CN106022474A - Reconstructible assembly line balancing optimization method - Google Patents

Abstract

The invention provides a reconstructible assembly line balancing optimization method adopting an improved memetic algorithm. The reconstructible assembly line balancing optimization method comprises steps of coding and decoding, initial population generating, sequence adjustment, adaptation degree calculation, parent selection, population update, and local searching. When an ideal state or set iteration frequency is acquired, a chromosome having a minimal adaption degree value is output, and then a task allocation way corresponding to the chromosome having the minimal adaption degree value is acquired. A productivity and assembly line smoothness degree weight function is used as an adaption degree value function. Compared with a common memetic algorithm and a common genetic algorithm, the reconstructible assembly line balancing optimization method is advantageous in that the acquired adaption degree value is low, and the optimizing capability of the algorithm is effectively improved, and more reasonable solution is acquired.

Description

A kind of reconfigurable assembly line balance optimizing method

Technical field

The present invention relates to a kind of reconfigurable assembly line balance optimizing method, belong to Mechanical Design Automatization technical field.

Background technology

Restructural assembling line equilibrium problem (Assembly Line Balancing Problem, ALBP) one of subject matter always perplexing vast manufacturing enterprise, how improving the assembly productivity of enterprise is that enterprise wins the market competition, the necessary links that obtains bigger profit.Assembly line balancing is the precedence relationship according to assembling process of products, if the fittage of dryed product is arranged into suitably assembling place or work station, and ensures that the Assembling Production time of each work station is necessarily less than or equal to the production beat drafted.Put it briefly, the final purpose of Product Assembly line balance is to ensure that the assembling load balancing of each work station, ensure that idle running production time and the overload production time of each work station are minimum, make assembling goods and materials run held stationary, it is to avoid goods and materials block or the generation of assembly line idle running situation.Meta-heuristic algorithm conventional such issues that of solution includes genetic algorithm, simulated annealing, tabu search algorithm and ant group algorithm etc., but genetic algorithm and ant group algorithm the most easily occur that local search ability is low and the shortcoming such as poor astringency, simulated annealing and tabu search algorithm shortcoming are that the situation to global search space is understood seldom, and operation efficiency is low.Therefore, more novel algorithm is used can to solve large-scale problem within the rational time the most important.

Summary of the invention

Purpose: in order to overcome the deficiencies in the prior art, the present invention provides a kind of reconfigurable assembly line balance optimizing method, it is intended to realize productivity ratio and the optimal effect of assembly line flatness.

Technical scheme: for solving above-mentioned technical problem, the technical solution used in the present invention is:

A kind of reconfigurable assembly line balance optimizing method, comprises the following steps:

(1) priority order matrix between assembling work task is read according to practical condition；

(2) N number of chromosome corresponding to number of tasks is randomly generated；I.e. task sequence is decoded, uses random topology sort algorithm to adjust task sequence and make it meet priority constraint；

(3) principle exchanged in pairs by neighboring gene is improved initializing the chromosome produced, and sequence adjusts process and can terminate after fitness value no longer changes；

(4) utilizing fitness function to determine the good and bad degree of every chromosome, its value is the least, represents this chromosome outstanding, and its fitness is the highest；Use productivity ratio and the optimal formula of smoothness as algorithm fitness function；

$f={\mathrm{\λ}}_1\sqrt{\frac{\underset{l=1}{\overset{L}{\Σ}}{\[\underset{i=1}{\overset{n}{\Σ}}(x_{il}\·t_i)-C\]}^2}{L}}-{\mathrm{\λ}}_2\frac{\underset{i=1}{\overset{n}{\Σ}}{t}_i}{L\×C}$

Wherein, λ₁,λ₂For the weighting function of target, practical set demand determine and λ₁+λ₂=1；L is minimum work station number；C is productive temp；t_iFor completing the time used by i-th operation element；Represent the total time that All Jobs element completes；x_ilFor operation constraint factor, when operation element i is assigned to work station l, x_il=1, it is otherwise 0；

(5) taking Propertional model to select individuality, the chromosome making fitness high is obtained in that bigger survival probability；First each chromosome i cumulative probability p is calculated according to following formula_i, arrange according to ascending order according to the size of cumulative probability；Then generate (0,1] between random number x, by p_iCompare with x, if x is < p_i, then select first chromosome, otherwise select i-th chromosome, until Chromosome number reaches standard；

$p_i=\underset{h=1}{\overset{i}{\&Sigma;}}\left(f\right(h)/\underset{i=1}{\overset{N}{\&Sigma;}}f(i\left)\right)$

Wherein, f (i) represents the fitness value of chromosome i；

(6) sequence crossover using sequence and the method exchanging variation generate new chromosome, reach the purpose of Population Regeneration；

(7) at random gene a certain in chromosome is extracted and inserts other position to avoid the chromosome after updating to be absorbed in local optimum；

(8) if the iterations of perfect condition or setting reaches, then the chromosome that output fitness value is minimum, obtain the corresponding task method of salary distribution, otherwise return step (4).

Further, in step (2), random topology sort algorithm particularly as follows:

(21) null set M is initialized；

(22) initialize 0-1 and assemble precedence constraint matrix P_i,j, generate operation element set N；

(23) operation element being classified as 0 in set N is put into null set M；

(24) operation element chosen in set M is allocated；

(25) delete the row and column at (24) allocated operation element place, update set N；

(26) if All Jobs element is complete distribution in set N, terminate to run, otherwise, turn to (23).

Further, in step (6), sequence crossover is specific as follows:

Gene order in overstriking grid is the sequence that holding is constant, it is possible to entail filial generation after the intersection；Gene order after overstriking grid is moved to prostatitis, obtains new parent, as follows: in order to preferably state the concrete operations mechanism of the method, to use example to be illustrated herein, but be not limited to this example:

By gene elmination identical with keeping constant genome in another original series in new sequence, as: will parent 2 ' be deleted with the part of gene [BCD] in parent 1, so deleting one " D ", one " B " and one " C " forward in parent 2 ', and the thickened portion in upper table, the result obtained is as shown in bracket；

In parent 1/2, constant gene order obtains filial generation in the combination of remaining gene order in being inserted respectively into parent 2 '/1 '；As: the constant genome [BCD] in parent 1 is inserted in parent 2 ' remaining genome BBCAB, after leading portion genome BBC is placed in constant genome [BCD], back segment genome AB is placed in before, obtain following progeny sequences:

Further, in step (6), exchange variation specific as follows:

In chiasmatypy, any two gene location reaches the effect of variation；As shown in Figure 8.

Beneficial effect: a kind of reconfigurable assembly line balance optimizing method that the present invention provides, use improve cultural gene algorithm, comprise the following steps: encode and decode, the generation of initial population, sequence adjustment, fitness calculating, Juvenile stage, population recruitment, Local Search；If reaching the iterations of perfect condition or setting, then the chromosome that output fitness value is minimum, obtain the chromosome corresponding task method of salary distribution that fitness value is minimum, the present invention chooses productivity ratio and assembly line smoothness weighting function as fitness value function.Compared to common cultural gene algorithm and genetic algorithm, the fitness value that the present invention is obtained is relatively low, can the optimizing ability of effective boosting algorithm, obtain the most reasonably solving.

Accompanying drawing explanation

Fig. 1 is dominance relation schematic diagram；

Fig. 2 is 0-1 precedence constraint matrix；

Fig. 3 is that product A/B/C preferentially schemes；

Fig. 4 is that the integration of product A/B/C is the most preferentially schemed；

Fig. 5 is cultural gene algorithm flow chart；

Fig. 6 is that motor assembly line integrates total preferential figure；

Fig. 7 is that work station loads block diagram；

Fig. 8 is that the method exchanging variation carries out variation process schematic diagram.

Detailed description of the invention

Below in conjunction with the accompanying drawings the present invention is further described.

These accompanying drawings are the schematic diagram of simplification, and the basic structure of the present invention is described the most in a schematic way, and therefore it only shows the composition relevant with the present invention.

Reconfigurable assembly line equilibrium problem classified description

Assembly line balancing refers to, under the restriction premise determined, quantitative task be arranged into the work station of fixed number, makes the activity duration of each work station meet the beat that regulation requires, reduces idle running and the overload time of work station.The parameter describing reconfigurable assembly line equilibrium problem generally comprises three kinds: 1. operation element；Operation element refers to operating unit minimum during production assembles or task.Operation element not merely comprises an operation action, it is also possible to be multiple actions.The operation element time has referred to an operation element required time consumed, and typically uses t_iRepresent.2. work station；Work station refers in Assembling Production, the position at complete rear operation element fittage place or equipment.Same work station can distribute one or some producers, it is also possible to complete latter or multi-mode operation element fittage, but a job task can only complete in a work station, it is impossible to is assigned to two and above work station.3. productive temp；Productive temp has referred to the average time of a Product Assembly required by task.At present, assembly line balancing problem (Assembly Line Balancing Problem, ALBP) has become as one of manufacturing study hotspot.Both at home and abroad the criteria for classification of assembly line balancing problem is mainly according to the difference of optimization aim, is roughly divided into following three types:

I class assembly line balancing problem (ALBP-I): given productive temp C, solves minimum work station number L.

Class ii assembly line balancing problem (ALBP-II): given work station number L, solves minimum production beat C.

SI class assembly line balancing problem (ALBP-SI): give productive temp C and work station number L simultaneously, make work station load balancing on assembly line, describes with Smoothness Index SI.

Assembling precedence constraints chart and precedence constraint matrix

Preferential figure (Precedence Diagram, PD) is a kind of sensing figure that can preferably express assembly precedence relations, and it can effectively describe the precedence relationship of Complicated Flow.Its structure fomula is the set of each operation element during PD=(E, P), node E representative is assembled, and P represents the set of before and after's operation element dominance relation, as shown in Figure 1.

In Fig. 1, the numeral in "○" represents each operation element or task, what the Arabic alphabet on "○" top represented complete this operation element or the duration that required by task is wanted, the sensing of arrow shows the sequencing of its operation element connected, as fulfiled assignment, 1. and the most just element can carry out operation 3., and 8. the element operation 4. and 5. that fulfils assignment just can be carried out.

Although assembling precedence constraints chart can show the sequencing between each operation element or task intuitively, but it cannot be by computer identification and process as picture language, so the number language that computer can identify must be converted into, the most conventional method is constraint matrix method.

Order

In brief, m_i,j(i=1,2 ..., n；J=1,2 ..., value n) is to be determined by the dominance relation of operation element i and j.The dominance relation be given in Fig. 1 can be changed into the 0-1 constraint matrix P of 13 × 13_{i , j}, as shown in Figure 2.

The balance of reconfigurable assembly line can be described as: in planning cycle T_GIn, producing the series of products of M kind, the demand of jth kind product is K_j(j=1,2 ..., J), the product aggregate demand of J kind isBy on all production operation Elemental partition to minimum work station, and it is made to be optimized.

According to previously described precedence constraints chart, utilize its theory of constitution, multiple preferential figures can be combined as one and integrate total preferential figure, replace the equilibrium problem of restructural assembling line with relatively simple single assembly line balancing problem.If t_ij(i=1,2 .., I；J=1,2 .., J) represent operating time of the i-th operation element of jth kind product, the demand of jth kind product is K_j(j=1,2 ..., J), then in integrating total preferential figure, the installation time of i-th operation element can be calculated by following formula as follows.

${\stackrel{\&OverBar;}{t}}_i=\frac{\underset{j=1}{\overset{J}{\&Sigma;}}(t_{ij}\&times;K_j)}{\underset{j=1}{\overset{J}{\&Sigma;}}{K}_j}$

Such as: on a reconfigurable assembly line, assemble product A, product B and products C, its product demand ratio is 2:1:2 simultaneously.The preferential figure of A, B, C is as shown in Figure 3.

The most preferentially scheme, as shown in Figure 4 by calculating the integration that can obtain tri-kinds of products of A/B/C.

Reconfigurable assembly line equilibrium problem algorithm designs

Step 1: the generation of initial population.Cultural gene algorithm (Memetic Algorithm, MA) proposed in 1989 by Moscato, its optimization mechanism simulates the basis of cultural volution, a kind of global search based on population and coalition based on individual partial heuristic search.The method that the present invention uses random topology to sort generates initial population, comprises the following steps that shown:

(1) null set M is initialized；

(2) initialize 0-1 and assemble precedence constraint matrix P_i,j, generate operation element set N；

(3) operation element being classified as 0 in set N is put into null set M；

(4) operation element chosen in set M is allocated；

(5) delete the row and column at (4) allocated operation element place, update set N；

(6) if All Jobs element is complete distribution in set N, terminate to run, otherwise, turn to (3).

Step 2: sequence adjusts: the principle exchanged in pairs by neighboring gene is improved initializing the chromosome produced, sequence adjusts process and can terminate after fitness value no longer changes.

Step 3: fitness calculates: in algorithm searching process, utilizing fitness function to determine the good and bad degree of every chromosome, its value is the least, represents this chromosome outstanding, and its fitness is the highest.The goal in research of the present invention is to look for productivity ratio and the optimal result of smoothness.The present invention uses following formula as algorithm fitness function.

$f={\mathrm{\&lambda;}}_1\sqrt{\frac{\underset{l=1}{\overset{L}{\&Sigma;}}{\&lsqb;\underset{i=1}{\overset{n}{\&Sigma;}}(x_{il}\&CenterDot;t_i)-C\&rsqb;}^2}{L}}-{\mathrm{\&lambda;}}_2\frac{\underset{i=1}{\overset{n}{\&Sigma;}}{t}_i}{L\&times;C}$

Such as, weight selection function is λ₁=0.7, λ₂=0.3.Its fitness value is

$f=0.7\&times;\sqrt{\frac{{(14-15)}^2+{(14-15)}^2+{(12-15)}^2+{(12-15)}^2}{5}}-0.3\&times;\frac{14+14+15+12+12}{5\&times;15}=1.132$

Step 4: Juvenile stage: the purpose of Juvenile stage is in order to the chromosome making fitness high is obtained in that bigger survival probability, takes Propertional model to select individuality herein.First each chromosome i cumulative probability p is calculated according to following formula_i, arrange according to ascending order according to the size of cumulative probability.Then generate (0,1] between random number x, by p_iCompare with x, if x is < p_i, then select first chromosome, otherwise select i-th chromosome, until Chromosome number reaches standard.

$p_i=\underset{h=1}{\overset{i}{\&Sigma;}}\left(f\right(h)/\underset{i=1}{\overset{N}{\&Sigma;}}f(i\left)\right)$

Wherein, f (i) represents the fitness value of chromosome i.

Step 5: population recruitment: the present invention mainly uses the intersection of sequence and the method for variation to generate new chromosome, reaches the purpose of Population Regeneration, in order to preferably state the concrete operations mechanism of the method, uses example to be illustrated herein.

(1) intersect

Intersecting and include many types, the present invention uses the most conveniently sequence crossover.As follows:

Gene order in overstriking grid is the sequence that holding is constant, it is possible to entail filial generation after the intersection.Gene order after overstriking grid is moved to prostatitis, obtains new parent, as follows:

By gene elmination identical with keeping constant genome in another original series in new sequence, as: will parent 2 ' be deleted with the part of gene [BCD] in parent 1, so deleting one " D ", one " B " and one " C " forward in parent 2 ', and the thickened portion in upper table, the result obtained is as shown in bracket.

In parent 1/2, constant gene order obtains filial generation in the combination of remaining gene order in being inserted respectively into parent 2 '/1 '.As: the constant genome [BCD] in parent 1 is inserted in parent 2 ' remaining genome BBCAB, after leading portion genome BBC is placed in constant genome [BCD], back segment genome AB is placed in before, obtain following progeny sequences:

(2) variation

The present invention uses the method exchanging variation to carry out variation process, namely any two gene in chiasmatypy, as shown in Figure 8.

Step 6: Local Search: in order to avoid the chromosome after updating is absorbed in local optimum, Local Search must be carried out, insertion algorithm is used to be optimized herein, i.e. at random gene a certain in chromosome is extracted and inserts other position, Local Search can continue always, until the fitness value of chromosome no longer changes.

Step 7: algorithm end condition: when algorithm reaches the iterations of setting or fitness value no longer changes when, algorithm terminates, and the chromosome that output fitness value is minimum, the gene order of this chromosome is the most rational operation element sequence of operation.Otherwise, return to step 3 and iterate, until meeting end condition.

In order to intuitively express the step of inventive algorithm, The present invention gives the algorithm flow chart such as Fig. 5.

The effect of the present invention can be illustrated by the electric motor of automobile reconfigurable assembly line balance optimizing example of certain electric motor of automobile assembling factory.

One electric motor of automobile reconfigurable assembly line of certain plant equipment company limited is balanced analyzing by the present invention, it is 62ZYT001 that this assembly line can assemble model, 100ZYT001,62ZYT-SUV, four kinds of motors of 78ZYT001, this enterprise receives certain cloud manufacturing order, and it is 500,400,400 and 300 to the quantity required of these four kinds of products respectively.By above-mentioned computing formula and preferential figure combinatorial principle, determining that the integration of these four kinds of products is the most preferentially schemed as shown in Figure 6, this preferential figure includes 30 job tasks, through early stage balanced design and Investigation on market demand, determining that its work station L is 7, productive temp C is 33.5s.

The present invention uses Matlab to write Algorithm for Solving program, and hardware platform is Intel (R) Core (TM) i5-4200H CPU@2.80GHz, RAM 8G.Population number is 50, intersects and the probability that makes a variation is respectively 0.8 and 0.09, weighting function λ₁=0.6, λ₂=0.4.If after iteration 30 times, target function value tends towards stability, then algorithm terminates.Being drawn by computing and be 7 at work station, when productive temp is 33.5s, the minima of object function and the job task distribution scheme of correspondence, as shown in the table.Can be seen that optimization solves fruit by the block diagram of Fig. 7 more stable smooth.

The load Smoothness Index SI=1.81 of assembly line, production efficiency after balance optimizingBalancing delay rate β=1-95.28%=4.72%, the evaluation criterion be given according to pertinent literature, the balancing delay rate assembly line less than 10% belongs to excellent assembly line, so balance optimizing concept feasible is effective.

The above is only the preferred embodiment of the present invention; it is noted that, for those skilled in the art; under the premise without departing from the principles of the invention, it is also possible to make some improvements and modifications, these improvements and modifications also should be regarded as protection scope of the present invention.

Claims (4)

1. a reconfigurable assembly line balance optimizing method, comprises the following steps:

(1) priority order matrix between assembling work task is read according to practical condition；

(2) N number of chromosome corresponding to number of tasks is randomly generated；I.e. task sequence is decoded, uses random topology sort algorithm to adjust task sequence and make it meet priority constraint；

(3) principle exchanged in pairs by neighboring gene is improved initializing the chromosome produced, and sequence adjusts process and can terminate after fitness value no longer changes；

(4) utilizing fitness function to determine the good and bad degree of every chromosome, its value is the least, represents this chromosome outstanding, and its fitness is the highest；Use productivity ratio and the optimal formula of smoothness as algorithm fitness function；

Wherein, λ₁,λ₂For the weighting function of target, practical set demand determine and λ₁+λ₂=1；L is minimum work station number；C is productive temp；t_iFor completing the time used by i-th operation element；Represent the total time that All Jobs element completes；x_ilFor operation constraint factor, when operation element i is assigned to work station l, x_il=1, it is otherwise 0；

(5) taking Propertional model to select individuality, the chromosome making fitness high is obtained in that bigger survival probability；First each chromosome i cumulative probability p is calculated according to following formula_i, arrange according to ascending order according to the size of cumulative probability；Then generate (0,1] between random number x, by p_iCompare with x, if x is < p_i, then select first chromosome, otherwise select i-th chromosome, until Chromosome number reaches standard；

Wherein, f (i) represents the fitness value of chromosome i；

(6) sequence crossover using sequence and the method exchanging variation generate new chromosome, reach the purpose of Population Regeneration；

(7) at random gene a certain in chromosome is extracted and inserts other position to avoid the chromosome after updating to be absorbed in local optimum；

(8) if the iterations of perfect condition or setting reaches, then the chromosome that output fitness value is minimum, obtain the corresponding task method of salary distribution, otherwise return step (4).

Reconfigurable assembly line balance optimizing method the most according to claim 1, it is characterised in that: in step (2), random topology sort algorithm particularly as follows:

(21) null set M is initialized；

(22) initialize 0-1 and assemble precedence constraint matrix P_i,j, generate operation element set N；

(23) operation element being classified as 0 in set N is put into null set M；

(24) operation element chosen in set M is allocated；

(25) delete the row and column at (24) allocated operation element place, update set N；

(26) if All Jobs element is complete distribution in set N, terminate to run, otherwise, turn to (23).

Reconfigurable assembly line balance optimizing method the most according to claim 1, it is characterised in that: in step (6), sequence crossover is specific as follows: be enumerated as

Gene order in overstriking grid is the sequence that holding is constant, it is possible to entail filial generation after the intersection；Gene order after overstriking grid is moved to prostatitis, obtains new parent, as follows:

By gene elmination identical with keeping constant genome in another original series in new sequence, as: will parent 2 ' be deleted with the part of gene [BCD] in parent 1, so deleting one " D ", one " B " and one " C " forward in parent 2 ', and the thickened portion in upper table, the result obtained is as shown in bracket；

In parent 1/2, constant gene order obtains filial generation in the combination of remaining gene order in being inserted respectively into parent 2 '/1 '；As: the constant genome [BCD] in parent 1 is inserted in parent 2 ' remaining genome BBCAB, after leading portion genome BBC is placed in constant genome [BCD], back segment genome AB is placed in before, obtain following progeny sequences:

Reconfigurable assembly line balance optimizing method the most according to claim 1, it is characterised in that: in step (6), exchange variation specific as follows:

In chiasmatypy, any two gene location reaches the effect of variation；As shown in Figure 8.