CN113011612A - Production and maintenance scheduling method and system based on improved wolf algorithm - Google Patents

Production and maintenance scheduling method and system based on improved wolf algorithm Download PDF

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CN113011612A
CN113011612A CN202110310814.5A CN202110310814A CN113011612A CN 113011612 A CN113011612 A CN 113011612A CN 202110310814 A CN202110310814 A CN 202110310814A CN 113011612 A CN113011612 A CN 113011612A
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wolf
workpiece
algorithm
maintenance
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CN113011612B (en
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钱晓飞
胡朝明
刘心报
陆少军
周谧
周志平
崔龙庆
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Hefei University of Technology
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/20—Administration of product repair or maintenance
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    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/004—Artificial life, i.e. computing arrangements simulating life
    • G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
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    • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
    • G06Q10/063—Operations research, analysis or management
    • G06Q10/0631—Resource planning, allocation, distributing or scheduling for enterprises or organisations
    • G06Q10/06312—Adjustment or analysis of established resource schedule, e.g. resource or task levelling, or dynamic rescheduling
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
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Abstract

The invention provides a production and maintenance scheduling method and system based on an improved wolf algorithm, and relates to the technical field of production and maintenance scheduling. The method comprises the steps of randomly generating N one-dimensional vectors for workpieces in the production and maintenance processes to form an initial solution of a gray wolf algorithm, then improving iteration parameters and an iteration mode in the original gray wolf algorithm, simultaneously adding a neighborhood search mechanism based on probability, optimizing the original gray wolf algorithm, finally inputting the initial solution into the improved gray wolf algorithm to solve a global optimal solution, and carrying out cooperative scheduling on production and maintenance by utilizing a workpiece processing sequence and a maintenance opportunity scheme corresponding to the global optimal solution. The method enhances the searching capability of the wolf pack, ensures the updating efficiency of the wolf pack, not only improves the diversity of the pack, but also enhances the convergence capability at the final stage of the algorithm to a certain extent, and solves the problem that the prior art can not carry out cooperative scheduling on production and maintenance when a plurality of influence factors are considered at the same time.

Description

Production and maintenance scheduling method and system based on improved wolf algorithm
Technical Field
The invention relates to the technical field of production and maintenance scheduling, in particular to a production and maintenance scheduling method and system based on an improved wolf algorithm.
Background
The problem of production and maintenance coordinated scheduling is paid more and more attention in recent years, is a typical combined optimization problem, and is widely applied to various industries in the manufacturing field, such as smelting industry, chip industry, high-end equipment manufacturing industry and the like. Different from the traditional scheduling mode of taking a maintenance plan as production constraint, the production and maintenance cooperative scheduling takes maintenance activities as part of decision and schedules the maintenance activities together with production tasks.
Currently, although there is a certain research on the cooperative decision problem of production and maintenance, there are few researches considering the reliability degradation of equipment and imperfect maintenance. Especially, when a plurality of influence factors such as processing sequence, maintenance opportunity, service life of machine equipment, comprehensive operation and maintenance cost of different workpieces need to be considered at the same time, the traditional scheduling model cannot be well solved. In addition, in terms of the method, although the principle is simple and easy to implement, and the gray wolf algorithm can show good performance when solving some specific problems, the gray wolf algorithm has the defect of being easy to fall into local optimization when solving a large-scale problem, so that the traditional gray wolf algorithm is not suitable for solving a complex production and maintenance cooperative scheduling problem.
Based on this, the prior art can not carry out coordinated scheduling to production and maintenance when simultaneously considering a plurality of influence factors.
Disclosure of Invention
Technical problem to be solved
Aiming at the defects of the prior art, the invention provides a production and maintenance scheduling method and system based on an improved wolf algorithm, and solves the problem that the prior art cannot perform cooperative scheduling on production and maintenance when a plurality of influence factors are considered at the same time.
(II) technical scheme
In order to achieve the purpose, the invention is realized by the following technical scheme:
in a first aspect, the present invention first provides a production and maintenance scheduling method based on an improved grayling algorithm, where the method includes:
s1, initializing the input parameters of the algorithm, including the number n of the workpieces and the delivery date d of the workpiecesjDelay cost per unit time w of workpiecejUnit production cost clTime t required for preventive maintenance activitiespAnd cost cpTime t required for a corrective maintenance activityrAnd cost crVirtual working life of the machine at its initial moment
Figure BDA0002989474380000021
And the number of preventive maintenance passes m;
s2, setting execution parameters of the algorithm, wherein the execution parameters comprise the number t of previous iterations as 1 and the maximum number t of iterationsmaxNeighborhood search probability ε, neighborhood maximum search times smaxAccording to the iteration parameter a of the nonlinear reduction;
s3, initializing the population, randomly generating N one-dimensional vectors as the initial solution of the algorithm, wherein each one-dimensional vector represents the position of a wolf, and the position of the kth wolf is defined as
Figure BDA0002989474380000022
1,2, N, wherein
Figure BDA0002989474380000023
For any real number, the work piece is according to
Figure BDA0002989474380000024
The absolute value of (A) is processed from small to large in sequence if
Figure BDA0002989474380000025
If the absolute value of (a) is negative, preventive maintenance is performed before the workpiece j starts to be machined;
s4, defining a population structure, calculating the fitness value of each individual in the population, setting the best three individuals in the wolf group as alpha, beta and gamma wolfs, and setting the rest wolfs as omega wolfs;
s5, calculating a learning factor epsilon based on weight1、ε2、ε3All ω wolves update their positions based on the weight-based learning factor and the position information of α, β, and γ wolves;
s6, updating the population;
s7, increasing a neighborhood searching mechanism based on probability, and generating a random number p between 0 and 1 for each individual in the wolf group i1,2, N, judge piWhether epsilon is not more than epsilon is true, if yes, performing neighborhood search on the ith individual, and if not, retaining the position information of the original individual;
s8, updating the population;
s9, defining a population structure, calculating the fitness value of each individual in the population, setting the best three individuals in the wolf group as alpha, beta and gamma wolfs, and setting the rest wolfs as omega wolfs;
s10, making t equal to t +1, updating the iteration parameter a, and judging that t is less than or equal to tmaxIf not, the step S11 is executed, otherwise, the step S5 is executed again;
and S11, finishing algorithm execution, and outputting the position of the global optimal solution alpha wolf, the fitness value of the global optimal solution alpha wolf and a production and maintenance scheduling scheme.
Preferably, the iteration parameter a can be expressed by the following formula:
Figure BDA0002989474380000031
wherein t is (1, 2, 3, …, t)max) Is shown asNumber of preceding iterations, tmaxThe maximum number of iterations is indicated.
Preferably, said epsilon1、ε2、ε3Expressed by the following formula:
Figure BDA0002989474380000032
Figure BDA0002989474380000033
Figure BDA0002989474380000034
wherein epsilon1、ε2、ε3Learning factors of omega wolf to alpha, beta and gamma wolf respectively; xα、Xβ、XγRepresent the positions of alpha, beta and gamma wolves, respectively; f (X)α)、f(Xβ)、f(Xγ) Respectively, the fitness values of alpha, beta and gamma wolves.
Preferably, the S7 includes:
s71: inputting a wolf group individual
Figure BDA0002989474380000035
Generating a random probability p for the individuali；
S72: if random probability piIf the probability is less than the neighborhood searching probability epsilon, the step S73 is entered, otherwise, the input solution is reserved;
s73: randomly generating 3 integers d, b and c between [1 and n ] which are not equal to each other, wherein n represents the number of workpieces;
s74: switching
Figure BDA0002989474380000041
And
Figure BDA0002989474380000042
and is given a value of
Figure BDA0002989474380000043
Is equal to a random number;
s75: calculating the fitness value of the new individual;
s76: judgment of f (X'k)＜f(Xk) If yes, assigning Xk' to Xk and finishing the search; if not, go to step S77;
s77: and judging whether the set maximum searching times is reached, if not, returning to the step S73, and if so, keeping the input solution.
Preferably, calculating the fitness value for each individual in the population comprises:
step 1: input solution vector
Figure BDA0002989474380000044
Step 2: reading the decision variables according to the following decoding rules, the work piece according to
Figure BDA0002989474380000045
The absolute value of (A) is processed from small to large in sequence if
Figure BDA0002989474380000046
If negative, preventive maintenance is performed before the workpiece j begins to be machined;
Figure BDA0002989474380000047
Figure BDA0002989474380000048
and step 3: calculating the virtual working life of the machine when the workpiece at each position starts to be machined and finishes to be machined according to the following recursion formula;
Figure BDA0002989474380000049
Figure BDA00029894743800000410
representing the virtual service life of the machine at the start of machining the workpiece in the i-th position;
Figure BDA00029894743800000411
representing the virtual working life of the machine at the end of the machining of the workpiece in the i-th position; p is a radical of[i]Indicating the processing time of the workpiece at the ith position;
and 4, step 4: calculating the expected failure times of the workpieces at all positions in the machining process;
Figure BDA0002989474380000051
Figure BDA0002989474380000052
indicating the number of preventive maintenance operations the machine undergoes at the start of processing the workpiece at the ith position; wherein m is the number of preventive maintenance times the machine experienced at T-0; η, β are parameters in the failure rate function;
and 5: calculating the expected finishing time of the workpiece at each position;
Figure BDA0002989474380000053
E(N[1]) Indicating the expected number of times of machine failure of the workpiece at the ith position in the machining process; e (N)[i]) Representing a desired finish time of the workpiece at the ith position;
step 6: calculating the fitness according to the following formula;
Figure BDA0002989474380000054
clrepresents the production cost per unit time; w is ajUnit extension representing workpiece jA term penalty cost; c. CpRepresents the cost of a preventive maintenance activity; c. CrRepresents the cost of a corrective maintenance activity at one time; e (T)[i]) Indicating the expected delay time of the workpiece at the ith position.
In a second aspect, the present invention provides a production and maintenance scheduling system based on an improved graying algorithm, the system comprising:
a processing unit for performing the steps of:
s1, initializing the input parameters of the algorithm, including the number n of the workpieces and the delivery date d of the workpiecesjDelay cost per unit time w of workpiecejUnit production cost clTime t required for preventive maintenance activitiespAnd cost cpTime t required for a corrective maintenance activityrAnd cost crVirtual working life of the machine at its initial moment
Figure BDA0002989474380000061
And the number of preventive maintenance passes m;
s2, setting execution parameters of the algorithm, wherein the execution parameters comprise the number t of previous iterations as 1 and the maximum number t of iterationsmaxNeighborhood search probability ε, neighborhood maximum search times smaxAccording to the iteration parameter a of the nonlinear reduction;
s3, initializing the population, randomly generating N one-dimensional vectors as the initial solution of the algorithm, wherein each one-dimensional vector represents the position of a wolf, and the position of the kth wolf is defined as
Figure BDA0002989474380000062
1,2, N, wherein
Figure BDA0002989474380000063
For any real number, the work piece is according to
Figure BDA0002989474380000064
The absolute value of (A) is processed from small to large in sequence if
Figure BDA0002989474380000065
If the absolute value of (a) is negative, preventive maintenance is performed before the workpiece j starts to be machined;
s4, defining a population structure, calculating the fitness value of each individual in the population, setting the best three individuals in the wolf group as alpha, beta and gamma wolfs, and setting the rest wolfs as omega wolfs;
s5, calculating a learning factor epsilon based on weight1、ε2、ε3All ω wolves update their positions based on the weight-based learning factor and the position information of α, β, and γ wolves;
s6, updating the population;
s7, increasing a neighborhood searching mechanism based on probability, and generating a random number p between 0 and 1 for each individual in the wolf group i1,2, N, judge piWhether epsilon is not more than epsilon is true, if yes, performing neighborhood search on the ith individual, and if not, retaining the position information of the original individual;
s8, updating the population;
s9, defining a population structure, calculating the fitness value of each individual in the population, setting the best three individuals in the wolf group as alpha, beta and gamma wolfs, and setting the rest wolfs as omega wolfs;
s10, making t equal to t +1, updating the iteration parameter a, and judging that t is less than or equal to tmaxIf not, the step S11 is executed, otherwise, the step S5 is executed again;
s11, finishing the algorithm execution;
and the output unit is used for outputting the position of the global optimal solution alpha wolf, the fitness value of the global optimal solution alpha wolf and a production and maintenance scheduling scheme.
Preferably, the iteration parameter a during the execution of the processing unit can be expressed by the following formula:
Figure BDA0002989474380000071
wherein t is (1, 2, 3, …, t)max) Representing the current number of iterations, tmaxThe maximum number of iterations is indicated.
Preference is given toOf the processing unit1、ε2、ε3Expressed by the following formula:
Figure BDA0002989474380000072
Figure BDA0002989474380000073
Figure BDA0002989474380000074
wherein epsilon1、ε2、ε3Learning factors of omega wolf to alpha, beta and gamma wolf respectively; xα、Xβ、XγRepresent the positions of alpha, beta and gamma wolves, respectively; f (X)α)、f(Xβ)、f(Xγ) Respectively, the fitness values of alpha, beta and gamma wolves.
Preferably, the processing unit executing step S7 includes:
s71: inputting a wolf group individual
Figure BDA0002989474380000075
Generating a random probability p for the individuali；
S72: if random probability piIf the probability is less than the neighborhood searching probability epsilon, the step S73 is entered, otherwise, the input solution is reserved;
s73: randomly generating 3 integers d, b and c between [1 and n ] which are not equal to each other, wherein n represents the number of workpieces;
s74: switching
Figure BDA0002989474380000076
And
Figure BDA0002989474380000077
and is given a value of
Figure BDA0002989474380000078
Is equal to a random number;
s75: calculating the fitness value of the new individual;
s76: judgment of f (X'k)＜f(Xk) If yes, assigning Xk' to Xk and finishing the search; if not, go to step S77;
s77: and judging whether the set maximum searching times is reached, if not, returning to the step S73, and if so, keeping the input solution.
Preferably, the calculating the fitness value of each individual in the population during the execution of the processing unit includes:
step 1: input solution vector
Figure BDA0002989474380000081
Step 2: reading the decision variables according to the following decoding rules, the work piece according to
Figure BDA0002989474380000082
The absolute value of (A) is processed from small to large in sequence if
Figure BDA0002989474380000083
If negative, preventive maintenance is performed before the workpiece j begins to be machined;
Figure BDA0002989474380000084
Figure BDA0002989474380000085
and step 3: calculating the virtual working life of the machine when the workpiece at each position starts to be machined and finishes to be machined according to the following recursion formula;
Figure BDA0002989474380000086
Figure BDA0002989474380000087
representing the virtual service life of the machine at the start of machining the workpiece in the i-th position;
Figure BDA0002989474380000088
representing the virtual working life of the machine at the end of the machining of the workpiece in the i-th position; p is a radical of[i]Indicating the processing time of the workpiece at the ith position;
and 4, step 4: calculating the expected failure times of the workpieces at all positions in the machining process;
Figure BDA0002989474380000089
Figure BDA00029894743800000810
indicating the number of preventive maintenance operations the machine undergoes at the start of processing the workpiece at the ith position; wherein m is the number of preventive maintenance times the machine experienced at T-0; η, β are parameters in the failure rate function;
and 5: calculating the expected finishing time of the workpiece at each position;
Figure BDA0002989474380000091
E(N[1]) Indicating the expected number of times of machine failure of the workpiece at the ith position in the machining process; e (N)[i]) Representing a desired finish time of the workpiece at the ith position;
step 6: calculating the fitness according to the following formula;
Figure BDA0002989474380000092
clrepresents the production cost per unit time; w is ajRepresenting the unit postponed penalty cost of the workpiece j;cprepresents the cost of a preventive maintenance activity; c. CrRepresents the cost of a corrective maintenance activity at one time; e (T)[i]) Indicating the expected delay time of the workpiece at the ith position.
(III) advantageous effects
The invention provides a production and maintenance scheduling method and system based on an improved wolf algorithm. Compared with the prior art, the method has the following beneficial effects:
the invention relates to a production and maintenance scheduling method and a system based on an improved wolf algorithm. The improved wolf algorithm enhances the searching capability of the wolf colony, ensures the updating efficiency of the wolf colony, not only improves the diversity of the colony, but also enhances the convergence capability at the end of the algorithm to a certain extent, solves the problem that the prior art can not carry out cooperative scheduling on production and maintenance when a plurality of influence factors are considered simultaneously, has high efficiency and accuracy in cooperative scheduling, improves the reliability of machine operation, and reduces the operation cost of enterprises.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flowchart of a production and maintenance scheduling method based on an improved Grey wolf algorithm according to an embodiment of the present invention;
FIG. 2 is a comparison graph of the parameter a in the improved gray wolf algorithm and the original gray wolf algorithm according to the embodiment of the present invention;
FIG. 3 is a schematic diagram of a manufacturing and maintenance process according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention are clearly and completely described, and it is obvious that the described embodiments are a part of the embodiments of the present invention, but not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment of the application provides a production and maintenance scheduling method and system based on an improved wolf algorithm, and solves the problem that in the prior art, production and maintenance cannot be cooperatively scheduled when multiple influence factors are considered simultaneously.
In order to solve the technical problems, the general idea of the embodiment of the application is as follows:
in order to carry out cooperative scheduling on production and maintenance when a plurality of influence factors are considered simultaneously, the method comprises the steps of firstly randomly generating N one-dimensional vectors for workpieces in the production and maintenance process to form an initial solution of a gray wolf algorithm, then improving iteration parameters and an iteration mode in the original gray wolf algorithm, simultaneously adding a neighborhood search mechanism based on probability, optimizing the original gray wolf algorithm, finally inputting the initial solution into the improved gray wolf algorithm to solve a global optimal solution, and carrying out cooperative scheduling on the production and the maintenance by utilizing a workpiece processing sequence and a maintenance opportunity scheme corresponding to the global optimal solution.
In order to better understand the technical solution, the technical solution will be described in detail with reference to the drawings and the specific embodiments.
The method aims to select the most suitable workpiece processing sequence and maintenance time scheme by making a decision on the processing sequence of workpieces with different delivery dates and making a decision on the maintenance time of a machine so as to minimize the total cost of production and maintenance of equipment. Assuming that n workpieces are to be processed on one machine, the most suitable workpiece processing sequence and maintenance timing scheme is selected in order to minimize the total cost of production and equipment maintenance, taking into account the information of the workpieces' processing time, delivery date, unit time delay cost, processing cost, time required for a preventive maintenance activity, cost required for a preventive maintenance activity, time required for a corrective maintenance, cost required for a corrective maintenance, historical maintenance times, and initial equipment service life.
The Grey Wolf optimization algorithm (GWOlf Optimizer) is a group intelligent optimization algorithm, is an optimized search method developed by inspiring Grey Wolf prey activities, has strong convergence performance, and has the characteristics of few parameters, easiness in implementation and the like. The general steps of the gray wolf algorithm include: (1) initializing a wolf group; (2) constructing a wolf cluster structure, selecting three individuals with the best fitness in the wolf cluster as alpha, beta and gamma wolfs, and setting the rest wolfs as omega wolfs; (3) the omega wolf in the wolf group searches the prey (updates the position) according to the guidance of the alpha, beta and gamma wolf; (4) repeating the steps (2) and (3), and searching an optimal solution in the whole space; (5) after the number of times of reaching the termination condition, the position of the wolf (alpha wolf) closest to the prey in the wolf group is output.
Example 1:
in a first aspect, the present invention first provides a production and maintenance scheduling method based on an improved grayish wolf algorithm, referring to fig. 1, the method includes:
s1, initializing the input parameters of the algorithm, including the number n of the workpieces and the delivery date d of the workpiecesjDelay cost per unit time w of workpiecejUnit production cost clTime t required for preventive maintenance activitiespAnd cost cpTime t required for a corrective maintenance activityrAnd cost crVirtual working life of the machine at its initial moment
Figure BDA0002989474380000111
And the number of preventive maintenance passes m;
s2, settingDetermining the execution parameters of the algorithm, wherein the execution parameters comprise the number t of previous iterations as 1 and the maximum number t of iterationsmaxNeighborhood search probability ε, neighborhood maximum search times smaxAccording to the iteration parameter a of the nonlinear reduction;
s3, initializing the population, randomly generating N one-dimensional vectors as the initial solution of the algorithm, wherein each one-dimensional vector represents the position of a wolf, and the position of the kth wolf is defined as
Figure BDA0002989474380000121
1,2, N, wherein
Figure BDA0002989474380000122
For any real number, the work piece is according to
Figure BDA0002989474380000123
The absolute value of (A) is processed from small to large in sequence if
Figure BDA0002989474380000124
If the absolute value of (a) is negative, preventive maintenance is performed before the workpiece j starts to be machined;
s4, defining a population structure, calculating the fitness value of each individual in the population, setting the best three individuals in the wolf group as alpha, beta and gamma wolfs, and setting the rest wolfs as omega wolfs;
s5, calculating a learning factor epsilon based on weight1、ε2、ε3All ω wolves update their positions based on the weight-based learning factor and the position information of α, β, and γ wolves;
s6, updating the population;
s7, increasing a neighborhood searching mechanism based on probability, and generating a random number p between 0 and 1 for each individual in the wolf group i1,2, N, judge piWhether epsilon is not more than epsilon is true, if yes, performing neighborhood search on the ith individual, and if not, retaining the position information of the original individual;
s8, updating the population;
s9, defining a population structure, calculating the fitness value of each individual in the population, setting the best three individuals in the wolf group as alpha, beta and gamma wolfs, and setting the rest wolfs as omega wolfs;
s10, making t equal to t +1, updating the iteration parameter a, and judging that t is less than or equal to tmaxIf not, the step S11 is executed, otherwise, the step S5 is executed again;
and S11, finishing algorithm execution, and outputting the position of the global optimal solution alpha wolf, the fitness value of the global optimal solution alpha wolf and a production and maintenance scheduling scheme.
It can be seen that the production and maintenance scheduling method based on the improved grayling algorithm provided by the embodiment of the invention includes the steps of firstly randomly generating N one-dimensional vectors for workpieces in the production and maintenance process to form an initial solution of the grayling algorithm, then improving iteration parameters and an iteration mode in the original grayling algorithm, simultaneously adding a neighborhood search mechanism based on probability to optimize the original grayling algorithm, finally inputting the initial solution into the improved grayling algorithm to solve a global optimal solution, and performing collaborative scheduling on the production and maintenance by utilizing a workpiece processing sequence and a maintenance opportunity scheme corresponding to the global optimal solution. The improved wolf algorithm enhances the searching capability of the wolf colony, ensures the updating efficiency of the wolf colony, not only improves the diversity of the colony, but also enhances the convergence capability at the end of the algorithm to a certain extent, solves the problem that the prior art can not carry out cooperative scheduling on production and maintenance when a plurality of influence factors are considered simultaneously, has high efficiency and accuracy in cooperative scheduling, improves the reliability of machine operation, and reduces the operation cost of enterprises.
In the method of the embodiment of the invention, in order to improve the global search capability of the gray wolf algorithm in the iterative process and to make the solving of the gray wolf algorithm more accurate, the iterative parameters and the iterative mode of the gray wolf algorithm need to be improved, on one hand, the iterative parameter a in the gray wolf algorithm is improved, so that the attenuation of the improved iterative parameter a in the early stage of the algorithm iteration is slower, the global search capability of the gray wolf algorithm in the iterative process is improved, and the later iterative parameter a accelerates the attenuation, thereby ensuring the convergence of the algorithm; a preferred way to do this is to use the iteration parameter a as follows:
Figure BDA0002989474380000131
wherein t is (1, 2, 3, …, t)max) Representing the current number of iterations, tmaxRepresenting the maximum number of iterations;
on the other hand, the learning factor in the gray wolf algorithm is improved, and the learning factor epsilon based on weight is designed1、ε2、ε3The learning rate of the wolf group to alpha wolf with higher fitness is higher, the solving of the gray wolf algorithm is more accurate, and a better processing mode is that the learning factor epsilon based on the weight is1、ε2、ε3Expressed by the following formula:
Figure BDA0002989474380000141
Figure BDA0002989474380000142
Figure BDA0002989474380000143
wherein epsilon1、ε2、ε3Learning factors of omega wolf to alpha, beta and gamma wolf respectively; xα、Xβ、XγRepresent the positions of alpha, beta and gamma wolves, respectively; f (X)α)、f(Xβ)、f(Xγ) Respectively, the fitness values of alpha, beta and gamma wolves.
In practice, in order to enhance the global search capability of the grayish wolf algorithm, the present invention adds a domain search mechanism based on probability, so that the wolf colony will search the neighborhood with a certain probability after updating the location, and a preferred processing manner at this time is that the S7 includes:
s71: inputting a wolf group individual
Figure BDA0002989474380000144
Generating a random probability p for the individuali；
S72: if random probability piIf the probability is less than the neighborhood searching probability epsilon, the step S73 is entered, otherwise, the input solution is reserved;
s73: randomly generating 3 integers d, b and c between [1 and n ] which are not equal to each other, wherein n represents the number of workpieces;
s74: switching
Figure BDA0002989474380000145
And
Figure BDA0002989474380000146
and is given a value of
Figure BDA0002989474380000147
Is equal to a random number;
s75: calculating the fitness value of the new individual;
s76: judgment of f (X'k)＜f(Xk) If yes, assigning Xk' to Xk and finishing the search; if not, go to step S77;
s77: and judging whether the set maximum searching times is reached, if not, returning to the step S73, and if so, keeping the input solution.
In addition, in order to enhance the global search capability of the grayish wolf algorithm, and finally obtain a more accurate location and fitness value of the globally optimal solution α wolf of the grayish wolf algorithm, and a production and maintenance scheduling scheme, a preferred processing manner is to calculate the fitness value of each individual in the population, including:
step 1: input solution vector
Figure BDA0002989474380000151
Step 2: reading the decision variables according to the following decoding rules, the work piece according to
Figure BDA0002989474380000152
The absolute value of (A) is processed from small to large in sequence if
Figure BDA0002989474380000153
If negative, preventive maintenance is performed before the workpiece j begins to be machined;
Figure BDA0002989474380000154
Figure BDA0002989474380000155
and step 3: calculating the virtual working life of the machine when the workpiece at each position starts to be machined and finishes to be machined according to the following recursion formula;
Figure BDA0002989474380000156
Figure BDA0002989474380000157
representing the virtual service life of the machine at the start of machining the workpiece in the i-th position;
Figure BDA0002989474380000158
representing the virtual work-life of the machine at the end of the machining of the workpiece in the i-th position; p is a radical of[i]Indicating the processing time of the workpiece at the ith position;
and 4, step 4: calculating the expected failure times of the workpieces at all positions in the machining process;
Figure BDA0002989474380000159
Figure BDA00029894743800001510
indicating the number of preventive maintenance operations the machine undergoes at the start of processing the workpiece at the ith position; wherein m is the number of preventive maintenance times the machine experienced at T-0; eta are provided for each of the first and second planes,β is a parameter in the failure rate function;
and 5: calculating the expected finishing time of the workpiece at each position;
Figure BDA00029894743800001511
E(N[1]) Indicating the expected number of times of machine failure of the workpiece at the ith position in the machining process; e (N)[i]) Representing a desired finish time of the workpiece at the ith position;
step 6: calculating the fitness according to the following formula;
Figure BDA0002989474380000161
clrepresents the production cost per unit time; w is ajRepresenting the unit postponed penalty cost of the workpiece j; c. CpRepresents the cost of a preventive maintenance activity; c. CrRepresents the cost of a corrective maintenance activity at one time; e (T)[i]) Indicating the expected delay time of the workpiece at the ith position.
The following explains a specific implementation procedure of an embodiment of the present invention in conjunction with detailed descriptions of steps S1-S11.
Fig. 1 is a flowchart of a production and maintenance scheduling method based on an improved grey wolf algorithm of the present invention, and referring to fig. 1, a specific process of the production and maintenance scheduling method based on the improved grey wolf algorithm includes:
s1, initializing the input parameters of the algorithm, including the number n of the workpieces and the delivery date d of the workpiecesjDelay cost per unit time w of workpiecejUnit production cost clTime t required for preventive maintenance activitiespAnd cost cpTime t required for a corrective maintenance activityrAnd cost crVirtual working life of the machine at its initial moment
Figure BDA0002989474380000162
And the number of preventive maintenance passes m.
S2, setting execution parameters of the algorithm, wherein the execution parameters comprise the number t of previous iterations as 1 and the maximum number t of iterationsmaxNeighborhood search probability ε, neighborhood maximum search times smaxAccording to an iteration parameter a which decreases nonlinearly.
And improving an iteration parameter a in the original gray wolf algorithm, and setting the iteration parameter a as the iteration parameter a reduced according to nonlinearity. In the original gray wolf optimization algorithm (GWO), the parameter a decreases linearly from 2 to 0 in an iterative process, and the fluctuation range of A is [ -a, a [ -a]. When the number of iterations reaches
Figure BDA0002989474380000163
When the value of | a | is constantly less than 1, the wolf pack is forced to start to get closer to α, β, and γ, which results in a reduction in the global search capability of the entire graywolf algorithm. In this embodiment, the iteration parameter a is set to be a non-linearly decreasing iteration parameter a:
Figure BDA0002989474380000171
wherein t is (1, 2, 3, …, t)max) Representing the current iteration number; t is tmaxThe maximum iteration number is represented, the attenuation of the iteration parameter a with nonlinear reduction is slow in the early stage of the iteration of the algorithm, the global search capability of the algorithm in the iteration process is improved, the attenuation of the iteration parameter a in the later stage is accelerated, and the convergence of the algorithm is guaranteed. Referring to fig. 2, the iteration parameter a in the original grayish wolf algorithm is linearly decreased along with the iteration of the algorithm, and when the iteration number reaches tmaxAt/2, all wolves start to close towards alpha, beta and gamma wolves, and the newly defined iteration parameter a is compared with the original iteration parameter a, when the iteration number reaches 2tmaxAt/3, all wolves start to converge towards alpha, beta and gamma wolves, and the newly defined iterative parameter a essentially expands the time of the global search of the wolves.
S3, initializing the population, randomly generating N one-dimensional vectors as the initial solution of the algorithm, wherein each one-dimensional vector represents the position of a wolf, and the position of the kth wolf is defined as
Figure BDA0002989474380000172
1,2, N, wherein
Figure BDA0002989474380000173
For any real number, the work piece is according to
Figure BDA0002989474380000174
The absolute value of (A) is processed from small to large in sequence if
Figure BDA0002989474380000175
If the absolute value of (a) is negative, preventive maintenance is performed before the workpiece j starts to be machined.
And S4, defining a population structure, calculating the fitness value of each individual in the population, setting the best three individuals in the wolf group as alpha, beta and gamma wolfs, and setting the rest wolfs as omega wolfs.
Fig. 3 is a schematic diagram of the production and maintenance process of the embodiment of the present invention, referring to fig. 3, the total cost of equipment production and maintenance is minimized by making decisions on the machining sequence of workpieces with different delivery dates and making decisions on the maintenance timing of the machine, and the minimized total cost of equipment production and maintenance is used as an objective function for obtaining the fitness value. Among them, the workpiece at the i-1 th position (i.e., (i-1) th jobin the figure), the workpiece at the i-th position (ith jobi), the workpiece at the i +1 th position (i +1) th jobi in the figure), Preventive Maintenance (PM), fault maintenance (CM), and virtual service life (virtual age). Specifically, the process of calculating the fitness value of each individual in the population includes the following steps 1-6:
step 1: input solution vector
Figure BDA0002989474380000181
Step 2: reading the decision variables according to the following decoding rules, the work piece according to
Figure BDA0002989474380000182
The absolute value of (A) is processed from small to large in sequence if
Figure BDA0002989474380000183
If the absolute value of (a) is negative, preventive maintenance is performed before the workpiece j starts to be machined;
Figure BDA0002989474380000184
Figure BDA0002989474380000185
and step 3: calculating the virtual working life of the machine when the workpiece at each position starts to be machined and finishes to be machined according to the following recursion formula;
Figure BDA0002989474380000186
Figure BDA0002989474380000187
represents the virtual service life of the machine at the start of machining the workpiece in the i-th position (i.e. the length of time the machine has been working since the last preventive maintenance);
Figure BDA0002989474380000188
representing the virtual work-life of the machine at the end of the machining of the workpiece in the i-th position; p is a radical of[i]Indicating the processing time of the workpiece at the ith position;
and 4, step 4: calculating the expected failure times of the workpieces at all positions in the machining process;
Figure BDA0002989474380000189
Figure BDA00029894743800001810
indicating the number of preventive maintenance operations experienced by the machine when starting to process the workpiece at the ith position; wherein m is T-0 time machineNumber of preventive maintenance passes; η, β are parameters in the failure rate function;
and 5: calculating the expected finishing time of the workpiece at each position;
Figure BDA0002989474380000191
E(N[1]) Indicating the expected number of times of machine failure of the workpiece at the ith position in the machining process; e (N)[i]) Representing a desired finish time of the workpiece at the ith position;
step 6: calculating the fitness according to the following formula;
Figure BDA0002989474380000192
clrepresents the production cost per unit time; w is ajRepresenting the unit postponed penalty cost of the workpiece j; c. CpRepresents the cost of a preventive maintenance activity; c. CrRepresents the cost of a corrective maintenance activity at one time; e (T)[i]) Indicating the expected delay time of the workpiece at the ith position.
S5, calculating a learning factor epsilon based on weight1、ε2、ε3All ω wolves update their positions based on the weight-based learning factor and the position information of α, β, and γ wolves.
In the original gray wolf optimization algorithm (GWO), the learning rates of wolf clusters for alpha, beta, and gamma wolfs are the same 1/3. In practice, however, the learning rate of the wolf group is higher for the α wolf with higher fitness, so the weight-based learning factor is defined as follows:
Figure BDA0002989474380000193
Figure BDA0002989474380000194
Figure BDA0002989474380000195
wherein epsilon1、ε2、ε3Learning factors of omega wolf to alpha, beta and gamma wolf respectively; xα、Xβ、XγRepresent the positions of alpha, beta and gamma wolves, respectively; f (X)α)、f(Xβ)、f(Xγ) Respectively, the fitness values of alpha, beta and gamma wolves.
And S6, updating the population.
S7, increasing a neighborhood searching mechanism based on probability, and generating a random number p between 0 and 1 for each individual in the wolf group i1,2, N, judge piAnd whether epsilon is more than or equal to epsilon is established, if yes, performing neighborhood search on the ith individual, and if not, keeping the position information of the original individual.
In the original gray wolf optimization algorithm (GWO), wolf clusters search for prey only according to the guidance of alpha, beta and gamma wolfs, so the algorithm is more dependent on the initial solution and the whole algorithm is easy to fall into local optimum. To enhance the global search capability of the algorithm, a neighborhood structure is defined. After updating the position, the wolf pack searches the neighborhood. Specifically, the method comprises the following steps:
s71: inputting a wolf group individual
Figure BDA0002989474380000201
Generating a random probability p for the individuali；
S72: if random probability piIf the probability is less than the neighborhood searching probability epsilon, the step S73 is entered, otherwise, the input solution is reserved;
s73: randomly generating 3 integers d, b and c between [1, n ] which are not equal to each other, wherein n represents the number of the workpieces, namely randomly selecting three workpieces d, b and c from 1 to n workpieces.
S74: switching
Figure BDA0002989474380000202
And
Figure BDA0002989474380000203
and is given a value of
Figure BDA0002989474380000204
The method is equal to a random number, namely the positions of the d and b workpieces are exchanged, and the workpiece c is changed to a random position, so that the main purpose is to expand the search range of the wolf colony and jump out the local optimum through the disturbance of the step.
S75: calculating the fitness value of the new individual;
s76: judgment of f (X'k)＜f(Xk) If yes, assigning Xk' to Xk and finishing the search; if not, go to step S77;
s77: and judging whether the set maximum searching times is reached, if not, returning to the step S73, and if so, keeping the input solution.
And S8, updating the population.
And S9, defining a population structure, calculating the fitness value of each individual in the population, setting the best three individuals in the wolf group as alpha, beta and gamma wolfs, and setting the rest wolfs as omega wolfs.
The fitness value of each individual was calculated in the same manner as in the step of S4.
S10, making t equal to t +1, updating the iteration parameter a, and judging that t is less than or equal to tmaxIf not, the step S11 is executed, otherwise, the step S5 is executed again;
and S11, finishing algorithm execution, and outputting the position of the global optimal solution alpha wolf, the fitness value of the global optimal solution alpha wolf and a production and maintenance scheduling scheme.
The global optimal solution (namely the position of the output alpha wolf) obtained through the iterative process is decoded to obtain the optimal processing sequence and the machine maintenance decision of the workpiece, so that the minimum total cost of equipment production and maintenance can be realized.
Therefore, the whole process of the production and maintenance scheduling method based on the improved wolf algorithm is completed.
Example 2:
in a second aspect, the present invention further provides a production and maintenance scheduling system based on the improved grayling algorithm, including:
a processing unit for performing the steps of:
s1, initializing the input parameters of the algorithm, including the number n of the workpieces and the delivery date d of the workpiecesjDelay cost per unit time w of workpiecejUnit production cost clTime t required for preventive maintenance activitiespAnd cost cpTime t required for a corrective maintenance activityrAnd cost crVirtual working life of the machine at its initial moment
Figure BDA0002989474380000211
And the number of preventive maintenance passes m;
s2, setting execution parameters of the algorithm, wherein the execution parameters comprise the number t of previous iterations as 1 and the maximum number t of iterationsmaxNeighborhood search probability ε, neighborhood maximum search times smaxAccording to the iteration parameter a of the nonlinear reduction;
s3, initializing the population, randomly generating N one-dimensional vectors as the initial solution of the algorithm, wherein each one-dimensional vector represents the position of a wolf, and the position of the kth wolf is defined as
Figure BDA0002989474380000212
1,2, N, wherein
Figure BDA0002989474380000213
For any real number, the work piece is according to
Figure BDA0002989474380000214
The absolute value of (A) is processed from small to large in sequence if
Figure BDA0002989474380000222
If the absolute value of (a) is negative, preventive maintenance is performed before the workpiece j starts to be machined;
s4, defining a population structure, calculating the fitness value of each individual in the population, setting the best three individuals in the wolf group as alpha, beta and gamma wolfs, and setting the rest wolfs as omega wolfs;
s5, calculating a learning factor epsilon based on weight1、ε2、ε3All ω wolves update their positions based on the weight-based learning factor and the position information of α, β, and γ wolves;
s6, updating the population;
s7, increasing a neighborhood searching mechanism based on probability, and generating a random number p between 0 and 1 for each individual in the wolf group i1,2, N, judge piWhether epsilon is not more than epsilon is true, if yes, performing neighborhood search on the ith individual, and if not, retaining the position information of the original individual;
s8, updating the population;
s9, defining a population structure, calculating the fitness value of each individual in the population, setting the best three individuals in the wolf group as alpha, beta and gamma wolfs, and setting the rest wolfs as omega wolfs;
s10, making t equal to t +1, updating the iteration parameter a, and judging that t is less than or equal to tmaxIf not, the step S11 is executed, otherwise, the step S5 is executed again;
s11, finishing the algorithm execution;
and the output unit is used for outputting the position of the global optimal solution alpha wolf, the fitness value of the global optimal solution alpha wolf and a production and maintenance scheduling scheme.
Optionally, the iteration parameter a during the execution process of the processing unit may be represented by the following formula:
Figure BDA0002989474380000221
wherein t is (1, 2, 3, …, t)max) Representing the current number of iterations, tmaxThe maximum number of iterations is indicated.
Optionally, epsilon in the execution process of the processing unit1、ε2、ε3Expressed by the following formula:
Figure BDA0002989474380000231
Figure BDA0002989474380000232
Figure BDA0002989474380000233
wherein epsilon1、ε2、ε3Learning factors of omega wolf to alpha, beta and gamma wolf respectively; xα、Xβ、XγRepresent the positions of alpha, beta and gamma wolves, respectively; f (X)α)、f(Xβ)、f(Xγ) Respectively, the fitness values of alpha, beta and gamma wolves.
Optionally, the executing of step S7 by the processing unit includes:
s71: inputting a wolf group individual
Figure BDA0002989474380000234
Generating a random probability p for the individuali；
S72: if random probability piIf the probability is less than the neighborhood searching probability epsilon, the step S73 is entered, otherwise, the input solution is reserved;
s73: randomly generating 3 integers d, b and c between [1 and n ] which are not equal to each other, wherein n represents the number of workpieces;
s74: switching
Figure BDA0002989474380000235
And
Figure BDA0002989474380000236
and is given a value of
Figure BDA0002989474380000237
Is equal to a random number;
s75: calculating the fitness value of the new individual;
s76: judgment of f (X'k)＜f(Xk) If true, assign Xk' to Xk, and ending the search; if not, go to step S77;
s77: and judging whether the set maximum searching times is reached, if not, returning to the step S73, and if so, keeping the input solution.
Optionally, the calculating, by the processing unit, the fitness value of each individual in the population during execution includes:
step 1: input solution vector
Figure BDA0002989474380000238
Step 2: reading the decision variables according to the following decoding rules, the work piece according to
Figure BDA0002989474380000239
The absolute value of (A) is processed from small to large in sequence if
Figure BDA00029894743800002310
If negative, preventive maintenance is performed before the workpiece j begins to be machined;
Figure BDA0002989474380000241
Figure BDA0002989474380000242
and step 3: calculating the virtual working life of the machine when the workpiece at each position starts to be machined and finishes to be machined according to the following recursion formula;
Figure BDA0002989474380000243
Figure BDA0002989474380000244
represents the virtual service life of the machine at the start of machining the workpiece in the i-th position (i.e. the length of time the machine has been working since the last preventive maintenance);
Figure BDA0002989474380000245
representing the virtual work-life of the machine at the end of the machining of the workpiece in the i-th position; p is a radical of[i]Indicating the processing time of the workpiece at the ith position;
and 4, step 4: calculating the expected failure times of the workpieces at all positions in the machining process;
Figure BDA0002989474380000246
Figure BDA0002989474380000247
indicating the number of preventive maintenance operations the machine undergoes at the start of processing the workpiece at the ith position; wherein m is the number of preventive maintenance times the machine experienced at T-0; η, β are parameters in the failure rate function;
and 5: calculating the expected finishing time of the workpiece at each position;
Figure BDA0002989474380000248
E(N[1]) Indicating the expected number of times of machine failure of the workpiece at the ith position in the machining process; e (N)[i]) Representing a desired finish time of the workpiece at the ith position;
step 6: calculating the fitness according to the following formula;
Figure BDA0002989474380000249
clrepresents the production cost per unit time; w is ajRepresenting the unit postponed penalty cost of the workpiece j; c. CpRepresents the cost of a preventive maintenance activity; c. CrRepresents the cost of a corrective maintenance activity at one time; e (T)[i]) Indicating the expected delay time of the workpiece at the ith position.
It can be understood that, the production and maintenance scheduling system based on the improved grey wolf algorithm provided in the embodiment of the present invention corresponds to the production and maintenance scheduling method based on the improved grey wolf algorithm, and the explanation, examples, and beneficial effects of the relevant contents thereof may refer to the corresponding contents in the production and maintenance scheduling method based on the improved grey wolf algorithm, and are not described herein again.
In summary, compared with the prior art, the method has the following beneficial effects:
1. the invention relates to a production and maintenance scheduling method and a system based on an improved wolf algorithm. The improved wolf algorithm enhances the searching capability of the wolf colony, ensures the updating efficiency of the wolf colony, not only improves the diversity of the colony, but also enhances the convergence capability at the end of the algorithm to a certain extent, solves the problem that the prior art can not carry out cooperative scheduling on production and maintenance when a plurality of influence factors are considered simultaneously, has high efficiency and accuracy in cooperative scheduling, improves the reliability of machine operation, and reduces the operation cost of enterprises.
2. The iterative parameter and the iterative mode of the gray wolf algorithm are improved, on one hand, the iterative parameter a in the gray wolf algorithm is improved, the improved iterative parameter a is slowly attenuated in the early stage of the algorithm iteration, the global search capability of the algorithm in the iteration process is improved, the later iterative parameter a is attenuated in an accelerated manner, and the convergence of the algorithm is ensured; on the other hand, the learning factor in the gray wolf algorithm is improved, and the learning factor epsilon based on weight is designed1、ε2、ε3The learning rate of the wolf group to alpha wolfs with higher fitness is higher, and the solving of the grey wolf algorithm is more accurate;
3. the invention increases a domain searching mechanism based on probability, so that the wolf pack can search the neighborhood with certain probability after updating the position, thereby enhancing the global searching capability of the wolf algorithm.
It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (10)

1. A production and maintenance scheduling method based on an improved Grey wolf algorithm is characterized by comprising the following steps:
s1, initializing the input parameters of the algorithm, including the number n of the workpieces and the delivery date d of the workpiecesjDelay cost per unit time w of workpiecejUnit production cost clTime t required for preventive maintenance activitiespAnd cost cpTime t required for a corrective maintenance activityrAnd cost crMachine for the production of a plastic materialVirtual working age of initial moment
Figure FDA0002989474370000011
And the number of preventive maintenance passes m;
s2, setting execution parameters of the algorithm, wherein the execution parameters comprise the number t of previous iterations as 1 and the maximum number t of iterationsmaxNeighborhood search probability ε, neighborhood maximum search times smaxAccording to the iteration parameter a of the nonlinear reduction;
s3, initializing the population, randomly generating N one-dimensional vectors as the initial solution of the algorithm, wherein each one-dimensional vector represents the position of a wolf, and the position of the kth wolf is defined as
Figure FDA0002989474370000012
Wherein
Figure FDA0002989474370000013
For any real number, the work piece is according to
Figure FDA0002989474370000014
The absolute value of (A) is processed from small to large in sequence if
Figure FDA0002989474370000015
If the absolute value of (a) is negative, preventive maintenance is performed before the workpiece j starts to be machined;
s4, defining a population structure, calculating the fitness value of each individual in the population, setting the best three individuals in the wolf group as alpha, beta and gamma wolfs, and setting the rest wolfs as omega wolfs;
s5, calculating a learning factor epsilon based on weight1、ε2、ε3All ω wolves update their positions based on the weight-based learning factor and the position information of α, β, and γ wolves;
s6, updating the population;
s7, increasing a neighborhood searching mechanism based on probability, and generating a random number p between 0 and 1 for each individual in the wolf groupi1,2, N, judge piWhether epsilon is not more than epsilon is true, if yes, performing neighborhood search on the ith individual, and if not, retaining the position information of the original individual;
s8, updating the population;
s9, defining a population structure, calculating the fitness value of each individual in the population, setting the best three individuals in the wolf group as alpha, beta and gamma wolfs, and setting the rest wolfs as omega wolfs;
s10, making t equal to t +1, updating the iteration parameter a, and judging that t is less than or equal to tmaxIf not, the step S11 is executed, otherwise, the step S5 is executed again;
and S11, finishing algorithm execution, and outputting the position of the global optimal solution alpha wolf, the fitness value of the global optimal solution alpha wolf and a production and maintenance scheduling scheme.
2. The method of claim 1, wherein the iteration parameter a is represented by the following formula:
Figure FDA0002989474370000021
wherein t is (1, 2, 3, …, t)max) Representing the current number of iterations, tmaxThe maximum number of iterations is indicated.
3. The method of claim 1, wherein epsilon1、ε2、ε3Expressed by the following formula:
Figure FDA0002989474370000022
Figure FDA0002989474370000023
Figure FDA0002989474370000024
wherein epsilon1、ε2、ε3Learning factors of omega wolf to alpha, beta and gamma wolf respectively; xα、Xβ、XγRepresent the positions of alpha, beta and gamma wolves, respectively; f (X)α)、f(Xβ)、f(Xγ) Respectively, the fitness values of alpha, beta and gamma wolves.
4. The method of claim 1, wherein the S7 includes:
s71: inputting a wolf group individual
Figure FDA0002989474370000025
Generating a random probability p for the individuali；
S72: if random probability piIf the probability is less than the neighborhood searching probability epsilon, the step S73 is entered, otherwise, the input solution is reserved;
s73: randomly generating 3 integers d, b and c between [1 and n ] which are not equal to each other, wherein n represents the number of workpieces;
s74: switching
Figure FDA0002989474370000031
And
Figure FDA0002989474370000032
and is given a value of
Figure FDA0002989474370000033
Is equal to a random number;
s75: calculating the fitness value of the new individual;
s76: judgment of f (X'k)＜f(Xk) If yes, assigning Xk' to Xk and finishing the search; if not, go to step S77;
s77: and judging whether the set maximum searching times is reached, if not, returning to the step S73, and if so, keeping the input solution.
5. The method of claim 1, wherein calculating the fitness value for each individual in the population comprises:
step 1: input solution vector
Figure FDA0002989474370000034
Step 2: reading the decision variables according to the following decoding rules, the work piece according to
Figure FDA0002989474370000035
The absolute value of (A) is processed from small to large in sequence if
Figure FDA0002989474370000036
If negative, preventive maintenance is performed before the workpiece j begins to be machined;
Figure FDA0002989474370000037
Figure FDA0002989474370000038
and step 3: calculating the virtual working life of the machine when the workpiece at each position starts to be machined and finishes to be machined according to the following recursion formula;
Figure FDA0002989474370000039
Figure FDA0002989474370000041
representing the virtual service life of the machine at the start of machining the workpiece in the i-th position;
Figure FDA0002989474370000042
indicating the workpiece in the i-th positionThe virtual working life of the machine at the end of the process; p is a radical of[i]Indicating the processing time of the workpiece at the ith position;
and 4, step 4: calculating the expected failure times of the workpieces at all positions in the machining process;
Figure FDA0002989474370000043
Figure FDA0002989474370000044
indicating the number of preventive maintenance operations the machine undergoes at the start of processing the workpiece at the ith position; wherein m is the number of preventive maintenance times the machine experienced at T-0; η, β are parameters in the failure rate function;
and 5: calculating the expected finishing time of the workpiece at each position;
Figure FDA0002989474370000045
E(N[1]) Indicating the expected number of times of machine failure of the workpiece at the ith position in the machining process; e (N)[i]) Representing a desired finish time of the workpiece at the ith position;
step 6: calculating the fitness according to the following formula;
Figure FDA0002989474370000046
clrepresents the production cost per unit time; w is ajRepresenting the unit postponed penalty cost of the workpiece j; c. CpRepresents the cost of a preventive maintenance activity; c. CrRepresents the cost of a corrective maintenance activity at one time; e (T)[i]) Indicating the expected delay time of the workpiece at the ith position.
6. A production and maintenance scheduling system based on an improved graying algorithm, the system comprising:
a processing unit for performing the steps of:
s1, initializing the input parameters of the algorithm, including the number n of the workpieces and the delivery date d of the workpiecesjDelay cost per unit time w of workpiecejUnit production cost clTime t required for preventive maintenance activitiespAnd cost cpTime t required for a corrective maintenance activityrAnd cost crVirtual working life of the machine at its initial moment
Figure FDA0002989474370000051
And the number of preventive maintenance passes m;
s2, setting execution parameters of the algorithm, wherein the execution parameters comprise the number t of previous iterations as 1 and the maximum number t of iterationsmaxNeighborhood search probability ε, neighborhood maximum search times smaxAccording to the iteration parameter a of the nonlinear reduction;
s3, initializing the population, randomly generating N one-dimensional vectors as the initial solution of the algorithm, wherein each one-dimensional vector represents the position of a wolf, and the position of the kth wolf is defined as
Figure FDA0002989474370000052
Wherein
Figure FDA0002989474370000053
For any real number, the work piece is according to
Figure FDA0002989474370000054
The absolute value of (A) is processed from small to large in sequence if
Figure FDA0002989474370000055
If the absolute value of (a) is negative, preventive maintenance is performed before the workpiece j starts to be machined;
s4, defining a population structure, calculating the fitness value of each individual in the population, setting the best three individuals in the wolf group as alpha, beta and gamma wolfs, and setting the rest wolfs as omega wolfs;
s5, calculating a learning factor epsilon based on weight1、ε2、ε3All ω wolves update their positions based on the weight-based learning factor and the position information of α, β, and γ wolves;
s6, updating the population;
s7, increasing a neighborhood searching mechanism based on probability, and generating a random number p between 0 and 1 for each individual in the wolf groupi1,2, N, judge piWhether epsilon is not more than epsilon is true, if yes, performing neighborhood search on the ith individual, and if not, retaining the position information of the original individual;
s8, updating the population;
s9, defining a population structure, calculating the fitness value of each individual in the population, setting the best three individuals in the wolf group as alpha, beta and gamma wolfs, and setting the rest wolfs as omega wolfs;
s10, making t equal to t +1, updating the iteration parameter a, and judging that t is less than or equal to tmaxIf not, the step S11 is executed, otherwise, the step S5 is executed again;
s11, finishing the algorithm execution;
and the output unit is used for outputting the position of the global optimal solution alpha wolf, the fitness value of the global optimal solution alpha wolf and a production and maintenance scheduling scheme.
7. The system of claim 6, wherein the iteration parameter a during execution by the processing unit is expressed by the following formula:
Figure FDA0002989474370000061
wherein t is (1, 2, 3, …, t)max) Representing the current number of iterations, tmaxThe maximum number of iterations is indicated.
8. The system of claim 6, wherein the processing unit executes1、ε2、ε3Expressed by the following formula:
Figure FDA0002989474370000062
Figure FDA0002989474370000063
Figure FDA0002989474370000064
wherein epsilon1、ε2、ε3Learning factors of omega wolf to alpha, beta and gamma wolf respectively; xα、Xβ、XγRepresent the positions of alpha, beta and gamma wolves, respectively; f (X)α)、f(Xβ)、f(Xγ) Respectively, the fitness values of alpha, beta and gamma wolves.
9. The system of claim 6, wherein the processing unit performing step S7 includes:
s71: inputting a wolf group individual
Figure FDA0002989474370000065
Generating a random probability p for the individuali；
S72: if random probability piIf the probability is less than the neighborhood searching probability epsilon, the step S73 is entered, otherwise, the input solution is reserved;
s73: randomly generating 3 integers d, b and c between [1 and n ] which are not equal to each other, wherein n represents the number of workpieces;
s74: switching
Figure FDA0002989474370000071
And
Figure FDA0002989474370000072
value of (A)And make an order
Figure FDA0002989474370000073
Is equal to a random number;
s75: calculating the fitness value of the new individual;
s76: judgment of f (X'k)＜f(Xk) If yes, assigning Xk' to Xk and finishing the search; if not, go to step S77;
s77: and judging whether the set maximum searching times is reached, if not, returning to the step S73, and if so, keeping the input solution.
10. The system of claim 6, wherein the processing unit, in performing the calculating the fitness value for each individual in the population, comprises:
step 1: input solution vector
Figure FDA0002989474370000074
Step 2: reading the decision variables according to the following decoding rules, the work piece according to
Figure FDA0002989474370000075
The absolute value of (A) is processed from small to large in sequence if
Figure FDA0002989474370000076
If negative, preventive maintenance is performed before the workpiece j begins to be machined;
Figure FDA0002989474370000077
Figure FDA0002989474370000078
and step 3: calculating the virtual working life of the machine when the workpiece at each position starts to be machined and finishes to be machined according to the following recursion formula;
Figure FDA0002989474370000079
Figure FDA00029894743700000710
representing the virtual service life of the machine at the start of machining the workpiece in the i-th position;
Figure FDA00029894743700000711
representing the virtual working life of the machine at the end of the machining of the workpiece in the i-th position; p is a radical of[i]Indicating the processing time of the workpiece at the ith position;
and 4, step 4: calculating the expected failure times of the workpieces at all positions in the machining process;
Figure FDA0002989474370000081
Figure FDA0002989474370000082
indicating the number of preventive maintenance operations the machine undergoes at the start of processing the workpiece at the ith position; wherein m is the number of preventive maintenance times the machine experienced at T-0; η, β are parameters in the failure rate function;
and 5: calculating the expected finishing time of the workpiece at each position;
Figure FDA0002989474370000083
E(N[1]) Indicating the expected number of times of machine failure of the workpiece at the ith position in the machining process; e (N)[i]) Representing a desired finish time of the workpiece at the ith position;
step 6: calculating the fitness according to the following formula;
Figure FDA0002989474370000084
clrepresents the production cost per unit time; w is ajRepresenting the unit postponed penalty cost of the workpiece j; c. CpRepresents the cost of a preventive maintenance activity; c. CrRepresents the cost of a corrective maintenance activity at one time; e (T)[i]) Indicating the expected delay time of the workpiece at the ith position.
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