CN107316107B - Warp knitting machine assembly line balancing method oriented to multi-objective optimization - Google Patents

Warp knitting machine assembly line balancing method oriented to multi-objective optimization Download PDF

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CN107316107B
CN107316107B CN201710450531.4A CN201710450531A CN107316107B CN 107316107 B CN107316107 B CN 107316107B CN 201710450531 A CN201710450531 A CN 201710450531A CN 107316107 B CN107316107 B CN 107316107B
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张卫
王敏其
王水
陆宝春
黄龙振
胡西彪
刘冬
王菡珠
高至恺
汤重九
陈传强
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Wuyang Textile Machinery Co ltd
Nanjing University of Science and Technology
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Abstract

The invention discloses a warp knitting machine assembly line balancing method for multi-objective optimization, which comprises the following steps: determining a balance mathematical model of a warp knitting machine assembly line; defining assembly line parameters; defining a particle swarm algorithm; performing algorithm iteration: initializing a particle population, calculating a fitness function value to update a current optimal position and a global optimal position, updating the speed and the position of each particle, performing cross replacement operation on the population, and checking an evolution termination condition; outputting an optimal scheme and each evaluation index: decoding the finally output particle space position, converting the particle space coordinates containing position information into corresponding workstation task allocation information, outputting an assembly process scheme allocated in each workstation and simultaneously outputting an evaluation index under the optimal scheme; the method well avoids the problem of falling into the local optimal solution, and is suitable for balancing of the warp knitting machine assembly line with multi-objective optimization.

Description

Warp knitting machine assembly line balancing method oriented to multi-objective optimization
Technical Field
The invention belongs to the fields of artificial intelligence theory and mechanical assembly of automation technology, and particularly relates to a warp knitting machine assembly line balancing method for multi-objective optimization.
Background
The balancing of the assembly line is to balance people or machines as much as possible, and all assembly processes are assigned to the work stations, so that each work station is busy in the beat (i.e. the interval between two adjacent products passing through the tail end of the assembly line) to complete the maximum amount of operation, thereby minimizing the non-working time (idle time) of each work station, which is a main link in the design process of the assembly line.
The general method is that on the premise of giving production takt, based on the operation time of the assembly process and the constraint relation before and after the assembly process, the reasonable assembly process distribution is searched by carrying out multi-objective optimization on the number loss rate of the workstations, the loss rate of the assembly line and the relative smoothness index, and the actual assembly line design is guided. However, the assembly line balancing problem is essentially an NP combinatorial optimization problem, i.e., a decision problem solved with an uncertainty polynomial algorithm. Especially, when the assembly line balance problem is caused by a large number of assembly processes, a general calculation method presents huge calculation difficulty, so that a particle swarm algorithm is introduced. However, in terms of the study of algorithms, the literature: an improved particle swarm optimization algorithm for the multi-target disassembly line balance problem, modern manufacturing engineering, 2016 (4): 8-15, introducing a simulated annealing sampling mechanism on the basis of the PSO algorithm to provide a mixed PSO algorithm, so as to avoid the defect that the PSO group algorithm is easy to fall into precocity; the literature: application of immune particle swarm algorithm in mixed flow assembly line sequencing industrial engineering and management, 2011, 16 (4): 16-20, introducing an immune algorithm into a PSO algorithm for improvement, maintaining population diversity and preventing particles from falling into precocity; the literature: a hybrid PSO algorithm for a multi-objective organizing protocol with flexible operation times, sequence-dependent settings and learning effect, International Journal of Production Economics, 2013, 141 (1): 99-111. the optimization capability is improved by fusing the variable domain algorithm and the PSO algorithm. However, the methods generally have the problems of slow convergence, incapability of comprehensively optimizing convergence precision and low matching degree in combination with specific problems.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a warp knitting machine assembly line balancing method oriented to multi-objective optimization, which solves the problem that production factors are integrated in the actual production process, and the optimal mixed-flow assembly line balancing is completed.
The technical solution for realizing the purpose of the invention is as follows:
a warp knitting machine assembly line balancing method for multi-objective optimization comprises the following steps:
step 1, determining a balance mathematical model of a warp knitting machine assembly line: analyzing and determining an assembly constraint priority relation graph among all operation elements according to an assembly process flow, and establishing a mathematical model of the mixed flow assembly line on the premise of production beat and operation priority relation;
step 2, defining assembly line parameters: define standard man-hours ti(ii) a Defining an assembly precedence constraint relation matrix MAPC(ii) a Defining a production beat CT and the number N of workstations;
step 3, defining a particle swarm algorithm:
3.1, algorithm coding: matching the specific assembly sequence to a space coordinate of a particle swarm algorithm;
3.2, defining algorithm parameters: defining algorithm parametersSeveral parts of population scale Q, iteration times n, maximum evolution stagnation times G, inertia weight w and learning factor c1，c2Evaluating an index f;
and 4, performing algorithm iteration: initializing a particle population, calculating a fitness function value to update a current optimal position and a global optimal position, updating the speed and the position of each particle, performing cross replacement operation on the population, and checking an evolution termination condition;
and 5, outputting the optimal scheme and each evaluation index: decoding the final output particle space position, converting the particle space coordinate containing position information into corresponding workstation task allocation information, outputting the assembly process scheme distributed in each workstation and simultaneously outputting the evaluation index f under the optimal scheme, the number loss rate LWS of the workstations, the assembly line loss efficiency LLE and the smoothness index SI, the working time T of the workstationskAnd the tact time CT.
Compared with the prior art, the invention has the following remarkable advantages: combining the technical scheme
(1) Based on reality, global influence factors such as time for cleaning parts and the like in the assembly and production process of a factory are taken into consideration, and a particle swarm algorithm is combined to abstract a concrete problem into a mathematical model, so that the problem that a concrete assembly sequence is converted into an assembly priority relation matrix to carry out particle swarm algorithm iteration to solve the optimal assembly line balance is solved;
(2) the particle swarm algorithm improved by practical population cross operation not only meets the requirement of high convergence speed, but also well avoids the problem of trapping in a local optimal solution.
Drawings
FIG. 1 is a general scheme of a warp knitting machine assembly line balancing method based on an improved particle swarm algorithm.
Fig. 2 is a schematic diagram of particle swarm position encoding and decoding.
FIG. 3 is an example assembly task contextual relationship diagram.
Detailed Description
For the purpose of illustrating the technical solutions and technical objects of the present invention, the present invention will be further described with reference to the accompanying drawings and specific embodiments.
The invention relates to a warp knitting machine assembly line balancing method oriented to multi-objective optimization, which is combined with a figure 1 and comprises the following steps:
step 1, determining a balance mathematical model of a warp knitting machine assembly line:
and analyzing and determining an assembly constraint priority relation diagram among all operation elements according to the assembly process flow, and establishing a mathematical model of the mixed-flow assembly line on the premise of production beat and operation priority relation so as to optimize a multi-target fitness function integrating the number loss rate of the work stations, the efficiency of the assembly line and the smoothness index.
Setting a mathematical model:
(1) the operation elements of each product meet the assembly priority constraint relationship;
(2) the sum of the operating time on each workstation cannot exceed the theoretical takt;
(3) there is no parallel operation on the line and the workpiece transit time on the assembly line is negligible.
The mathematical model of the assembly line balance problem is set as follows:
s.t. Sx∩Sy＝Φ x≠y x，y＝1，2，…，N (1)
S1∪S2∪......∪SN＝E (2)
Figure BDA0001322300090000031
pj∈Syif m isij1, x is less than or equal to y (3)
Tk≤CT k＝1，2，…，m
Figure BDA0001322300090000032
Wherein s.t. is expressed as satisfying the following constraint, Sx、SyTask sets of the x workstation and the y workstation respectively; phi is a null set; skFor a set of tasks assigned to the kth workstation, i.e. Sk＝{piI task piAssigned to the kth station }; e is a post on the assembly lineWith a set of assembly processes, E ═ p1，p2，...，pII is the total number of assembly procedures; m isijAssembling a priority constraint relation for the task, if the task piFor task pjThe immediately preceding element of (i.e. p)jThe assembly process is based on piM when the assembly process is completedij1, otherwise mij＝0；TkIs the total working time of the kth station. Equation (1) indicates that any task must also be assigned to only one workstation; equation (2) ensures that each task is assigned; the distribution of each task in the formula (3) must meet the assembly priority constraint relation; equation (4) represents the unit time of the job scheduled to any one workstation and the tempo time cannot be exceeded.
Step 2, defining assembly line parameters: define standard man-hours ti(ii) a Defining an assembly precedence constraint relation matrix MAPC(ii) a Defining a production beat CT and the number N of workstations;
2.1, defining standard working hours ti
According to the actual assembly condition, counting and standardizing the standard working hours t of each warp knitting machine part assembly procedureiAnd i represents an assembly process number, and the counting includes the time for arranging parts and the like.
2.2 defining an assembly precedence constraint relation matrix MAPC: numbering and sequencing the assembly processes of the warp knitting machine, and defining a preferential constraint relation matrix M based on the numbering and sequencingAPC
According to the equipment process of the whole machine, and according to the number p of the equipment before and after the processiRepresenting the ith assembly procedure, and establishing a priority constraint relation matrix model as follows:
Figure BDA0001322300090000041
MAPCto assemble precedence constraint relationship matrices, pi、pjFor the ith and jth assembly processes, I is the total number of processes, mijThe assembly priority constraint relation between the ith assembly process and the jth assembly process, when there is no connection relation between the assembly processes, mij0, otherwise m ij1. In conjunction with FIG. 3, forThe specific warp knitting machine assembly procedure generates a precedence order priority relation matrix M between two adjacent assembly proceduresAPCThe description is given.
Referring to fig. 3, in this embodiment, assembly processes of a certain type of warp knitting machine are numbered, and taking 50 processes as an example, a priority relationship matrix M between two adjacent assembly processes is generated for a specific assembly process of the warp knitting machineAPCThe description is as follows:
the assembly process is explained as 1, 2, 3, 4, 5, 6: 1 is a pre-process of 2, 4, 2 is a pre-process of 3, 4 is a pre-process of 5, 4, 5 are both pre-processes of 6, so m is12＝1，m14＝1，m23＝1，m45＝1， m36＝1，m 561 and the rest are 0, and according to the rule, a 50-order assembly precedence constraint relation matrix can be obtained.
2.3 defining the production beat CT and the number of workstations N
The calculation formula of the assembly line beat is as follows:
Figure BDA0001322300090000042
in the formula (1), CT is the time difference between two continuous adjacent products on the assembly line in the theoretical tempo, T is the effective working time, namely the actual assembly working time, β is the working hour utilization rate, T0Is the total time of the job, i.e., the standard operating time of the plant, and Q is the total projected production.
The theoretical minimum workstation number is calculated by the formula:
Figure BDA0001322300090000043
in the formula, ∑ tiThe total time to complete all jobs. In practice, N.gtoreq.N is selectedminAnd rounding is performed.
And step 3: defining a particle swarm algorithm
3.1, algorithm coding: matching the specific assembly sequence to a space coordinate of a particle swarm algorithm;
the method comprises the steps of representing particles as a mode of spatial coordinates containing distributed workstation information, firstly determining an I-dimensional particle according to the total number I of assembly processes, wherein the dimension corresponds to the serial number of the assembly processes, then carrying out dimension coordinate distribution, and randomly assigning 1-N corresponding to Roman numerals in the particle dimension to represent the serial number of the workstation distributed by the assembly processes according to the number N of the workstations.
The coding of the algorithm is explained in detail in connection with fig. 2: taking 14 assembly processes and 6 workstations as examples, firstly, a 14-dimensional particle is defined, 14 assembly processes exist corresponding to 14 dimensions, corresponding coordinate values I-VI are randomly assigned in the dimensions, the coordinate values represent the common workstation numbers, for example, the coordinate values in the dimensions 1, 2 and 5 are I, namely, the assembly processes assigned to the workstation I are represented as the process 1, the process 2 and the process 5.
3.2, defining algorithm parameters: defining the population scale Q, the iteration number n, the maximum evolution stagnation number G, the inertia weight w and the learning factor c of the parameter part of the algorithm1，c2Evaluation index f
3.2.1, defining the population size Q, and determining the iteration number n: considering that the actual calculation amount is large, but in order to achieve both convergence speed and accuracy, the number of medium-scale population and the number of medium iterations are taken, Q is 20, and n is 200.
3.2.2, defining the maximum evolution stagnation time G: the value of the maximum evolution stagnation times is an improvement key judgment index of the algorithm, and in order to fully determine whether the search is really trapped in the local optimal solution, G is taken as 20. When the evolution stagnation number reaches 20, the particles are subjected to cross operation.
3.2.3 defining inertia weight w, learning factor c1，c2: after a plurality of times of simulation of the warp knitting machine data, the learning factor c is found when the inertia weight w is 0.21＝2，c21.5, which is the closest to the actual result.
3.2.4, defining evaluation index f: adopting the station number loss rate LWS, the assembly line loss efficiency LLE and the smoothness index SI as comprehensive calculation evaluation indexes f fitness values;
(1) station count loss rate LWS: the method is used for evaluating the difference value between the number of the actual assembly line workstations and the number of the theoretical minimum assembly line workstations, the smaller the LWS is, the less the number of workstations, staff and floor space requirements are required for the assembly line, the better the production efficiency is, and the formula is as follows:
Figure BDA0001322300090000051
(2) assembly line loss efficiency LLE: the method is used for evaluating the efficiency and continuity indexes of an assembly line, and the smaller the LLE is, the better the efficiency and continuity of the assembly line is shown, and the formula is as follows:
Figure BDA0001322300090000052
(3) smoothing index SI: the method is used for evaluating the deviation degree between the operation time and the production rhythm of each workstation in the assembly line, and the smaller the SI is, the smaller the operation time deviation of each workstation in the assembly line is, the more balanced the load of the assembly line is, and the formula is as follows:
Figure BDA0001322300090000061
wherein N is the number of workstations and CT is the tact; t is tiThe ith assembling working hour is that I assembling working hours are provided in total; t iskIs the kth workstation working time.
Comprehensively considering the three evaluation indexes, and obtaining the optimal weighting coefficient omega through multiple times of simulation1＝0.4、ω2＝0.3、ω30.3, the fitness value f of the assembly line balance problem is expressed as a function of equation 10:
f＝ω1·LWS+ω2·LLE+ω3·SI (10)
step 4, performing algorithm iteration
4.1, initializing particle population: assigning particle initial spatial position and velocity
Initializing the position in the working space of each particle in the population in 1 iteration
Figure BDA0001322300090000062
And velocity
Figure BDA0001322300090000063
A set of random initial solutions is obtained,
Figure BDA0001322300090000064
4.2, calculating the fitness function value and updating the current optimal position
Figure BDA00013223000900000614
And a global optimum position Pg
Evaluating the nth of the nth iteration
Figure BDA0001322300090000065
Fitness value of individual particle
Figure BDA0001322300090000066
Finding fitness value in particle swarm
Figure BDA0001322300090000067
And records the current nth value in the nth iteration
Figure BDA0001322300090000069
Optimal spatial position of individual particles
Figure BDA0001322300090000068
And all particles global optimal spatial position PgAll represented by row vectors of the I columns. Wherein the current optimal spatial position
Figure BDA00013223000900000613
Is a specific coordinate value in the particle space. PgIn the nth iteration
Figure BDA00013223000900000610
Comparing the minimum value with the minimum fitness value f in the previous n-1 iterations, selecting the smaller of the twoThe spatial position.
4.3 updating the velocity of each particle
Figure BDA00013223000900000612
And position
Figure BDA00013223000900000611
In searching for an optimal solution, the first
Figure BDA00013223000900000615
Each particle adjusts its own velocity and position according to a velocity update equation and a position update equation. Velocity update equation of the particle:
Figure BDA00013223000900000616
in the formula
Figure BDA00013223000900000617
Is the nth iteration
Figure BDA00013223000900000618
The new velocity of the individual particles is,
Figure BDA00013223000900000619
is the nth iteration
Figure BDA00013223000900000620
Velocity of individual particles, c1、c2Is a learning factor, w is an inertial weight, r1、r2Is [0, 1 ]]Random numbers obeying a normal distribution.
Figure BDA00013223000900000621
Is the nth iteration
Figure BDA00013223000900000622
The position of the particle. Particles
Figure BDA00013223000900000623
Position update equation of (1):
Figure BDA00013223000900000624
in the formula (I), the compound is shown in the specification,
Figure BDA0001322300090000071
is the n +1 th iteration
Figure BDA0001322300090000072
The position of the particles is determined by the position of the particles,
Figure BDA0001322300090000073
is the nth iteration
Figure BDA0001322300090000074
The position of the particle.
4.4, performing cross-over replacement operation: judging whether the updating stagnation algebra G is larger than or equal to G, and if so, operating the cross variation population;
if it is not
Figure BDA0001322300090000075
The updating stagnation algebra g is g +1, otherwise the updating stagnation algebra is set to zero g is 0. If G is larger than or equal to G, carrying out variant group strategy operation to generate new v.N random particles, and cross-replacing the speed and position of the v.N particles in the existing population, wherein v is a replacement proportion; otherwise go to step 4.5.
4.5 checking the evolution termination condition
If n is less than 200, the particle swarm algorithm is cycled from 4.2 to 4.4; if the number of iterations has reached 200, the iteration is terminated and step 5 is entered.
Step 5, outputting the optimal scheme and each evaluation index
And decoding the finally output particle space position, and converting the particle space coordinates containing the position information into corresponding workstation task allocation information. Outputting the assembly process schemes distributed in each workstation and outputting the assembly process schemes simultaneouslyThe evaluation index f, the station number loss rate LWS, the assembly line loss efficiency LLE and the smoothness index SI under the optimal scheme, and the station operation time TkAnd the tact time CT.
In the actual decoding process, decoding is carried out based on the space position of the finally output particles, the space position of the final particles is composed of dimensions 1-I and Roman numerical coordinate values representing workstation serial numbers under the dimensions, and dimension serial number values (different assembly processes) of the same coordinate value (the same workstation) are collected to obtain a final assembly line workstation distribution assembly process scheme.
The decoding method is specifically explained with reference to fig. 2: take the final optimal particle as 14 assembly sequences, 6 workstations as an example. I in the coordinates of dimension 1, 2 and 5, i.e. the assembly steps assigned to workstation I in the final project are assembly steps 1, 2 and 5. And the coordinates in the dimensions 3, 6 and 11 are II, namely the assembly steps divided in the workstation II in the corresponding final scheme are 3, 6 and 11. Similarly, the assembly steps divided in the workstation III are assembly steps 4, 7 and 10; the assembly steps divided in the workstation IV are assembly steps 6 and 9; the assembly steps divided in the workstation V are assembly steps 12 and 13; the assembly step divided in the workstation VI is the assembly step 14.

Claims (7)

1. A warp knitting machine assembly line balancing method for multi-objective optimization is characterized by comprising the following steps:
step 1, determining a balance mathematical model of a warp knitting machine assembly line: analyzing and determining an assembly constraint priority relation graph among all operation elements according to an assembly process flow, and establishing a mathematical model of the mixed flow assembly line on the premise of production beat and operation priority relation; the warp knitting machine assembly line balance mathematical model is as follows:
s.t.Sx∩Sy＝Φ x≠yx，y＝1，2，…，N (1)
S1∪S2∪......∪SN＝E (2)
Figure FDA0002617338110000011
Figure FDA0002617338110000012
wherein s.t. is expressed as satisfying the following constraint, Sx、SyTask sets of the x workstation and the y workstation respectively; phi is a null set; skFor a set of tasks assigned to the kth workstation, i.e. Sk＝{piI task piAssigned to the kth station }; e is the set of all assembly processes on the assembly line, E ═ p1，p2，...，pII is the total number of assembly procedures; m isijAssembling a priority constraint relation for the task, if the task piFor task pjThe immediately preceding element of (i.e. p)jThe assembly process is based on piM when the assembly process is completedij1, otherwise mij＝0；TkIs the total working time of the kth workstation;
step 2, defining assembly line parameters: define standard man-hours ti(ii) a Defining an assembly precedence constraint relation matrix MAPC(ii) a Defining a production beat CT and the number N of workstations; the specific process of defining the assembly line parameters comprises the following steps:
2.1, defining standard working hours ti: counting and standardizing standard working hours t of each warp knitting machine part assembly procedureiI represents the number of the assembly process, and the counting time includes the time for arranging parts and the like;
2.2 defining an assembly precedence constraint relation matrix MAPC: numbering and sequencing the assembly processes of the warp knitting machine, and defining a preferential constraint relation matrix M based on the numbering and sequencingAPC：
Figure FDA0002617338110000013
Wherein p isi、pjFor the ith and jth assembly processes, I is the total number of processes, mijThe assembly priority constraint relation between the ith assembly process and the jth assembly process, when there is no connection relation between the assembly processes, mij0, otherwise mij＝1；
2.3, defining the production beat CT and the number of workstations N:
the calculation formula of the assembly line beat is as follows:
Figure FDA0002617338110000021
in the formula (5), T is the effective working time, β is the working hour utilization rate, T0Is the total time of the job, i.e. the standard working time of the plant, Q is the total planned production;
the theoretical minimum workstation number is calculated by the formula:
Figure FDA0002617338110000022
in the formula, ∑ tiIn order to complete the total time of all the operations, in practice, N is selected to be more than or equal to NminAnd rounding;
step 3, defining a particle swarm algorithm:
3.1, algorithm coding: matching the specific assembly sequence to a space coordinate of a particle swarm algorithm;
3.2, defining algorithm parameters: defining the population scale Q, the iteration number n, the maximum evolution stagnation number G, the inertia weight w and the learning factor c of the parameter part of the algorithm1，c2Evaluating an index f; calculating a fitness value by taking the station number loss rate LWS, the assembly line loss efficiency LLE and the smoothness index SI as evaluation indexes f;
(1) station count loss rate LWS:
Figure FDA0002617338110000023
(2) assembly line loss efficiency LLE:
Figure FDA0002617338110000024
(3) smoothing index SI:
Figure FDA0002617338110000025
f＝ω1·LWS+ω2·LLE+ω3·SI (10)
wherein N is the number of workstations, NminFor the theoretical minimum number of workstations, CT is the tact; t iskIs the kth station operating time, ω1、ω2、ω3Is the optimal weighting coefficient;
and 4, performing algorithm iteration: the method comprises the steps of 4.1 initializing a particle population, 4.2 calculating a fitness function value to update a current optimal position and a global optimal position, 4.3 updating the speed and the position of each particle, 4.4 performing cross replacement operation on the population, and 4.5 checking evolution termination conditions;
and 5, outputting the optimal scheme and each evaluation index: decoding the final output particle space position, converting the particle space coordinate containing position information into corresponding workstation task allocation information, outputting the assembly process scheme distributed in each workstation and simultaneously outputting the evaluation index f under the optimal scheme, the number loss rate LWS of the workstations, the assembly line loss efficiency LLE and the smoothness index SI, the working time T of the workstationskAnd the tact time CT.
2. The warp knitting machine assembly line balancing method oriented to multi-objective optimization as claimed in claim 1, wherein the specific process of step 3.1 algorithm coding is as follows:
the method comprises the steps of representing particles as a mode of spatial coordinates containing distributed workstation information, firstly determining an I-dimensional particle according to the total number I of assembly processes, wherein the dimension corresponds to the serial number of the assembly processes, then carrying out dimension coordinate distribution, and randomly assigning 1-N corresponding to Roman numerals in the particle dimension to represent the serial number of the workstation distributed by the assembly processes according to the number N of the workstations.
3. The warp knitting machine assembly line balancing method oriented to multi-objective optimization as claimed in claim 1, wherein in step 3.2, the population size Q is 20, and the iteration number n is 200; the maximum evolution stagnation number G is 20; step 3.2 inertiaSex weight w is 0.2, learning factor c1＝2，c2＝1.5。
4. The multi-objective optimization-oriented warp knitting machine assembly line balancing method as claimed in claim 1, wherein the current optimal position and the global optimal position, the global optimal position P, are updated in step 4gIn the nth iteration
Figure FDA0002617338110000031
The minimum value is compared with the minimum fitness value f in the previous n-1 iterations, and the spatial position of the smaller of the two is selected.
5. The multi-objective optimization-oriented warp knitting machine assembly line balancing method as claimed in claim 1, wherein in the step 4, the particles are used for balancing
Figure FDA0002617338110000032
The velocity update equation of (1):
Figure FDA0002617338110000033
in the formula
Figure FDA0002617338110000034
Is the n +1 th iteration
Figure FDA0002617338110000036
The new velocity of the individual particles is,
Figure FDA0002617338110000035
is the nth iteration
Figure FDA0002617338110000037
Velocity of individual particles, c1、c2Is a learning factor, w is an inertial weight, r1、r2Is [0, 1 ]]Random numbers following a normal distribution;
particles
Figure FDA0002617338110000038
Position update equation of (1):
Figure FDA0002617338110000039
in the formula (I), the compound is shown in the specification,
Figure FDA00026173381100000310
is the n +1 th iteration
Figure FDA00026173381100000311
The position of the particles is determined by the position of the particles,
Figure FDA00026173381100000312
is the nth iteration
Figure FDA00026173381100000313
The position of the particle.
6. The warp knitting machine assembly line balancing method oriented to multi-objective optimization as claimed in claim 1, wherein the specific process of performing the cross replacement operation in the step 4 is as follows:
judging whether the updating stagnation algebra G is larger than or equal to G, and if so, operating the cross variation population; if it is not
Figure FDA00026173381100000314
Updating the stagnation algebra g to be g +1, otherwise, updating the stagnation algebra to be zero g to be 0; if G is larger than or equal to G, carrying out variant group strategy operation to generate new v.N random particles, and cross-replacing the speed and position of the v.N particles in the existing population, wherein v is a replacement proportion; otherwise, the evolution termination condition is checked.
7. The warp knitting machine assembly line balancing method for multi-objective optimization as claimed in claim 1, wherein the termination conditions in step 4 are as follows: if n is less than 200, the particle swarm algorithm is cycled from 4.2 to 4.4; if the number of iterations has reached 200, the iteration is terminated and step 5 is entered.
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