CN105975701A - Parallel scheduling disassembly path forming method based on mixing fuzzy model - Google Patents

Abstract

The invention discloses a parallel scheduling disassembly path forming method based on a mixing fuzzy model; the method comprises the following steps: building a fuzzy time scheduling disassembly process model, and deriving a fuzzy boundary and detachable constraint conditions; hybrid coding the disassembly sequence of all parts on stations and station sequence numbers of each disassembly step; using an improved heredity algorithm to optimize so as to obtain the minimum time and cost. The method can solve fuzzy time complex equipment parallel disassembly path forming and disassembly station scheduling optimization problems, thus shortening disassembly process time and reducing disassembly cost, improving production efficiency, introducing the gauss function into optimization solving, improving variation operation quality, accelerating convergence speed, and obtaining a better result.

Description

Parallel scheduling disassembly path generation method based on hybrid fuzzy model

Technical Field

The invention relates to the field of mechanical engineering and the technical field of computer application. And more particularly, to a parallel scheduling disassembly path generation method based on a hybrid fuzzy model.

Background

Along with the contradiction of environmental protection requirements, the production and life are increasingly prominent, and the disassembly, recovery and reuse of products become an important subject faced by people. The product inevitably faces disassembly problems during its life cycle because of the need for maintenance, inspection and recycling. The complex product contains spare part quantity many, and the assembly relation is also comparatively diversified and complicated, often needs the cooperation operation of a plurality of stations and a large amount of manpowers, consequently, and parallel dismantlement can improve dismantlement machining efficiency, optimizes resource allocation.

At present, many domestic and foreign scholars have conducted intensive research in this regard. Li et al propose a maintenance-oriented intelligent disassembly path planning method, which can deduce all possible disassembly operations with disassembled parts through a disassembly constraint graph and obtain the sequence of all disassembly operation combinations through a genetic algorithm; the Ayuce Aydemir-Karadag AND the like solve the problem of multi-target optimization of the balance of the disassembly line with parallel stations, provide a new genetic algorithm to solve the multi-target optimization problem, AND optimize the balance AND design cost of the disassembly production line by using an AND/OR graph; jeremy l.rickli et al propose a genetic algorithm to solve the local disassembly path optimization problem based on disassembly cost, recovery reprocessing cost, profit and environmental impact. In China, Liu Chong Hua and the like (application number 201310173004.5) propose a method and a device for planning a selective disassembly path, which are used for solving the problems of low automation degree and poor universality of the method for planning the selective disassembly path in the prior art; cao rock et al (application No. 201310671532.3) proposes an assembly time evaluation method based on an artificial neural network and virtual assembly, aiming at solving the problems of long assembly period, high cost and poor effect of products. Song guard and the like provide a product disassembly path planning based on constraint satisfaction problems, and provide a product disassembly path planning solving flow and algorithm based on constraint satisfaction problems; zhangxiufen and the like provide a parallel disassembly path planning method based on a fuzzy rough set, and establish a parallel disassembly fuzzy rough set mapping model to generate an optimal path.

In summary, the research on the disassembly path at home and abroad is mainly focused on the aspects of the disassembly path generation method and the optimization algorithm thereof. However, in the existing research, the parallel disassembly station scheduling and the disassembly path generation are rarely mixed and coded to solve, so that the situation that only local optimization is obtained in the algorithm solving is easily caused. In addition, uncertain researches are mostly focused on uncertain product disassembly quality states and uncertain product disassembly capacity or uncertain planning paths, and the uncertainty of processing time of each disassembly procedure, namely time ambiguity, is rarely researched, so that the deviation of final results is easily caused.

Disclosure of Invention

The invention aims to provide a parallel scheduling disassembly path generation method based on a hybrid fuzzy model, and aims to solve the problems that in the actual situation, the disassembly processing process is influenced by various uncertain factors, the processing time of each disassembly procedure fluctuates within a certain range instead of an accurate numerical value, and complex mechanical equipment is usually cooperatively disassembled on a plurality of stations in the actual disassembly process, namely, the disassembly is performed in parallel.

The embodiment of the invention adopts the technical scheme that:

step one, disassembling a product comprising L assemblies by taking the assemblies as a unit, specifically, disassembling the assemblies into parts, sequentially completing the disassembly of the assemblies on different stations through different processes, wherein each station corresponds to a plurality of processes, fuzzy completion time and fuzzy disassembly cost in the disassembly process are represented and calculated by adopting a triangular fuzzy function set, and normalization processing is performed;

the step one is to adopt a triangular fuzzy function set to represent the fuzzy completion time of the disassembling processAnd fuzzy disassembly costs. The basic algorithm for any two trigonometric fuzzy functions is defined as follows: if it is not Is two triangular blur Functions, where a_L,a_M,a_H，b_L,b_M,b_HAre all the quantity values of the raw materials,respectively represent by a_L,a_M,a_H，And b_L,b_M,b_HThe formed matrix is as follows:

and (3) addition operation:

subtraction:

multiplication operation:

division operation:

trigonometric fuzzy functionThe reciprocal operation of (a):

taking a big operation:

taking a small operation:

and (3) comparison operation: will be provided withAnd ═ b_L，b_M，b_H) A comparison operation is defined, as shown in table 1:

TABLE 1 comparison of operational criteria

Wherein, a_LAnd b_LIs thatAndlower limit of (a)_MAnd b_MIs thatAndmean value of a_HAnd b_HIs thatandThe upper limit of >, < is the greater and smaller sign in the fuzzy function, respectively.

The invention thus forms a model that yields the following parameters:

a component set AP: AP ═ AP₁… ap_i… ap_LL denotes the total number of components, i denotes the ordinal number of the component;

OP (OP) { OP)₁… op_i… op_L}；

Process set op of ith component_i：op_i＝{op_i，1… op_i，j… op_i，w(i)}；

Station set ST: ST ═ { ST ═ ST₁… st_k… st_N}；

Set of processes on the kth station SOP: SO (SO)_k＝{so_k，1… so_k，h… so_k，NU(k)The NU (k) represents a function of the number of finished processes of each station;

the parameters are specifically shown in table 2:

TABLE 2 model parameters for fuzzy time scheduling disassembly Process

The invention constructs a fuzzy time scheduling disassembly process model and aims to balance disassembly time and disassembly cost.

Because the time cannot be accurately represented by a triangular fuzzy function, from the historical records, the upper limit, the middle value and the lower limit are distributed according to the longest time, the average time and the shortest time of the disassembling process, so that the fuzzy time scheduling disassembling process model constructs the following four preconditions.

TABLE 3 four preconditions for model building of fuzzy time scheduling disassembly Process

Step two: taking the fuzzy completion time and the fuzzy disassembly cost of all the components obtained in the step one as optimized target values, weighting and summing the normalized fuzzy completion time and the normalized fuzzy disassembly cost in order to improve the model calculation efficiency, establishing a fuzzy time scheduling disassembly process model, and solving through a fuzzy matter element matrix to obtain weighted weights;

and step three, generating each fuzzy time dismounting path by the fuzzy time scheduling dismounting process model, and performing optimization solution by adopting a genetic algorithm to obtain an optimized dismounting path, the shortest dismounting time and the lowest dismounting cost so as to finish the generation of the parallel scheduling dismounting paths.

In the fuzzy time scheduling disassembly process model, each station can only operate one disassembly process of one assembly at the same time, each disassembly process of each assembly cannot be interrupted, the stations and the processes are independent, and different processes have no priority sequencing. And the time for setting the station and the time for moving the parts are ignored.

In the parallel disassembly process, in the first step, the total fuzzy completion time T and the total fuzzy disassembly cost C in the disassembly process are respectively expressed by the following formulas:

$T=\underset{k=1}{\overset{N}{\&Sigma;}}\underset{h=1}{\overset{NU\left(k\right)}{\&Sigma;}}t({\mathrm{st}}_k,{\mathrm{so}}_{k,h})$

$C=\underset{k=1}{\overset{N}{\&Sigma;}}\underset{h=1}{\overset{NU\left(k\right)}{\&Sigma;}}c({\mathrm{st}}_k,{\mathrm{so}}_{k,h})$

wherein, f is t (st)_k，so_k，h) The fuzzy completion time function of the h-th procedure on the k-th station is shown, g ═ c (st)_k，so_k，h) A fuzzy disassembly cost function representing a h-th process on a k-th station, k representing a serial number of the station, N representing a total number of the stations, h representing a serial number of the process, NU (k) representing a function of the total number of the processes on the k-th station, st_kDenotes the kth station, so_k，hShowing the h-th procedure on the k-th station;

because the time and the cost expression magnitude have larger difference, a linear normalization function is adopted, and the following formulas are adopted for carrying out unified normalization processing on each fuzzy completion time and each fuzzy disassembly cost:

$x=\frac{x-x_{min}}{x_{max}-x_{min}}.$

wherein x represents a normalized value, x_minRepresenting the minimum of all fuzzy completion times or fuzzy disassembly costs, x_minRepresenting the maximum of all fuzzy completion times or fuzzy disassembly costs.

The fuzzy time scheduling disassembly process model is expressed by the following formula:

$s.t.\left\{\begin{array}{c}\underset{k=1}{\overset{N}{\&Sigma;}}NU\left(k\right)=\underset{i=1}{\overset{L}{\&Sigma;}}W\left(i\right),\\ 1\&le;NU\left(k\right)\&le;\underset{i=1}{\overset{L}{\&Sigma;}}W\left(i\right)+1-N,\\ W\left(i\right)\&GreaterEqual;1,\\ {\mathrm{so}}_{k,h}\&Element;OP,\\ t({\mathrm{st}}_k,{\mathrm{so}}_{k,h})=\left(\begin{array}{ccc}{t}_{k,h}^1& t_{k,h}^2& t_{k,h}^3\end{array}\right).\end{array}\right.$

wherein W (i) represents the number of processes required to be completed when the ith component is completely disassembled, i represents the serial number of the component,and weights representing the blur completion time and the blur removal cost, respectively.

Fuzzy completion time weights in the fuzzy time scheduling disassembly process modelAnd solving the fuzzy disassembly cost weight by adopting a fuzzy matter element matrix in the following mode:

a) establishing a composite fuzzy matter element matrix R with l samples and two evaluation indexes_l,2：

$R_{l,2}=\left[\begin{array}{cc}{T}_1& C_1\\ T_2& C_2\\ .& .\\ .& .\\ .& .\\ T_l& C_l\end{array}\right]$

Wherein, T_lShowing the fuzzy time required for the first assembly to be completely disassembled, C_lExpressing the fuzzy disassembly cost required by the complete disassembly of the first component;

b) the smaller and more optimal transformation mode is adopted, the optimal mode is introduced to transform the composite fuzzy matter element matrix into a membership degree matrix, and the transformation formula is as follows:

${\mathrm{\&mu;}}_{j,i}=\frac{\min A_{j,i}}{A_{j,i}}$

wherein, mu_j,iThe degree of membership of the i-th evaluation index of the j-th component, A_j,iA quantity value representing the ith evaluation index of the jth component;

c) obtaining a correlation coefficient matrix R_ξAs a matrix of degrees of membershipComprises the following steps:

$R_{\mathrm{\&xi;}}=\stackrel{\&OverBar;}{R_{l,2}}=\left[\begin{array}{cc}{\mathrm{\&mu;}}_{1,1}& {\mathrm{\&mu;}}_{1,2}\\ {\mathrm{\&mu;}}_{2,1}& {\mathrm{\&mu;}}_{2,2}\\ .& .\\ .& .\\ .& .\\ {\mathrm{\&mu;}}_{l,1}& {\mathrm{\&mu;}}_{l,2}\end{array}\right]$

wherein,representing a matrix of degrees of membership, R_ξIs a matrix of correlation coefficients, mu_l,1Degree of membership, μ, of the first evaluation index of the first component_l,2Expressing the degree of membership of the second evaluation index of the ith component;

with R_wWeight complex element for each evaluation index, represented by R_kAnd expressing a relevance composite fuzzy object element consisting of two relevance, and performing weighted average centralized processing by adopting the following formula:

R_k＝R_w⊙R_ξ

wherein, the weight compound element R of each evaluation index_wIs represented by R_w＝(W₁,W₂)，W₁Weight complex element, W, representing the first evaluation index, i.e. the fuzzy disassembly time₂A weight compound element representing the fuzzy disassembly cost as a second evaluation index, ⊙ represents an operator, and an association degree compound fuzzy element R consisting of two association degrees is obtained_k：

$R_k=\left(\begin{array}{cc}{K}_1& K_2\end{array}\right)=\left(\begin{array}{cc}\underset{i=1}{\overset{n}{\&Sigma;}}{W}_1{\mathrm{\&mu;}}_{l,1}& \underset{i=1}{\overset{n}{\&Sigma;}}{W}_2{\mathrm{\&mu;}}_{l,2}\end{array}\right)$

Wherein, K₁、K₂Respectively representing the relevance values;

the obtained relevance values are sorted, and K is two relevance values according to the following formula₁、K₂Finding out the maximum value K of the correlation value^*：

K^*＝max(K₁K₂)

According to the relevance value K₁、K₂The completion time weight of the model is obtained by calculation according to the following formulaAnd a cost of disassembly weight:

the finally formed model of the fuzzy time scheduling and disassembling process is expressed as follows:

when K is₁≥K₂，

$\min E\&lsqb;\frac{K^{*}}{K_1+K_2}\underset{k=1}{\overset{N}{\&Sigma;}}\underset{h=1}{\overset{NU\left(k\right)}{\&Sigma;}}t({\mathrm{st}}_k,{\mathrm{so}}_{k,h})+(1-\frac{K^{*}}{K_1+K_2})\underset{k=1}{\overset{N}{\&Sigma;}}\underset{h=1}{\overset{NU\left(k\right)}{\&Sigma;}}c({\mathrm{st}}_k,{\mathrm{so}}_{k,h})\&rsqb;$

When K is₁<K₂

$\min E\&lsqb;(1-\frac{K*}{K_1+K_2})\underset{k=1}{\overset{N}{\&Sigma;}}\underset{h=1}{\overset{NU\left(k\right)}{\&Sigma;}}t({\mathrm{st}}_k,{\mathrm{so}}_{k,h})+\frac{K*}{K_1+K_2}\underset{k=1}{\overset{N}{\&Sigma;}}\underset{h=1}{\overset{NU\left(k\right)}{\&Sigma;}}c({\mathrm{st}}_k,{\mathrm{so}}_{k,h})\&rsqb;$

$s.t.\left\{\begin{array}{c}\underset{k=1}{\overset{N}{\&Sigma;}}NU\left(k\right)=\underset{i=1}{\overset{L}{\&Sigma;}}W\left(i\right),\\ 1\&le;NU\left(k\right)\&le;\underset{i=1}{\overset{L}{\&Sigma;}}W\left(i\right)+1-N,\\ W\left(i\right)\&GreaterEqual;1,\\ {\mathrm{so}}_{k,h}\&Element;OP,\\ t({\mathrm{st}}_k,{\mathrm{so}}_{k,h})=\left(\begin{array}{ccc}{t}_{k,h}^1& t_{k,h}^2& t_{k,h}^3\end{array}\right).\end{array}\right..$

The third step is to take the coding information of a single station or a single procedure as a gene and a single parallel scheduling and disassembling path as a chromosome to form a population taking all parallel scheduling and disassembling paths generated by a fuzzy time scheduling and disassembling process model as a group, and the following steps are adopted for specific treatment:

1) taking the obtained procedure and station mixed codes under the disassembly requirement as parallel scheduling disassembly paths, wherein the first half section of the mixed codes represents procedure information of all assemblies to be disassembled, and the second half section represents station information corresponding to each procedure gene of the first half section;

2) establishing a fitness function according to the optimization target, and assigning an initial value to the fitness;

3) and carrying out selection operation, cross operation and variation operation on the population to obtain an optimized disassembly path, the shortest fuzzy disassembly time and the shortest fuzzy disassembly cost.

The fitness value function of the step 2) is as follows:

wherein,and weights representing a fuzzy completion time and a fuzzy disassembly cost, respectively, n and m represent a total number of components and a total number of processes, respectively, t represents a time, c represents a cost, t represents a cost_i,jFuzzy disassembly time representing the completion of the disassembly of the jth process of the ith module, c_i,jRepresenting the fuzzy disassembly cost of the jth process of the ith module.

Fitness value is a criterion for the algorithm to select offspring individuals. In general, the total time for completing all the disassembling processes can be directly calculated to obtain an accurate value, which is recorded as fixness q/ZT, where ZT refers to the time for completing the disassembling of all the parts, and the smaller the fitness value, the better the chromosome is. However, time is often not the only consideration in actual production, and cost can play a significant role in solution decision making. Therefore, in the method, the actual situation is considered, the cost is introduced into the optimization process of the disassembly route generation, the disassembly cost is added into the fitness value formula of q/ZT, and ZT refers to the completion time of the disassembly of all the assemblies.

The selecting operation of the population in the step 3) is to adopt a roulette method to sequentially select parallel scheduling disassembly paths with better fitness to the population of the next generation until the number of calculation reaches the threshold of iteration times, and the probability pi (i) of each parallel scheduling disassembly path being selected is as follows:

$pi\left(i\right)=Fitness\left(i\right)/\underset{i-1}{\overset{n}{\&Sigma;}}Fitness\left(i\right)$

wherein, fitness (i) ═ 1/fitness (i), i represents the serial number of the component, n represents the number of the component, n, fitness (i) represents the reciprocal of the fitness value fitness (i), fitness (i) represents the fitness value of the ith component;

the step 3) of crossing the population specifically includes selecting two parallel scheduling disassembly paths randomly from the population by an integer crossing method, and selecting the front of each of the two parallel scheduling disassembly pathsBits, k denotes the total number of components in the disassembly path, i denotes the ith disassembled component, n_iIndicating the components, i ∈ (1,2, …,k)，m_jshowing a disassembly process;

then randomly selecting a crossing position for crossing, and then adjusting the process or station codes in the parallel scheduling disassembly path: and when the codes of the working procedures or the stations are repeated and redundant in the two parallel scheduling and disassembling paths, the codes at the positions are adjusted to the codes before crossing.

Because the parallel scheduling disassembly path adopted by the invention is used as a chromosome, and the coding form is an integer, an integer crossing method is adopted.

The population performing mutation operations comprises: firstly, randomly selecting a mutated parallel scheduling disassembly path from all parallel scheduling disassembly paths by using a mutation operator: for the first half segment of codes, reversing the process codes of the variation positions and the station codes corresponding to the process; and for the second half segment code, two variation positions are randomly selected, the station code of the first variation position is subjected to Gaussian variation by a variation method based on Gaussian distribution, and the station code of the second variation position is subjected to compensation variation to meet the model constraint condition.

The Gaussian mutation of the station code of the first mutation position is specifically as follows:

probability density function of gaussian distribution expressed by the following formula:

$f\left(x\right)=\frac{1}{\sqrt{2\mathrm{\&pi;}}\mathrm{\&sigma;}}{e}^{-{(x-\mathrm{\&mu;})}^2/\left(2{\mathrm{\&sigma;}}^2\right)},-\mathrm{\&infin;}<x<\mathrm{\&infin;}$

where σ is the variance of the gaussian distribution, μ is the expected value, and x is expressed. . . And e represents. . . ,

the variation from parent individuals to child individuals when the Gaussian variation is different adopts the following formula:

of formula (II) to (III)'_kRepresents the descendant (after mutation) of the kth station code, y_kRepresents the parent (before mutation) of the coding of the kth station, N (mu, sigma) represents a Gaussian variable with the expectation value of mu and the variance of sigma,to obtain the most ideal effect, the operator expressed by rounding down is assumed to have μ equal to 0, and the variance σ varies with the number of iterations of the gaussian variation s (t) as follows:

$\mathrm{\&sigma;}\left(t\right)=1-0.9\&times;\frac{g}{G}$

wherein G is the current genetic algebra, G is the total genetic algebra, and t represents the iteration number.

The parallel scheduling of the invention refers to that the working procedure operation is carried out simultaneously on multiple stations, the disassembly of the product assembly is completed, and the disassembly efficiency is improved.

The invention has the beneficial effects that:

the present invention introduces fuzzy mathematic theory and uses triangular fuzzy number rather than precise numerical value to express the detaching time of each part on a certain working position.

The parallel disassembly path planning of the invention shortens the disassembly process time, reduces the disassembly cost and improves the production efficiency. In the optimization solving process, the genetic algorithm is improved, and a Gaussian function is introduced to improve the quality of variation operation so as to accelerate the convergence speed of the algorithm and obtain a better result.

Drawings

FIG. 1 is an example of crossover and mutation of population in example 1.

FIG. 2 is the exploded view of the hydraulic machine and the main components of the embodiment 2.

In the figure: 1. a column; 2. an upper cross beam; 3. an oil cylinder; 4. stamping a sliding block; 5. a blank pressing slide block; 6. a work table; 7. a lower cross beam.

FIG. 3 shows the results of the algorithm of example 2 after 150 iterations at different initial mutation probabilities, where the initial mutation probability of (part a) is 0.6, (part b) is 0.3, and part c is 0.1.

Fig. 4 is a fuzzy time distribution of the parallel disassembly of seven components of example 2 at 9 stations.

Fig. 5 is the cost of the optimal parallel disassembly path of seven components of example 2 at 9 stations.

Fig. 6 is a variation of the present invention and the fast growing random number algorithm, where fig. 6(a), 6(c) and 6(e) are the results using the present method, and fig. 6(b), 6(d) and 6(f) are the results using the fast growing random number algorithm.

Detailed Description

The invention is further illustrated by the following figures and examples.

The method comprises the steps of firstly establishing a fuzzy time scheduling and disassembling process model and deducing fuzzy boundaries and detachable constraint conditions. And then, carrying out mixed coding on the disassembly sequence of all parts on the stations and the station serial number of each disassembly process, and finally, optimizing by adopting an improved genetic algorithm to obtain the minimum time and cost.

The examples of the invention are as follows:

example 1

Example 1 is a specific example for step three:

1) procedure and station hybrid coding under disassembly requirements

For example, the mixed code for the disassembled process and station, such as the code for a certain individual, is: 1, 3,4, 2, 4, 1, 3, 2, 1, 4, 1,2 | 2, 5, 3, 3, 1, 4, 2, 5, 4, 2, 1, 5, and the process and station information is shown in table 4, which contains 4 parts and 5 stations. The correspondence between parts and stations is shown in table 5:

TABLE 4 table of information decomposition of certain mixed code individual process and station

TABLE 5 correspondence between parts and stations

2) Establishing a fitness function according to the optimization target, and assigning an initial value to the fitness;

3) and carrying out selection operation, cross operation and mutation operation on the population.

Population selection

And selecting chromosomes with better fitness to the population of the next generation by adopting a roulette method. Therefore, the probability that the individual with larger fitness value is selected is higher, so that the evolution is always towards the optimization direction of the result.

Group crossing

For example, fig. 1 shows a chromosome crossing an extremum, and the crossing position is selected to be 6.

After the adjustment is performed after the intersection, the information of the intersected individual may be duplicated or incomplete, the supply and demand of some parts may be missing (e.g., parts 3 and 4 in the example), and the process of some parts may be redundant (e.g., part 1). According to the station before the intersection, the missing information is added to the semi-segment gene of the individual in the method.

Population variation

Firstly, a mutation operator randomly selects mutation individuals from a population, the first half segment of the individuals adopts selection mutation positions pos1 and pos2, for example, 2 and 7 are respectively selected for coding, and the disassembling processes of pos1 and pos2 in the individuals and corresponding station serial numbers are reversed.

For the second half of the individual code, a variation method based on Gaussian distribution is introduced, for two randomly selected variation positions pos3 and pos4, the gene at the first position is subjected to Gaussian variation, and the variation is complemented at the second position to meet the model constraint condition. For example, a certain somatometric pos1 is 2, pos2 is 7, pos3 is 3, and pos4 is 7, the total number of generations is 10, and the current number of generations is 8, as shown in fig. 1.

For example, in fig. 1, the amount of the complementary change of the position code of the second mutation position is specifically: the individual mutation positions are 3 and 7, the total number of genetic generations is 10, the current number of genetic generations is 8, and then the sigma is 0.28. The gene is 4 after pos3 mutation, since the post-individual half-segment gene lacks station 5 after pos3 mutation and does not meet the constraint condition, the gene mutation at position 7 is 5, and the mutation process and the result are as follows:

resulting in an optimized disassembly path and minimum disassembly time and minimum disassembly cost.

Example 2

Embodiment 2 specifically describes the embodiment with reference to a disassembly process of a hydraulic machine of a certain type, and specifically includes the following steps:

step one, summarizing the disassembly process of a hydraulic machine of a certain model. The explosion diagram of the hydraulic machine is shown in figure 2, and the hydraulic machine of the type totally comprises 7 main structural components 1, a stand column; 2. an upper cross beam; 3. an oil cylinder; 4. stamping a sliding block; 5. a blank pressing slide block; 6. a work table; 7. a lower cross beam. All the disassembling processes are completed on 10 optional stations, and the disassembling process of each part is less than or equal to 6.

Step two, according to historical data of a certain disassembly workshop, giving an optional station table corresponding to all part disassembly processes, as shown in table 6:

table 6 optional stations corresponding to each process

Step three, according to the historical data of the disassembly workshop, a triangular fuzzy number set of the disassembly time of the working procedure on the corresponding station is given, and as shown in a table 7:

TABLE 7 triangular fuzzy number set of disassembling time of working procedure on corresponding station

Step four, according to the historical data of the disassembly workshop, the cost required to be spent in each process is shown in table 8:

TABLE 8 cost per procedure

And fifthly, solving the fuzzy time disassembly path optimization based on the genetic algorithm.

The basic parameters of the algorithm are: the population number was 40, the crossover probability was set to 0.8, the mutation probability was set to 0.6, and the gully value was 0.9. Fig. 3a to 3c show the results of the method after 150 iterations when the initial mutation probabilities are 0.6, 0.3 and 0.1. Fig. 4 and 5 show the best disassembly path obtained when the number of iterations is 50.

Example 2 results:

the comparison of the run results and run time results obtained from the embodiments of the method of the present invention and the fast-growing random tree algorithm using the same raw data input at 50, 100, and 150 iterations respectively is shown in table 9.

TABLE 9 comparison between the results of the algorithms

As can be seen from Table 9, the optimal solutions obtained in the method of the present invention are all superior to the solutions of the fast search random number algorithm, and the runtime phrase fast search random number algorithm. The comparison between the present invention and the conventional fast growing random number algorithm is shown in fig. 6(a) to 6(f), and it can be seen that the algorithm of the present invention has a faster convergence rate.

Claims (10)

1. A parallel scheduling disassembly path generation method based on a hybrid fuzzy model is characterized by comprising the following steps:

step one, disassembling a product comprising L assemblies by taking the assemblies as a unit, sequentially completing the disassembly of the assemblies on different stations through different procedures, representing and calculating the fuzzy completion time and the fuzzy disassembly cost in the disassembly procedure by adopting a triangular fuzzy function set, and performing normalization processing;

step two: taking the fuzzy completion time and the fuzzy disassembly cost of all the components obtained in the step one as optimized target values, carrying out weighted summation on the normalized fuzzy completion time and the normalized fuzzy disassembly cost, establishing a fuzzy time scheduling disassembly process model, and solving through a fuzzy matter element matrix to obtain weighted weight;

and step three, generating each fuzzy time dismounting path by the fuzzy time scheduling dismounting process model, and performing optimization solution by adopting a genetic algorithm to obtain an optimized dismounting path, the shortest dismounting time and the lowest dismounting cost so as to finish the generation of the parallel scheduling dismounting paths.

2. The parallel scheduling disassembly path generation method based on the hybrid fuzzy model according to claim 1, wherein: in the fuzzy time scheduling disassembly process model, each station can only operate one disassembly process of one assembly at the same time, each disassembly process of each assembly cannot be interrupted, the stations and the processes are independent, and different processes have no priority sequencing.

3. The parallel scheduling disassembly path generation method based on the hybrid fuzzy model according to claim 1, wherein: in the first step, the total fuzzy completion time T and the total fuzzy dismantling cost C in the dismantling process are respectively expressed by the following formulas:

wherein, f is t (st)_k，so_k，h) The fuzzy completion time function of the h-th procedure on the k-th station is shown, g ═ c (st)_k，so_k，h) Representing a fuzzy disassembly cost function of the h-th procedure on the k-th station, wherein k represents the serial number of the station, N represents the total number of the station, h represents the serial number of the procedure, NU_(k)Indicating the process at the kth stationFunction of the total number, st_kDenotes the kth station, so_k，hShowing the h-th procedure on the k-th station;

and performing unified normalization processing on each fuzzy completion time and each fuzzy disassembly cost by adopting the following formulas:

wherein x represents a normalized value, x_minRepresenting the minimum of all fuzzy completion times or fuzzy disassembly costs, x_minRepresenting the maximum of all fuzzy completion times or fuzzy disassembly costs.

4. The parallel scheduling disassembly path generation method based on the hybrid fuzzy model according to claim 1, wherein: the fuzzy time scheduling disassembly process model is expressed by the following formula:

wherein W (i) represents the number of processes required to be completed when the ith component is completely disassembled, i represents the serial number of the component,and weights representing the blur completion time and the blur removal cost, respectively.

5. The parallel scheduling disassembly path generation method based on the hybrid fuzzy model according to claim 4, wherein: fuzzy completion time weights in the fuzzy time scheduling disassembly process modelAnd solving the fuzzy disassembly cost weight by adopting a fuzzy matter element matrix in the following mode:

a) establishing a composite fuzzy matter element matrix R with l samples and two evaluation indexes_l,2：

Wherein, T_lShowing the fuzzy time required for the first assembly to be completely disassembled, C_lExpressing the fuzzy disassembly cost required by the complete disassembly of the first component;

b) introducing a preferred mode to transform the composite fuzzy matter element matrix into a membership matrix, wherein the transformation formula is as follows:

wherein, mu_j,iThe degree of membership of the i-th evaluation index of the j-th component, A_j,iA quantity value representing the ith evaluation index of the jth component;

c) obtaining a correlation coefficient matrix R_ξAs a matrix of degrees of membershipComprises the following steps:

wherein,representing a matrix of degrees of membership, R_ξIs a matrix of correlation coefficients, mu_l,1Degree of membership, μ, of the first evaluation index of the first component_l,2Expressing the degree of membership of the second evaluation index of the ith component;

with R_wWeight complex representing each evaluation indexElement with R_kAnd expressing a relevance composite fuzzy object element consisting of two relevance, and performing weighted average centralized processing by adopting the following formula:

R_k＝R_w⊙R_ξ

wherein, the weight compound element R of each evaluation index_wIs represented by R_w＝(W₁,W₂)，W₁Weight complex element, W, representing the first evaluation index, i.e. the fuzzy disassembly time₂A weight compound element representing the fuzzy disassembly cost as a second evaluation index, ⊙ represents an operator, and an association degree compound fuzzy element R consisting of two association degrees is obtained_k：

Wherein, K₁、K₂Respectively representing the relevance values;

the obtained relevance values are sorted, and K is two relevance values according to the following formula₁、K₂Finding out the maximum value K of the correlation value^*：

K^*＝max(K₁K₂)

According to the relevance value K₁、K₂The completion time weight of the model is obtained by calculation according to the following formulaAnd a cost of disassembly weight:

6. the parallel scheduling disassembly path generation method based on the hybrid fuzzy model according to claim 1, wherein: the third step is to take the coding information of a single station or a single procedure as a gene and a single parallel scheduling and disassembling path as a chromosome to form a population taking all parallel scheduling and disassembling paths generated by a fuzzy time scheduling and disassembling process model as a group, and the following steps are adopted for specific treatment:

1) taking the obtained procedure and station mixed codes under the disassembly requirement as parallel scheduling disassembly paths, wherein the first half section of the mixed codes represents procedure information of all assemblies to be disassembled, and the second half section represents station information corresponding to each procedure gene of the first half section;

2) establishing a fitness function according to the optimization target, and assigning an initial value to the fitness;

3) and carrying out selection operation, cross operation and variation operation on the population to obtain an optimized disassembly path, the shortest fuzzy disassembly time and the shortest fuzzy disassembly cost.

7. The parallel scheduling disassembly path generation method based on the hybrid fuzzy model according to claim 6, wherein: the fitness value function of the step 2) is as follows:

wherein,and weights representing a fuzzy completion time and a fuzzy disassembly cost, respectively, n and m represent a total number of components and a total number of processes, respectively, t represents a time, c represents a cost, t represents a cost_i,jFuzzy disassembly time representing the completion of the disassembly of the jth process of the ith module, c_i,jRepresenting the fuzzy disassembly cost of the jth process of the ith module.

8. The parallel scheduling disassembly path generation method based on the hybrid fuzzy model according to claim 6, wherein: the selecting operation of the population in the step 3) is to adopt a roulette method to sequentially select parallel scheduling disassembly paths to the population of the next generation until the calculation number reaches an iteration number threshold, and the probability pi (i) of each parallel scheduling disassembly path being selected is as follows:

where, 1/fitness (i), i represents the serial number of the component, n represents the reciprocal of the fitness value fitness (i), and fitness (i) represents the fitness value of the ith component.

9. The parallel scheduling disassembly path generation method based on the hybrid fuzzy model according to claim 6, wherein: the step 3) of crossing the population specifically includes selecting two parallel scheduling disassembly paths randomly from the population by an integer crossing method, and selecting the front of each of the two parallel scheduling disassembly pathsBits, k denotes the total number of components in the disassembly path, i denotes the ith disassembled component, n_iRepresenting component, i ∈ (1,2, …, k), m_jShowing a disassembly process;

then randomly selecting a crossing position for crossing, and then adjusting the process or station codes in the parallel scheduling disassembly path: and when the codes of the working procedures or the stations are repeated and redundant in the two parallel scheduling and disassembling paths, the codes at the positions are adjusted to the codes before crossing.

10. The parallel scheduling disassembly path generation method based on the hybrid fuzzy model according to claim 6, wherein: the population performing mutation operations comprises:

firstly, randomly selecting a mutated parallel scheduling disassembly path from all parallel scheduling disassembly paths by using a mutation operator: for the first half segment of codes, reversing the process codes of the variation positions and the station codes corresponding to the process;

for the second half segment code, two variation positions are randomly selected, the station code of the first variation position is subjected to Gaussian variation through a variation method based on Gaussian distribution, and the station code of the second variation position is subjected to complement variable quantity:

the gaussian variation is a probability density function of the gaussian distribution expressed by the following formula:

where σ is the variance of the gaussian distribution, μ is the expected value, and x is expressed. . . And e represents. . . ,

the variation from parent individuals to child individuals when the Gaussian variation is different adopts the following formula:

of formula (II) to (III)'_kRepresents the descendant (after mutation) of the kth station code, y_kRepresents the parent (before mutation) of the coding of the kth station, N (mu, sigma) represents a Gaussian variable with the expectation value of mu and the variance of sigma,the operator is expressed as a rounded-down operator, the expectation is taken to be 0, and the variance σ changes with the number of iterations of the gaussian variation σ (t) as:

wherein G is the current genetic algebra, G is the total genetic algebra, and t represents the iteration number.