set TS, namely a dynamic job shop original feature set, comprise shop related, workpiece related and machine related features;

the set ITER parameter is an end condition of the algorithm, when ITER is larger than ITER, the algorithm is ended and an excellent scheduling rule set of a dynamic job shop scene is given, and one scheduling rule corresponds to one multi-gene chromosome in the GEP-VNS algorithm; the popsize parameter is the total number of chromosomes to be generated, the popsize chromosomes making up a population; the gene consists of a head part and a tail part, and the length of the head part and the tail part satisfies tail ═ head × (n-1) + 1; the function nodes of the algorithm use FS { +, -, ×, ÷, min, max }, where +, -, ×, ÷ is the basic arithmetic operator and "÷" is the protective division, i.e., returns 1 when the divisor is zero; "min" and "max" are the acceptance of two parameters and the return of a smaller or larger value, respectively; the terminal set TS, namely the original feature set of the dynamic job shop, is shown in table 1;

TABLE 1 dynamic job shop raw feature set

S2, carrying out random initialization operation on the population according to the function set FS, the terminal set TS and the algorithm parameters in the S1 to obtain an initial population Pop with the size of the population being popsize, namely a candidate scheduling rule set R, wherein each individual in the population represents a workshop scheduling rule R, and R belongs to the R;

s21, coding multigene chromosomes, wherein each chromosome is composed of 3 genes, each gene is divided into a head part and a tail part, elements of the head part are from a function set FS and a terminal set TS, elements of the tail part are only from the terminal set TS, the head part length of each gene is 8, the tail part length of each gene is 9, and sub-expression trees formed by mapping the genes are connected in an 'adding' mode to form a large and complex multi-sub-tree expression tree; (ii) a

S22, carrying out random initialization operation on the population to obtain an initial population Pop with the population size of popsize, namely a candidate dispatching rule set R, wherein each chromosome in the population represents a workshop dispatching rule R, and R belongs to R;

s23, performing a decoding operation on the multigene chromosome, specifically as follows:

(1) converting each gene of the chromosome in the initial population into a sub-expression tree respectively according to the inverse process of depth-first traversal;

(2) connecting the sub-expression trees in an 'adding' mode to form a multi-subtree expression tree with a complex structure;

and S3, evaluating the fitness of population individuals. Transferring the initial population Pop obtained in the step S2 to a dynamic job shop scene, evaluating the fitness of population individuals according to the performance index of the scene, taking out 10% of excellent individuals, storing the excellent individuals into an elite library, and enabling the cycle number iter to be 0;

s31, setting basic structure parameters of the job shop, and recording the equipment number m and the product type x; consider 4 key variables in the plant uncertainty: the total number N of workpieces, the urgent delivery date factor C, the equipment fault level F and the workshop utilization rate Ug, J (J is more than or equal to 3) parameter levels can be set for all the key variables, and J is combined ⁴ Planting production scenes so as to construct a job shop dynamic multi-scene set S; in the invention, three levels are set for the key variables, 81 production scenes can be combined, and the multi-scene structure parameter setting of the dynamic job shop is shown in a table 2;

TABLE 2 Multi-scene Structure parameter Table

S32, the initial population Pop obtained in S2, namely the candidate dispatching rule set R is applied to the dynamic job workshop scene S _i ,s _i Scheduling by belonging to S, and using a candidate scheduling rule R belonging to R to wait for a processing workpiece queue on the machine when the machine is idle, and selecting a workpiece with the highest priority to be processed on the machine; in this example, the scene 58 is taken as an example, and the scene structure is represented as s ₅₈ ＝{N＝100；C＝2；F＝10；U _a ＝90％}，s ₅₈ ∈S；

S33, according to the dynamic workshop scene S ₅₈ To minimize the average delay time

Calculating the fitness value of each scheduling rule R, R belongs to R, and defining a fitness function as

Wherein, f (r, s) _i (I) Means that the scheduling rule r is applied to the dynamic plant scenario s _i The performance index value f of the scheduling scheme obtained in (1) _ref (s _i (I) Means that the reference scheduling rule is applied to the plant scene s _i The performance index value of the scheduling scheme obtained in (1),

representing a scene s _i I denotes an example, N is the total number of processed workpieces, c _j For finishing time of the work, d _j Is the delivery date of the workpiece;

s34, taking 10% of excellent individuals from the initial population Pop and storing the excellent individuals into an elite library according to the calculation result of the fitness value, and enabling the cycle number iter to be 0;

s4, averagely dividing the initial population Pop into L sub-populations, performing genetic operation (mutation, item shift and recombination) in each sub-population according to Gene Expression Programming (GEP), evaluating the fitness value of each individual in each sub-population, storing the optimal individual in each sub-population into an elite library, and replacing L poor solutions in the original elite library;

s41, dividing the whole population (including 10% of individuals stored in elite library) into L sub-populations on average, and dividing each sub-population after grouping by a variation probability p _m Probability of item shift p _s Recombination probability p _r Carrying out genetic manipulation;

s42, mutation;

the variation may occur anywhere on the chromosome. First, randomly selecting a chromosomeDry the location and then replace it with another element. In order to ensure that the structure of the gene is not changed, mutation generates a legal new individual, and the replacement operation is provided with the following steps: any symbol in the head of a gene can be changed to another symbol representing a function or a terminal, while a terminal symbol in the tail of a gene can only be changed to another terminal symbol. For example chromosomes

The third position "+" and the "NOR" of the eleventh position are selected as the positions where mutation occurs, and the chromosome after mutation becomes

S43, item shifting;

the transposition operation IS to activate a certain gene segment in the chromosome, the activated gene segment IS called a transposition factor, and the transposition factor IS jumped to another position of the chromosome to form a new chromosome, and the transposition operation comprises three transposition items, namely IS transposition item, RIS transposition item and gene transposition item;

s431, IS item shifting. IS factor (arbitrary gene fragment) IS randomly selected among genes of chromosome, its copy IS inserted into any position of gene head except head position, and the end of gene head IS deleted with the same number of symbols as translocation factor to ensure head and tail division line not to be destroyed. For example chromosomes

SL IS selected as the IS factor and the chromosome obtained by transposition after the insertion point of its copy IS selected as the second position IS

The tail parts of the genes before and after the transposition can be seen to be unchanged;

s432, RIS shift item. The RIS factor (arbitrary gene fragment starting with a function) is randomly selected from among chromosomal genes, and its copy is inserted at the head of the gene, and the end of the gene head is deleted by the same number as the number of the translocation factorTo ensure that the head and tail parting lines are not broken. For example chromosomes

The gene fragment "X. AT" in (1) is selected as the RIS factor, and its copy is inserted into the first position of the gene, and the chromosome obtained by transposition is

It can be seen that the tail of the gene remains unchanged before and after the transposition;

s433, gene transposition. First, a gene to be moved IS randomly selected, and then the selected gene IS entirely inserted into the starting position of the chromosome, unlike IS transposition and RIS transposition, the gene at the original position IS entirely deleted, rather than being duplicated.

S44, recombining;

the recombination operation is to make two chromosomes into a pair and exchange partial substances to form two new chromosomes, and comprises three kinds of recombination operation, namely single-point recombination, two-point recombination and gene recombination;

and S441, single-point recombination. Two ancestral chromosomes form a pair and then the same position is cut, and the substances behind the cut position are exchanged;

s442, two-point recombination. Randomly selecting two cross points after the two parent chromosomes are paired, and then interchanging the substances between the cross points between the two parent chromosomes to generate two new child chromosomes;

s443, gene recombination. In the single-point recombination and the two-point recombination, the interchangeable partial substance of the counterpart chromosome may be arbitrary, and in the gene recombination, the interchangeable partial substance of the counterpart chromosome is the whole gene. Genes involved in the crossover are randomly selected and swapped at designated positions;

s45, according to the dynamic workshop scene S ₅₈ To minimize the average delay time

By a fitness function

Calculating the fitness value of each individual in each sub-population, storing the optimal individual in each sub-population into the elite library, and replacing L poor solutions in the original elite library;

s5, constructing four different neighborhood structures, and performing adaptive neighborhood-variant search (VNS) on the optimal individuals in the elite library obtained in the above steps;

s51, initialization parameters: initial solution x, iteration number P, determining neighborhood structure Nz (z is 1,2,3,4), loop variable i is 1, neighborhood search success and failure number are respectively expressed as N _s ＝0，N _f ＝0；

S511, four different neighborhood structures Nz are designed (z ═ 1,2,3, 4):

neighborhood structure N ₁ -an insertion neighborhood, randomly selecting two points in the gene tail of the chromosome, the points of the gene tail being from the set of raw features TS of the workshop, inserting the gene of the latter position before the gene of the former position;

neighborhood structure N ₂ -a two-point crossover neighborhood, randomly selecting two points in the gene tail, to crossover the genes at the two positions with each other;

neighborhood structure N ₃ Randomly shuffling the neighborhood, randomly selecting four positions in the gene tail, shuffling the order of the four elements, and then shuffling;

neighborhood structure N ₄ -a reverse-order neighborhood, randomly selecting two positions in the gene tail, and then arranging the elements between the two positions in reverse order to obtain a new gene;

s52, judging whether the termination criterion (i > P) is met, if so, outputting a local optimal solution X, otherwise, turning to the step S53;

s53, if i is less than P/3, randomly selecting neighborhood Nz to search neighborhood to obtain new solution X', otherwise, according to

And

calculating the selection probability eta value to select a neighborhood Nz, performing neighborhood search to obtain a new solution X', wherein a parameter xi is used for measuring the improvement degree of the chromosome,

denotes the relative fitness value, f (X) ^* ) Representing the global optimal solution obtained in the current elite library, wherein f (q) is the fitness value of the chromosome in the current neighborhood search, and the selection probability eta value of each neighborhood is calculated according to the zeta value in the search process;

s54, if f (X') < f (X) ^* ) Then X ^* ＝X′，N _s ＝N _s +1，N _f ＝N _f +1；

S55, updating the selection probability eta values of each field, and turning to S52;

FIG. 2 shows a flow chart of an adaptive variable neighborhood search process;

s6, updating individuals, generating a new population, making ITER be ITER +1, judging whether the algorithm meets the termination condition ITER > ITER, if so, outputting an optimized population

Otherwise, go to step S3 to execute until the termination condition is satisfied;

s7, optimizing the population obtained by the step S6

The individuals in the method are sorted according to the fitness, and the first K excellent individuals are selected to be put into an optimal scheduling rule set

S71, according to the dynamic workshop scene S ₅₈ Through a fitness function

Optimized population of final output of calculation algorithm

Due to dynamic job shop scenario s ₅₈ The target of (1) is a non-decreasing function of completion time, the smaller the fitness is, the more excellent the individuals are, therefore, the individuals are sorted from small to large according to the fitness value, and the first K excellent individuals are selected to be put into an optimal scheduling rule set

In (1), the value of K is set to 30;

s8, comprehensively considering the optimal scheduling rule set

The fitness of the medium rule and the contribution of the characteristics to the rule are subjected to characteristic selection to obtain a dynamic job shop scene s _i The set of key features TS;

s81, in dynamic workshop scenario S ₅₈ In the method, each feature t in the feature set TS is calculated, and the t belongs to the TS pair optimal scheduling rule set

Each scheduling rule in

The contribution degree of (A) is shown in the following formula;

wherein

Representing a scene s in a dynamic job shop _i Medium scheduling rules

A fitness value of;

to fix the characteristic t as constantScheduling rules for number 1

The feature is fixed to a constant of 1, meaning that the scheduling rule does not select the feature, then

Representing a scene s in a dynamic job shop _i Scheduling rules without selection feature t

A fitness value of;

s82, dynamic Job shop scenario S ₅₈ The target of the scheduling is the non-decreasing function of the completion time, the voting weight of each rule is defined as the monotone decreasing function of the fitness, and each scheduling rule is calculated

For each feature t, t ∈ TS, the voting weight is given by the following formula:

s83, judging the characteristic contribution value calculated in the step S81

If the threshold value theta is larger than the threshold value theta, the threshold value theta is set to be 0.001, and if the threshold value theta is larger than the threshold value theta

Scheduling rule

The support ticket is thrown to t, otherwise, a negative ticket is thrown;

FIG. 3 shows a dynamic job shop scenario s ₅₈ The contribution condition of the candidate features to the optimal scheduling rule. In dynamic job shop scenarios s ₅₈ Performing independent simulation for 30 times, and calculating the optimal scheduling rule set of each feature t pair in the original feature set TS

The contribution profile of (1). From the figure, it can be seen that in a dynamic job shop scenario s ₅₈ In, to the optimal scheduling rule set

The contribution of the characteristic(s) exceeds the threshold value theta by 11 characteristics, namely AT, PT, NPT, OWT, NOINQ, NOR, DD, RPT, SL, FDD and MWT, wherein the contribution of the characteristic AT has an upper limit close to 0.45, a lower limit close to 0.3 and an average value close to 0.35, namely the characteristic pair dynamic workshop scene s ₅₈ The generation of the optimal scheduling rule plays a very important role; the contribution of the NOPS, WIQ, WNIQ features is approximately equal to a threshold, indicating that these features are contributing to the dynamic job shop scenario s ₅₈ The generation of the optimal scheduling rule has little effect; the contribution degree of the characteristic NOIQ is lower than a threshold value, which shows that the characteristic NOIQ plays a role in generating an optimal scheduling rule;

FIG. 4 shows a dynamic job shop scenario s ₅₈ The voting weight of the candidate feature. In dynamic job shop scenarios s ₅₈ Performing independent simulation for 30 times, and calculating an optimal scheduling rule set

Each scheduling rule in (1)

The average value of the voting weight of each feature t in the original feature set TS shows that the support weight of AT, NPT, NOR, DD, SL, FDD and MWT is greater than the rejection weight, which indicates that these seven features contribute most to the objective of minimizing the average delay in the plant scene. The support weight of the feature AT is the largest, and the method has important influence on the calculation of the priority of the workpiece. The support weights of NPT and NOR are also larger, the probability of workpiece delay is obviously increased due to too long processing time of the subsequent process of the workpiece and large residual workload, and the machine is biased to select the workpiece with short processing time and small residual number of processes to process preferentially. The delivery date urgency degree of the workpiece affects the average weighted delay time, the delivery date is less relative to the workpiece delay time than the urgency, the probability of workpiece delay with abundant delivery date is larger, SL is the workpiece relaxation time, namely, the larger the difference between the residual time before the delivery date and the residual processing time is, the workpiece is less likely to arrive late, the smaller the relaxation time is, the less the residual processing time is, and the conclusion is consistent with the general conclusion of the neighborhood of the scheduling research and is logical. Also, the less machine waiting time in the shop floor, the less the probability of workpiece delay. These seven features are consistent with the logic for optimizing the average weighted delay time. In contrast, the veto weight of PT, OWT, NOPS, WIQ, NOINQ, RPT, and W is greater than the support weight, indicating that these features are in the dynamic job shop scenario s ₅₈ The contribution of the characteristics WINQ and NOIQ to the minimization of the average delay is small, and the weight obtained by the characteristics WINQ and NOIQ is not contributed to the workshop scene or even is counterproductive, which shows that the correlation between the total processing time of the working procedures in the waiting set of the processing equipment of the subsequent working procedure of the workpiece and the delay condition of all the working procedures in the current waiting queue to the workpiece is not large.

S84, if the weight of the support ticket obtained by each feature t in the original feature set TS is larger than the weight of the negative ticket, selecting the feature t and putting the feature t into the key feature set TS;

s85, repeating the steps S91 to S94 for each feature t in the original feature set TS, and finally selecting a dynamic workshop scene S ₅₈ Is the set of key features TS, scene s ₅₈ Has a key feature set of

In order to verify the effectiveness of the invention, the running time of the algorithm provided by the invention is analyzed and compared. Table 3 shows the running time mean and standard deviation of the standard GEP feature selection algorithm and the GEP-VNS feature selection algorithm that run independently 30 times on three dynamic job shop scene training sets, where the scheduling targets of the scenes are all the minimum mean delay. As can be seen from Table 3, the running time of the GEP-VNS feature selection algorithm on the training sets of the three dynamic job shop scenarios is less than that of the standard GEP feature selection algorithm, the training time of the GEP-VNS is at least 51.01% of that of the standard GEP, and the efficiency of feature selection is obviously improved by embedding the VNS algorithm into the GEP algorithm.

TABLE 3 mean and standard deviation of run time of standard GEP and GEP-VNS feature selection algorithms on a scene training set

Based on dynamic job shop scene s ₅₈ The key feature set in (1)

And (3) taking the minimized average delay time as a scheduling optimization target, and performing simulation analysis to compare the scheduling rules generated before and after the feature selection of the GEP-VNS algorithm and other representative reference rules on the test performance under the scene. The test performance of a scheduling rule r is defined as the percentage deviation from its reference scheduling rule on the dynamic job shop scenario test set, i.e., 100 (fir (r, s) _i ) -1) wherein

Setting the WATC rule as a dynamic Job shop scenario s in this example ₅₈ Reference scheduling rule(s). Wilson rank-sum test is performed between the scheduling rules generated before and after the feature selection of the GEP-VNS algorithm in Table 4, and statistically significantly better results are marked in bold.

TABLE 4 GEP-VNS Algorithm feature selection front and back generation scheduling rule Performance comparison analysis

Scene test set	WEDD	WESD	WSPT	W(CR+SPT)	WCOVERT	GEP-VNS(TS)	GEP-VNS(TS * )
								S 58-1	30.96	4.86	0.06	0.53	0.58	-11.35±1.67	-13.68±1.26
S 58-2	37.78	6.76	0.37	0.32	0.27	-6.63±0.85	-10.52±1.17
								S 58-3	39.23	11.25	0.18	0.03	-0.57	-4.46±0.75	-9.32±1.06
S 58-4	34.69	8.89	0.07	0.36	0.08	-4.13±0.69	-9.12±0.93
								S 58-5	31.95	10.52	0.25	-0.12	0.02	-5.74±0.81	-6.73±0.78
S 58-6	33.26	9.56	-0.15	0.28	0.93	-5.12±0.79	-5.58±0.85
								S 58-7	36.62	10.81	0.37	1.04	-0.51	-8.84±1.23	-8.99±1.06
S 58-8	39.55	9.33	0.18	0.41	0.01	-7.69±0.98	-9.63±0.87

As can be seen from table 4, the GEP-VNS algorithm achieves better results than the benchmark rule both before and after feature selection, which indicates the advantage of generating the scheduling rules using the GEP-VNS algorithm (negative values indicate the advantage over the reference scheduling rules). In addition, it can be seen in the table that the performance of the GEP-VNS (TS) on most scene test sets is obviously better than that of the GEP-VNS (TS), that is, the performance of the scheduling rule generated by using the key feature after feature selection as the terminal attribute is better than that of the scheduling rule generated by the original feature. To further validate the GEP-VNS feature selection algorithm, GEP-VNS (TS) and GEP-VNS (TS) are respectively applied to the dynamic job shop scene s ₅₈ On the 18 training sets of the training set, learning being performed on each training setThe sets are respectively and independently operated for 30 times, the performance of the optimal scheduling rule obtained by each operation is tested on 18 verification sets, and fig. 5 shows the comparison result of the performance of the scheduling rule generated by adopting the original feature set and the performance of the scheduling rule generated after feature selection. Irrelevant features are removed after feature selection through a GEP-VNS algorithm to obtain a key feature set of a dynamic job shop scene, the problems of large search space and low algorithm efficiency of directly generating a scheduling rule through gene expression programming are solved, and meanwhile, the generated scheduling rule structure is simpler and is easy to understand.

The above-mentioned embodiments are merely illustrative of the principles and effects of the present invention, and some embodiments may be used, not restrictive; it should be noted that, for those skilled in the art, various changes and modifications can be made without departing from the inventive concept of the present invention, and these changes and modifications belong to the protection scope of the present invention.

Claims (5)

1. A feature selection method in a dynamic job shop scheduling rule based on GEP-VNS evolution comprises the following steps:

s1, setting basic parameters of the GEP-VNS algorithm: total iteration number ITER, population size popsize, gene number n, head length head, tail length tail, variation probability p _m Recombination probability p _r Sum and shift probability p _s The number z of neighborhoods, a function set FS { +, -, ×, +/-min, max, if }, and a terminal set TS, namely a dynamic job shop original feature set, comprise shop related, workpiece related and machine related features;

the set ITER parameter is an end condition of the algorithm, when ITER is larger than ITER, the algorithm is ended and an excellent scheduling rule set of a dynamic job shop scene is given, and one scheduling rule corresponds to one multi-gene chromosome in the GEP-VNS algorithm; the popsize parameter is the total number of chromosomes to be generated, the popsize chromosomes making up a population; the gene consists of a head part and a tail part, and the length of the head part and the tail part satisfies tail ═ head × (n-1) + 1; the function nodes of the algorithm use FS { +, -, ×, ÷, min, max }, where +, -, ×, ÷ is the basic arithmetic operator and "÷" is the protective division, i.e., returns 1 when the divisor is zero; "min" and "max" are the acceptance of two parameters and the return of a smaller or larger value, respectively; the terminal set TS, i.e. the set of raw features of the dynamic job shop, is shown in the following table:

serial number Feature name Meaning of characteristic 1 AT Current time of day 2 PT Processing time of current working procedure of workpiece 3 NPT Processing time of subsequent process of workpiece 4 OWT Waiting time of process 5 NOPS Number of steps of workpiece 6 WIQ Total processing time of processes in waiting set of processing equipment of current process of workpiece 7 WINQ Total processing time of processes in waiting set of processing equipment for subsequent processes of workpiece 8 NOIQ All the number of processes in the current waiting queue 9 NOINQ All the number of processes in the next waiting queue 10 DD Delivery date of workpieces 11 RPT Remaining processing time of workpiece 12 SL Time of workpiece relaxation 13 MWT Machine latency 14 NOR Number of remaining steps of workpiece 15 FDD Flow time of process 16 W Workpiece weight

S2, carrying out random initialization operation on the population according to the function set FS, the terminal set TS and the algorithm parameters in the S1 to obtain an initial population Pop with the size of the population being popsize, namely a candidate scheduling rule set R, wherein each individual in the population represents a workshop scheduling rule R, and R belongs to the R;

s21, coding multigene chromosomes, wherein each chromosome is composed of 3 genes, each gene is divided into a head part and a tail part, elements of the head part are from a function set FS and a terminal set TS, elements of the tail part are only from the terminal set TS, the head part length of each gene is 8, the tail part length of each gene is 9, and sub-expression trees formed by mapping the genes respectively are connected in an 'adding' mode to form a multi-sub-tree expression tree;

s22, carrying out random initialization operation on the population to obtain an initial population Pop with the population size of popsize, namely a candidate dispatching rule set R, wherein each chromosome in the population represents a workshop dispatching rule R, and R belongs to R;

s23, performing a decoding operation on the multigene chromosome, specifically as follows:

converting each gene of the chromosome in the initial population into a sub-expression tree respectively according to the inverse process of depth-first traversal;

connecting the sub-expression trees in an 'adding' mode to form a multi-subtree expression tree with a complex structure;

s3, evaluating the fitness of population individuals: transferring the initial population Pop obtained in the step S2 to a dynamic job shop scene, evaluating the fitness of population individuals according to the performance index of the scene, taking out 10% of excellent individuals, storing the excellent individuals into an elite library, and enabling the cycle number iter to be 0;

s31, setting basic structure parameters of the job shop, and recording the equipment number m and the product type x; consider 4 key variables in the plant uncertainty: the total number N of workpieces, the urgent delivery date factor C, the equipment fault level F and the workshop utilization rate Ug, J (J is more than or equal to 3) parameter levels can be set for all the key variables, and J is combined ⁴ Planting production scenes so as to construct a job shop dynamic multi-scene set S;

s32, the initial population Pop obtained in S2, namely the candidate dispatching rule set R is applied to the dynamic job workshop scene S _i ，s _i Scheduling by belonging to S, and using a candidate scheduling rule R belonging to R to wait for a processing workpiece queue on the machine when the machine is idle, and selecting a workpiece with the highest priority to be processed on the machine;

s33, according to the dynamic workshop scene S _i (i＝1，…J ⁴ ) The scheduling target calculates the fitness value of each scheduling rule R, R belongs to R, and the fitness function is defined as

Wherein, f (r, s) _i (I) Means that the scheduling rule r is applied to the dynamic plant scenario s _i The performance index value f of the scheduling scheme obtained in (1) _ref (s _i (I) Means that the reference scheduling rule is applied to the plant scene s _i The performance index value of the scheduling scheme obtained in (II) _train Representing a scene s _i I denotes an example, the scheduling goal of the scenario is to minimize the maximum completion time, or minimize the average flow-through time or minimize the average delay time;

s34, taking 10% of excellent individuals from the initial population Pop and storing the excellent individuals into an elite library according to the calculation result of the fitness value, and enabling the cycle number iter to be 0;

s4, averagely dividing the initial population Pop into L sub-populations, performing genetic operation in each sub-population according to a gene expression programming GEP, wherein the genetic operation comprises variation, item shifting and recombination, evaluating the fitness value of each individual in each sub-population, storing the optimal individual in each sub-population into an elite library, and replacing L poor solutions in the elite library;

s41, dividing the whole population into L sub-populations, and dividing each sub-population into groups according to variation probability p _m Probability of item shift p _s Recombination probability p _r Carrying out genetic manipulation;

s42, mutation;

first, several positions are randomly selected in the chromosome and then replaced with another element: any symbol in the head of the gene can be changed into another symbol representing a function or a terminal, and the terminal character in the tail of the gene can only be changed into another terminal character;

s43, item shifting;

the transposition operation IS to activate a certain gene segment in the chromosome, the activated gene segment IS called a transposition factor, and the transposition factor IS jumped to another position of the chromosome to form a new chromosome, and the transposition operation comprises three transposition items, namely IS transposition item, RIS transposition item and gene transposition item;

s431, IS term shift: randomly selecting any gene segment, namely IS factor, from the gene of the chromosome, inserting the copy of the IS factor into any position of the head of the gene except the head position, and simultaneously deleting the same number of symbols as the transposition factors from the tail end of the head of the gene so as to ensure that the head and tail division lines are not damaged;

s432, RIS shift item: randomly selecting any gene segment, namely RIS factor, starting with a function from the gene of the chromosome, inserting the copy of the RIS factor into the head position of the head of the gene, and simultaneously deleting the same number of symbols as the transposition factors from the tail end of the head of the gene so as to ensure that the head and tail division lines are not damaged;

s433, gene transposition: firstly, randomly selecting genes to be moved, then inserting the whole selected genes into the initial position of a chromosome, and deleting the whole genes on the original position;

s44, recombining;

the recombination operation is to make two chromosomes into a pair and exchange partial substances to form two new chromosomes, and comprises three kinds of recombination operation, namely single-point recombination, two-point recombination and gene recombination;

s441, single-point recombination: two ancestral chromosomes form a pair and then the same position is cut, and the substances behind the cut position are exchanged;

s442, two-point recombination: randomly selecting two cross points after the two parent chromosomes are paired, and then interchanging materials between the cross points between the two parent chromosomes to generate two new child chromosomes;

s443, gene recombination: the interchange part of the paired chromosomes is the whole gene, and the genes involved in interchange are randomly selected and exchanged at the designated positions;

s45, according to the dynamic workshop scene S _i (i＝1，…J ⁴ ) To minimize the average delay time

By a fitness function

Calculating the fitness value of each individual in each sub-population, storing the optimal individual in each sub-population into the elite library, and replacing L poor solutions in the original elite library;

s5, constructing four different neighborhood structures, performing neighborhood-variable search on the optimal individuals in the elite library obtained in the above steps, and searching a better solution near the local optimal solution to further optimize the population;

s6, updating individuals, generating a new population, making ITER be ITER + l, judging whether the algorithm meets the termination condition ITER is larger than ITER, if yes, outputting an optimized population

Otherwise, go to step S3 to execute until the termination condition is satisfied;

s7, optimizing the population obtained by the step S6

The individuals in the method are sorted according to the fitness, and the first K excellent individuals are selected to be put into an optimal scheduling rule set

S71, according to the dynamic workshop scene S _i (i＝1，…J ⁴ ) Through a fitness function

Optimized population of final output of calculation algorithm

Selecting the first K excellent individuals to put into an optimal scheduling rule set

Performing the following steps;

s8, comprehensively considering the optimal scheduling rule set

The fitness of the medium rule and the contribution of the characteristics to the rule are subjected to characteristic selection to obtain a dynamic job shop scene s _i The set of key features TS:

s81, in dynamic workshop scenario S _i (i＝1，…J ⁴ ) In the method, each characteristic t in the feature set TS is calculated, and each scheduling rule in the optimal scheduling rule set R is subjected to t e TS

The contribution degree of (A) is shown in the following formula;

wherein

Representing scheduling rules in a dynamic job shop scenario s

A fitness value of;

scheduling rules for fixing the characteristic t to a constant 1

The feature is fixed to a constant of 1, meaning that the scheduling rule does not select the feature, then

Representing a scene s in a dynamic job shop _i Scheduling rules without selection feature t

A fitness value of;

s82, dynamic Job shop scenario S _i (i＝1，…J ⁴ ) The target of the scheduling is the non-decreasing function of the completion time, the voting weight of each rule is defined as the monotone decreasing function of the fitness, and each scheduling rule is calculated

For each feature t, t ∈ TS, the voting weight is given by the following formula:

s83, judging the characteristic contribution value calculated in the step S81

Whether or not it is greater than a threshold value

The threshold is set to 0.001 if

Scheduling rule

The support ticket is thrown to t, otherwise, a negative ticket is thrown;

s84, if the weight of the support ticket obtained by each feature t in the original feature set TS is larger than the weight of the negative ticket, selecting the feature t and putting the feature t into the key feature set TS;

s85, repeating the steps S81 to S84 for each feature t in the original feature set TS, and finally selecting a dynamic workshop scene S _i (i＝1，…J ⁴ ) The set of key features.

2. The method for selecting the features in the GEP-VNS evolution-based dynamic job shop scheduling rule according to claim 1, wherein: in the step S33, according to the dynamic workshop scene S _i (i＝1，…J ⁴ ) With the aim of minimizing the mean delay time

Wherein N is the total number of the processed workpieces, c _j For finishing time of the work, d _j Is the delivery date of the workpiece.

3. The method for selecting the features in the GEP-VNS evolution-based dynamic job shop scheduling rule according to claim 1, wherein: the step S5 specifically includes the following steps:

s51, initializing parameters: initial solution x, iteration number P, determining neighborhood structure Nz (z is 1,2,3,4), loop variable i is 1, neighborhood search success and failure number are respectively expressed as N _s ＝0，N _f ＝0；

S511, four different neighborhood structures Nz are designed (z ═ 1,2,3, 4):

neighborhood structure N ₁ -an insertion neighborhood, randomly selecting two points in the gene tail of the chromosome, the points of the gene tail being from the set of raw features TS of the workshop, inserting the gene of the latter position before the gene of the former position;

neighborhood structure N ₂ -a two-point crossover neighborhood, randomly selecting two points in the gene tail, to crossover the genes at the two positions with each other;

neighborhood structure N ₃ Randomly shuffling the neighborhood, randomly selecting four positions in the gene tail, shuffling the order of the four elements, and then shuffling;

neighborhood structure N ₄ -a reverse-order neighborhood, randomly selecting two positions in the gene tail, and then arranging the elements between the two positions in reverse order to obtain a new gene;

s52, judging whether the termination criterion is satisfied (i > P), if so, outputting a local optimal solution X, otherwise, turning to the step S53;

s53, if i is less than P/3, randomly selecting neighborhood Nz to search neighborhood to obtain new solution X', otherwise, according to

And

calculating the selection probability eta value to select a neighborhood Nz, performing neighborhood search to obtain a new solution X', wherein a parameter xi is used for measuring the improvement degree of the chromosome,

denotes the relative fitness value, f (X) ^* ) Representing the global optimal solution obtained in the current elite library, wherein f (q) is the fitness value of the chromosome in the current neighborhood search, and the selection probability eta value of each neighborhood is calculated according to the zeta value in the search process;

s54, if f (X ') < f (X'), then X ^* ＝X′，N _s ＝N _s +1，N _f ＝N _f +1；

And S55, updating the selection probability eta values of each field, and turning to S52.

4. The method for selecting the features in the GEP-VNS evolution-based dynamic job shop scheduling rule according to claim 1, wherein: the step S5 specifically includes the following steps:

s51, initialization parameters: initially solving X, iterating for a time P, determining a neighborhood structure Nz (z is 1,2,3 and 4), and a loop variable i is 1;

s511, four different neighborhood structures Nz are designed (z ═ 1,2,3, 4):

neighborhood structure N ₁ -an insertion neighborhood, randomly selecting two points in the gene tail of the chromosome, the points of the gene tail being from the set of raw features TS of the workshop, inserting the gene of the latter position before the gene of the former position;

neighborhood structure N ₂ -a two-point crossover neighborhood, randomly selecting two points in the gene tail, to crossover the genes at the two positions with each other;

neighborhood structure N ₃ Randomly shuffling the neighborhood, randomly selecting four positions in the gene tail, shuffling the order of the four elements, and then shuffling;

neighborhood structure N ₄ - -reverse order neighborhood, two randomly chosen in the gene tailThen, elements between the two points are arranged in a reverse order to obtain a new gene;

s52, judging whether the termination criterion is satisfied (i > P), if so, outputting a local optimal solution X, otherwise, turning to the step S53;

s53, randomly selecting a neighborhood structure Nz to generate a new solution X', and comparing the fitness value of the new solution X with the fitness value of the initial solution X;

s54, if f (X') < f (X) ^* ) If so, outputting z, where X is X', replacing the initial solution with a new solution with a larger fitness value, and continuing to search in the neighborhood structure Nz; otherwise, z is z + 1;

s55, if z > 4, returning to step S52; otherwise, returning to step S53, entering the next neighborhood structure for searching.

5. The GEP-VNS evolution-based feature selection method in dynamic job shop scheduling rules according to any one of claims 1 to 4, wherein: the value of K is set to 30 in said step S71.

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