CN111652392B - Low-carbon efficient disassembly line balance optimization method for waste mobile terminal - Google Patents
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Abstract
The invention belongs to the technical field of mobile terminal recovery, and discloses a low-carbon efficient disassembly line balance optimization method for waste mobile terminals. The invention effectively provides a decision maker with a selection reference of various schemes, can improve the efficiency of the workstation and reduce the carbon emission, and is efficient and environment-friendly.
Description
Technical Field
The invention relates to a low-carbon efficient disassembly line balance optimization method for a waste mobile terminal, and relates to a mobile terminal recovery technology.
Background
With the development and application of mobile interconnection technology and intelligent manufacturing technology, the intelligent manufacturing industry has an increasingly heavy influence proportion in daily life, electronic mobile terminals have been increased year by year from both yield and popularity, and the updating of mobile terminals has also been faster and faster, with the fact that the speed of replacing mobile terminals has also been increased year by year, and old and useless mobile terminals have been routinely discarded in landfill sites in the last stage of their lives in the past. However, in the last decade, environmental awareness manufacturing and product recycling has become an obligation for many companies due to new government regulations and consumer interests. Compared with the traditional waste electronic products, the waste mobile terminals have the characteristics of high residual value and long residual service life. Accordingly, enterprises are increasingly interested in how to effectively disassemble their produced products. The method and the system have the advantages that time, money and engineering expertise are invested in to determine how customers return scrapped products (reverse logistics) and how to make the recovery process of the products profitable, or the parts of the waste mobile terminals are recycled in an industrialized and large-scale manner with the lowest cost so as to achieve the purposes of developing circular economy and reducing environmental pollution, and have great economic and social benefits.
The low-carbon and high-efficiency disassembly of waste mobile terminals is a typical disassembly line balancing and multi-objective optimization problem, and the selection of an optimal disassembly sequence is critical for effective processing of the product at the end of its lifetime. A disassembly sequence is a list of disassembly operations (e.g., separating a component into two or more components, or deleting one or more connections between components). Disassembly is performed during remanufacturing, recycling and disposal, with disassembly lines being the best choice for automation. The problem of the disassembly sequence of the mobile phone shell on a disassembly line is solved, a feasible sequence is found, and the number of work stations, the idle time index, the work load smoothness and the carbon emission are minimized.
For the multi-objective optimization problem of the disassembly line balance, a dictionary method can be adopted to gradually study each objective or convert the multi-objective problem into a single-objective problem by distributing objective weight values, the dictionary method only pays attention to the optimization of one or more objectives, and other objectives are ignored, so that the balance among the objectives can not be realized, and the diversity of solutions is lost. For the weighting method, different targets have different dimensions, and how to reasonably and accurately set the weight value is difficult. Based on Pareto criteria, multiple targets are simultaneously optimized, multiple balance solutions are obtained, and balance among multiple targets is achieved. Based on the Pareto solution set, the congestion distance is introduced as a non-inferior solution filtering strategy, so that the solution performance is further improved. Therefore, it is appropriate to design an intelligent algorithm based on Pareto solution sets to solve the multi-objective disassembly line balancing problem.
Disclosure of Invention
Aiming at the technical problems, the invention provides a low-carbon and high-efficiency disassembly line balance optimization method for a waste mobile terminal, which applies a genetic algorithm method based on Pareto multi-objective optimization to low-carbon and high-efficiency disassembly of the waste mobile terminal so as to solve the problems of time consuming, low efficiency, pollution and the like of the disassembly of the waste mobile terminal, realize the purposes of efficient, environment-friendly and environment-friendly disassembly and achieve the industrialization and large-scale recycling of waste products.
In order to achieve the above purpose, the present invention provides the following technical solutions: a low-carbon efficient disassembly line balance optimization method for a waste mobile terminal comprises the following steps:
step one, initializing a population according to a priority relation matrix p;
secondly, rapid non-dominant sorting is conducted on the primary population, population layering is conducted according to the non-dominant solution level of the individuals, and the purpose is to guide searching to be conducted in the Pareto optimal solution set direction;
step three, calculating fitness function values;
designing a niche function, and solving a real Pareto layering level;
step five, classical PPX, the priority protection crosses, before which the predefining of the filial generation is carried out;
step six, mutating individuals of which the population meets the mutation condition to obtain offspring of which the population size is N=50;
step seven, rapidly and non-dominantly sorting the variant offspring again;
step eight, elite selection is carried out, and the father and the offspring are combined into a new whole; pareto non-dominant sorting is performed according to the objective function value of each individual, the first 50% of the individuals in the population are reserved, and the rest 50% are removed;
step nine, judging whether the iteration times reach the iteration limit G=200, if not, updating the external archive omega and storing the non-dominant solution set P t+1 Returning to the second step for continuous execution, and outputting the external file if the iteration limit times are reachedAnd (3) obtaining an optimal disassembly sequence by the non-inferior solution in (3).
Further, in the first step, the basic parameters of the waste mobile terminals are set in advance as the number N of parts of each waste mobile terminal 1 =25, decision variable number v=n 1 =25, the number of objective functions m=4, the population size n=50, the iteration number g=200, the variation probability p m =0.1, initializing the population according to a priority relation matrix p, the matrix p being N 1 *N 1 Is represented by y (i, j) representing the dominance of the ith individual to the jth individual, i=1, 2, …, N 1 ，j＝1,2,…,N 1 Set up external filesTo store Pareto non-dominant solutions. In particular:
y (i, j) =1, indicating that the ith individual dominates the jth individual (i individual is prioritized over j individual);
y (i, j) =0, and indicates that the i-th individual and the j-th individual do not form a dominant relationship with each other.
Further, in the third step, the calculation formula of the fitness function of the objective function is:
individuals of the same class have the same fitness function value, ensuring that solutions of the same class have the same regeneration rate, wherein F (X) is the fitness function value of a single individual X, m represents the largest class, j (X) represents the class of individual X, n j Indicating the number of individuals to which the rank j corresponds.
Further, in step four, in order to ensure that the search of the optimal solution does not converge on the local solution of the feasible domain and that the population evolves consistently along the Pareto optimal front, a sharing function is required as follows:
wherein delta (X, Y) represents a shared function of different individuals, sigma is a distance parameter, d (X, Y) is the Euclidean distance between different individuals X and Y, h represents the number of objective functions, and X (F) i ) And Y (F) i ) The values of the objective function i for individual X and individual Y, respectively.
Further, in the fifth step, four targets of the number of workstations, the idle time index, the work load smoothness and the carbon emission are modeled respectively. Thus, four objective functions can be established as follows:
f 1 ＝NWS
f 4 ＝811.2·(E 1 +E 2 +E 3 +E 4 )
f＝min[f 1 ,f 2 ,f 3 ,f 4 ]
wherein NWS is the number of workstations on; CT represents the longest available time for each workstation; ST (ST) j Indicating the operation time of the j-th workstation, j=1, 2, …, NWS; f includes respective minima of the four objective functions; e (E) 1 Indicating the total disassembly energy consumption; e (E) 2 Representing the total turnover energy consumption; e (E) 3 Representing the total conveyor belt energy consumption; e (E) 4 Representing the total standby energy consumption of the mechanical arm; DS (DS) j Representing the disassembly energy consumption of the single part; DR (digital radiography) j Representing single overturning energy consumption; the energy consumption units are Kw.h.
In step eight, elite selection is performed, the parent and the offspring are combined into a new whole, pareto non-dominant ranking is performed according to the objective function value of each individual, the first 50% of individuals in the population are reserved, the rest 50% of the individuals are removed, and the optimal non-dominant solution set Γ is obtained 1 Preferential addition of P t+1 Then Γ 2 Sequentially proceeding until P is disabled t+1 Accommodate more individuals, assuming Γ i The set is the last non-dominant solution set that can be put in, beyond which the remaining following non-dominant solution sets cannot be accommodated, at which time a determination needs to be made:
if from Γ 1 To Γ i The sum of all the set additions of (a) is equal to the population number N=50, and the step nine is executed;
if from Γ 1 To Γ i The sum of all the set additions of (a) is greater than the population number n=50, and the crowding comparison operator p is required to be used for accurately selecting excellent individuals n For gamma i The solutions of the fronts are ordered and the new father P is selected to be filled t+1 The optimal solution required;
5) Repeating 2-4 steps for different objective functions to obtain crowding distance L [ i ] of individual i] d The individuals with larger crowded distances are preferably selected, so that the calculation results can be distributed uniformly in the target space, and the diversity of the groups is maintained.
Further, the distance parameter sigma represents a mean value of the sum of Euclidean distances between individuals except for X individuals in the population, and the expression is:
f' (X) represents an objective function of an individual X after sharing the function, n represents population size, Y i Refers to individuals in the population other than X.
Further, the individual crowding degree calculating process comprises the following steps:
1) Initializing individual distance of same layer to make L [ i ]] d ＝0；
2) Individuals on the same layer are arranged in ascending order according to the mth objective function value;
3) For each objective function, a boundary solution (solution with minimum and maximum function values) is given an infinite distance value, L1] d ＝L[i] d All other intermediate solutions are given a distance value equal to the absolute normalized difference of the function values of two adjacent solutions;
4) The overall congestion distance value is calculated as the sum of the individual distance values corresponding to each target. Each objective function is normalized before the congestion distance is calculated. Crowding distance expression:
wherein: l [ i+1 ]] m The mth objective function value for the i+1th individual,and->Is the maximum and minimum of the mth objective function.
Further, in the fifth step, a roulette function is adopted to select the father.
Further, in step seven, the process of rapidly non-dominantly sorting the mutated offspring is to sort the parent population P again t And offspring population Q t R combined to form population size 2N t Then for the new population R t Computing R using a fast dominant ranking algorithm t Leading edge ordering of the population R in descending order t Individual selection to the next parent P t+1 。
Compared with the prior art, the invention has the following beneficial effects:
according to the method, a multi-objective function to be optimized is constructed based on the number of workstations, idle time indexes, work load smoothness and total carbon emission, and the multi-objective function is solved by utilizing a Pareto multi-objective genetic algorithm, so that a non-dominant solution set of a low-carbon efficient disassembly strategy of a group of waste mobile terminals is obtained. The invention effectively provides a decision maker with a selection reference of various schemes, can improve the efficiency of the workstation and reduce the carbon emission, and is efficient and environment-friendly.
Drawings
FIG. 1 is an algorithm flow chart of a low-carbon efficient disassembly line balance optimization method for a waste mobile terminal;
fig. 2 is a diagram illustrating PPX principle.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
In the description of the present invention, it should be noted that the directions or positional relationships indicated by the terms "upper", "lower", "inner", "outer", "front", "rear", "both ends", "one end", "the other end", etc. are based on the directions or positional relationships shown in the drawings, are merely for convenience of description of the present invention, and are not intended to indicate or imply that the apparatus or elements referred to must have a specific orientation, be configured and operated in a specific orientation, and thus should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and the like, are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In the description of the present invention, it should be noted that, unless explicitly specified and limited otherwise, the terms "mounted," "provided," "connected," and the like are to be construed broadly, and may be fixedly connected, detachably connected, or integrally connected, for example; can be mechanically or electrically connected; can be directly connected or indirectly connected through an intermediate medium, and can be communication between two elements. The specific meaning of the above terms in the present invention will be understood in specific cases by those of ordinary skill in the art.
Referring to the drawings, the optimization targets considered by the method are the number of workstations on the disassembly line of the waste mobile terminal, the idle time index, the work load smoothness and the total carbon emission. The number N of parts of each waste mobile terminal 1 =25, decision variable number v=n 1 =25, the number of objective functions m=4, the population size n=50, the iteration number g=200, the variation probability p m For example, =0.1, a detailed description will be given of the embodiments of the present invention.
An algorithm flow chart of a low-carbon efficient disassembly line balance optimization method for a waste mobile terminal, as shown in fig. 1, comprises the following steps:
step one, initializing a population according to a priority relation matrix p. Matrix p is N 1 *N 1 Is represented by y (i, j) representing the dominance of the ith individual to the jth individual, i=1, 2, …, N 1 ，j＝1,2,…,N 1 . Set up external filesTo store Pareto non-dominant solutions. In particular:
y (i, j) =1, indicating that the ith individual dominates the jth individual (i individual is prioritized over j individual);
y (i, j) =0, and indicates that the i-th individual and the j-th individual do not form a dominant relationship with each other.
Step 1.1, randomly selecting an unassigned task i from the disassembly priority matrix p, wherein the task i has no immediately preceding task or a task before which is assigned (i.e. the tasks in each column in p are all zero) as the disassembly task at the current position.
Step 1.2, deleting the constraint with priority relation to the task i from p:let y ia ＝0，y ai ＝0。
And step 1.3, repeating the step 1.1 and the step 1.2 until all tasks are distributed to obtain a sequence which is an initial feasible disassembly sequence.
And step two, rapid non-dominant sorting of the primary population. Population stratification is performed according to the non-dominant solution level of the individuals, with the aim of directing the search to the Pareto optimal solution set direction. The pseudo code is as follows:
in particular, n p : the number of solutions that govern the individual p in the population. S is S p : a set of solutions governed by individual p. P is population size, P is individual number, Γ i A set of individuals is unassigned for the i-th level.
for each p∈P
n p ＝0
for each q∈P
if(p p q)then
S p ＝S p ∪{q}
else if(q p p)then
n p ＝n p +1
if n p ＝0 then
p rank ＝1
Γ 1 ＝Γ 1 ∪{p}
i＝1
for each p∈Γ i
for each q∈S p
n q ＝n q -1
if n q ＝0 then
q rank ＝i+2
Q＝Q∪{q}
i＝i+1
Γ 1 ＝Q
Step 2.1, finding all n in the population p Individual =0, i.e. all individuals p in the population not dominated by other individuals, and store these individuals in the current Γ 1 (first non-dominant layer) assigning individuals in the set to non-dominant order p rank And removing the individuals from the whole population, wherein the individuals in the remaining population are all the individuals which are not dominated by other populations.
Step 2.2 for Γ 1 Each individual q of (a) has their corresponding set of individuals S p S to be accessed p Each individual q in the collection is subjected to nq-1 processing.
Step 2.3, if nq-1=0, storing the individual q in Γ 2 While individuals within the set are all assigned the same non-dominant order q rank (second non-dominant layer). Then to Γ 2 The same ranking operation is performed as described above, returning to step 2.2, until all individuals are ranked.
And 2.4, updating the external archive omega.
Step three, calculating fitness function values:
individuals of the same level have the same fitness function value, and the solutions of the same level are guaranteed to have the same regeneration rate. Wherein F (X) is a single individual X fitness function value, m represents the maximum rank, j (X) represents the rank of individual X, n j Indicating the number of individuals to which the rank j corresponds.
And fourthly, designing a niche function, wherein the purpose is to solve a real Pareto layering level.
Step 4.1, in order to ensure that the search of the optimal solution does not converge on the local solution of the feasible domain and that the population evolves consistently along the pareto optimal front, a sharing function is required, as follows:
wherein delta (X, Y) represents a shared function of different individuals, sigma is a distance parameter, d (X, Y) is the Euclidean distance between different individuals X and Y, h represents the number of objective functions, and X (F) i ) And Y (F) i ) The values of the objective function i for individual X and individual Y, respectively.
In particular, the distance parameter σ represents the mean of the sum of the Euclidean distances of individuals other than X individuals in the population and the expression:
and 4.2, punishing the aggregated individuals in the population to reduce the fitness function value. Redefinition of the objective function is as follows:
f' (X) denotes that individual X passes through the shared functionThe objective function after counting, n refers to population scale, Y i Refers to individuals in the population other than X. Thus, after the processing of the niche function is completed, each individual corresponds to a niche value and is recorded in a real Pareto level, namely, the objective function values of 50 non-dominant solutions are obtained, and the order corresponding to the individuals is unchanged.
Step five, classical PPX (preferential protection crossover), before which the predefining of the offspring is performed. The innovation of this embodiment is that the roulette function is used to select the parent. The method comprises the following specific steps:
and 5.1, selecting a parent 1 and a parent 2 from the population individuals respectively by using a roulette function.
And 5.2, crossing by taking the selected parent 1 and the selected parent 2 as parameters to obtain a gene sequence of the offspring. The principle will now be briefly described with the present example of algorithm of fig. 2. For a feasible solution:
X1＝{4,1,2,3,9,7,5,10,11,12,8,6,16,14,13,17,15,18,21,19,22,20,23,25,24}
X2＝{2,4,7,8,1,5,6,3,10,11,9,15,16,18,13,14,17,12,19,21,22,20,23,25,24}
the algorithm for PPX is as follows:
1) PPX first creates a mask consisting of random 1 and 2, indicating from which parent information should be obtained; the mask for the child is 2,1,1,1,2,1,2,2,2,2,1,1,1,2,1,2,1,1,2,1,2,1,2,2,1 (1 represents taken from parent 1 and 2 represents taken from parent 2). The first gene in parent 2 and the second gene in parent 1 (from left to right) will constitute the first two genes of the offspring (while these genes will be deleted from the parts obtained from parent 1 and parent 2);
2) The first available gene in parent 1 (i.e., not deleted) will constitute the third gene of the offspring, while the gene will be deleted from the parts obtained from parent 1 and parent 2;
3) Obtaining a fourth gene of the offspring from the fourth mask 1 as a fourth gene of the parent 1, deleting the fourth gene from the obtaining parts of the parent 1 and the parent 2, and obtaining a fifth available gene 7 in the parent 2 from the fifth mask 2 to form a fifth gene of the offspring;
4) Deleting a fifth gene of the offspring from the part obtained from the parent 1 and the parent 2, obtaining a sixth gene of the offspring from the sixth mask 1 as a next available gene 9 in the parent 1, and so on;
5) The last five genes of the father 1 and the father 2 are the same, and the 21 st to 25 th genes of the filial generation are formed, and finally a new filial generation gene sequence is obtained.
And 5.3, setting the sequence of the obtained offspring as a variable for testing whether the sequence accords with logic. If the test sequence does not accord with the test sequence, returning to the step 5.2 until the test sequence accords with the test sequence, and normally retaining the test sequence to the next step.
And 5.4, substituting the final obtained child sequence into the multi-objective function as the independent variable parameter. And finally outputting target vectors, namely the number of workstations, the idle time index, the work load smoothness and the total carbon emission. Thereby four objective functions f can be established 1 、f 2 、f 3 、f 4 The following are provided:
f 1 ＝NWS (5.1)
f 4 ＝811.2·(E 1 +E 2 +E 3 +E 4 ) (5.4)
f＝min[f 1 ,f 2 ,f 3 ,f 4 ] (5.5)
wherein NWS is the number of workstations on; CT represents the longest available time for each workstation; ST (ST) j Indicating the operation time of the j-th workstation, j=1, 2, …, NWS; f includes respective minima of the four objective functions; e (E) 1 Indicating the total disassembly energy consumption; e (E) 2 Representing the total turnover energy consumption; e (E) 3 Representing the total conveyor belt energy consumption; e (E) 4 Representing the total standby energy consumption of the mechanical arm; DS (DS) j Representing the disassembly energy consumption of the single part; DR (digital radiography) j Representing single overturning energy consumption; the energy consumption units are Kw.h.
In particular, the data of carbon emission factors of each region in 2015 provided by http:// cdm.ccchina.org.cn/archive/cdmcn/UpFile/Files/defaults/20160606120244478242. Pdf are shown in table 1, and the carbon emission factors of the east China regional power grid are selected for calculation in this embodiment.
TABLE 1
And step six, mutating the individuals of which the population meets the mutation condition (the mutation probability is smaller than 0.1) to obtain the offspring of which the new gene sequence and the population size is N=50.
And step seven, rapidly and non-dominantly sorting the variant offspring again. And then the parent population P t And offspring population Q t R combined to form population size 2N t Then for the new population R t Computing R using a fast dominant ranking algorithm t Is a leading edge ordering of (c). The population R is sorted in descending order t Individual selection to the next parent P t+1 。
Step eight, performingElite selection. The parent and child are combined into a new whole. Pareto non-dominant ranking was performed according to the objective function value for each individual, keeping the top 50% of the individuals in the population, and rejecting the remaining 50%. Optimal non-dominant solution set Γ 1 Preferential addition of P t+1 Then Γ 2 Sequentially proceeding until P is disabled t+1 Accommodating more individuals. Assume Γ i The set is the last non-dominant solution set that can be placed beyond which the remaining following non-dominant solution sets cannot be accommodated. At this time, a judgment needs to be made:
if from Γ 1 To Γ i Is equal to the population number n=50, step nine is performed.
If from Γ 1 To Γ i The sum of all the set additions of (a) is greater than the population number n=50, and the crowding comparison operator p is required to be used for accurately selecting excellent individuals n For gamma i The solutions of the fronts are ordered and the new father P is selected to be filled t+1 The best solution required.
In particular, the individual congestion level calculation process is briefly described here:
1) Initializing individual distance of same layer to make L [ i ]] d ＝0。
2) Individuals on the same layer are arranged in ascending order of the mth objective function value.
3) For each objective function, a boundary solution (solution with minimum and maximum function values) is given an infinite distance value, L1] d ＝L[i] d = infinity. All other intermediate solutions are assigned a distance value equal to the absolute normalized difference of the function values of two adjacent solutions.
4) The overall congestion distance value is calculated as the sum of the individual distance values corresponding to each target. Each objective function is normalized before the congestion distance is calculated. Crowding distance expression:
wherein: l [ i+1 ]] m Individual =i+1Is set to be the m-th objective function value of (c),and->Is the maximum and minimum of the mth objective function.
5) Repeating 2-4 steps for different objective functions to obtain crowding distance L [ i ] of individual i] d The individuals with larger crowded distances are preferably selected, so that the calculation results can be distributed uniformly in the target space, and the diversity of the groups is maintained.
In particular, crowding comparison operatorsAnd also to direct the various stages of the algorithm toward the best evenly distributed Pareto front.
And step nine, judging whether the iteration times reach an iteration limit G=200. If not, the external archive Ω is updated and the non-dominant solution set P is stored t+1 And returning to the second step to continue execution. And if the iteration limit times are reached, outputting non-inferior solutions in the external files to obtain an optimal disassembly sequence.
The algorithm program of the embodiment is run by Matlab software, the simulation results are shown in Table 2, the following 19 conditions are all the final non-dominant solutions, all the final non-dominant solutions are candidate solutions, and various disassembly scheme references are provided for a decision maker.
TABLE 2
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Claims (5)
1. A low-carbon efficient disassembly line balance optimization method for a waste mobile terminal is characterized by comprising the following steps of:
step one, initializing a population according to a priority relation matrix p;
secondly, rapid non-dominant sorting is conducted on the primary population, population layering is conducted according to the non-dominant solution level of the individuals, and the purpose is to guide searching to be conducted in the Pareto optimal solution set direction;
step three, calculating fitness function values;
designing a niche function, and solving a real Pareto layering level;
step five, classical PPX, the priority protection crosses, before which the predefining of the filial generation is carried out;
step six, mutating individuals of which the population meets the mutation condition to obtain offspring of which the population size is N=50;
step seven, rapidly and non-dominantly sorting the variant offspring again;
step eight, elite selection is carried out, and the father and the offspring are combined into a new whole; pareto non-dominant sorting is performed according to the objective function value of each individual, the first 50% of the individuals in the population are reserved, and the rest 50% are removed;
step nine, judging whether the iteration times reach the iteration limit G=200, if not, updating the external archive omega and storing the non-dominant solution set P t+1 Returning to the second step for continuous execution, and if the iteration limit times are reached, outputting a non-inferior solution in the external file to obtain an optimal disassembly sequence;
in the first step, the basic parameters of the waste mobile terminals are set in advance as the number N of parts of each waste mobile terminal 1 =25, decision variable number v=n 1 =25, the number of objective functions m=4, the population size n=50, iterateThe number g=200, the probability of variation p m =0.1, initializing the population according to a priority relation matrix p, the matrix p being N 1 *N 1 Is represented by y (i, j) representing the dominance of the ith individual to the jth individual, i=1, 2, …, N 1 ，j＝1,2,…,N 1 Set up external filesFor storing Pareto non-dominant solutions,
y (i, j) =1, indicating that the ith individual dominates the jth individual, with the ith individual being prioritized over the jth individual;
y (i, j) =0, indicating that the i-th individual and the j-th individual do not form a dominant relationship with each other;
designing a niche function to obtain a real Pareto layering level;
step 4.1, in order to ensure that the search of the optimal solution does not converge on the local solution of the feasible domain and that the population evolves consistently along the Pareto optimal front, a sharing function is required as follows:
（4.1）
（4.2）
wherein delta (X, Y) represents a shared function of different individuals, sigma is a distance parameter, d (X, Y) is the Euclidean distance between different individuals X and Y, h represents the number of objective functions, and X (F) i ) And Y (F) i ) Objective functions F of individuals X and Y, respectively i Is a value of (2);
the distance parameter sigma represents the average of the sum of Euclidean distances of individuals except X individuals in the population and the individual X, and the expression is:
（4.3）
step 4.2, punishing the aggregated individuals in the population to reduce the fitness function value thereof; redefinition of the objective function is as follows:
（4.4）
f' (X) represents an objective function of the individual X after sharing the function, N represents population size, Y i Refers to individuals in the population other than X; after the processing of the niche function is finished, each individual corresponds to a niche value and is recorded in a real Pareto level, namely, the objective function values of 50 non-dominant solutions are obtained, and the order corresponding to the individuals is unchanged;
in the fifth step, classical PPX preferentially protects the crossover, predefining offspring is firstly carried out, and a roulette function is adopted to select a parent, and the specific steps are as follows:
step 5.1, selecting a father 1 and a father 2 from population individuals by using a roulette function;
step 5.2, crossing the selected parent 1 and parent 2 as parameters to obtain a gene sequence of the offspring;
step 5.3, setting the sequence of the obtained offspring as a variable for testing whether the sequence accords with logic; if the test sequence does not accord with the test sequence, returning to the step 5.2 until the test sequence accords with the test sequence, and keeping the test sequence normally to the next step;
step 5.4, substituting the final obtained child sequence into the multi-objective function as the independent variable parameter; the final output target vector is respectively the number of workstations, the idle time index, the work load smoothness and the total carbon emission; thereby four objective functions f can be established 1 、f 2 、f 3 、f 4 The following are provided:
（5.1）
（5.2）
（5.3）
（5.4）
（5.5）
（5.6）
（5.7）
（5.8）
（5.9）
wherein NWS is the number of workstations on; CT represents the longest available time for each workstation; ST (ST) j Indicating the operation time of the j-th workstation, j=1, 2, …, NWS; f includes respective minima of the four objective functions; e (E) 1 Indicating the total disassembly energy consumption; e (E) 2 Representing the total turnover energy consumption; e (E) 3 Representing the total conveyor belt energy consumption; e (E) 4 Representing the total standby energy consumption of the mechanical arm; DS (DS) j Representing the disassembly energy consumption of the single part; DR (digital radiography) j Representing single overturning energy consumption; the energy consumption units are Kw.h.
2. The method for optimizing balance of low-carbon and high-efficiency disassembly lines for waste mobile terminals according to claim 1, wherein in the third step, the calculation formula of the fitness function of the objective function is as follows:
individuals of the same class have the same fitness function value, ensuring that solutions of the same class have the same regeneration rate, wherein F (X) is the fitness function value of a single individual X, M represents the maximum class, J (X) represents the class of individual X, n J Indicating the number of individuals to which level J corresponds.
3. The method for optimizing balance of low-carbon and high-efficiency disassembly lines for waste mobile terminals according to claim 1, wherein in the eighth step, elite selection is performed, parents and offspring are combined into a new whole, pareto non-dominant ranking is performed according to objective function values of each individual, the first 50% of individuals in a population are reserved, the rest 50% of individuals in the population are removed, and an optimal non-dominant solution set Γ is obtained 1 Preferential addition of P t+1 Then Γ 2 Sequentially proceeding until P is disabled t+1 Accommodate more individuals, assuming Γ i The set is the last non-dominant solution set that can be put in, beyond which the remaining following non-dominant solution sets cannot be accommodated, at which time a determination needs to be made:
if from Γ 1 To Γ i The sum of all the set additions of (a) is equal to the population number N=50, and the step nine is executed;
if from Γ 1 To Γ i The sum of all the set additions of (a) is greater than the population number n=50, and the crowding comparison operator p is required to be used for accurately selecting excellent individuals n For gamma i The solutions of the fronts are ordered and the new father P is selected to be filled t+1 The best solution required.
4. The method for optimizing low-carbon efficient disassembly line balance for waste mobile terminals according to claim 3, wherein the individual crowding degree calculation process is as follows:
1) Initializing individual distance of same layer to make L [ i ]] d ＝0；
2) Individuals on the same layer are arranged in ascending order according to the mth objective function value;
3) For each objective function, a boundary solution, i.e. a solution with minimum and maximum function values, is given an infinite distance value, L1] d ＝L[i] d All other intermediate solutions are given a distance value equal to the absolute normalized difference of the function values of two adjacent solutions;
4) Calculating the total crowding distance value as the sum of the single distance values corresponding to each target, and normalizing each objective function before calculating the crowding distance; crowding distance expression:
wherein: l [ i+1 ]] m The mth objective function value for the i+1th individual,and->Is the maximum and minimum of the mth objective function;
5) Repeating 2-4 steps for different objective functions to obtain crowding distance L [ i ] of individual i] d The individuals with larger crowded distances are preferably selected, so that the calculation results can be distributed uniformly in the target space, and the diversity of the groups is maintained.
5. The method for optimizing balance of low-carbon and high-efficiency disassembly lines for waste mobile terminals according to claim 1, wherein in the seventh step, the process of rapidly and non-dominantly sorting the variant offspring is to sort the parent population P again t And offspring population Q t R combined to form population size 2N t Then for the new population R t Computing R using a fast dominant ranking algorithm t Leading edge ordering of the population R in descending order t Individual selection to the next parent P t+1 。
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