CN114819355A - Multi-target flexible job shop energy-saving scheduling method based on improved wolf algorithm - Google Patents
Multi-target flexible job shop energy-saving scheduling method based on improved wolf algorithm Download PDFInfo
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Abstract
The invention discloses a multi-target flexible job shop energy-saving scheduling method based on an improved wolf algorithm, which comprises the steps of firstly, constructing a flexible job shop energy-saving scheduling problem model; two-section coding based on natural numbers is adopted; discretizing the continuity problem by adopting a mode based on an LOV rule; introducing the aggregation rate among individuals to obtain an initial population with higher quality; evaluating individuals in the initial population, determining an alpha wolf set, a beta wolf set and a delta wolf set of the decision-making layer individuals according to a proportion, and adding a non-dominant solution into an external archive; by using a dual-mode parallel search mode, the tracking and searching capabilities are dynamically adjusted in the search process, improved tracking operation is introduced, the problem solving precision is improved, variable-field search is adopted in the search mode, the evolution speed is improved, and the local optimal solution is broken through. The invention reasonably arranges the processing sequence of the workpieces on each machine, and provides a better scheduling scheme for production enterprises from the three aspects of minimizing the maximum completion time, the total delay time and the total energy consumption of the system.
Description
Technical Field
The invention belongs to the technical field of load prediction, and particularly relates to a multi-target flexible job shop energy-saving scheduling method based on an improved wolf algorithm.
Background
The scheduling problem of the job shop reasonably arranges the processing sequence of the workpieces on each machine to obtain the expected production performance. Since the problem has strong theoretical and application background, the problem has been widely concerned by researchers at home and abroad since the proposal, and most FJSPs have proved to have NP-difficult characteristics. However, the conventional FJSP only considers economic indicators related to time, quality, cost, and the like, and does not pay attention to energy consumption indicators related to environment and the like, and it is difficult to guide an enterprise to obtain the maximum profit in the true sense.
Disclosure of Invention
The invention aims to provide a multi-target flexible job shop energy-saving scheduling method based on an improved wolf algorithm, and provides a better energy-saving scheduling scheme for production enterprises from the aspects of minimizing the maximum completion time, the total delay time and the total energy consumption of a system.
The technical scheme adopted by the invention is that the multi-target flexible job shop energy-saving scheduling method based on the improved wolf algorithm is implemented according to the following steps:
and 8, finishing the algorithm, outputting an external file, and obtaining the workshop equipment codes and the processing procedure codes through individuals in the external file.
(1) only one workpiece can be processed by one device at a time;
(2) the equipment does not stop once the processing is started in the middle;
(3) sequence constraint exists among the working procedures of the same workpiece, and the next working procedure starts to process after the previous working procedure is finished;
(4) the quality of the workpieces is not divided;
(5) the equipment is idle and does not stop;
(6) the preparation time before the equipment is processed and the time for loading and unloading the workpiece in the processing process are not considered;
(7) the device catastrophic failure condition is not considered.
the energy-saving scheduling problem model of the flexible job shop is constructed by the following objective functions:
f 1 ＝max(C iJi ) (1-1)
ST i(j) ≥CT i(j-1) ,i＝1,2,...n,j＝2,...J i ； (1-5)
x ijk ∈{0,1},i＝1,2,...n,j＝1,2,...J i ,k＝1,2,...m； (1-8)
z ijhgk ∈{0,1},i,h＝1,2,...n,j,g＝1,2,...m (1-9)
the specific process of the step 3 is as follows:
step 3.1, generating a wolf group G according to the formula (3-1) and the formula (3-2), wherein the position of an individual in the wolf group G is represented as S and is represented as follows:
wherein the position component of the individual S
Generated by the following equation:
wherein ub is 100, lb is-100, N is the total number of grey wolves of the group G, N is the total number of the work processes, dim represents the position dimension of the grey wolves, and each position component is
The value is [ -100,100 [)]；
Step 3.2, sequentially arranging according to the position components of the individual S to generate wolf group position vectors WoStruct
To obtain addWork order sequence WolStruct.bta;
randomly selecting equipment with the minimum available processing time as equipment selection codes according to the corresponding procedures of each position in the processing sequence;
step 3.3, taking Chm1, wherein Chm2 is a process processing sequence WolStruct.bta of two wolfsbane individual positions after LOV rule conversion, and calculating the aggregation of individuals in the population, wherein the calculation formula is as follows:
P(Chm1,Chm2)＝S(Chm1,Chm2)/n (3-4)
where Chm1(dim), Chm2(dim) represents the value of two wolsstruct.bta sequences in dimension dim, and when the two values are the same,
take a value of 0, if not equal, then
The value is 1; the value of S is called the Hamming distance; p represents the aggregation rate between the two bodies, and n represents the total number of work processes;
generating initial population individuals and ensuring the position P of each wolf S The specific operation is that > Pcmax is 0.5:
step a) generating a process sequence and machine selection code of an initial individual according to steps 3.1, 3.2;
step b) calculating the aggregation rate between the initial population and the initial population; if the number of the individuals is more than 0.5, storing the individuals into the initial population, otherwise, giving up the individuals;
repeatedly selecting the wolfsbane individuals to perform the steps a) and b) until the initial population number is N.
The specific process of the step 4 is as follows:
step 4.1, finding out the non-dominance optimal solution in the current population to form a first non-dominance optimal solution layer, assigning the grade of the individual to be 1 grade, removing the solutions from the population, finding out a new non-dominance solution from the rest individuals, assigning the grade of the individual to be 2 grades, and so on until all the individuals are graded;
step 4.2, calculating the crowding degree distance of the individuals, carrying out normalization processing, and sorting the individuals according to the non-dominant grade of the individuals in the population and the normalized crowding distance: for any two individuals, the lower ranked individuals rank first; if the two individual grades are the same, comparing the normalized congestion distances of the two individuals, and arranging the individuals with large normalized congestion distances in front;
the crowdedness distance is specifically represented as:
and (3) carrying out normalization processing on the individual crowdedness distance, namely:
P(i) distance ＝(P max -P(i) distance )/(P max -P min ) (4-2)
wherein, by P (i) distance Indicates the crowdedness distance of the individual y (i), p (i) m A function value representing the individual y (i) on the target m; p max And P min The maximum value and the minimum value of the individual crowdedness distance respectively;
selecting the individuals ranked at the top 30% from the population according to the sorting principle, and respectively using the individuals as three wolf sets of alpha, beta and delta to form a decision layer according to the quantity ratio of 1:2: 3;
4.3, adding the individuals with the non-dominance level of 1 into the external files to realize the updating of the external files; and if the number of individuals in the external file is larger than the external file size N', eliminating the individuals with smaller crowdedness until the number of non-dominant solutions is consistent with the external file size.
The specific process of finding the non-dominant optimal solution in step 4.1 is as follows: defining a dominance relationship: for the multi-objective optimization problem, when all target values of the individuals y (i) are better than the target values corresponding to the individuals y (j), defining the individuals y (i) to dominate the individuals y (j), otherwise, the individuals y (i) cannot dominate the individuals y (j);
and comparing the individuals in the population pairwise to obtain a dominance relation between any two individuals, wherein the individuals which are not dominated by other individuals are called non-dominated optimal solutions, and a set formed by the non-dominated optimal solutions is called a non-dominated optimal solution layer.
The specific process of the step 6 is as follows:
defining a tracking probability MR, representing the ratio of the number of individuals in the population to the whole population in the global tracking mode, and a searching probability 1-MR, representing the ratio of the number of individuals in the population to the whole population in the local searching mode, wherein the tracking probability MR is expressed as:
MR＝MR max -(MR max -MR min )×t/t max (6-1)
wherein, MR max And MR min 1 and 0, respectively; t and t max Respectively representing the current iteration times and the maximum iteration times of the algorithm;
selecting the wolf individuals according to the tracking probability MR to perform global tracking operation to obtain new individuals representing equipment codes and procedure code sequencing;
and selecting the Huilus wolf individuals according to the search probability 1-MR to perform local search operation to obtain new individuals aiming at equipment codes and process code sequencing.
The global tracking operation process is as follows:
introducing a discrete inter-individual distance formula, wherein the distance is expressed as the difference between two individuals and is expressed as:
the distance formula is normalized, namely:
wherein, with D ij Representing the discrete distance of the individuals i and j, n representing the number of workpieces, CT ik Representing the completion of a workpiece k in an individual iWorking time; d ijmax And D ijmin Respectively, the maximum and minimum of the discrete inter-individual distances;
determining information communication of alpha, beta and delta of the individual at the decision layer according to the distance between the individual and the optimal individual, wherein the information communication is expressed as follows:
wherein, the first and the second end of the pipe are connected with each other,
indicating that the individual i communicates with the individual alpha,
indicating that the individual i and the individual beta carry out information communication,
indicating that the individual i communicates information with the individual delta.
The content of the information communication between the individual i and the individual alpha, beta or delta comprises the information communication between the process code sorting part and the equipment selecting part;
the information exchange of the procedure coding sequencing part adopts a POX crossing mode, and the specific process comprises the following steps:
a, generating a random integer R (R is more than or equal to 1 and less than or equal to n), wherein n is the total number of workpieces;
step b, parent individual P 1 Copying the workpieces with the workpiece serial numbers less than or equal to R to the offspring individuals C 1 (ii) a Parent individual P 2 Copying the workpieces with the workpiece serial numbers larger than R to the offspring individuals C 2 Reserving the position of the device, and copying the corresponding device number to the corresponding position;
step c, copying the parent P 1 Not present in offspring C 2 To C of workpiece serial number 2 Copying the parent P 2 Not present in C 1 To child C 1 And preserving the sequence of the new individuals, and copying the equipment numbers to corresponding positions to obtain new individuals sorted based on procedure codes;
the tracking operation of the equipment selection part adopts a two-point crossing mode, and the following steps are specifically adopted:
for two new individuals completing the process coding information exchange, randomly setting two cross points, exchanging the equipment serial numbers corresponding to the processes of the parent individuals between the set two cross points, and obtaining new individuals based on process sequencing and equipment selection;
and selecting the superior individuals from the two new individuals based on the process sequence and equipment according to the domination relationship to serve as the new individuals, and if the two individuals are not dominated with each other, selecting one of the two individuals as the new individual.
The specific process of the local search operation is as follows:
3 neighborhood structures are designed aiming at individual process coding and equipment coding:
(1) neighborhood structure N 1 : optionally selecting two positions in the coding section of the process sequencing part, and carrying out exchange operation on elements between the two selected positions;
(2) neighborhood structure N 2 : optionally selecting two elements in a code segment of the procedure sorting part, and inserting the element positioned at the back of the two selected elements into the position in front of the element positioned at the front;
(3) neighborhood structure N 3 : selecting an element in the code segment of the machine distribution part, wherein the number of the machinable devices of the element is more than 1, and the machining device corresponding to the element is changed into the device with the shortest centralized machining time of the selectable machining devices;
based on the neighborhood structure, the specific steps of local search are as follows:
step 1), taking the current generation individual performing the variable domain search as an initial solution X', and setting a threshold value delta > 0, gamma being 1, rho being 1 and a termination condition gamma max ；
Step 2), rho represents a variable of 0 or 1 and is used for deciding which combined field search is executed by X', and N is selected in an equal probability mode during each iteration 1 ∪N 3 And N 2 ∪N 3 One of them is to perform a neighborhood search operation, if ρ is 1, X ″, N 1 (X')∪N 3 (X'); if ρ is 0, X ″N 2 (X')∪N 3 (X'), (u) means that two operations are performed;
step 3), judging whether C is satisfied max (X″)-C max (X')≤δ，C max Representing a maximum completion time; if so, then X '═ X'; otherwise, setting rho ═ rho-1 |;
step 4), enabling gamma to be gamma +1, and judging whether gamma is more than gamma or not max (ii) a If yes, turning to step 5); otherwise, go to step 2);
and 5) finishing local search, and outputting X 'as a child individual of X', wherein the child individual comprises equipment selection and process sequencing.
The invention has the beneficial effects that:
the multi-target flexible job shop energy-saving scheduling method based on the improved wolf algorithm can overcome the intermittency and the fluctuation of the household electricity load, trains a flow-based condition generation model through the source domain household electricity load data, and solves the problem of large load prediction error caused by less household electricity data accumulation by applying model migration.
Drawings
FIG. 1 is a schematic diagram of encoding of plant equipment and processing procedures in the present invention;
FIG. 2 is a schematic diagram of the structural data of the wolf unit according to the LOV rule in the present invention;
FIG. 3 is a schematic diagram of an improved wolf pack rating system of the present invention;
FIG. 4 is a schematic diagram of a portion of the process tracking operation of the present invention;
FIG. 5 is a maximum completion time convergence graph obtained by solving MK09 with two algorithms according to an embodiment of the invention;
FIG. 6 is a graph of the total delay time convergence obtained by solving MK09 with two algorithms according to an embodiment of the invention;
FIG. 7 is a graph of the convergence of total energy consumption of the system resulting from the solution of MK09 by two algorithms in an embodiment of the invention;
FIG. 8 is a chart of HV convergence curves resulting from two algorithms solving MK09 in an embodiment of the invention;
FIG. 9 is an IGD convergence graph obtained by solving MK09 with two algorithms according to an embodiment of the invention;
FIG. 10 is a Gantt chart obtained by solving MK09 using the improved Grey wolf algorithm in an embodiment of the invention;
FIG. 11 is a Gantt chart obtained by solving MK09 with the MOEA/D algorithm in the embodiment of the invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention relates to a multi-target flexible job shop energy-saving scheduling method based on an improved wolf algorithm, which is implemented according to the following steps:
the multi-target flexible job shop energy-saving scheduling problem is described as follows:
the flexible job shop scheduling problem is an extension of the classic job shop scheduling problem, and can be specifically described as follows: n workpieces are processed on m devices, each workpiece consisting of J i The working procedures are formed, and each working procedure can finish processing on a plurality of different devices at different time. However, in the classic flexible job shop scheduling problem, an important index of energy consumption is not generally considered, so that in the context of sustainable manufacturing, an environmental index of energy consumption is increased, so that the factors considered in the flexible job shop scheduling work can be more comprehensive, and the decision can be more accurate.
The equipment in the workshop has two working states of processing and no-load, the corresponding energy consumption is respectively processing energy consumption and no-load energy consumption, the scheduling optimization aims at minimizing three of maximum completion time, total delay time and total system energy consumption, wherein the total system energy consumption is composed of four parts of workshop fixed energy consumption, processing energy consumption, no-load energy consumption and transfer energy consumption. The model assumes that the model satisfies the following conditions:
(1) only one workpiece can be processed by one device at a time;
(2) the equipment does not stop once the processing is started in the middle;
(3) sequence constraint exists among the working procedures of the same workpiece, and the next working procedure starts to process after the previous working procedure is finished;
(4) the quality of the workpieces is not divided;
(5) the equipment is idle and does not stop;
(6) the preparation time before the equipment is processed and the time for loading and unloading the workpiece in the processing process are not considered;
(7) the device catastrophic failure condition is not considered.
The specific process of the step 1 is as follows: on the basis of model assumptions, J i Representing the total process number of the workpiece i; c iJi Representing the finishing time of the workpiece i; n represents the total number of workpieces; t is a unit of i Indicating the delivery date of the workpiece i; t is t ijk The processing time of the j-th procedure of the workpiece i on the equipment k is shown; x is the number of ijk Is a variable from 0 to 1, if the jth process of the workpiece i is processed on the equipment k, x ijk 1, otherwise x ijk 0; m represents the fixed energy consumption of the workshop per unit time; lambda [ alpha ] k Represents the average energy consumption per unit time during the processing of the equipment k; CT (computed tomography) k Representing the time of completion of the plant k, CT ij Showing the finishing time of the jth process of the workpiece i; theta k Represents the average energy consumption of the device k in unit time when the device k is idle; alpha represents the transfer energy consumption of the workpieces in the workshop; z represents the transfer times of the workshop workpieces; ST (ST) ij Indicating the starting time of the j-th process of the workpiece i; z is a linear or branched member ijhgk Z is a variable from 0 to 1 if the jth pass of workpiece i is not machining on machine k at the same time as the gth pass of workpiece h ijhgk 1, otherwise Z ijhgk ＝0；p ijk The processing time of the j-th process of the workpiece i on the machine k is shown;
the energy-saving scheduling problem model of the flexible job shop is constructed by the following objective functions:
f 1 ＝max(C iJi ) (1-1)
ST i(j) ≥CT i(j-1) ,i＝1,2,...n,j＝2,...J i ； (1-5)
x ijk ∈{0,1},i＝1,2,...n,j＝1,2,...J i ,k＝1,2,...m； (1-8)
z ijhgk ∈{0,1},i,h＝1,2,...n,j,g＝1,2,...m (1-9)。
equation (1-1) defines the maximum completion time minimization of the objective function of the EFJSP; the equation (1-2) defines that the total delay time of the target function of the EFJSP is shortest; the equation (1-3) defines that the total energy consumption of the EFJSP objective function system is minimum, and the total energy consumption of the system comprises fixed energy consumption, processing energy consumption, no-load energy consumption and transfer energy consumption; the formula (1-4) shows that the working procedure can not be interrupted during the processing process until the completion; the formula (1-5) indicates that the front and back sequence constraints exist among the processes of the same workpiece; the expression (1-6) shows that the same machine can only process one workpiece at the same time; the formula (1-7) shows that all the procedures can only be continuously finished on one device; the formula (1-8) represents a variable x of 0-1 ijk (ii) a The formula (1-9) represents a variable z of 0-1 ijghk 。
And 2, coding the workshop equipment and the processing procedures by adopting a machine-procedure-based coding method, namely, each scheduling solution comprises a front section and a rear section which are equal in length and respectively correspond to a machine selection scheme and a procedure sequencing scheme, as shown in figure 1. Wherein O is 12 The 2 nd process of the workpiece 1 is shown, and so on. In addition, the first halfThe segment element values represent the number of the machine where each process belongs, the second half element values represent the number of the workpiece where each process belongs, the same element values represent different processes of the same workpiece, and the sequence of appearance represents the sequence of processing of the processes. Adopting a natural number two-section type code based on process coding and equipment coding; creating an empty external archive A 0 Scale N'; setting algorithm parameters: initial population size N, current iteration number t, maximum iteration number t max Tracking probability MR, and searching probability 1-MR.
For solving the multi-target flexible job shop energy-saving scheduling problem, the processing path of each workpiece is known, the elements in the second half section of each scheduling solution are scanned from left to right during decoding, and the processing machine selected by each procedure is determined according to the values of the elements in the first half section. The process at the leftmost end of the second half is scheduled first to be processed as early as possible on the respective machine and to obtain the start time and the completion time of all the processes. And the rest procedures are analogized until all the procedures are scheduled.
And 3, directly determining the quality of the initial wolf pack in the later hunting process, wherein the good wolf pack improves the operation efficiency of the algorithm. The invention adopts an LOV (full name as Largest Order Value) rule to generate an initial population and calculates the aggregation rate among individuals to improve the quality of an initial solution.
The specific process is as follows:
step 3.1, generating a wolf group G according to the formula (3-1) and the formula (3-2), wherein the position of an individual in the wolf group G is represented as S and is represented as follows:
wherein the position component of the individual S
Generated by the following equation:
wherein ub is 100, lb is-100, N is the total number of grey wolves of the group G, N is the total number of the work processes, dim represents the position dimension of the grey wolves, and each position component is
The value is [ -100,100 [)]；
Step 3.2, sequentially arranging according to the position components of the individual S to generate wolf group position vectors WoStruct position, arranging WoStruct position variables in descending order according to the LOV rule to obtain an intermediate sequence WoStruct
Obtaining a processing sequence WolStruct.bta; taking two processes for each of two workpieces as an example, as shown in fig. 2, a workpiece process sequence wolstruct.seq 'is obtained, and a final machining sequence wolstruct.seq is obtained as a process sequence code according to the formula seq (dim) seq' (find (alp ═ (bta (dim))) (1 < dim < n);
randomly selecting equipment with the minimum available processing time as equipment selection codes according to the corresponding procedures of each position in the processing sequence;
and 3.3, in order to effectively solve the quality of the initial solution, ensure the diversity of the initialized population and improve the quality of the initial solution. The aggregability between the two locations is defined in terms of their process variability. Random generation
And then, taking Chm1, wherein Chm2 is a process processing sequence WoStruct.bta of the positions of two wolfsbane individuals after LOV rule conversion, and calculating the aggregative property of the individuals in the population, wherein the calculation formula is as follows:
P(Chm1,Chm2)＝S(Chm1,Chm2)/n (3-4)
wherein Chm1(dim) and Chm2(dim) represent two WolStruct.bta sequence's value in dimension dim, when the two values are the same,
take a value of 0, if not equal, then
The value is 1; the value of S is called the Hamming distance; p represents the aggregation rate between the two bodies, and n represents the total number of work processes;
generating initial population individuals and ensuring the position P of each wolf S Greater than Pcmax being 0.5, the diversity of the wolf colony generating individuals can be effectively ensured so as to improve the quality of the solution; the specific operation is as follows:
step a) generating a process sequence and machine selection code of an initial individual according to steps 3.1, 3.2;
step b) calculating the aggregation rate between the initial population and the initial population; if the number of the individuals is more than 0.5, storing the individuals into the initial population, otherwise, giving up the individuals;
repeatedly selecting the wolfsbane individuals to perform the steps a) and b) until the initial population number is N.
and 4.1, the multi-objective optimization problem cannot directly compare the quality of the individuals according to the fitness value, and the individuals in the population need to be divided into a plurality of non-dominant grades through Pareto sorting. Finding out the non-dominant optimal solution in the current population to form a first non-dominant optimal solution layer, assigning the grade of each individual to be 1 grade, removing the solutions from the population, finding out a new non-dominant solution from the rest individuals, assigning the grade of each individual to be 2 grades, and so on until all the individuals are graded; obviously, individuals with small numbers of ranks perform better.
The specific process of finding the non-dominant optimal solution is as follows: defining a dominance relationship: for the multi-objective optimization problem, when all target values of the individuals y (i) are better than the target values corresponding to the individuals y (j), defining the individuals y (i) to dominate the individuals y (j), otherwise, the individuals y (i) cannot dominate the individuals y (j);
and comparing the individuals in the population pairwise to obtain a dominance relation between any two individuals, wherein the individuals which are not dominated by other individuals are called non-dominated optimal solutions, and a set formed by the non-dominated optimal solutions is called a non-dominated optimal solution layer.
Step 4.2, because the multi-objective optimization problem can not directly determine the individual of the decision layer by comparing the size of the fitness value, the individual of the decision layer is obtained by adopting a method based on the non-dominant grade and the crowding distance: calculating the crowding degree distance of the individuals, carrying out normalization processing, and sequencing the individuals according to the non-dominant grade of the individuals in the population and the normalized crowding distance: for any two individuals, the lower ranked individuals ranked ahead; if the two individual grades are the same, comparing the normalized congestion distances of the two individuals, and ranking the individuals with large normalized congestion distances in front;
the crowdedness distance is specifically represented as:
and (3) carrying out normalization processing on the individual crowdedness distance, namely:
P(i) distance ＝(P max -P(i) distance )/(P max -P min ) (4-2)
wherein, by P (i) distance Represents the crowdedness distance of the individual y (i), p (i). f m A function value representing the individual y (i) on the target m; p max And P min The maximum value and the minimum value of the individual crowdedness distance respectively;
in order to improve the defect that the conventional algorithm only depends on three wolfs to promote the hunting process, the information exchange and cooperation among wolf group individuals limit the searching capability of the algorithm to a certain extent, the number of leader level individuals is increased, the concept of the wolf rate u is provided, u is 0.3, namely, the individuals ranked at the top 30% in the population are selected, and the number ratio is 12:3, respectively using the two as alpha, beta and delta wolf sets to form a decision layer; the number of the three wolfsbane individuals of alpha, beta and delta is 1:2:3, and dividing. The alpha wolf is in the highest leadership in the population, and the quantity is the least; the second rank of beta is more in the number of individuals; the δ wolf has the worst leadership and the largest number of individuals. The number of the wolfs heads is adjusted according to the size of the population, and the guidance of the wolfs heads is strengthened. The wolf clusters are sorted according to indexes such as fitness and the like, and a wolf set is screened according to the wolf rate. The improved wolf rank system is shown in FIG. 3, where u is 1 ＝0.05，u 2 ＝0.1，0u 3 ＝0.1，u 1 +u 2 +u 3 ＝u＝0.3。
Step 4.3, in order to store the non-dominated solution in the searching process, an external file A is established 0 And updating the Pareto dominant relationship based on the Pareto dominant relationship, wherein the updating method comprises the following steps: adding the individuals with the non-domination level of 1 into the external files to realize the updating of the external files; if the number of individuals in the external file is larger than the external file size N', the individuals with smaller crowdedness are removed until the number of non-dominant solutions is consistent with the external file size.
And 5, judging whether an algorithm termination condition is reached: t is t max If yes, turning to step 8, otherwise, executing step 6;
and 6, in the basic improved Greenwolf algorithm, the individual is updated only according to the information of the individual in the decision layer, so that the population diversity of the algorithm is reduced at the later stage of operation, and premature convergence occurs. The invention adopts a dual-mode parallel search mechanism of a tracking mode and a search mode, and respectively corresponds to tracking and searching. In each iteration, the algorithm divides the whole wolf group into two subgroups, and then performs tracking operation and searching operation on individuals in the subgroups respectively. In order to coordinate the tracking and searching capabilities of the algorithm, the number of individuals in each sub-population is dynamically adjusted in the searching process, so that the algorithm is focused on tracking in the early stage and on searching in the later stage.
Carrying out global tracking and local search on the wolf individuals in the external files according to the probability of the scale factor MR of the tracking mode, and obtaining new individuals through corresponding operation; the specific process is as follows:
defining a tracking probability MR which represents the ratio of the number of individuals in the population to the whole population in the tracking mode, and a searching probability 1-MR which represents the ratio of the number of individuals in the population to the whole population in the local searching mode, wherein the tracking probability MR is expressed as:
MR＝MR max -(MR max -MR min )×t/t max (6-1)
wherein, MR max And MR min 1 and 0, respectively; t and t max Respectively representing the current iteration times and the maximum iteration times of the algorithm;
selecting the wolf individuals according to the tracking probability MR to perform global tracking operation to obtain new individuals representing equipment codes and procedure code sequencing;
and selecting the wolf individuals according to the search probability 1-MR to perform local search operation to obtain new individuals aiming at equipment codes and process code sequencing.
The global tracking operation process is as follows:
introducing a discrete inter-individual distance formula, wherein the distance is expressed as the difference between two individuals and is expressed as:
the distance formula is normalized, namely:
wherein, with D ij Representing the discrete distance of the individuals i and j, n representing the number of workpieces, CT ik Representing the time of completion of the workpiece k in the individual i; d ijmax And D ijmin Respectively, the maximum and minimum of the discrete inter-individual distances;
on the basis, a two-point crossing-based discrete individual updating strategy is provided by combining the characteristics of a gray wolf algorithm search mode and FJSP (fuzzy inference processing), and information exchange is carried out on an individual and three head wolf sets of a decision layer alpha, beta and delta through tracking operation according to the distance between the individual and an optimal individual, as shown in a formula (6-4).
Wherein the content of the first and second substances,
indicating that the individual i communicates with the individual alpha,
indicating that the individual i and the individual beta carry out information communication,
indicating that the individual i communicates information with the individual delta.
The distance between the current individual and the optimal individual is more than or equal to
And then, the difference between the fitness value of the current individual and the discrete arrangement of the optimal individual is larger, and at this time, any individual in the alpha set of the decision layer is selected to perform tracking operation with the current individual, so that the information of the optimal individual is reserved for the next generation. The distance between the current individual and the optimal individual is less than or equal to
In the time, the difference between the fitness value of the current individual and the fitness value of the optimal individual is larger, but the difference between the fitness value of the current individual and the fitness value of the optimal individual is not large in discrete arrangement, and then any individual in the decision layer delta set is selected to perform tracking operation with the optimal individual, so that the diversity of the population is increased while the superior individual information is kept. When the distance between the current individual and the optimal individual is in a middle area, any one of the decision layer beta sets with the fitness value in a middle position in the decision layer is selected to perform tracking operation with the optimal individual.
The content of the information communication between the individual i and the individual alpha, beta or delta comprises the information communication between the process code sorting part and the equipment selecting part;
the information exchange of the procedure coding sequencing part adopts a POX crossing mode, and the specific process comprises the following steps:
a, generating a random integer R (R is more than or equal to 1 and less than or equal to n), wherein n is the total number of workpieces;
step b, parent individual P 1 Copying the workpieces with the workpiece serial numbers less than or equal to R to the offspring individuals C 1 (ii) a Parent individual P 2 Copying the workpieces with the workpiece serial numbers larger than R to the offspring individuals C 2 Reserving the position of the device, and copying the corresponding device number to the corresponding position;
step c, copying the parent P 1 Not present in offspring C 2 Workpiece number of C 2 Copying the parent P 2 Not present in C 1 To child C 1 And preserving the sequence, and copying the equipment number to the corresponding position to obtain a new individual based on the process coding sequence, wherein the process is shown in FIG. 4;
the tracking operation of the equipment selection part adopts a two-point crossing mode, and the following steps are specifically adopted:
for two new individuals completing the process coding information exchange, randomly setting two cross points, exchanging the equipment serial numbers corresponding to the processes of the parent individuals between the set two cross points, and obtaining new individuals based on process sequencing and equipment selection;
and selecting the superior individuals from the two new individuals based on the process sequence and equipment according to the domination relationship to serve as the new individuals, and if the two individuals are not dominated with each other, selecting one of the two individuals as the new individual.
Definition of governing relationship: for the multi-objective optimization problem, when all target values of the individuals y (i) are better than the target values corresponding to the individuals y (j), the individuals y (i) are defined to dominate the individuals y (j), otherwise, the individuals y (i) cannot dominate the individuals y (j). Selecting new individuals according to the dominating relationship: comparing a plurality of target values of the two individuals, and selecting the individual with the better target value as a next generation new individual.
The specific process of the local search operation is as follows:
as can be seen from the tracking mode, the individual is updated only according to the individual information of the decision layer. To avoid the algorithm from falling into a locally optimal solution, the search algorithm is embedded into the grayish optimization algorithm, which is referred to as a search operation. The search operation acts on the sub-population in the search mode at each iteration, thereby improving algorithm performance. In the search algorithm, 3 kinds of neighborhood structures are designed for individual process codes and equipment codes:
(1) neighborhood structure N 1 : optionally selecting two positions in the coding section of the process sequencing part, and carrying out exchange operation on elements between the two selected positions;
(2) neighborhood structure N 2 : optionally selecting two elements in a code segment of the procedure sorting part, and inserting the element positioned at the back of the two selected elements into the position in front of the element positioned at the front;
(3) neighborhood structure N 3 : selecting an element in a code segment of a machine distribution part, wherein the number of the processing equipment of the element is more than 1, and the processing equipment corresponding to the element is changed into equipment with the shortest centralized processing time of the selectable processing equipment;
based on the neighborhood structure, the specific steps of local search are as follows:
step 1), taking the current generation individual performing the variable domain search as an initial solution X', and setting a threshold value delta > 0, gamma being 1, rho being 1 and a termination condition gamma max ；
Step 2), rho represents a variable of 0 or 1 and is used for deciding which combined field search is executed by X', and N is selected in an equal probability mode during each iteration 1 ∪N 3 And N 2 ∪N 3 One of them is to perform a neighborhood search operation, if ρ is 1, X ″, N 1 (X')∪N 3 (X'); if ρ is 0, X ″, N 2 (X')∪N 3 (X'), (u) means that two operations are performed;
step 3), judging whether C is satisfied max (X″)-C max (X')≤δ，C max Representing a maximum completion time; if so, then X '═ X'; otherwise, setting rho ═ rho-1 |;
step 4), enabling gamma to be gamma +1, and judging whether gamma is more than gamma or not max (ii) a If so, then X ″, X', go toStep 5); otherwise, go to step 2);
and 5) finishing local search, and outputting X 'as a child individual of X', wherein the child individual comprises machine selection and process sequencing.
and 8, finishing the algorithm, outputting an external file, and obtaining the workshop equipment codes and the processing procedure codes through individuals in the external file.
Simulation verification
The invention adopts an improved Hui wolf algorithm and an MOEA/D algorithm to carry out simulation solution on 10 standard examples, wherein the simulation environment is as follows: the Matlab2017b is adopted for programming, and a win10 operating system is arranged on a computer with 8G memory and R53.2GHz. In order to effectively apply the algorithm of the invention to solve, the processing energy consumption rates of all the devices in the standard calculation examples are randomly generated on [5,18], the no-load energy consumption rates of all the devices are randomly generated on [1,3], the unit is kw/h, and the fixed energy consumption rate of the workshop and the transfer energy consumption of all the workpieces are respectively 30kw/h and 1.8 kw/time. Delivery date data for all workpieces is generated according to equation (1).
Wherein d is j Represents the delivery time of the jth workpiece, r j Representing the delivery time, t, of the jth workpiece j Representing the tightness, s, of the jth workpiece j Representing the number of processes of the jth workpiece, p l,j Represents the machining time of the l-th process of the j-th workpiece. t is t j There are three values: t is t j 2 denotes time variance, t j 1.5 denotes moderate time, t j 1 represents time stress. In each case, the number of workpieces with different degrees of tightness (tight, moderate, loose) in time was 34%, 33%, respectively.
The aggregation function in the MOEA/D algorithm adopts a Chebychef aggregation method (TA), the population size is set to be 62, the variation probability is set to be 1.0, the division number is set to be 10, the weight vector neighborhood size is set to be 20, the maximum replaceable number of each offspring solution is set to be 1, and the maximum iteration number is set to be 1200.
The parameters of the improved wolf algorithm are set as 200 population size, tracking probability MR, searching probability 1-MR, and according to the direct dynamic adjustment of MR, the maximum iteration number is 1200, and the wolf rate is 0.3. Wherein the value of MR can be adjusted by the formula (2) in which MR max And MR min 1 and 0, respectively; t and t max Respectively representing the current iteration number and the maximum iteration number of the algorithm.
MR＝MR max -(MR max -MR min )×t/t max (2)
The operation environment is the same as that of an enterprise example, the operation result of each operator takes an optimal value and an average value, and the simulation result of the invention and the existing algorithm is shown in a table 1:
TABLE 1
Analysis table 1 shows that, compared with the MOEA/D algorithm, the maximum completion time index is improved to obtain the optimal values of 10 cases of MK01, MK02, MK03, MK04, MK05, MK06, MK07, MK08, MK09 and MK10, and the better average values of 10 cases of MK01, MK02, MK03, MK04, MK05, MK06, MK07, MK08, MK09 and MK10 are obtained. And the MOEA/D algorithm obtains the optimal values of 3 cases of MK01, MK03 and MK04 and the better average value of 1 case of MK 01.
Compared with the MOEA/D algorithm, the improved Grey wolf algorithm achieves the optimal values of 6 examples of MK01, MK02, MK06, MK07, MK09 and MK10 and achieves the better average values of 7 examples of MK01, MK02, MK06, MK07, MK08, MK09 and MK10 on the index of the total delay time. The MOEA/D algorithm obtains the optimal value of 6 examples of MK02, MK03, MK04, MK05, MK06 and MK08 and the better average value of 5 examples of MK02, MK03, MK04, MK05 and MK 06.
Compared with the MOEA/D algorithm, the improved Grey wolf algorithm obtains the optimal values of 6 algorithms of MK05, MK06, MK07, MK08, MK09 and MK10 and obtains the better average values of 7 algorithms of MK03, MK05, MK06, MK07, MK08, MK09 and MK10 on the total energy consumption index. And the MOEA/D algorithm obtains the optimal values of 4 algorithms comprising MK01, MK02, MK03 and MK04 and the better average values of 3 algorithms comprising MK01, MK02 and MK 04.
Analysis shows that the improved wolf algorithm is superior to the MOEA/D algorithm on the whole in the aspect of solving the obtained optimized target value.
Fig. 5-9 show single target convergence curves of two algorithms for a single run of the example MK09, and IGD and HV convergence curves, and fig. 10 and 11 are corresponding gantt charts. As can be seen from the figure, in the process of solving the energy-saving scheduling problem of the multi-target flexible job shop, three optimization indexes of the two algorithms show a convergence trend on the whole, and in comparison, the convergence trend of the improved Hui wolf algorithm is more obvious; in the evolution process of IGD and HV multi-objective optimization indexes, the convergence trend of the two algorithms is more obvious when compared, and in comparison, the improved Hui wolf algorithm is better than the solution result of MOEA/D.
Through the mode, the multi-target flexible job shop energy-saving scheduling method based on the improved wolf algorithm disclosed by the invention comprises the following steps of firstly constructing a flexible job shop energy-saving scheduling problem model: the method comprises the steps of describing the energy-saving scheduling problem of the flexible job shop and assuming a model; two-section type coding based on natural numbers is adopted, wherein the two-section type coding is a procedure code and an equipment code respectively; then discretizing the continuity problem by adopting a mode based on an LOV rule; introducing the aggregation rate among individuals to obtain an initial population with higher quality; evaluating individuals in the initial population, determining an alpha wolf set, a beta wolf set and a delta wolf set of the decision-making layer individuals according to a proportion, and adding a non-dominant solution into an external archive; by using a dual-mode parallel search mode, the tracking and searching capabilities are dynamically adjusted in the searching process, improved tracking operation is introduced, the problem solving precision is improved, the variable-field searching is adopted in the searching mode, the evolutionary speed is improved, and the local optimal solution is broken through. The invention reasonably arranges the processing sequence of the workpieces on each machine, and provides a better scheduling scheme for production enterprises from the three aspects of minimizing the maximum completion time, the total delay time and the total energy consumption of the system.
Claims (10)
1. The multi-target flexible job shop energy-saving scheduling method based on the improved wolf algorithm is characterized by being implemented according to the following steps:
step 1, constructing an energy-saving scheduling problem model of a flexible job shop: the method comprises the steps of describing the energy-saving scheduling problem of the flexible job shop and assuming a model;
step 2, encoding workshop equipment and processing procedures, and adopting natural number two-section type encoding based on procedure encoding and equipment encoding; creating an empty external archive A 0 Scale N'; setting algorithm parameters: initial population size N, current iteration number t, maximum iteration number t max Tracking probability MR, and searching probability 1-MR;
step 3, obtaining an initial population by adopting a mode based on an LOV rule;
step 4, combining the current population with an external file, evaluating individuals in the combined population, determining an alpha wolf set, a beta wolf set and a delta wolf set of the individuals of the decision layer according to a proportion, and updating the external file through a non-dominant solution;
and 5, judging whether an algorithm termination condition is reached: t ═ t max If yes, turning to step 8, otherwise, executing step 6;
step 6, carrying out global tracking or local search on the wolf individuals in the external files according to the probability of the scale factor MR of the tracking mode, and obtaining new individuals through corresponding operation;
step 7, combining the newly generated individuals for executing the tracking operation and the searching operation to generate a new generation of wolf population; then turning to the step 4, and carrying out next iteration;
and 8, finishing the algorithm, outputting an external file, and obtaining the workshop equipment codes and the processing procedure codes through individuals in the external file.
2. The multi-target flexible job shop energy-saving scheduling method based on the improved wolf algorithm as claimed in claim 1, wherein the model in step 1 assumes that the model specifically satisfies the following conditions:
(1) only one workpiece can be processed by one device at a time;
(2) the equipment does not stop once the processing is started in the middle;
(3) the sequence constraint is formed among the working procedures of the same workpiece, and the next working procedure starts to process after the previous working procedure is finished;
(4) the quality of the workpieces is not divided;
(5) the equipment is idle and does not stop;
(6) the preparation time before the equipment is processed and the time for loading and unloading the workpiece in the processing process are not considered;
(7) the device catastrophic failure condition is not considered.
3. The multi-target flexible job shop energy-saving scheduling method based on the improved wolf algorithm as claimed in claim 1, wherein the specific process of step 1 is as follows: on the basis of model assumptions, J i Representing the total process number of the workpiece i;
representing the finishing time of the workpiece i; n represents the total number of workpieces; t is i Indicating the delivery date of the workpiece i; t is t ijk The processing time of the j-th procedure of the workpiece i on the equipment k is shown; x is the number of ijk Is a variable from 0 to 1, if the jth process of the workpiece i is processed on the equipment k, x ijk 1, otherwise x ijk 0; m represents the fixed energy consumption of the workshop per unit time; lambda [ alpha ] k Represents the average energy consumption per unit time during the processing of the equipment k; CT k Representing the time of completion of the plant k, CT ij Showing the finishing time of the j-th process of the workpiece i; theta k Represents the average energy consumption per unit time when the device k is idle; alpha represents the transfer energy consumption of the workpieces in the workshop; z represents the transfer times of the workshop workpieces; ST (ST) ij Indicating the starting time of the j-th process of the workpiece i; z ijhgk Z is a variable from 0 to 1 if the jth pass of workpiece i is not machining on machine k at the same time as the gth pass of workpiece h ijhgk 1, otherwise Z ijhgk ＝0；p ijk The processing time of the j-th process of the workpiece i on the machine k is shown;
the energy-saving scheduling problem model of the flexible job shop is constructed by the following objective functions:
ST i(j) ≥CT i(j-1) ,i＝1,2,...n,j＝2,...J i ； (1-5)
x ijk ∈{0,1},i＝1,2,...n,j＝1,2,...J i ,k＝1,2,...m； (1-8)
z ijhgk ∈{0,1},i,h＝1,2,...n,j,g＝1,2,...m (1-9)
4. the multi-target flexible job shop energy-saving scheduling method based on the improved wolf algorithm as claimed in claim 1, wherein the specific process of step 3 is as follows:
step 3.1, generating a wolf pack G according to the formula (3-1) and the formula (3-2), wherein the position of an individual in the wolf pack G is expressed as S and expressed as follows:
wherein the position component of the individual S
Generated by the following equation:
wherein ub is 100, lb is-100, N is the total number of grey wolves of the group G, N is the total number of the work processes, dim represents the position dimension of the grey wolves, and each position component is
The value is [ -100,100 [)]；
Step 3.2, sequentially arranging according to the position components of the individual S to generate wolf group position vectors WoStruct
Obtaining a processing sequence WolStruct.bta;
randomly selecting equipment with the minimum available processing time as equipment selection codes according to the corresponding procedures of each position in the processing sequence;
step 3.3, taking Chm1, wherein Chm2 is a process processing sequence WolStruct.bta of two wolfsbane individual positions after LOV rule conversion, and calculating the aggregation of individuals in the population, wherein the calculation formula is as follows:
P(Chm1,Chm2)＝S(Chm1,Chm2)/n(3-4)
where Chm1(dim), Chm2(dim) represents the value of two wolsstruct.bta sequences in dimension dim, and when the two values are the same,
take a value of 0, if not equal, then
The value is 1; the value of S is called the Hamming distance; p represents the aggregation rate between the two bodies, and n represents the total number of work processes;
generating initial population individuals and ensuring the position P of each wolf S The specific operation is that > Pcmax is 0.5:
step a) generating a process sequence and machine selection code of an initial individual according to steps 3.1, 3.2;
step b) calculating the aggregation rate between the initial population and the initial population; if the number of the individuals is more than 0.5, storing the individuals into the initial population, otherwise, giving up the individuals;
repeatedly selecting the wolfsbane individuals to perform the steps a) and b) until the initial population number is N.
5. The multi-target flexible job shop energy-saving scheduling method based on the improved wolf algorithm as claimed in claim 1, wherein the specific process of step 4 is as follows:
step 4.1, finding out the non-dominance optimal solution in the current population to form a first non-dominance optimal solution layer, assigning the grade of the individual to be 1 grade, removing the solutions from the population, finding out a new non-dominance solution from the rest individuals, assigning the grade of the individual to be 2 grades, and so on until all the individuals are graded;
step 4.2, calculating the crowding degree distance of the individuals, carrying out normalization processing, and sorting the individuals according to the non-dominant grade of the individuals in the population and the normalized crowding distance: for any two individuals, the lower ranked individuals ranked ahead; if the two individual grades are the same, comparing the normalized congestion distances of the two individuals, and arranging the individuals with large normalized congestion distances in front;
the crowdedness distance is specifically represented as:
and (3) carrying out normalization processing on the individual crowdedness distance, namely:
P(i) distance ＝(P max -P(i) distance )/(P max -P min ) (4-2)
wherein, by P (i) distance Represents the crowdedness distance of the individual y (i), p (i). f m A function value representing the individual y (i) on the target m; p max And P min The maximum value and the minimum value of the individual crowdedness distance respectively;
selecting the individuals ranked at the top 30% from the population according to the sorting principle, and respectively using the individuals as three wolf sets of alpha, beta and delta to form a decision layer according to the quantity ratio of 1:2: 3;
4.3, adding the individuals with the non-dominance level of 1 into the external files to realize the updating of the external files; if the number of individuals in the external file is larger than the size N' of the external file, the individuals with smaller crowdedness are removed until the number of non-dominant solutions is consistent with the size of the external file.
6. The multi-target flexible job shop energy-saving scheduling method based on the improved wolf algorithm as claimed in claim 5, wherein the specific process of finding the non-dominant optimal solution in step 4.1 is as follows: defining a dominance relationship: for the multi-objective optimization problem, when all target values of the individuals y (i) are better than the target values corresponding to the individuals y (j), defining the individuals y (i) to dominate the individuals y (j), otherwise, the individuals y (i) cannot dominate the individuals y (j);
and comparing the individuals in the population pairwise to obtain a dominance relation between any two individuals, wherein the individuals which are not dominated by other individuals are called non-dominated optimal solutions, and a set formed by the non-dominated optimal solutions is called a non-dominated optimal solution layer.
7. The multi-target flexible job shop energy-saving scheduling method based on the improved wolf algorithm as claimed in claim 1, wherein the specific process of step 6 is as follows:
defining a tracking probability MR which represents the ratio of the number of individuals in the population to the whole population in the tracking mode, and a searching probability 1-MR which represents the ratio of the number of individuals in the population to the whole population in the local searching mode, wherein the tracking probability MR is expressed as:
MR＝MR max -(MR max -MR min )×t/t max (6-1)
wherein, MR max And MR min 1 and 0, respectively; t and t max Respectively representing the current iteration times and the maximum iteration times of the algorithm;
selecting the wolf individuals according to the tracking probability MR to perform global tracking operation to obtain new individuals representing equipment codes and procedure code sequencing;
and selecting the wolf individuals according to the search probability 1-MR to perform local search operation to obtain new individuals aiming at equipment codes and process code sequencing.
8. The multi-target flexible job shop energy-saving scheduling method based on the improved wolf algorithm according to claim 1, wherein the global tracking operation process is as follows:
introducing a discrete inter-individual distance formula, wherein the distance is expressed as the difference between two individuals and is expressed as:
the distance formula is normalized, namely:
wherein, with D ij Representing the discrete distance of the individuals i and j, n representing the number of workpieces, CT ik Representing the time of completion of the workpiece k in the individual i; d ijmax And D ijmin Respectively, the maximum and minimum of the discrete inter-individual distances;
determining information communication of alpha, beta and delta of the individual at the decision layer according to the distance between the individual and the optimal individual, wherein the information communication is expressed as follows:
wherein, the first and the second end of the pipe are connected with each other,
indicating that the individual i communicates with the individual alpha,
indicating that the individual i and the individual beta carry out information communication,
indicating that the individual i communicates information with the individual delta.
9. The improved wolf algorithm-based multi-target flexible job shop energy-saving scheduling method for the flexible job shop, as claimed in claim 1, wherein the content of the information communication between the individual i and the individual α or β or δ comprises the information communication between the process coding ordering part and the equipment selecting part;
the information exchange of the procedure coding sequencing part adopts a POX crossing mode, and the specific process comprises the following steps:
a, generating a random integer R (R is more than or equal to 1 and less than or equal to n), wherein n is the total number of workpieces;
step b, parent individual P 1 Copying the workpieces with the workpiece serial numbers less than or equal to R to the offspring individuals C 1 (ii) a Parent individual P 2 Copying the workpieces with the workpiece serial numbers larger than R to the offspring individuals C 2 Retention ofIts position, and copy the correspondent device number to the corresponding position;
step c, copying the parent P 1 Not present in offspring C 2 To C of workpiece serial number 2 Copying parent P 2 Not present in C 1 To child C 1 Keeping the sequence of the new individuals, and copying the equipment numbers to corresponding positions to obtain new individuals sorted based on procedure codes;
the tracking operation of the equipment selection part adopts a two-point crossing mode, which comprises the following specific steps:
for two new individuals completing the process coding information exchange, randomly setting two cross points, exchanging the equipment serial numbers corresponding to the processes of the parent individuals between the set two cross points, and obtaining new individuals based on process sequencing and equipment selection;
and selecting the superior individuals from the two new individuals based on the process sequence and equipment according to the domination relationship to serve as the new individuals, and if the two individuals are not dominated with each other, selecting one of the two individuals as the new individual.
10. The multi-target flexible job shop energy-saving scheduling method based on the improved wolf algorithm as claimed in claim 1, wherein the specific process of the local search operation is as follows:
3 neighborhood structures are designed aiming at individual process coding and equipment coding:
(1) neighborhood structure N 1 : optionally selecting two positions in the coding section of the process sequencing part, and carrying out exchange operation on elements between the two selected positions;
(2) neighborhood structure N 2 : optionally selecting two elements in a code segment of the procedure sorting part, and inserting the element positioned at the back of the two selected elements into the position in front of the element positioned at the front;
(3) neighborhood structure N 3 : selecting an element in the code segment of the machine distribution part, wherein the number of the machinable devices of the element is more than 1, and the machining device corresponding to the element is changed into the device with the shortest centralized machining time of the selectable machining devices;
based on the neighborhood structure, the specific steps of local search are as follows:
step 1), taking the current generation individual performing the variable domain search as an initial solution X', and setting a threshold value delta > 0, gamma being 1, rho being 1 and a termination condition gamma max ；
Step 2), rho represents a variable of 0 or 1 and is used for deciding which combined field search is executed by X', and N is selected in an equal probability mode during each iteration 1 ∪N 3 And N 2 ∪N 3 One of them is to perform a neighborhood search operation, if ρ is 1, then X ═ N 1 (X')∪N 3 (X'); if ρ is 0, X ″ -N 2 (X')∪N 3 (X'), (u) means that two operations are performed;
step 3), judging whether C is satisfied max (X”)-C max (X')≤δ，C max Representing a maximum completion time; if so, then X' ═ X "; otherwise, setting rho ═ rho-1 |;
step 4), enabling gamma to be gamma +1, and judging whether gamma is more than gamma or not max (ii) a If yes, turning to step 5); otherwise, go to step 2);
and 5) finishing local search, and outputting X 'as a child individual of X', wherein the child individual comprises equipment selection and process sequencing.
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| CN115130789A (en) * | 2022-08-30 | 2022-09-30 | 武汉理工大学 | Distributed manufacturing intelligent scheduling method based on improved wolf optimization algorithm |
| CN115375193A (en) * | 2022-10-24 | 2022-11-22 | 埃克斯工业有限公司 | Method, device and equipment for optimizing double-target production scheduling and readable storage medium |
| CN115981262A (en) * | 2023-01-31 | 2023-04-18 | 武汉理工大学 | IMOEA-based hydraulic cylinder part workshop production scheduling method |
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2022
- 2022-04-29 CN CN202210465332.1A patent/CN114819355A/en active Pending
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| CN115130789A (en) * | 2022-08-30 | 2022-09-30 | 武汉理工大学 | Distributed manufacturing intelligent scheduling method based on improved wolf optimization algorithm |
| CN115375193A (en) * | 2022-10-24 | 2022-11-22 | 埃克斯工业有限公司 | Method, device and equipment for optimizing double-target production scheduling and readable storage medium |
| CN115375193B (en) * | 2022-10-24 | 2023-02-10 | 埃克斯工业有限公司 | Method, device and equipment for optimizing double-target production scheduling and readable storage medium |
| CN115981262A (en) * | 2023-01-31 | 2023-04-18 | 武汉理工大学 | IMOEA-based hydraulic cylinder part workshop production scheduling method |
| CN115981262B (en) * | 2023-01-31 | 2023-12-12 | 武汉理工大学 | IMOEA-based hydraulic cylinder part workshop production scheduling method |
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