CN114066065A - Multi-target mixed zero-idle replacement flow shop scheduling method and system - Google Patents
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Abstract
The invention relates to a scheduling method and a system for a multi-target mixed zero-idle replacement flow shop, wherein the method comprises the following steps: step S1: describing the scheduling problem of the multi-target mixed zero-space idle current conversion water workshop; step S2: establishing a constraint condition meeting the problem; step S3: establishing an expected objective function in the actual production process; step S4: constructing a group intelligent algorithm based on dynamic time warping distance; step S5: and (4) finishing iterative optimization according to the dynamic time warping distance, finding out the set of the optimal solution, and obtaining the final scheduling scheme. The method and the system are favorable for optimizing the mixed zero-air idle current conversion water shop scheduling, so that an effective scheduling scheme is provided for a factory to reasonably arrange the work piece procedures.
Description
Technical Field
The invention belongs to the field of flow shop scheduling, and particularly relates to a multi-target mixed zero-idle replacement flow shop scheduling method and system based on a dynamic time warping distance.
Background
The Problem of zero-idle Flow water Scheduling (NPFSP) is a Problem of modern industrial combination which is distributed in the electronic circuit production industry, the casting field and the like, the NPFSP is further restricted on the basis of the Scheduling of a replacement Flow Shop, and the NPFSP requires continuous processing of a machine so as to reduce the abrasion and maintenance of a valuable machine.
Since not all machines belong to high-energy-consumption and expensive machines, a mixed zero-idle PermutionLow sheet Scheduling Problim (MNPFSP) is introduced, and the mixed zero-idle PermutionLow Shop Scheduling Problem requires that a designated machine is in a zero-idle constraint state, and other machines are in a normal operation state. Due to the complexity of the problems, such as containing a plurality of targets, a plurality of constraints and having NP-Hard characteristics, the research problems have larger research value as the scale of the research problems is enlarged. At present, methods for solving the problems mainly comprise an accurate algorithm, a heuristic algorithm and an intelligent optimization algorithm, but the realization effect is poor mostly. Therefore, there is a need to develop a new method to optimize the hybrid zero-idle permutation flow shop scheduling.
Disclosure of Invention
The invention aims to provide a multi-target mixed zero-idle replacement flow shop scheduling method and system, which are beneficial to optimizing mixed zero-idle replacement flow shop scheduling, so that an effective scheduling scheme is provided for a factory to reasonably arrange work procedures.
In order to achieve the purpose, the invention adopts the technical scheme that: a multi-target mixed zero-idle replacement flow shop scheduling method comprises the following steps:
step S1: describing the scheduling problem of the multi-target mixed zero-space idle current conversion water workshop;
step S2: establishing a constraint condition meeting the problem;
step S3: establishing an expected objective function in the actual production process;
step S4: constructing a group intelligent algorithm based on dynamic time warping distance;
step S5: and (4) finishing iterative optimization according to the dynamic time warping distance, finding out the set of the optimal solution, and obtaining the final scheduling scheme.
In step S1, n is the total number of components, m is the total number of machines, and U ═ U { (U) }1，U2，…Ui，…UnU denotes the machining sequence of the workpiece, UiFor workpieces positioned at i in the sequence, fHIs the H objective function value, yjFor workpieces U subject to zero idle constraintiThe total time of push-up post-processing in machine j, the set of machines belonging to the zero idle state is
Further, in step S2, the constraint condition satisfying the problem is established as follows:
the finishing time constraint conditions for starting the processing are as follows: c1，1＝t1，1；
Constraints of the machine 1 processing: ci，1≥Ci-1，1+ti，1，(i＝2，…n)；
Workpiece U1Constraint conditions of processing: c1，j≥C1，j-1+t1，j+yj-1，(j＝2，…m)；
The constraint conditions to be met by the rest of the workpieces and the machine are as follows:
Ci，j≥max{Ci，j-1，Ci-1，j+yj-1}+ti，j，(i＝2，…n；j＝2，…m)；
zero idle constraint: when j is equal to N, Ci-1，j＝Si，j，(i＝2，…n)；
Each machine delay time constraint: y is1＝0，
Wherein S isi，jIs a workpiece UiStarting time of machining on machine j, Ci，jTo workPart UiTime of completion on machine j, ti，jIs a workpiece UiMachining time on machine j, n being total number of workpieces, m being total number of machines, yjFor workpieces U subject to zero idle constraintiThe total time of push-up post-processing in machine j, the set of machines belonging to the zero idle state is
Further, in the step S3, an objective function f of the maximum completion time is set1Objective function f of maximum delay time2Total inventory cost objective function f3Objective function f of total holdover cost4：
f1＝Cn，m；
f2＝max{max(0，Ci，m-di)}，i＝1，2…n；
In the formula, Cn，mIs a workpiece UnThe completion time on machine m, i.e. the maximum completion time; ci，mIs a workpiece UiTime of completion on machine m, diIs a workpiece UiRequired delivery time of alphaiIs a workpiece UiStorage cost per unit time, |iIs a workpiece UiActual delivery time ofiIs a workpiece UiThe delay cost per unit time.
Further, the step S4 includes the following steps:
step S41: defining a parameter of the problem under study;
step S42: encoding individuals in a group intelligent algorithm;
step S43: constructing distance expression based on dynamic time warping;
step S44: and taking the reciprocal of the dynamic time warping distance as the fitness value of the individual in the group intelligent algorithm, and selecting the strategy to carry out the selection operation of the individual in the algorithm according to the fitness value.
Further, in step S41, gen is defined as the number of iterations at this time, maxgen is the total number of iterations, popsize is the population size, pcross is the cross probability, pmutation is the variation probability, ω, ε, and δ are all the intervals [0, 1]Random number in (b) the v-th gene of the r individualrv，bmaxIs gene brvThe upper bound of (1) is the total number n of workpieces; bminIs gene brvA lower bound of 1;
in step S42, the individual codes are integer codes, specifically, an array with a length of workpiece number is randomly generated, and then the array is sorted according to size to obtain a sorted array which meets the research problem, where the total number of individuals is the population number.
Further, the step S43 includes the following steps:
step S431: calculating the objective function value of different individuals of the ith iteration of the population as
The maximum value of each objective function in all individuals is selected and recorded as
Selecting the minimum value of each objective function in all individuals and marking as
Step S432: the objective function values of different dimensions fall in the [0, 1] interval by min-max normalization, which is as follows:
wherein i represents a population overlapThe generation is carried out for the ith time,
normalizing the value for the H-th objective function after the individual normalization,
represents the H-th objective function value of the individual,
the minimum function value of the H-th objective function in the population is represented,
representing the maximum function value of the H-th objective function in the population;
step S433: calculating the dynamic time warping distance, taking the reciprocal of the dynamic time warping distance as the fitness value of each individual in the group intelligent algorithm, establishing an individual selection strategy according to the fitness value, sequencing the reciprocals of the dynamic time warping distances of all the individuals in the group according to the size, wherein the maximum value is the optimal solution with the highest similarity to the objective function value of the ideal solution in the group, and the objective function value of the ideal solution is the minimum value of all objective functions during single-target optimization.
Further, in step S433, the calculating the dynamic time warping distance specifically includes the following steps:
step S4331: assuming that the function target value min-max normalized sequence of any individual and the minimum value min-max normalized sequence of each target function in the population individuals are respectively
It is formed into an H pattern matrix MHD, i.e. the distance matrix:
elements in a matrix
Represents
And
manhattan distance between;
wherein i represents the ith iteration of the population,
the H-th objective function value normalized for the individual,
the value normalized by the minimum value of the H-th objective function in the population individuals, M represents the Manhattan distance, and the calculation formula is as follows:
step S4332: in the matrix MHD, the continuum of elements forms a plurality of paths, which are normalized paths and denoted by W: w ═ W1，w2…，wK)，H≤K≤2H-1；
The canonical path W satisfies the following constraint:
(1) boundary conditions: the regular paths being from the lower left corner of the matrix MHD
At the beginning, corresponding coordinate point w1To the upper right corner of (1, 1)
Ending, corresponding to the coordinate point wK＝(H，H)；
(2) Continuity: if the coordinate is (p, q), the conditions that the coordinate is moved to the next coordinate point (p ', q') need to satisfy are that p '-p is less than or equal to 1, and q' -q is less than or equal to 1, which means that a certain point cannot be skipped and only the coordinate is moved to the next point;
(3) monotonicity: the requirement that p '-p is more than or equal to 0 and q' -q is more than or equal to 0 is met, namely W is required to be monotonous;
step S4333: there are many regular paths that satisfy the condition, wherein the path with the minimum regular cost is:
wherein K is the number of passing points, wk' is a coordinate point wkSelecting a path to minimize the final total distance according to the corresponding value in the matrix MHD, wherein the total distance measures the similarity of the two sequences, and the smaller the value is, the higher the similarity is;
and calculating the accumulated distance D in a manner of accumulating from the lower left corner to the upper right corner of the distance matrix MHD, and accumulating the distances of the passing points to obtain the accumulated distance D, wherein the calculation formula is as follows:
wherein D (p-1, q) represents the accumulated distance when the vehicle travels to the point (p-1, q), D (p, q-1) represents the accumulated distance when the vehicle travels to the point (p, q-1), and D (p-1, q-1) represents the accumulated distance when the vehicle travels to the point (p-1, q-1); initial conditions
And finally, calculating the cumulative distance D (H, H) through iteration, wherein the distance is the total distance, the cumulative distance D (H, H) is the dynamic time warping distance DTW (P, Q), and the passed path is the path with the minimum warping cost.
Further, the step S44 includes the following steps:
step S441: initializing a population, randomly generating the population with the size of popsize, setting the iteration number i as 1, and starting iteration;
step S442: solving each objective function value of the population;
step S443: calculating a fitness value, wherein a dynamic time warping distance is used as an individual selection strategy, and the reciprocal of the dynamic time warping distance is the size of the fitness value;
step S444: updating external files, when two or more objective function values are superior to the objective function values of the parent population, saving the values, and finally removing the same individuals;
step S445: selecting by adopting a binary tournament method, randomly selecting two individuals from a parent population each time, wherein the probability of selecting the individuals is the same, determining the selected individuals according to the fitness value of each individual, selecting the individuals with large fitness values to enter a child population, and repeating for multiple times until the child population reaches the size of the parent population;
step S446: performing cross operation, randomly selecting two individuals from a population, and inheriting good aspects of old individuals to new individuals through exchange combination of the individuals so as to generate new excellent individuals; firstly, a real number crossing method is adopted for crossing, and then the crossed individual genes are sequenced from small to large; wherein the x-th individual and the y-th individual are inzThe crossing mode on the position is as follows:
bxz＝bxz(1-ω)+byzω；
byz＝byz(1-ω)+bxzω；
in the formula, bxzIs the z-th gene of the x-th individual, byzIs the z-th gene of the y-th individual, and omega is the interval [0, 1%]A random number within;
step S447: carrying out mutation operation, randomly selecting an individual from the population, firstly selecting any point in the individual for mutation, and then sequencing the mutated genes according to the sequence from small to large; wherein the variation pattern of the r-th individual at the v position is:
in the formula, brvIs the v-th gene of the r individual, bmaxIs gene brvThe upper bound of (1) is the total number n of workpieces; bminIs gene brvA lower bound of 1; f (g) δ (1-gen/maxgen)2Both epsilon and delta are the interval [0, 1]]The internal random number gen is the iteration number at the moment, and maxgen is the total iteration number;
step S448: and when i is less than maxgen, i is i +1, jumping to the step S443, otherwise, jumping out of the loop, and stopping the algorithm.
The invention also provides a multi-target mixed zero-idle replacement flow shop scheduling system, which comprises a memory, a processor and computer program instructions stored on the memory and capable of being executed by the processor, wherein when the processor executes the computer program instructions, the steps of the method can be realized.
Compared with the prior art, the invention has the following beneficial effects: the invention provides a multi-target mixed zero-idle replacement flow shop scheduling method based on dynamic time warping distance, which can quickly and accurately find a target value and improve the searching performance by combining constraint conditions possibly encountered by factory production and taking the maximum completion time, the maximum delay time, the total inventory cost and the total deadline cost which are highly concerned by a factory as optimization targets.
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FIG. 1 is a flow chart of an implementation of an embodiment of the present invention.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
As shown in fig. 1, this embodiment provides a method for scheduling a multi-target hybrid zero-idle replacement flow shop, including the following steps:
step S1: and describing the scheduling problem of the multi-target mixed zero-idle replacement flow shop.
In step S1, n is the total number of components, m is the total number of machines, and U ═ U { (U) }1，U2，…Ui，…UnU represents the machining sequence of the workpiece, UiFor workpieces positioned at i in the sequence, Ci，jIndicating the work UiFinish machining time on machine j, Si，j(i 1, 2, …, n, j 1, 2, …, m) represents a workpiece UiStarting time of machining on machine j, fHIs the H objective function value, F ═ F1，f2，…fH)TRepresenting the target vector, ti，jIs a workpiece UiMachining time on machine j, diIs a workpiece UiRequired delivery time of liIs a workpiece UiActual delivery time of alphaiIs a workpiece UiStorage cost per unit time, epsiloniIs a workpiece UiDelay cost per unit time, WpIs the actual delivery volume of the p-th batch, h is the maximum delivery volume of a single batch, b is the number of deliveries, yjFor workpieces U subject to zero idle constraintiThe total time of push-up post-processing in machine j, the set of machines belonging to the zero idle state is
Step S2: and establishing constraint conditions meeting the problems.
In step S2, the constraint conditions satisfying the problem are established as follows:
the finishing time constraint conditions for starting the processing are as follows: c1，1＝t1，1；
Constraints of the machine 1 processing: ci，1≥Ci-1，1+ti，1，(i＝2，…n)；
Workpiece U1Constraint conditions of processing: c1，j≥C1，j-1+t1，j+yj-1，(j＝2，…m)；
The constraint conditions to be met by the rest of the workpieces and the machine are as follows:
Ci，j≥max{Ci，j-1，Ci-1，j+yj-1}+ti，j，(i＝2，…n；j＝2，…m)；
zero idle constraint: when j is equal to N, Ci-1，j＝Si，j，(i＝2，…n)；
Each machine delay time constraint: y is1＝0，
Conveying amount constraint conditions: wp≤h，p＝1，2，…b；
Wherein S isi，jIs a workpiece UiStarting time of machining on machine j, Ci，jIs a workpiece UiTime of completion on machine j, ti，jIs a workpiece UiMachining time on machine j, n being total number of workpieces, m being total number of machines, yjFor workpieces U subject to zero idle constraintiThe total time of push-up post-processing in machine j, the set of machines belonging to the zero idle state is
Step S3: and establishing an objective function expected in the actual production process.
In step S3, the objective function f of the maximum completion time is set1Objective function f of maximum delay time2Total inventory cost objective function f3Objective function f of total holdover cost4：
f1＝Cn，m；
f2＝max{max(0，Ci，m-di)}，i＝1，2…n；
In the formula, Cn，mIs a workpiece UnThe completion time on machine m, i.e. the maximum completion time; ci，mIs a workpiece UiTime of completion on machine m, diIs a workpiece UiRequired delivery time of alphaiIs a workpiece UiStorage cost per unit time, |iIs a workpiece UiActual delivery time ofiIs a workpiece UiThe delay cost per unit time.
Step S4: and constructing a group intelligent algorithm based on the dynamic time warping distance.
The step S4 includes the steps of:
step S41: the parameters of the problem under study are defined.
In step S41, gen is defined as the number of iterations at this time, maxgen is the total number of iterations, popsize is the population size, pcross is the cross probability, pmutation is the variation probability, ω, ε, and δ are all the intervals [0, 1]Random number in (b) the v-th gene of the r individualrv，bmaxIs gene brvThe upper bound of (1) is the total number n of workpieces; bminIs gene brvA lower bound of 1.
Step S42: and encoding the individuals in the group intelligent algorithm.
In step S42, the individual codes are integer codes, specifically, an array with a length of workpiece number is randomly generated, and then the array is sorted according to size to obtain a sorted array which meets the research problem, where the total number of individuals is the population number.
Step S43: and constructing distance expression based on dynamic time warping.
The step S43 includes the steps of:
step S431: calculating the objective function value of different individuals of the ith iteration of the population as
The maximum value of each objective function in all individuals is selected and recorded as
Selecting the minimum value of each objective function in all individuals and marking as
Step S432: the objective function values of different dimensions fall in the [0, 1] interval by min-max normalization, which is as follows:
wherein i represents the ith iteration of the population,
normalizing the value for the H-th objective function after the individual normalization,
represents the H-th objective function value of the individual,
the minimum function value of the H-th objective function in the population is represented,
the maximum function value of the H-th objective function in the population is represented.
Step S433: calculating the dynamic time warping distance, taking the reciprocal of the dynamic time warping distance as the fitness value of each individual in the group intelligent algorithm, establishing an individual selection strategy according to the fitness value, sequencing the reciprocals of the dynamic time warping distances of all the individuals in the group according to the size, wherein the maximum value is the optimal solution with the highest similarity to the objective function value of the ideal solution in the group, and the objective function value of the ideal solution is the minimum value of all objective functions during single-target optimization.
In step S433, the calculating the dynamic time warping distance specifically includes the following steps:
step S4331: assuming that the function target value min-max normalized sequence of any individual and the minimum value min-max normalized sequence of each target function in the population individuals are respectively
It is formed into an H pattern matrix MHD, i.e. the distance matrix:
elements in a matrix
Represents
And
manhattan distance between;
wherein i represents the ith iteration of the population,
h th after standardization for individualsThe value of each of the objective function values,
the value normalized by the minimum value of the H-th objective function in the population individuals, M represents the Manhattan distance, and the calculation formula is as follows:
step S4332: in the matrix MHD, the continuum of elements may form a plurality of paths, which are normalized paths, and are generally denoted by W: w ═ W1，w2…，wK) H is not more than K is not more than 2H-1, example: path W { (1, 1), (2, 2), (2, 3), (3, 3), (4, 4) }.
The canonical path W needs to meet the following constraint:
(1) boundary conditions: the regular paths being from the lower left corner of the matrix MHD
At the beginning, corresponding coordinate point w1To the upper right corner of (1, 1)
Ending, corresponding to the coordinate point wK＝(H，H)；
(2) Continuity: if the coordinate is (p, q), the conditions that the coordinate is moved to the next coordinate point (p ', q') need to satisfy are that p '-p is less than or equal to 1, and q' -q is less than or equal to 1, which means that a certain point cannot be skipped and only the coordinate is moved to the next point;
(3) monotonicity: in addition to satisfying the requirement for continuity, it is also necessary to satisfy p '-p.gtoreq.0 and q' -q.gtoreq.0, i.e., W is required to be monotonous.
Step S4333: there are many regular paths that satisfy the condition, wherein the path with the minimum regular cost is:
wherein K is the number of passing points, wk' is a coordinate point wkSelecting a path to minimize the final total distance according to the corresponding value in the matrix MHD, wherein the total distance is used for measuring the similarity of the two sequences, and the smaller the value is, the higher the similarity is.
And calculating the accumulated distance D in a manner of accumulating from the lower left corner to the upper right corner of the distance matrix MHD, and accumulating the distances of the passing points to obtain the accumulated distance D, wherein the calculation formula is as follows:
wherein D (p-1, q) represents the accumulated distance when the vehicle travels to the point (p-1, q), D (p, q-1) represents the accumulated distance when the vehicle travels to the point (p, q-1), and D (p-1, q-1) represents the accumulated distance when the vehicle travels to the point (p-1, q-1); initial conditions
Through iteration, the cumulative distance D (H, H), i.e. the total distance mentioned above, can be finally obtained, and the cumulative distance D (H, H) is the dynamic time warping distance DTW (P, Q), and the path that is passed is also the path with the minimum warping cost.
Step S44: and taking the reciprocal of the dynamic time warping distance as the fitness value of the individual in the group intelligent algorithm, and selecting the strategy to carry out the selection operation of the individual in the algorithm according to the fitness value.
The step S44 includes the steps of:
step S441: and (5) initializing a population, randomly generating the population with the size of popsize, and starting iteration when the iteration number i is 1.
Step S442: and solving each objective function value of the population.
Step S443: and calculating the fitness value, wherein the dynamic time warping distance is used as an individual selection strategy, and the reciprocal of the dynamic time warping distance is the size of the fitness value.
Step S444: and updating the external file, when two or more objective function values are superior to the objective function value of the parent population, saving the two or more objective function values, and finally removing the same individual.
Step S445: selecting by adopting a binary tournament method, randomly selecting two individuals from a parent population each time, wherein the probability of the individuals being selected is the same, determining the selected individuals according to the fitness value of each individual, selecting the individuals with large fitness values to enter a child population, and repeating for multiple times until the child population reaches the size of the parent population.
Step S446: performing cross operation, randomly selecting two individuals from a population, and inheriting good aspects of old individuals to new individuals through exchange combination of the individuals so as to generate new excellent individuals; firstly, a real number crossing method is adopted for crossing, and then the crossed individual genes are sequenced from small to large; wherein the crossing mode of the x-th individual and the y-th individual at the z position is as follows:
bxz＝bxz(1-ω)+byzω；
byz＝byz(1-ω)+bxzω；
in the formula, bxzIs the z-th gene of the x-th individual, byzIs the z-th gene of the y-th individual, and omega is the interval [0, 1%]The random number in (c).
Step S447: carrying out mutation operation, randomly selecting an individual from the population, firstly selecting any point in the individual for mutation, and then sequencing the mutated genes according to the sequence from small to large; wherein the variation pattern of the r-th individual at the v position is:
in the formula, brvIs the v-th gene of the r individual, bmaxIs gene brvThe upper bound of (1) is the total number n of workpieces; bminIs gene brvA lower bound of 1; f (g) δ (1-gen/maxgen)2Both epsilon and delta are the interval [0, 1]]The random number in the table, gen is the number of iterations at this time, and maxgen is the total number of iterations.
Step S448: and when i is less than maxgen, i is i +1, jumping to the step S443, otherwise, jumping out of the loop, and stopping the algorithm.
Step S5: and (4) finishing iterative optimization according to the dynamic time warping distance, finding out the set of the optimal solution, and obtaining the final scheduling scheme.
The embodiment also provides a multi-target mixed zero-idle replacement flow shop scheduling system, which comprises a memory, a processor and computer program instructions stored on the memory and capable of being executed by the processor, wherein when the computer program instructions are executed by the processor, the method steps can be implemented.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The foregoing is directed to preferred embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow. However, any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention are within the protection scope of the technical solution of the present invention.
Claims (10)
1. A multi-target mixed zero-idle replacement flow shop scheduling method is characterized by comprising the following steps:
step S1: describing the scheduling problem of the multi-target mixed zero-space idle current conversion water workshop;
step S2: establishing a constraint condition meeting the problem;
step S3: establishing an expected objective function in the actual production process;
step S4: constructing a group intelligent algorithm based on dynamic time warping distance;
step S5: and (4) finishing iterative optimization according to the dynamic time warping distance, finding out the set of the optimal solution, and obtaining the final scheduling scheme.
2. The method for scheduling multiple target mixed zero-idle replacement flow shop according to claim 1, wherein the method is characterized in thatIn step S1, n is the total number of components, m is the total number of units, and U ═ U { (U) }1，U2，…Ui，…UnU denotes the machining sequence of the workpiece, UiFor workpieces positioned at i in the sequence, fHIs the H objective function value, yjFor workpieces U subject to zero idle constraintiThe total time of push-up post-processing in machine j, the set of machines belonging to the zero idle state is
3. The method for scheduling a multi-target hybrid zero-idle replacement flow shop according to claim 2, wherein in step S2, the constraint conditions satisfying the problem are established as follows:
the finishing time constraint conditions for starting the processing are as follows: c1，1＝t1，1；
Constraints of the machine 1 processing: ci，1≥Ci-1，1+ti，1，(i＝2，…n)；
Workpiece U1Constraint conditions of processing: c1，j≥C1，j-1+t1，j+yj-1，(j＝2，…m)；
The constraint conditions to be met by the rest of the workpieces and the machine are as follows:
Ci，j≥max{Ci，j-1，Ci-1，j+yj-1}+ti，j，(i＝2，…n；j＝2，…m)；
zero idle constraint: when j is equal to M, Ci-1，j＝Si，j，(i＝2，…n)；
Each machine delay time constraint: y is1＝0，
Wherein S isi，jIs a workpiece UiStarting time of machining on machine j, Ci，jTo workPart UiTime of completion on machine j, ti，jIs a workpiece UiMachining time on machine j, n being total number of workpieces, m being total number of machines, yjFor workpieces U subject to zero idle constraintiThe total time of push-up post-processing in machine j, the set of machines belonging to the zero idle state is
4. The method for scheduling multiple target mixed zero-idle replacement flow shop according to claim 3, wherein in step S3, the objective function f of the maximum completion time is set1Objective function f of maximum delay time2Total inventory cost objective function f3Objective function f of total holdover cost4：
f1＝Cn，m；
f2＝max{max(0，Ci，m-di)}，i＝1，2…n；
In the formula, Cn，mIs a workpiece UnThe completion time on machine m, i.e. the maximum completion time; ci，mIs a workpiece UiTime of completion on machine m, diIs a workpiece UiRequired delivery time of alphaiIs a workpiece UiStorage cost per unit time, |iIs a workpiece UiActual delivery time ofiIs a workpiece UiThe delay cost per unit time.
5. The method for scheduling a multi-target hybrid zero-idle replacement flow shop according to claim 4, wherein the step S4 includes the steps of:
step S41: defining a parameter of the problem under study;
step S42: encoding individuals in a group intelligent algorithm;
step S43: constructing distance expression based on dynamic time warping;
step S44: and taking the reciprocal of the dynamic time warping distance as the fitness value of the individual in the group intelligent algorithm, and selecting the strategy to carry out the selection operation of the individual in the algorithm according to the fitness value.
6. The method as claimed in claim 5, wherein in step S41, gen is defined as the number of iterations at that time, maxgen is the total number of iterations, popsize is the population size, pcross is the cross probability, pmutation is the variation probability, ω, ε, and δ are all the intervals [0, 1]Random number in (b) the v-th gene of the r individualrv，bmaxIs gene brvThe upper bound of (1) is the total number n of workpieces; bminIs gene brvA lower bound of 1;
in step S42, the individual codes are integer codes, specifically, an array with a length of workpiece number is randomly generated, and then the array is sorted according to size to obtain a sorted array which meets the research problem, where the total number of individuals is the population number.
7. The method for scheduling a multi-target hybrid zero-idle replacement flow shop according to claim 6, wherein the step S43 includes the steps of:
step S431: calculating the objective function value of different individuals of the ith iteration of the population as
The maximum value of each objective function in all individuals is selected and recorded as
Selecting the minimum value of each objective function in all individuals and marking as
Step S432: the objective function values of different dimensions fall in the [0, 1] interval by min-max normalization, which is as follows:
wherein i represents the ith iteration of the population,
normalizing the value for the H-th objective function after the individual normalization,
represents the H-th objective function value of the individual,
the minimum function value of the H-th objective function in the population is represented,
representing the maximum function value of the H-th objective function in the population;
step S433: calculating the dynamic time warping distance, taking the reciprocal of the dynamic time warping distance as the fitness value of each individual in the group intelligent algorithm, establishing an individual selection strategy according to the fitness value, sequencing the reciprocals of the dynamic time warping distances of all the individuals in the group according to the size, wherein the maximum value is the optimal solution with the highest similarity to the objective function value of the ideal solution in the group, and the objective function value of the ideal solution is the minimum value of all objective functions during single-target optimization.
8. The multi-target hybrid zero-idle replacement flow shop scheduling method according to claim 7, wherein in the step S433, the calculating the dynamic time warping distance specifically includes the following steps:
step S4331: assuming that the function target value min-max normalized sequence of any individual and the minimum value min-max normalized sequence of each target function in the population individuals are respectively
It is formed into an H pattern matrix MHD, i.e. the distance matrix:
elements in a matrix
Represents
And
manhattan distance between;
wherein i represents the ith iteration of the population,
the H-th objective function value normalized for the individual,
the value normalized by the minimum value of the H-th objective function in the population individuals, M represents the Manhattan distance, and the calculation formula is as follows:
step S4332: in the matrix MHD, the continuum of elements forms a plurality of paths, which are normalized paths and denoted by W: w ═ W1，w2…，wK)，H≤K≤2H-1；
The canonical path W satisfies the following constraint:
(1) boundary conditions: the regular paths being from the lower left corner of the matrix MHD
At the beginning, corresponding coordinate point w1To the upper right corner of (1, 1)
Ending, corresponding to the coordinate point wK＝(H，H)；
(2) Continuity: if the coordinate is (p, q), the conditions that the coordinate is moved to the next coordinate point (p ', q') need to satisfy are that p '-p is less than or equal to 1, and q' -q is less than or equal to 1, which means that a certain point cannot be skipped and only the coordinate is moved to the next point;
(3) monotonicity: the requirement that p '-p is more than or equal to 0 and q' -q is more than or equal to 0 is met, namely W is required to be monotonous;
step S4333: there are many regular paths that satisfy the condition, wherein the path with the minimum regular cost is:
wherein K is the number of passing points, wk' is a coordinate point wkSelecting a path to minimize the final total distance according to the corresponding value in the matrix MHD, wherein the total distance measures the similarity of the two sequences, and the smaller the value is, the higher the similarity is;
and calculating the accumulated distance D in a manner of accumulating from the lower left corner to the upper right corner of the distance matrix MHD, and accumulating the distances of the passing points to obtain the accumulated distance D, wherein the calculation formula is as follows:
wherein D (p-1, q) represents the accumulated distance when the vehicle travels to the point (p-1, q), D (p, q-1) represents the accumulated distance when the vehicle travels to the point (p, q-1), and D (p-1, q-1) represents the accumulated distance when the vehicle travels to the point (p-1, q-1); initial conditions
And finally, calculating the cumulative distance D (H, H) through iteration, wherein the distance is the total distance, the cumulative distance D (H, H) is the dynamic time warping distance DTW (P, Q), and the passed path is the path with the minimum warping cost.
9. The method for scheduling a multi-target hybrid zero-idle replacement flow shop according to claim 8, wherein the step S44 includes the steps of:
step S441: initializing a population, randomly generating the population with the size of popsize, setting the iteration number i as 1, and starting iteration;
step S442: solving each objective function value of the population;
step S443: calculating a fitness value, wherein a dynamic time warping distance is used as an individual selection strategy, and the reciprocal of the dynamic time warping distance is the size of the fitness value;
step S444: updating external files, when two or more objective function values are superior to the objective function values of the parent population, saving the values, and finally removing the same individuals;
step S445: selecting by adopting a binary tournament method, randomly selecting two individuals from a parent population each time, wherein the probability of selecting the individuals is the same, determining the selected individuals according to the fitness value of each individual, selecting the individuals with large fitness values to enter a child population, and repeating for multiple times until the child population reaches the size of the parent population;
step S446: performing cross operation, randomly selecting two individuals from a population, and inheriting good aspects of old individuals to new individuals through exchange combination of the individuals so as to generate new excellent individuals; firstly, a real number crossing method is adopted for crossing, and then the crossed individual genes are sequenced from small to large; wherein the crossing mode of the x-th individual and the y-th individual at the z position is as follows:
bxz＝bxz(1-ω)+byzω；
byz＝byz(1-ω)+bxzω；
in the formula, bxzIs the z-th gene of the x-th individual, byzIs the z-th gene of the y-th individual, and omega is the interval [0, 1%]A random number within;
step S447: carrying out mutation operation, randomly selecting an individual from the population, firstly selecting any point in the individual for mutation, and then sequencing the mutated genes according to the sequence from small to large; wherein the variation pattern of the r-th individual at the v position is:
in the formula, brvIs the v-th gene of the r individual, bmaxIs gene brvThe upper bound of (1) is the total number n of workpieces; bminIs gene brvA lower bound of 1; f (g) δ (1-gen/maxgen)2Both epsilon and delta are the interval [0, 1]]The internal random number gen is the iteration number at the moment, and maxgen is the total iteration number;
step S448: and when i is less than maxgen, i is i +1, jumping to the step S443, otherwise, jumping out of the loop, and stopping the algorithm.
10. A multi-objective hybrid zero-idle replacement flow shop scheduling system comprising a memory, a processor, and computer program instructions stored on the memory and executable by the processor, the computer program instructions when executed by the processor being operable to perform the method steps of claims 1-9.
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