CN110580547B - Method for arranging parallel incomplete disassembly lines for disassembling waste products - Google Patents

Method for arranging parallel incomplete disassembly lines for disassembling waste products Download PDF

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CN110580547B
CN110580547B CN201910811495.9A CN201910811495A CN110580547B CN 110580547 B CN110580547 B CN 110580547B CN 201910811495 A CN201910811495 A CN 201910811495A CN 110580547 B CN110580547 B CN 110580547B
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张则强
朱立夏
管超
刘思璐
蒋晋
谢梦柯
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Abstract

The invention discloses a method for setting a parallel incomplete disassembly line for disassembling waste products, which comprises the following steps: (1) constructing a mathematical model with the aim of minimizing the disassembly depth, the number of workstations, the idle time balance index of the workstations and the quantity of disassembly resources; (2) generating an initial population; (3) acquiring neighborhood individuals of the initial population; (4) comparing objective function values of a mixed population consisting of the neighborhood individuals and the population individuals through Pareto, updating the population and outputting a Pareto better solution to an external archive; (5) carrying out simulated annealing operation on the population updated in the step (4) to obtain a new population; (6) comparing the objective function value of a mixed population consisting of the population subjected to the simulated annealing operation and an external file by using Pareto, and outputting a Pareto better solution to the external file; (7) repeating the steps (3) - (6) according to the set times; (8) outputting Pareto in the external file as a disassembly task allocation scheme. The invention has simple realization and stronger searching capability.

Description

Method for arranging parallel incomplete disassembly lines for disassembling waste products
Technical Field
The invention relates to the technical field of product disassembly, in particular to a method for setting a parallel incomplete disassembly line for disassembling waste products.
Background
Along with the continuous development of social economy, the material living standard of people is continuously improved, the updating speed of various products is continuously increased, and according to statistics, the quantity of theoretically scrapped household appliances per year in China reaches 1 to 1.2 hundred million, and the quantity of the theoretically scrapped household appliances per year is continuously increased by 20 percent on average per year. If the waste products are directly buried or burned, the environment is badly affected, and the waste of resources is caused. In order to minimize environmental pollution caused by waste products and to sufficiently extract recyclable resources contained in the waste products, the waste products must be recovered and remanufactured. The disassembly is a key ring for implementing recovery and remanufacture of waste products, and in order to adapt to large-scale disassembly production, the disassembly line becomes a preferred disassembly production mode of each disassembly enterprise. In order to improve the operating efficiency of the disassembly line, the workload of each disassembly station should be as full and balanced as possible, and therefore, the disassembly line balancing problem has been proposed and widely studied.
The current research on the balance problem of the disassembly line is mainly focused on the balance problem of the complete disassembly line in the form of a single linear layout, and the balance problem of the complete disassembly line in the form of the single linear layout is researched on how to distribute a series of disassembly tasks of one or more products to be disassembled to a plurality of assembly line workstations arranged in the form of the linear layout so as to meet one or more optimization targets, however, in practical dismantling enterprises, the dismantling process flows of different products are greatly different and are generally dismantled in different production lines, and in order to improve the disassembly yield and reduce the disassembly cost, the waste products are generally not completely disassembled from the whole product to each part, but the disassembly depth is determined according to the EOL (End-of-life) condition of the product and the requirements and harmfulness of each part. Generally, the parts of the waste products that can be reused and remanufactured need to be removed as required parts, and in addition, in view of environmental protection, the harmful parts, whether used for reuse, remanufactured or recycled, must be removed, for example, when a waste CRT (Cathode Ray Tube) television is disassembled, the screen glass must be removed due to the existence of fluorescent powder substances, other parts may be removed or not, and after all the parts that need to be disassembled are removed, the remaining undetached parts enter the crushing and sorting stage in an integrated manner to extract raw materials, so that the actual disassembling enterprises usually adopt an incomplete disassembling manner for disassembling production.
In order to improve the labor hour utilization rate and the Disassembly efficiency of workers, Seda Hezer et al put forward a Parallel Disassembly Line Balancing Problem (PDLBP) for the first time, and solve by using a shortest path model based on a Disassembly priority relationship network diagram with the minimum number of work stations as an optimization target. Seda Hezer et al indicate that parallel disassembly lines are superior to single straight disassembly lines in reducing idle time of the work stations, reducing the number of open work stations, reducing the number of disassembly workers, reducing line length, and improving production efficiency.
The parallel disassembly line balance problem belongs to an NP-hard (NP is all called non-deterministic polynomial, and NP-hard refers to a problem that all NP problems can be reduced within polynomial time complexity) combined optimization problem as the single linear disassembly line balance problem which is researched more, and the solution complexity of the problem increases exponentially along with the increase of the problem scale. Seda Hezer et al apply a heuristic method to solve PDLBP, although the heuristic algorithm is simple and easy to implement, and can quickly obtain a near-optimal solution or even an optimal solution for a problem of a smaller scale, the solution results are far from the ideal when solving a problem of a large scale. At present, the problem of NP-hard combined optimization is solved by using a meta-heuristic algorithm such as a genetic algorithm, a simulated annealing algorithm, an ant colony algorithm and the like, but the problems of poor convergence, long search time, poor solving quality and the like exist. Therefore, a more efficient method is sought to solve PDLBP to obtain a split line setup scheme.
Disclosure of Invention
The invention mainly aims to provide a setting method of a parallel incomplete disassembly line for disassembling waste products so as to obtain a better setting scheme of the disassembly line.
In order to achieve the above object, the present invention provides a setting method of a parallel incomplete disassembly line for disassembling waste products. The setting method of the parallel incomplete disassembly line for disassembling the waste products comprises the following steps:
(1) constructing a mathematical model with the aim of minimizing the disassembly depth, the number of workstations, the idle time balance index of the workstations and the quantity of disassembly resources;
(2) generating an initial population;
(3) acquiring neighborhood individuals of the initial population;
(4) comparing objective function values of a mixed population consisting of the neighborhood individuals and the population individuals through Pareto, updating the population and outputting a Pareto better solution to an external archive;
(5) carrying out simulated annealing operation on the population updated in the step (4) to obtain a new population;
(6) comparing the objective function value of a mixed population consisting of the population subjected to the simulated annealing operation and an external file by using Pareto, and outputting a Pareto better solution to the external file;
(7) repeating the steps (3) - (6) according to the set times;
(8) outputting Pareto in the external file as a disassembly task allocation scheme.
The method takes the practical application background of disassembly production, designs a parallel incomplete disassembly line on the basis of the existing single linear disassembly line, and constructs a multi-objective mathematical model aiming at the balance problem of the parallel incomplete disassembly line, wherein the multi-objective mathematical model takes the minimum disassembly depth, the minimum number of workstations, the minimum idle time balance index of the workstations and the minimum disassembly resource number as the targets; the multi-target mixed group neighborhood searching algorithm is creatively provided, namely step three, the method is simple to realize and high in searching capability, and the global optimization capability of the algorithm is further enhanced by introducing simulated annealing operation so as to obtain a better solving effect.
The invention is further described with reference to the following figures and detailed description. Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, are included to assist in understanding the invention, and are included to explain the invention and their equivalents in the description and should not be taken to limit the invention to the proper form disclosed herein. In the drawings:
fig. 1 is a schematic view of a parallel disassembly line in the setting method of a parallel incomplete disassembly line for disassembling waste products of the present invention.
Fig. 2 is a schematic diagram of an adjacent domain search based on an embedding operation in the setting method of the parallel incomplete disassembly line for disassembling the waste products of the present invention.
Fig. 3 is a schematic diagram of neighbor search based on exchange operation in the setup method of parallel incomplete disassembly line for disassembling waste products of the present invention.
FIG. 4 is a flowchart of a multi-target mixed group neighborhood search algorithm in the method for setting a parallel incomplete disassembly line for disassembling scrap products according to the present invention.
Fig. 5 is a view showing the relationship of the priorities of the tasks of disassembling the used refrigerator according to embodiment 1 of the present invention.
Fig. 6 is a priority relationship diagram of the disassembly tasks of the used tv set in embodiment 1 of the present invention.
Fig. 7 is an operation allocation diagram obtained by using the Pareto better solution scheme with the solution number of 1 in embodiment 1 of the present invention.
Detailed Description
The invention will be described more fully hereinafter with reference to the accompanying drawings. Those skilled in the art will be able to implement the invention based on these teachings. Before the present invention is described in detail with reference to the accompanying drawings, it is to be noted that:
the technical solutions and features provided in the present invention in the respective sections including the following description can be combined with each other without conflict.
Furthermore, the embodiments of the present invention described in the following description are generally only a part of the embodiments of the present invention, and not all of the embodiments. Therefore, all other embodiments obtained by a person of ordinary skill in the art based on the embodiments of the present invention without any creative effort shall fall within the protection scope of the present invention.
With respect to terms and units in the present invention. The terms "comprising," "having," and any variations thereof in the description and claims of this invention and the related sections are intended to cover non-exclusive inclusions.
The product types that the enterprise was retrieved through different channels are disassembled in different, but these products need be unified to be dismantled, and present dismantlement line layout form is that the same kind of product is dismantled on solitary linear type assembly line, nevertheless through investigation on the spot we discover, and the workman on the line is dismantled to the list has the busy uneven condition of idle time, and partial workman has idle time longer to lead to workman man-hour utilization ratio low, has also led to the waste of resource simultaneously. To this end, the present invention provides a parallel production line for the simultaneous disassembly of different products as shown in fig. 1, the first disassembly line 21 of the first to-be-disassembled product 11 and the second disassembly line 22 of the second to-be-disassembled product 21 are arranged in parallel at respective adjacent positions, and through the uniform distribution of all the disassembly tasks for disassembling the products on the two lines, the worker in the workstation 3 can operate one disassembly line alone or operate the operations on the two disassembly lines simultaneously, thereby reducing the idle time of the worker as much as possible, improving the man-hour utilization rate of the worker, and the residual undetached parts will enter the raw material extraction chamber 4 in an integrated manner for the extraction of the raw material.
In order to reduce the disassembly cost as much as possible and improve the disassembly benefit, and simultaneously reduce the harm of the disassembly of the waste products to the environment to the minimum, the products on the parallel disassembly line are not completely disassembled, specifically, on the basis of following the disassembly priority relation of the products, the worker stops the disassembly after completely disassembling the required and harmful parts in the waste products along a certain disassembly path, and the rest parts enter a crushing and sorting machine in an integral mode to refine and sort the raw materials.
In order to improve the production efficiency of a parallel disassembly line and aim at the balance problem of a parallel incomplete disassembly line, a multi-objective mathematical model which takes the minimum disassembly depth, the minimum work station number, the minimum idle time balance index and the minimum quantity of resources required by disassembly as targets is established, an optimal scheme for synchronously distributing all disassembly tasks on the parallel line is sought under the constraint of the priority relation of the disassembly tasks of all products and the constraint conditions of part requirements, hazards and the like, the number of the opened work stations is minimized while the disassembly depth is minimized, the work loads in all the work stations are full and balanced as much as possible, and the quantity of the resources used for disassembly is minimized.
Specifically, the setting method of the parallel incomplete disassembly line for disassembling the waste products comprises the following specific steps:
1. assumption of conditions
(1) Two parallel lines respectively dismantle a waste product;
(2) enough waste products are arranged on the disassembly line, so that the parallel disassembly line can continuously run;
(3) the operation time of each disassembly task of each product is determined and known, and uncertain factors in operation are ignored;
(4) each workstation is allocated with one worker, and each worker is a multi-skill worker and can be competent for all disassembly tasks;
(5) neglecting the walking time of the disassembling worker between the two parallel lines;
(6) other burst conditions are ignored.
2. Description of the symbols
For convenience of description, the symbols referred to in the present invention have the meanings shown in table 1.
TABLE 1
Figure BDA0002185182530000041
Figure BDA0002185182530000051
3. Mathematical model
Constructing a multi-objective mathematical model of a parallel incomplete disassembly line balance problem with the objective of minimizing disassembly depth, minimizing the number of workstations, minimizing idle time balance indexes of workstations and minimizing the number of disassembly resources as follows:
F＝min[f1,f2,f3,f4] (1)
Figure BDA0002185182530000052
Figure BDA0002185182530000061
Figure BDA0002185182530000062
Figure BDA0002185182530000063
constraint conditions are as follows:
Figure BDA0002185182530000064
Figure BDA0002185182530000065
Figure BDA0002185182530000066
Figure BDA0002185182530000067
Figure BDA0002185182530000068
Figure BDA0002185182530000069
Figure BDA00021851825300000610
Figure BDA00021851825300000611
in the above mathematical model: equation (1) represents four objective functions f to be optimized1,f2,f3,f4(ii) a Target f1The formula (2) shows that the disassembly depth is minimized, namely, in order to reduce the disassembly cost as much as possible and increase the disassembly benefit, the disassembly depth is minimized as much as possible, namely, the number of the disassembled parts is minimized; target f2Minimizing the number of open stations as shown in equation (3); target f3The method is represented by the formula (4), namely the idle index is minimized, namely the work load of each workstation is enabled to be as full and balanced as possible; target f4The method is represented by the formula (5) that the number of resources required for disassembly is minimized, namely, the disassembly tasks using the same resources are distributed to the same workstation as much as possible;
in the above constraints: equation (6) indicates that the disassembly tasks are inseparable, each disassembly task being allowed to be assigned to only one workstation; formula (7) indicates that the hazardous part must be removed; formula (8) indicates that the required component must be removed; equation (9) indicates that the sum of the time allotted to all the disassembly tasks in each workstation k cannot exceed a predetermined tact time; equation (10) indicates that the allocation of disassembly tasks on each disassembly line must follow the respective disassembly priorities for each product; equation (11) indicates that if a certain task j on the tear-down line l is executed, the task i immediately before the task j must also be executed; equation (12) indicates that the workstations are turned on in sequence, and there are no empty workstations to which tasks are not assigned; equation (13) indicates that if a tear down task i using resource r is allocated to a workstation k, the workstation k must be equipped with the corresponding resource r accordingly.
4. And solving a disassembly task allocation scheme by adopting a multi-target mixed group neighborhood search algorithm creatively provided.
4.1 population initialization
The multi-target mixed group neighborhood searching algorithm provided by the invention is an algorithm based on group neighborhood searching, and a group needs to be initialized before the algorithm enters iteration. Because the solved parallel incomplete disassembly line balance problem has a discrete characteristic, each individual in the population corresponds to a solution of the solved problem by adopting a disassembly task-based coding mode, namely corresponds to a disassembly task sequence, the population initialization process also corresponds to a generation process of a series of disassembly task sequences, and in the decoding stage, the series of disassembly task sequences are sequentially distributed to a plurality of workstations according to the production beat constraint of the disassembly line to determine the objective function value of each optimization index, namely determine the multi-objective solution scheme of the solved problem.
In order to ensure the diversity of the initial population, the invention adopts a random mode to generate the initial population, the initial population follows the priority order relation constraint between the disassembly tasks, and the operation order on two disassembly lines needs to be considered simultaneously.
The specific process for generating the initial population Pop is as follows:
step 1: aiming at each current population pop _ num, according to respective operation priority relation matrixes P of disassembled products on the disassembling line I and the disassembling line II1And P2Respectively finding out the job in all the disassembling tasks as empty or the job in which the job in the immediate front is distributed, i.e. respectively finding out P1And P2The sum of all the column elements in the task set C is 0, and the task set C to be allocated is formed;
step 2: randomly selecting a disassembly task i from a task set C to be distributed to the current position of the pop _ num of the current population individual;
step 3: if the disassembly task I is a job on the disassembly line I, then all immediate constraints associated with the disassembly task I are removed, i.e., P is about to occur1Setting a row element where the middle disassembly task i is located as 0; if the disassembly task i is a job on the disassembly line II, all immediate constraints associated with the disassembly task i are released, i.e. P is released2Setting the row element of the middle task i as 0;
step 4: repeating Step 1 to Step 3 until all the operations on the two disassembly lines are distributed;
step 5: repeating Step 1 to Step 4 until all Pop _ num population individuals are initialized;
and (3) outputting: the initial population Pop is the number of Pop _ num;
4.2 neighborhood search operation
In order to ensure the quality of neighborhood search and the diversity of neighborhood individuals, the neighborhood search of the population individuals is carried out by respectively adopting the optimal embedding operation and the optimal exchange operation, namely Pareto comparison is carried out on all feasible solutions generated by embedding operation and exchange operation of a certain disassembly task arbitrarily selected in each disassembly task sequence, and an optimal solution is selected as a final neighborhood solution. For number S1The population individuals generate neighborhood individuals through optimal embedding operation, and the number of the neighborhood individuals is S2Generating neighborhood individuals by optimal exchange operation of population individuals, S1+S2Pop _ num. Preferably, S1＝S2At this time, the objective function value of the obtained disassembly task allocation scheme is small.
Fig. 2 is a schematic diagram of neighborhood search based on an embedding operation, in which an item of task 6 is randomly selected in a current solution sequence, such as [1-2-3-4-5-6-7-8], and tasks immediately before and after the task 6 are determined to be 3 and 7 respectively through a job priority order relationship matrix, the task 6 may be embedded in any one of positions 1 and 2 indicated by dotted arrows, so that two neighborhood solutions may be generated, and a better solution is screened as a final neighborhood individual through Pareto comparison in the two neighborhood solutions.
Fig. 3 is a schematic diagram of neighborhood search based on a swap operation, in which if task 6 swaps its location with task 2, the task priority relationship constraint is violated, and the generated task sequence is not feasible, so task 6 only allows a certain task corresponding to two locations 1 and 2 shown by dotted lines to swap, and thus two neighborhood solutions can be generated, and similarly, a Pareto better solution is screened as a final neighborhood individual from the two neighborhood solutions generated by the swap operation.
4.3 population renewal
After a current population individual generates a neighborhood individual through neighborhood search operation, performing Pareto comparison and screening on a mixed population composed of the population individual and all neighborhood individuals, and reserving screened Pareto better solutions, if the number of the Pareto better solutions exceeds the population number, calculating crowding distances of the screened Pareto better solutions in order to obtain Pareto better solutions with more uniform spatial distribution, then sorting all the Pareto better solutions according to the calculated crowding distances from large to small, and selecting the Pareto better individuals with the population number from the Pareto better individuals to form a new generation of population; if the number of the screened Pareto better solutions is smaller than the number of the populations, randomly selecting a certain number of individuals from the remaining mixed populations after screening, and forming a new generation of population with the screened Pareto better solutions.
The calculation formula of the crowding distance is as follows:
Figure BDA0002185182530000081
in the formula, CDaRepresenting the crowding distance of the Pareto better individual a, U being the number of optimization targets, XPop_numAnd X1Respectively representing individuals having the maximum value and the minimum value in the u-th objective function, the crowding distance of the two individuals being defined as infinity, fu(Xa+1) And fu(Xa-1) The u-th objective function values of two adjacent individuals a +1 and a-1 of the individual a respectively.
Pareto comparison procedure is as follows: calculating the objective function value of each individual in the mixed population according to the sequence number X1、 X2、···、XnNumbering; firstly, X is put in1Deposit into empty matrix M0Then X is added2Is an objective function value X of1Performing Pareto comparison on the objective function value of (1), if X is1Quilt X2Dominant, i.e. X2＜X1Then X will be2Adding M0Neutralizing and reacting X1Slave matrix M0Deletion is then carried out by X3And X2Comparing the objective function values of (1); if X2Quilt X1Dominant, i.e. representing X2If not, deleting X2Then X is carried out3And X1Comparing; if X1And X2If they do not dominate each other, then X will be2Adding M0In then X3One by one with X1And X2And (6) comparing. And so on. Final M when Pareto comparisons were completed for all individuals in the mixed population0The selected Pareto is the better solution of the population individuals.
4.4 simulated annealing operation
The updating and algorithm iteration are carried out through the neighborhood search operation of population individuals, a better search effect is achieved in the early stage, but the local optimization is easy to fall into in the later stage, and in order to improve the global search performance of the algorithm, a local search operation combined with simulated annealing is added in the algorithm, so that the algorithm receives the worse solution in the optimization searching process with a certain probability, and the algorithm jumps out of the local optimization. Since the disassembly line balance problem researched by the invention is a multi-objective optimization problem, the Metropolis criterion needs to be improved, and the improvement is as follows: if new solution XnAnd the current solution XcAre not dominant or newly solved by XnGoverning the current solution XcThen receive XnSubstitution of Xc(ii) a If the current solution XcGoverning a new solution XnThen a random number rand within the interval (0,1) is randomly generated, if rand<And P, accepting the new solution to replace the current solution, and abandoning the new solution if not, wherein P is an acceptance probability, and the calculation formula is shown as the following formula (14):
Figure BDA0002185182530000091
wherein, U is the number of optimization targets, and U is 4; u is the {1,2,3, 4}, fu(Xc) For the current solution XcValue of the u-th objective function, fu(Xn) New solutions X generated for perturbationsnThe corresponding u-th objective function value, T, is the temperature at the current iteration.
The simulated annealing operation of each population individual after population updating comprises the following specific steps:
step 1: for current population individual XcGenerating a new solution X by means of a swap operationn；
Step 2: if XnDominating XcOr XnAnd XcDo not dominate each other, then Xc＝Xn(ii) a If XcDominating XnEntering Step 3;
step 3: randomly generating a random number rand within a range (0,1) if P>rand, i.e. Xc＝XnOtherwise, give up new solution Xn。
To sum up, the flow of the multi-objective mixed group neighborhood search algorithm is shown in fig. 4, and the specific implementation steps are as follows:
step 1: initializing algorithm parameters, including: iteration times Iter of the algorithm, population quantity Pop _ num, population individual neighborhood solution quantity neighbor _ count, and simulated annealing operation initial temperature T0Temperature reduction coefficient q, chain length Lk(ii) a Inputting question parameters, including: the takt time CT of the disassembly line, wherein the relevant information of each disassembly task comprises the operation time, the hazard attribute, the demand attribute, the disassembly resource type and the priority sequence of the disassembly tasks;
step 2: randomly initializing population individuals according to the method in section 4.1 to generate an initial population Pop;
and step 3: setting an iteration count iter as 1, and entering algorithm iteration;
and 4, step 4: as described in section 4.2, neighbor search based on the optimal embedding operation is performed on each population individual in the first half to generate neighbor _ count neighbor individuals, and neighbor search based on the optimal exchanging operation is performed on each population individual in the second half to generate neighbor _ count neighbor individuals;
and 5: as described in section 4.3, Pareto comparison is performed on a mixed population composed of the current population individuals and all neighborhood individuals, Pareto better solutions are screened, the screened Pareto better solutions are stored in an external archive Q, and then the population is updated;
step 6: performing simulated annealing operation on each population individual updated in the step 5 as described in section 4.4 to obtain a new population;
and 7: performing Pareto comparison on a mixed population consisting of the new population subjected to the simulated annealing operation and the external archive, screening out a Pareto better solution, and outputting the Pareto better solution to an external archive Q;
and 8: if Iter is less than Iter, making Iter equal to Iter +1, and returning to step 4; if Iter count Iter is equal to Iter, go to step 9;
and step 9: and (4) stopping the algorithm, and outputting the Pareto better solution in the final external file as a disassembly task allocation scheme.
The setting method of the parallel incomplete disassembly line for disassembling the waste products utilizes the established mathematical model and the multi-target mixed group neighborhood search algorithm to be applied to the parallel disassembly line of two waste products, and can perform integrated line balance optimization on the disassembly task flows of the two waste products. The advantageous effects of the present invention are illustrated below by specific examples.
Example 1
The information of the waste refrigerator and the waste television of a certain enterprise obtained by research is as follows:
1. the data information of the disassembly task of the used refrigerator is shown in table 1, and the data information of the disassembly task of the used television is shown in table 2, wherein: in the hazard attribute, "0" indicates no hazard, and "1" indicates hazardous; in the requirement attribute, "0" indicates no requirement, "1" indicates requirement; disassembling resources means disassembling tools corresponding to various disassembling tasks, 1 represents a screwdriver, 2 represents scissors, 3 represents a word screwdriver, 4 represents a clamp, and 5 represents fixed heavy equipment tools such as a cutting machine, a punching machine and the like.
TABLE 1
Figure BDA0002185182530000101
Figure BDA0002185182530000111
TABLE 2
Figure BDA0002185182530000112
2. The priority relation diagram of the disassembly tasks of the waste refrigerator is shown in fig. 5, and the priority relation diagram of the disassembly tasks of the waste television is shown in fig. 6; taking disassembly tasks 2 and 3 in FIG. 5 as examples, disassembly task 2 is the immediately preceding task of disassembly task 3, plij＝pl2,3＝1，plij＝pl3,2＝0。
3. The disassembly production beats of the waste refrigerator and the waste television are respectively 130s and 60 s.
The multi-target mathematical model of the refrigerator and television parallel incomplete disassembly line balance problem is solved by applying the setting method of the parallel incomplete disassembly line for disassembling the waste products, and parameters of a multi-target mixed group neighborhood search algorithm are set as follows: the population quantity Pop _ num is 50, the iteration number Iter is 200, the population individual neighborhood solution quantity neighbor _ count is 3, and the simulated annealing operation initial temperature T0100, cooling coefficient q 0.9, chain length LkThe takt time CT for the parallel detachment of the wires is taken to be 780s, the least common multiple of the takts of the two products. The 34 Pareto better solution sets (solution numbers 1-34) of the solved parallel disassembly line on the four optimization indexes are shown in table 3.
TABLE 3
Figure BDA0002185182530000121
TABLE 4
Figure BDA0002185182530000122
Figure BDA0002185182530000131
TABLE 5
Figure BDA0002185182530000132
In order to prove the advantages of the proposed parallel disassembly line compared with the single linear disassembly line, a Pareto better solution set of the single linear disassembly line of the two products on four optimization indexes is solved on the premise of keeping the algorithm parameters unchanged, wherein 9 Pareto better solutions exist in the waste refrigerator as shown in table 4, and 16 Pareto better solutions exist in the waste television as shown in table 5.
The results of the comparison of table 3 with tables 4 and 5 are as follows:
(1) all Pareto better solution schemes solved by parallel layout mode are in f2The targets are 8, if the two products are independently optimized, the number of required workstations is 9, and 1 workstation is started more than that in a parallel layout mode;
(2) parallel layout mode Pareto better solution scheme 13 at target f3The optimal result is 5797, and if the two products are independently optimized, all Pareto better solution schemes are obtained in the balance index f3Is more than 20000, is obviously inferior to the parallel layout mode;
(3) parallel layout mode Pareto better solution schemes 23 and 30 at target f4The optimal result is 13, if the two products are independently optimized, the Pareto optimal solution schemes 7 and 9 obtained by independently optimizing the refrigerator disassembly line are in the target f4The optimal result is 9, and the Pareto better solution scheme obtained by independently optimizing the television dismounting line is in the target f4The optimal result is 8, so the total amount of the required disassembly resources under the condition of individual optimization is 17;
(4) the number of the Pareto parallel layout modes is as much as 34 compared with the optimal solution schemes, so that more selection schemes can be provided for enterprises, and the parallel layout modes have higher practicability than a single linear dismounting line.
In conclusion, the parallel disassembly line layout mode is better than the optimized results of the single linear disassembly line of two products in four indexes of reducing the number of workstations, reducing the idle time of the workstations, balancing the operation load on each workstation and reducing the use number of disassembly resources.
In this embodiment, Step 1 in the simulated annealing operation adopts pairwise exchange operation, i.e. randomly selecting XcTwo disassembly tasks in the sequence are exchanged to obtain a new sequence, and if the new sequence meets the priority relation between the disassembly tasks, the new sequence is the new solution XnIf the new sequence does not meet the priority relation between the disassembly tasks, two disassembly tasks are reselected for exchange until a new solution X is obtainedn。
The job assignment map obtained by using the Pareto preferred solution with the solution number of 1 is shown in fig. 7, for example, workstation 1 only completes the disassembly tasks 1-2 of the tv, workstation 2 only completes the disassembly tasks 1-2, 14-15 and 18 of the refrigerator, and workstation 3 completes both the disassembly task 4 of the tv and the disassembly tasks 3-4, 8 and 21 of the refrigerator; the television removal line does not require the removal tasks 20 and 27 and the refrigerator removal line does not require the removal tasks 25, thereby achieving incomplete removal.
The explanation about "dominance" is as follows: unlike a single target, the mutual constraint and limitation among the sub-targets of multiple targets cannot make all the sub-targets optimal at the same time. In order to select a relatively better scheme, the method for judging the fitness function of the disassembly sequence by combining the Pareto thought is as follows: suppose j' th of two disassembly sequences A, B
Figure BDA0002185182530000142
The function values of the sub-targets are AFjAnd BFjK th, k
Figure BDA0002185182530000141
The function values of the sub-targets are AFkAnd BFkIf AFjAnd BFj、 AFkAnd BFkSatisfies the following conditions: AFj≤BFj、AFk＜BFkThen, it is called that a dominates B, B is the dominated solution, a is the non-inferior solution, i.e., the superior solution, and the solution set formed by all the non-inferior solutions is the Pareto solution set.
The contents of the present invention have been explained above. Those skilled in the art will be able to implement the invention based on these teachings. All other embodiments, which can be derived by a person skilled in the art from the above description without inventive step, shall fall within the scope of protection of the present invention.

Claims (9)

1. The setting method of the parallel incomplete disassembly line for disassembling the waste products comprises the following steps:
(1) constructing a mathematical model with the aim of minimizing the disassembly depth, the number of workstations, the idle time balance index of the workstations and the quantity of disassembly resources;
(2) generating an initial population with the quantity of Pop _ num;
(3) acquiring neighborhood individuals of a population;
(4) comparing objective function values of a mixed population consisting of the neighborhood individuals and the population individuals through Pareto, updating the population and outputting a Pareto better solution to an external archive;
(5) carrying out simulated annealing operation on the population updated in the step (4) to obtain a new population;
(6) comparing the objective function value of a mixed population consisting of the population subjected to the simulated annealing operation and an external file by using Pareto, and outputting a Pareto better solution to the external file;
(7) repeating the steps (3) - (6) according to the set times;
(8) outputting a Pareto better solution in the external file as a disassembly task allocation scheme;
the mathematical model in step (1) is as follows:
an objective function: f is min [ F ═1，f2，f3，f4]
f1To minimize the disassembly depth function:
Figure FDA0003374479690000011
f2to minimize the number of stations turned on function:
Figure FDA0003374479690000012
f3to minimize the station idle time equalization indicator function:
Figure FDA0003374479690000013
f4to minimize the number of torn down resources function:
Figure FDA0003374479690000014
in the formula, l is the number of a disassembly line, and belongs to {1,2 }; i is a disassembly task number; n is a radical oflThe number of the disassembly tasks on the disassembly line l is K, the number of the work stations is K, K belongs to {1,2, …, K }, and K is the number of the work stations; x is the number ofilk1 denotes that a disassembly task i in the disassembly line l is assigned to a workstation k, otherwise xilk＝0；Zk1 means workstation k is open, otherwise Zk0; CT is the beat time of the parallel disassembly line; t is tilThe working time of the disassembly task i in the disassembly line l is set; r is the disassembly resource type number; r is the number of the types of the disassembly resources; mrk1 denotes that the tear down resource class r is allocated into workstation k, otherwise Mrk＝0。
2. The setup method of parallel incomplete disassembly lines for disassembling old and useless products according to claim 1, characterized in that: the step (1) is carried out under the following constraint conditions:
(1) the disassembly tasks are inseparable, and each disassembly task is only allowed to be distributed to one work station;
(2) hazardous parts must be removed;
(3) the required parts must be removed;
(4) the sum of the time allotted to all the disassembly tasks in each workstation cannot exceed a predetermined takt time;
(5) the allocation of the disassembly tasks on each disassembly line must follow the respective disassembly priority of each product;
(6) if a certain task on the disassembly line is executed, the task immediately before the task must also be executed;
(7) the workstations are started in sequence, and no empty workstation with no task allocated exists;
(8) if a tear down task using a certain resource is allocated to a workstation, the workstation must be equipped with the resource accordingly.
3. The setup method of parallel incomplete disassembly lines for disassembling old and useless products according to claim 1, characterized in that: the specific flow of the step (2) is as follows:
step 1: aiming at each current population pop _ num, according to respective operation priority relation matrixes P of disassembled products on the disassembling line I and the disassembling line II1And P2Respectively finding out the job in all the disassembling tasks as empty or the job in which the job in the immediate front is distributed, i.e. respectively finding out P1And P2The sum of all the column elements in the task set C is 0, and the task set C to be allocated is formed;
step 2: randomly selecting a disassembly task i from a task set C to be distributed to the current position of the pop _ num of the current population individual;
step 3: if the disassembly task I is a job on the disassembly line I, all immediate constraints associated with the disassembly task I are released, i.e. P is released1Setting a row element where the middle disassembly task i is located as 0; if the disassembly task i is a job on the disassembly line II, all immediate constraints associated with the disassembly task i are released, i.e. P is released2Setting the row element of the middle task i as 0;
step 4: repeating Step 1 to Step 3 until all the operations on the two disassembly lines are distributed;
step 5: repeating Step 1 to Step 4 until all Pop _ num population individuals are initialized;
and (3) outputting: an initial population Pop;
wherein, Pop _ num is the number of the population individuals, and the total number of Pop _ num population individuals.
4. The setup method of parallel incomplete disassembly lines for disassembling old and useless products according to claim 1, characterized in that: in step (3), for the number S1The population individuals generate neighborhood individuals through optimal embedding operation, and the number of the neighborhood individuals is S2The population individuals generate neighborhood individuals through optimal exchange operation S1+S2＝Pop_num。
5. The setup method of parallel incomplete disassembly lines for disassembling old and useless products according to claim 4, characterized in that: s1＝S2。
6. The setup method of parallel incomplete disassembly lines for disassembling old and useless products according to claim 1, characterized in that: in the step (4), the population updating process is as follows: if the number of Pareto better solutions is larger than the number of the populations, calculating crowding distances of the screened Pareto better solutions, and then sorting the Pareto better solutions of the population number from large to small according to the crowding distances to form a new generation of population; if the number of the screened Pareto better solutions is smaller than the number of the populations, randomly selecting a certain number of population individuals from the remaining mixed populations after screening, and forming a new generation of population with the screened Pareto better solutions.
7. The setup method of parallel incomplete disassembly line for disassembling old and useless products according to claim 6, characterized in that: the calculation formula of the crowding distance is as follows:
Figure FDA0003374479690000031
in the formula, CDaRepresenting the crowding distance of the Pareto better individual a, U being the number of optimization targets, XPop_numAnd X1The function values respectively representing the u-th sub-object take the individuals of the maximum value and the minimum value, the crowdedness distance of the two individuals is defined as infinity, fu(Xa+1) And fu(Xa-1) The function values of the u-th sub-objectives of two adjacent individuals a +1 and a-1, respectively, of the individual a.
8. The setup method of parallel incomplete disassembly lines for disassembling old and useless products according to claim 1, characterized in that: the simulated annealing operation process of each population in the step (5) is as follows:
step 1: for current population individual XcGenerating a new solution X by means of a swap operationn；
Step 2: if XnDominating XcOr XnAnd XcDo not dominate each other, then Xc＝Xn(ii) a If XcDominating XnEntering Step 3;
step 3: randomly generating a random number rand within a range (0,1) if P>rand, then Xc＝XnOtherwise, give up new solution Xn；
Wherein P is the acceptance probability.
9. The setup method of parallel incomplete disassembly line for disassembling old and useless products according to claim 8, characterized in that:
Figure FDA0003374479690000032
wherein, U is the number of optimization targets, and U is 4; u is the {1,2,3, 4}, fu(Xc) For the current solution XcValue of the u-th objective function, fu(Xn) New solutions X generated for perturbationsnThe corresponding u-th objective function value, T, is the temperature at the current iteration.
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