A balance control method for a U-shaped incomplete disassembly line for mixed waste products

Abstract

The application discloses a kind of U-shaped incomplete disassembly line balance control methods for mixed waste products, comprising the following steps: S1, construct the disassembly line balance optimization model with minimizing workstation quantity, hazard index, disassembly depth and maximizing workstation load smoothness as target;S2, adopt MonteCarlo simulation initialization method to generate parent population;S3, adopt two-stage crossover, variation method to process parent population, generate offspring population;S4, merge parent population and offspring population, generate hybrid population;S5, adopt global multi-level elite strategy to screen hybrid population, generate parent population, export parent population to external file;S6, repeat steps S3-5 according to the number of iterations;S7, output Pareto optimal solution in external file as disassembly scheme.The application expands the traditional disassembly to U-shaped incomplete disassembly of mixed waste products, improves the disassembly efficiency.

Description

Technical Field

[0001] This invention relates to the field of dismantling line balancing technology, and in particular to a U-shaped incomplete dismantling line balancing control method for mixed waste products. Background Technology

[0002] With the rapid development of technology and the increasingly faster pace of product upgrades, a large number of waste products are generated. These waste products contain functional parts and recyclable raw materials, but also harmful substances that pollute the environment. If these waste products are left unattended, it will lead to resource waste and environmental pollution, placing enormous economic and environmental pressure on society. Therefore, recycling and reusing waste products is an essential path to achieving sustainable development.

[0003] Dismantling operations on a dismantling line are the optimal choice for large-scale dismantling. The layout of the dismantling line is a crucial factor affecting dismantling efficiency. Currently, dismantling line layouts are mainly categorized as straight, double-sided, parallel, and U-shaped. Among these, the U-shaped dismantling line layout is an important method. It consists of an entrance side and an exit side. In a U-shaped dismantling line, operators can simultaneously perform dismantling tasks on both the entrance and exit sides, thus offering advantages such as high dismantling efficiency, flexible task allocation, and minimal factory space requirements. In production practice, achieving balance in a U-shaped dismantling line is of significant practical value to dismantling companies. However, the solution space for the U-shaped dismantling line balancing problem is large, and the solution is difficult. Existing solution methods all suffer from poor solution quality when solving the U-shaped dismantling line balancing problem.

[0004] With technological advancements, automated crushers and sorting machines have been introduced into the dismantling process, making incomplete dismantling a mainstream method. Incomplete dismantling requires the removal of parts with both demand and hazard attributes; the remaining parts can be dismantled based on optimization objectives and the priority of dismantling tasks. Compared to traditional complete dismantling, incomplete dismantling, utilizing automated crushers and sorting machines to break down and automatically sort unnecessary parts, significantly improves dismantling efficiency and reduces costs. Consequently, incomplete dismantling has garnered widespread attention from dismantling companies, giving rise to the problem of incomplete dismantling line balancing. Currently, there are few methods for handling incomplete dismantling line balancing; therefore, modeling this problem and providing high-performance solution methods are urgent issues to be addressed.

[0005] Given the diversity of waste products and the wide variety of components, a dismantling line with a specific dismantling scheme for each type of waste product would result in a significant waste of resources. Therefore, a mixed-product dismantling line capable of dismantling multiple products is urgently needed, leading to the mixed-product dismantling line balancing problem. Solving the mixed-product dismantling line balancing problem is highly challenging because it requires optimizing predefined objectives and determining the dismantling scheme for each product while satisfying the priority constraints of each product. Furthermore, as the number of mixed products increases, the dismantling tasks also increase, leading to a continuously expanding solution space and a rising difficulty in solving the problem. Therefore, a method that can efficiently handle the mixed-product dismantling line balancing problem is required.

[0006] Integrating the advantages of U-shaped dismantling line layout, incomplete dismantling operation methods, and mixed product dismantling lines, this paper establishes a U-shaped incomplete dismantling line balancing problem for mixed waste products, and provides an efficient solution method, which is of great significance to dismantling operations. Currently, scholars both domestically and internationally have conducted in-depth research on dismantling line balancing problems, proposing various problems, including those with fixed workstations, those considering tool change energy consumption, those considering human-machine collaboration, and those considering mixed waste products. However, no one has yet proposed a U-shaped incomplete dismantling line balancing problem specifically for mixed waste products. Therefore, we propose a U-shaped incomplete dismantling line balancing problem (MUPDLBP) for mixed waste products, aiming to minimize the number of workstations, hazard indicators, dismantling depth, and maximize workstation load smoothness.

[0007] Besides proposing the disassembly line equilibrium problem, scholars at home and abroad have proposed many methods to solve it. These methods include improved NSGA II algorithm, improved multi-objective particle swarm optimization algorithm, improved brainstorming algorithm, and improved artificial bee colony algorithm. However, the solution quality of these methods is difficult to be satisfactory when solving complex disassembly line equilibrium problems. The convergence, diversity and uniformity of the obtained Pareto front are poor, especially when solving MUPDLBP, the performance is even worse.

[0008] Therefore, there is a need to provide a balancing control method for a U-shaped incomplete dismantling line for mixed waste products, to establish a mathematical model for the U-shaped incomplete dismantling line for mixed waste products, and to be able to find the optimal balancing scheme for the U-shaped incomplete dismantling line for mixed waste products based on the dismantling task information, thus providing an efficient dismantling operation method. Summary of the Invention

[0009] In view of this, it is necessary to provide a balance control method for a U-shaped incomplete dismantling line for mixed waste products to achieve efficient dismantling operations.

[0010] To achieve the above objectives, the present invention provides the following technical solution:

[0011] This invention provides a method for balancing a U-shaped incomplete dismantling line for mixed waste products, comprising the following steps:

[0012] S1. Construct a disassembly line balancing optimization model with the objectives of minimizing the number of workstations, hazard indicators, disassembly depth, and maximizing workstation load smoothness, and establish a priority relationship matrix for each product to be disassembled; wherein, the disassembly line balancing optimization model is:

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[0020] In the above formulas, equations (1)-(4) are objective functions, and equations (5)-(7) are constraints; equation (1) is the function to minimize the number of open workstations; equation (2) is the function to minimize the hazard index; equation (3) is the function to minimize the dismantling depth; equation (4) is the function to maximize the workstation load smoothness; equation (5) is the priority relationship constraint between dismantling tasks; equation (6) is the dismantling necessity constraint; equation (7) is the cycle time constraint; HI is the hazard index; DD is the dismantling depth; SI is the workstation load smoothness; k is the workstation number, k∈{1,2,…,K}, K is the number of workstations; m is the waste product type number; i is the dismantling task number; Nap is the number of waste product types; Nm is the total dismantling task volume of the m-th waste product; Tk is the sum of the times of all dismantling tasks executed in workstation k. Tc is the maximum value among all Tk. ; Let i be the hazard attribute of the part corresponding to disassembly task i in product m. If the part is hazardous, then =1, otherwise =0; Let i be the operation time for disassembly task i in product m; Let i be the set of dismantling tasks immediately preceding dismantling task i in waste product m; Let i be the set of dismantling tasks immediately following dismantling task i in waste product m; Enable state variables for workstations; if workstation k is enabled, then... =1, otherwise =0; To decompose the task execution order variable, , Assign variables to the disassembly tasks. If the i-th disassembly task of the m-th product is assigned to the entrance side of the k-th workstation of the U-shaped disassembly line, then... , ,otherwise , ;

[0021] S2. Generate a parent population of size Pop_num using the Monte Carlo simulation initialization method;

[0022] S3. Use a two-stage crossover method and a two-stage mutation method to process individuals in the parent population to generate the offspring population;

[0023] S4. Merge the parent population and the offspring population to generate a mixed population, and calculate the objective function value of all individuals in the mixed population;

[0024] S5. Use a global multi-level elite strategy to screen the mixed population, generate a new parent population, and output the new parent population to an external archive.

[0025] S6. Repeat S3-S5 according to the predetermined number of iterations;

[0026] S7. Output the Pareto optimal solution from the external file as the disassembly scheme.

[0027] Further, in step S2, the population is composed of multiple sets of feasible dismantling task sequences, with each set of feasible dismantling task sequences serving as an individual in the population; each set of feasible dismantling task sequences is represented by a two-dimensional integer encoding method; the absolute value of each integer in the first dimension encoding of each set of feasible dismantling task sequences represents the number of the waste product to be dismantled; the absolute value of each integer in the second dimension encoding of each set of feasible dismantling task sequences represents the dismantling task number of the product to be dismantled corresponding to the first dimension encoding; the sign of the integer in the second dimension encoding represents the position of the corresponding dismantling task assigned to the U-shaped dismantling line; a positive integer in the second dimension encoding indicates that the corresponding dismantling task is assigned to the entrance side of the U-shaped dismantling line for execution, and a negative integer in the second dimension encoding indicates that the corresponding dismantling task is assigned to the exit side of the U-shaped dismantling line for execution.

[0028] Furthermore, the specific process of step S2 is as follows:

[0029] S201. Determine the set E of the discarded products that need to be dismantled, E={1,2,…Nap};

[0030] S202. Select the discarded product m to be dismantled from set E, m=1;

[0031] S203. For each individual pop_m in the current population, based on the priority relationship matrix between dismantling tasks of the discarded product m. Shadow Priority Relationship Matrix Among all unassigned dismantling tasks, identify the dismantling tasks whose preceding work is empty, forming a set C of unassigned dismantling tasks to be assigned. This is equivalent to identifying the dismantling tasks corresponding to the columns in P where the sum of all column elements is 0, and removing the dismantling tasks already recorded in pop_m. Next, among all unassigned dismantling tasks, identify the dismantling tasks whose succeeding work is empty, forming a shadow set Cs of unassigned dismantling tasks to be assigned. The dismantling tasks corresponding to the columns where the sum of all column elements is 0 are identified, and dismantling tasks already recorded in pop_m are removed.

[0032] S204. Randomly select a dismantling task i from the set {C, Cs}. If the dismantling task i comes from the set C, first record the number of the dismantling task i as +i, and then record +i in the current position of the current population individual pop_m; if the dismantling task i comes from the set Cs, first record the number of the dismantling task i as -i, and then record -i in the current position of the current population individual pop_m.

[0033] S205. If the dismantling task i selected in S204 comes from set C, then remove all preceding constraints associated with dismantling task i, that is, set the row element containing dismantling task i in P to 0; if the dismantling task i selected in S204 comes from set Cs, then remove all succeeding constraints associated with dismantling task i, that is... Set the element in the row containing the disassembly task i to 0;

[0034] S206. Repeat S203-S205 until all dismantling tasks of the waste product m have been assigned, and a set of feasible dismantling task sequences is obtained, pop_m as a population individual;

[0035] S207, Repeat S203-S206 until Pop_m individuals are generated for waste product m;

[0036] S208. Take out the first D elements of the current population individual pop_m, generate an incomplete disassembly sequence icpop_m of depth D, and output icpop_m to the incomplete disassembly sequence set Q;

[0037] S209, repeat S208, until all population individuals in S207 have generated the corresponding incomplete disassembly sequence;

[0038] S210. Remove duplicates from Q to generate a set of incompletely disassembled sequences Q_d without repetition.

[0039] S211. Sequentially extract the element q_d from Q_d;

[0040] S212. Calculate the frequency of q_d in Q, fq_d;

[0041] S213. Pop q_d as the current population individual pop_m, and repeat S203-S205 until all dismantling tasks of the waste product m have been assigned.

[0042] S214. Repeat S213 until Pop_m×fq_d population individuals are generated for waste product m;

[0043] S215. Repeat S211-S214 until all elements in Q_d have been removed;

[0044] S216. Repeat S201-S215 until Pop_m individuals are generated for all the waste products that need to be dismantled in set E.

[0045] S217. Randomly select one individual from the population of each product;

[0046] S218. While keeping the order of disassembly tasks within each product population unchanged, randomly combine the disassembly tasks of different products to obtain a mixed product population.

[0047] S219. Repeat S217-S218 until Pop_m mixed product populations are generated;

[0048] S220. Take the Pop_m mixed product populations obtained in S219 and form a parent population, and output the parent population.

[0049] Furthermore, the specific process of the two-stage crossover method described in step S3 is as follows:

[0050] S301. Randomly select two individuals from the parent population and define two paired individuals, denoted as Pop_1 and Pop_2 respectively.

[0051] S302. Randomly select two identical points on the feasible disassembly sequence of the paired individuals, map the elements between the two points on the feasible disassembly sequence to each other and move their positions so that the paired individuals form two new disassembly sequences respectively. The two new disassembly sequences are denoted as Seq_1 and Seq_2 respectively.

[0052] S303. Select Pop_1 and Seq_1 as the current parent individual NowPop and the current new disassembly sequence NowSeq;

[0053] S304. Compare NowPop with NowSeq, find the element whose sign has changed in the second dimension of the dismantling sequence as the current element NowEle, and determine the waste product number m and dismantling task number i corresponding to NowEle.

[0054] S305. Determine the sign of the second dimension of NowEle's code. If it is positive, proceed to S306; otherwise, proceed to S307.

[0055] S306, Locate all preceding jobs of NowEle and proceed to S308;

[0056] S307. Locate all of NowEle's immediate successor works and proceed to S309;

[0057] S308. Determine whether all the codes corresponding to the immediate predecessors of NowEle in NowSeq are positive. If so, go to S314; otherwise, go to S310.

[0058] S309. Determine whether all the codes corresponding to the immediate successor work of NowEle in NowSeq are negative. If so, go to S315; otherwise, go to S312.

[0059] S310. Under the condition that the absolute value of the second dimension of NowEle remains unchanged, modify the second dimension of NowEle to a negative integer;

[0060] S311, Locate all of NowEle's immediate successor works and proceed to S315;

[0061] S312. Under the condition that the absolute value of the second dimension of NowEle remains unchanged, modify the second dimension of NowEle to a positive integer;

[0062] S313, Locate all of NowEle's preceding work and proceed to S314;

[0063] S314. In NowSeq, adjust the position of NowEle to any position after all preceding disassembly tasks to obtain a new feasible disassembly sequence as the child individual Pop_child, and go to S316.

[0064] S315. In NowSeq, adjust the position of NowEle to any position before all subsequent disassembly tasks to obtain a new feasible disassembly sequence as the child individual Pop_child, and go to S316.

[0065] S316. Generate a random number α in the interval [0,1). If α>a, go to S317; otherwise, go to S318.

[0066] S317. Use a two-stage mutation method to process Pop_child and add the processed Pop_child to the offspring population. Proceed to S319.

[0067] S318. Add Pop_child to the offspring population, then proceed to S319.

[0068] S319. Select Pop_2 and Seq_2 as the current parent individual NowPop and the current new disassembly sequence NowSeq;

[0069] S320, Repeat S304-S316 once;

[0070] S321. Repeat S301-S320 until Pop_m offspring individuals are generated;

[0071] S322. Form a sub-population from all offspring individuals and output the sub-population.

[0072] Where a is a real number, and 0 ≤ a < 1.

[0073] Furthermore, the specific process of the two-stage mutation method described in step S317 is as follows:

[0074] S31701. Randomly select a position on the feasible disassembly sequence of the individual pop_mutation that is undergoing two-stage mutation, determine the element corresponding to the position as the mutation element MutationEle, and determine the waste product number m and disassembly task number i corresponding to MutationEle.

[0075] S31702, Find all predecessor and successor activities of MutationEle;

[0076] S31703. Find all elements in pop_mutation whose second dimension is negative and which are the immediate predecessors of MutationEle. Record the positions of these elements in pop_mutation and take the first position as A.

[0077] S31704. Find all elements in pop_mutation whose second dimension is negative and which are the next work of MutationEle. Record the position of these elements in pop_mutation and take the last position as B.

[0078] S31705. Find all elements in pop_mutation whose second dimension is positive and which are the immediate predecessors of MutationEle. Record the positions of these elements in pop_mutation and take the last position as C.

[0079] S31706. Find all elements in pop_mutation whose second dimension is positive and which are the next work of MutationEle. Record the position of these elements in pop_mutation and take the first position as D.

[0080] S31707. Determine the sign of the second dimension of MutationEle's encoding. If it is positive, go to S31708; otherwise, go to S31709.

[0081] S31708. Determine whether all the codes corresponding to the immediate successor work in pop_mutationMutationEle are negative. If so, go to S31710; otherwise, go to S31715.

[0082] S31709. Determine whether all the codes corresponding to the immediate successor work in pop_mutationMutationEle are positive. If so, go to S31711; otherwise, go to S31714.

[0083] S31710. Generate a random number β in the interval [0,1). If β>0.5, go to S31712; otherwise, go to S31715.

[0084] S31711. Generate a random number β in the interval [0,1). If β>0.5, go to S31713; otherwise, go to S31714.

[0085] S31712. Under the condition that the absolute value of the second dimension of MutationEle remains unchanged, modify the second dimension of MutationEle to a negative integer and go to S31714.

[0086] S31713. Under the condition that the absolute value of the second dimension of MutationEle remains unchanged, modify the second dimension of MutationEle to a positive integer and go to S31715.

[0087] S31714. In pop_mutation, adjust the position of MutationEle to any position between B and A to obtain the mutated individual Pop_M;

[0088] S31715. In pop_mutation, adjust the position of MutationEle to any position between C and D to obtain the mutated individual Pop_M.

[0089] Furthermore, in step S4, the specific steps for calculating the objective function value of all individuals in the mixed population are as follows:

[0090] S401. Merge the parent population and the offspring population to generate a mixed population, and use the mixed population as the current population;

[0091] S402. For each current population individual pop_m, determine the corresponding disassembly task sequence, and further determine the position of the disassembly task with the hazardous attribute of the corresponding part in the disassembly sequence, and record the last position position_1; further determine the position of the disassembly task with the demand attribute of the corresponding part in the disassembly sequence, and record the last position position_2; take position_max=max{ position_1, position_2}.

[0092] S403. Delete the dismantling tasks after position_max in the dismantling task sequence corresponding to pop_m to obtain the current individual pop_m_true. The number of dismantling tasks in the dismantling task sequence corresponding to pop_m_true is the dismantling depth DD of individual pop_m.

[0093] S404, Set L=1, HI=0;

[0094] S405. Take out the Lth disassembly task Task_L in pop_m_true, set HI to HI plus L multiplied by the hazard attribute of the part corresponding to Task_L. If L=1, go to S405; otherwise, go to S406.

[0095] S406, Open a new workstation k k=1, s k Operation time T k The execution time t_task_L is set to task_L. k The disassembly task set in the middle is set to ζ k , ζ k ={task_L};

[0096] S407. Determine if the disassembly task Task_L can be performed on the current workstation. k The process is executed, and T is judged. k The relationship between +t_task_L and cycle time CT, if T kIf +t_task_L < CT, go to S407; otherwise, go to S408;

[0097] S408. Set T k = T k + t_task_L, and add the disassembly task Task_L to ζ k ;

[0098] S409. Open a new workstation, set k = k + 1, and set the operation time T k of s k to the execution time t_task_L of task_L, and set the disassembly task set in s k to ζ k , ζ k = { task_L};

[0099] S410. If L ≠ position_max, set L = L + 1, set HI equal to HI plus the hazard attribute of the part corresponding to Task_L multiplied by L, and repeat steps S404 - S408; otherwise, output the disassembly plan, output k as the number of workstations NS turned on, and output HI as the hazard index;

[0100] S411. Select the maximum value in T k as Tc;

[0101] S412. Substitute Tk and Tc into the following formula (8) to calculate the workstation load smoothness SI.

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[0103] Furthermore, the specific process of step S5 is as follows: If the number of Pareto-optimal solutions in the mixed population is greater than the population size Pop_m, calculate the global multi-level crowding distance for the selected Pareto-optimal solutions, then sort them in ascending order according to the global multi-level crowding distance, and select the Pareto-optimal solutions with the population size to form a new parental population; If the number of selected Pareto-optimal solutions is less than the population size, randomly select a certain number of population individuals from the remaining mixed population after screening and combine them with the selected Pareto-optimal solutions to form a new generation of parental population, and output the new parental population to the external archive; The calculation method of the global multi-level crowding distance is shown in the following formula (9):

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[0105] In the formula, o is the number of the objective, o = (1, 2, 3, 4), O is the number of objectives, O = 4, pop and pop´ are both Pareto-optimal population individuals, pop of is the set of all individuals in the population that achieve the optimal value of the function for the o-th objective. o Let be the o-th objective function.

[0106] Further, the specific process of step S7 is as follows: If the number of Pareto better solutions in the external archive is greater than the population size Pop_m, then the global multi-level congestion distance is calculated for the selected Pareto better solutions, and then the Pareto better solutions with the largest population size are selected as the dismantling scheme output according to the global multi-level congestion distance sorted from smallest to largest; if the number of Pareto better solutions selected from the external archive is less than the population size, then a certain number of population individuals are randomly selected from the remaining solutions after screening in the external archive and combined with the selected Pareto better solutions to form the dismantling scheme output.

[0107] The beneficial effects of this invention are as follows:

[0108] The above scheme establishes a dismantling line balancing optimization model for the U-shaped incomplete dismantling line balancing problem (MUPDLBP) of mixed waste products. It provides a control method for the U-shaped incomplete dismantling line balancing of mixed waste products, which is a Pareto discrete NSGAⅡ algorithm (NPNSGAⅡ) improved from the fast elite multi-objective genetic algorithm based on the characteristics of the U-shaped incomplete dismantling line balancing problem of mixed waste products. A Monte Carlo simulation initialization method is designed to effectively solve the problem of low coverage of the entire solution space by random initialization methods. The designed two-stage crossover and two-stage mutation methods ensure that the dismantling task sequence corresponding to the newly generated individuals is a feasible solution sequence. The designed global multi-level elite strategy can better evaluate the quality of each solution in the same Pareto front, improving the convergence, diversity, and uniformity of the Pareto front. Experimental results show that NPNSGAⅡ can solve MUPDLBP well, providing high-quality dismantling schemes and improving dismantling efficiency. Attached Figure Description

[0109] Figure 1 This is an overall flowchart of the present invention;

[0110] Figure 2 This is a priority relationship diagram of the dismantling tasks of a discarded television set according to an embodiment of the present invention;

[0111] Figure 3 This is a priority relationship diagram of the dismantling tasks of a used refrigerator according to an embodiment of the present invention;

[0112] Figure 4 This is a priority relationship diagram of the dismantling tasks of a waste printer according to an embodiment of the present invention;

[0113] Figure 5This is a box plot showing the supervolume index when comparing four algorithms in the embodiments of the present invention;

[0114] Figure 6 This is a supervolume iteration curve of NPNSGAⅡ in the embodiments of the present invention;

[0115] Figure 7 This is a disassembly scheme with the minimum disassembly depth obtained from the solutions in the embodiments of the present invention.

[0116] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0117] It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0118] This embodiment will describe the balance problem of the U-shaped incomplete disassembly line of discarded products such as televisions, refrigerators and printers in practice.

[0119] Reference Figure 1 This invention provides a method for balancing a U-shaped incomplete dismantling line for mixed waste products, comprising the following steps:

[0120] S1. Construct a disassembly line balancing optimization model with the goal of minimizing the number of workstations, hazard indicators, disassembly depth, and maximizing the smoothness of workstation load, and establish a priority relationship matrix for each product to be disassembled.

[0121] S101. Construct a disassembly line balancing optimization model with the objectives of minimizing the number of workstations, hazard indicators, disassembly depth, and maximizing workstation load smoothness:

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[0129] In the above formulas, equations (1)-(4) are objective functions, and equations (5)-(7) are constraints; equation (1) is the function to minimize the number of open workstations; equation (2) is the function to minimize the hazard index; equation (3) is the function to minimize the dismantling depth; equation (4) is the function to maximize the workstation load smoothness; equation (5) is the priority relationship constraint between dismantling tasks; equation (6) is the dismantling necessity constraint; equation (7) is the cycle time constraint; HI is the hazard index; DD is the dismantling depth; SI is the workstation load smoothness; k is the workstation number, k∈{1,2,…,K}, K is the number of workstations; m is the waste product type number; i is the dismantling task number; Nap is the number of waste product types; Nm is the total dismantling task volume of the m-th waste product; Tk is the sum of the times of all dismantling tasks executed in workstation k. Tc is the maximum value among all Tk. ; Let i be the hazard attribute of the part corresponding to disassembly task i in product m. If the part is hazardous, then =1, otherwise =0; Let i be the operation time for disassembly task i in product m; Let i be the set of dismantling tasks immediately preceding dismantling task i in waste product m; Let i be the set of dismantling tasks immediately following dismantling task i in waste product m; Enable state variables for workstations; if workstation k is enabled, then... =1, otherwise =0; To decompose the task execution order variable, , Assign variables to the disassembly tasks. If the i-th disassembly task of the m-th product is assigned to the entrance side of the k-th workstation of the U-shaped disassembly line, then... , ,otherwise , ;

[0130] S102. Establish a priority relationship matrix for each product to be disassembled;

[0131] Specifically, since the method of this invention can disassemble multiple different types of products simultaneously, it is necessary to count and number the components within each product. For a product m to be disassembled, a set mI is used as the set of numbers for each component in that product, where mI = {1, 2, ..., mi, ..., N}. m}, N m This represents the upper limit of the number of each component in the product to be disassembled.

[0132] In products to be disassembled, the disassembly of some components can only proceed after the disassembly of another component has been completed. This means there is a predecessor / successor relationship between the two components. Therefore, it is necessary to record the components with this predecessor / successor relationship.

[0133] In summary, this step requires treating each component of the product to be disassembled as a disassembly task, assigning a number to each task, and constructing a priority relation matrix to record the preceding and succeeding tasks among the components. The priority relation matrix for the product m to be disassembled is defined as follows: For N m ×N m TP matrix m One of the elements is TP. m ij =1 (1≤i≤N m , 1≤j≤N m When i ≠ j, it indicates that disassembly task i is the immediate predecessor of disassembly task j. m ij =0 indicates that disassembly task i is not the preceding task of disassembly task j.

[0134] S2. The initial parent population is generated using the Monte Carlo simulation initialization method;

[0135] Specifically, in this invention, the population consists of multiple sets of feasible dismantling task sequences, with each set of feasible dismantling task sequences serving as an individual in the population. Each set of feasible dismantling task sequences is represented using a two-dimensional integer encoding method. The absolute value of each integer in the first dimension of each feasible dismantling task sequence represents the number of the waste product to be dismantled. The absolute value of each integer in the second dimension of each feasible dismantling task sequence represents the dismantling task number of the product to be dismantled corresponding to the first dimension. The sign of the integer in the second dimension indicates the position of the corresponding dismantling task assigned to the U-shaped dismantling line. A positive integer in the second dimension indicates that the corresponding dismantling task is assigned to the entrance side of the U-shaped dismantling line for execution, and a negative integer in the second dimension indicates that the corresponding dismantling task is assigned to the exit side of the U-shaped dismantling line for execution.

[0136] The specific implementation process for this step is as follows:

[0137] S201. Determine the set E of the discarded products that need to be dismantled, E={1,2,…,m,…N}. ap};

[0138] S202. Select the discarded product m to be dismantled from set E, m=1;

[0139] S203 For each individual pop_m in the current population, according to the priority relationship matrix P between the dismantling tasks of the waste product m. m And shadow priority relation matrix P m T Among all unassigned dismantling tasks, find the dismantling tasks whose immediate predecessor is empty, and form a set C of unassigned dismantling tasks to be assigned. This means finding the dismantling tasks corresponding to the columns in P where the sum of all column elements is 0, and removing the dismantling tasks already recorded in pop_m. Among all unassigned dismantling tasks, find the dismantling tasks whose immediate successor is empty, and form a shadow set C of unassigned dismantling tasks to be assigned. s That is, to find P T The dismantling tasks corresponding to the columns where the sum of all column elements is 0 are identified, and dismantling tasks already recorded in pop_m are removed.

[0140] S204. In the set {C, C...} s Randomly select a dismantling task i from set C. If dismantling task i comes from set C, first record the number of dismantling task i as +i, and then record +i in the current position of the individual pop_m in the current population; if dismantling task i comes from set C... s If so, first record the number of disassembly task i as -i, and then record -i in the current position of the current population individual pop_m;

[0141] S205. If the dismantling task i selected in S204 comes from set C, then remove all preceding constraints associated with dismantling task i, that is, set the row element containing dismantling task i in P to 0; if the dismantling task i selected in S204 comes from set C s Then, all immediate successor constraints associated with disassembly task i are released, that is, P... T Set the element in the row containing the disassembly task i to 0;

[0142] S206. Repeat S203-S205 until all dismantling tasks of the waste product m have been assigned, and a set of feasible dismantling task sequences is obtained, pop_m as a population individual;

[0143] S207, Repeat S203-S206 until Pop_m individuals are generated for waste product m;

[0144] S208. Take out the first D elements of the current population individual pop_m, generate an incomplete disassembly sequence icpop_m of depth D, and output icpop_m to the incomplete disassembly sequence set Q;

[0145] S209, repeat S208, until all population individuals in S207 have generated the corresponding incomplete disassembly sequence;

[0146] S210. Remove duplicates from Q to generate a set of incompletely disassembled sequences Q_d without repetition.

[0147] S211. Sequentially extract the element q_d from Q_d;

[0148] S212. Calculate the frequency of q_d in Q, fq_d;

[0149] S213. Pop q_d as the current population individual pop_m, and repeat S203-S205 until all dismantling tasks of the waste product m have been assigned.

[0150] S214. Repeat S213 until Pop_m×fq_d population individuals are generated for waste product m;

[0151] S215. Repeat S211-S214 until all elements in Q_d have been removed;

[0152] S216. Repeat S201-S215 until Pop_m individuals are generated for all the waste products that need to be dismantled in set E.

[0153] S217. Randomly select one individual from the population of each product;

[0154] S218. While keeping the order of disassembly tasks within each product population unchanged, randomly combine the disassembly tasks of different products to obtain a mixed product population.

[0155] S219. Repeat S217-S218 until Pop_m mixed product populations are generated;

[0156] S220. Take the Pop_m mixed product populations obtained in S219 and form a parent population, and output the parent population.

[0157] S3. Use a two-stage crossover and two-stage mutation method to process individuals in the parent population to generate the offspring population. The specific steps are as follows:

[0158] S301: Randomly select two individuals from the parent population to define two paired individuals, and denote the two paired individuals as Pop_1 and Pop_2 respectively;

[0159] S302: Randomly select two identical points on the feasible disassembly sequence of the paired individuals, map the elements between the two points on the feasible disassembly sequence to each other and move their positions, so that the paired individuals form two new disassembly sequences respectively. The two new disassembly sequences are denoted as Seq_1 and Seq_2 respectively.

[0160] S303: Select Pop_1 and Seq_1 as the current parent individual NowPop and the current new disassembly sequence NowSeq;

[0161] S304: Compare NowPop with NowSeq, find the element whose sign has changed in the second dimension of the dismantling sequence as the current element NowEle, and determine the waste product number m and dismantling task number i corresponding to NowEle;

[0162] S305: Determine the sign of the second dimension of NowEle's code. If it is positive, proceed to S306; otherwise, proceed to S307.

[0163] S306: Locate all of NowEle's immediate predecessors and proceed to S308;

[0164] S307: Locate all of NowEle's immediate successor tasks and proceed to S309;

[0165] S308: Determine whether all the codes corresponding to the immediate predecessor tasks of NowEle in NowSeq are positive. If so, go to S314; otherwise, go to S310.

[0166] S309: Determine whether all the codes corresponding to the immediate successor tasks of NowEle in NowSeq are negative. If so, go to S315; otherwise, go to S312.

[0167] S310: Modify the second dimension of NowEle to a negative integer while keeping the absolute value of NowEle's second dimension unchanged;

[0168] S311: Locate all of NowEle's immediate successor tasks and proceed to S315;

[0169] S312: Modify the second dimension of NowEle to a positive integer while keeping the absolute value of NowEle's second dimension unchanged;

[0170] S313: Locate all of NowEle's immediate predecessors and proceed to S314;

[0171] S314: In NowSeq, adjust the position of NowEle to any position after all preceding disassembly tasks to obtain a new feasible disassembly sequence as the child individual Pop_child, and then go to S316;

[0172] S315: In NowSeq, adjust the position of NowEle to any position before all subsequent disassembly tasks to obtain a new feasible disassembly sequence as the child individual Pop_child, and go to S316;

[0173] S316: Generate a random number α in the interval [0,1). If α>a, go to S317; otherwise, go to S318.

[0174] S317: Process Pop_child using a two-stage mutation method, and add the processed Pop_child to the offspring population. Proceed to S319; the specific two-stage mutation method operation is as follows:

[0175] S31701: Randomly select a position on the feasible disassembly sequence of the individual pop_mutation undergoing two-stage mutation, determine the element corresponding to that position as the mutation element MutationEle, and determine the waste product number m and disassembly task number i corresponding to MutationEle;

[0176] S31702. Find all predecessor and successor tasks of MutationEle;

[0177] S31703. Find all elements in pop_mutation whose second dimension is negative and which are the immediate predecessors of MutationEle. Record the positions of these elements in pop_mutation and take the first position as A.

[0178] S31704. Find all elements in pop_mutation whose second dimension is negative and which are the immediate successors of MutationEle. Record the positions of these elements in pop_mutation and take out the last position as B.

[0179] S31705. Find all elements in pop_mutation whose second dimension is positive and which are the immediate predecessors of MutationEle. Record the positions of these elements in pop_mutation and take out the last position as C.

[0180] S31706. Find all elements in pop_mutation whose second dimension is positive and which are the immediate successors of MutationEle. Record the positions of these elements in pop_mutation and take the first position as D.

[0181] S31707. Determine the sign of the second dimension of MutationEle's encoding. If it is positive, go to S31708; otherwise, go to S31709.

[0182] S31708. Determine whether all the codes corresponding to the immediate successor tasks of pop_mutationMutationEle are negative. If so, go to S31710; otherwise, go to S31715.

[0183] S31709. Determine whether all the codes corresponding to the immediate successor tasks of pop_mutationMutationEle are positive. If so, go to S31711; otherwise, go to S31714.

[0184] S31710. Generate a random number β in the interval [0,1). If β>0.5, go to S31712; otherwise, go to S31715.

[0185] S31711. Generate a random number β in the interval [0,1). If β>0.5, go to S31713; otherwise, go to S31714.

[0186] S31712. Under the condition that the absolute value of the second dimension of MutationEle remains unchanged, modify the second dimension of MutationEle to a negative integer and go to S31714.

[0187] S31713. Under the condition that the absolute value of the second dimension of MutationEle remains unchanged, modify the second dimension of MutationEle to a positive integer and go to S31715.

[0188] S31714. In pop_mutation, adjust the position of MutationEle to any position between B and A to obtain the mutated individual Pop_M;

[0189] S31715. In pop_mutation, adjust the position of MutationEle to any position between C and D to obtain the mutated individual Pop_M.

[0190] S318: Add Pop_child to the offspring population, then proceed to S319;

[0191] S319: Select Pop_2 and Seq_2 as the current parent individual NowPop and the current new disassembly sequence NowSeq;

[0192] S320: Repeat S304-S316 once;

[0193] S321: Repeat S301-S320 until Pop_m offspring individuals are generated;

[0194] S322: Combine all offspring individuals into an offspring population and output the offspring population;

[0195] Where a is a real number, and 0 ≤ a < 1;

[0196] S4. Merge the parent and offspring populations to generate a mixed population, and calculate the objective function value for all individuals in the mixed population. The specific steps are as follows:

[0197] S401. Merge the parent population and the offspring population to generate a mixed population, and use the mixed population as the current population;

[0198] S402. For each current population individual pop_m, determine the corresponding disassembly task sequence, and further determine the position of the disassembly task with the hazardous attribute of the corresponding part in the disassembly sequence, and record the last position position_1; further determine the position of the disassembly task with the demand attribute of the corresponding part in the disassembly sequence, and record the last position position_2; take position_max=max{ position_1, position_2}.

[0199] S403. Delete the dismantling tasks after position_max in the dismantling task sequence corresponding to pop_m to obtain the current individual pop_m_true. The number of dismantling tasks in the dismantling task sequence corresponding to pop_m_true is the dismantling depth DD of individual pop_m.

[0200] S404, Set L=1, HI=0;

[0201] S405. Take out the Lth disassembly task Task_L in pop_m_true, set HI to HI plus L multiplied by the hazard attribute of the part corresponding to Task_L. If L=1, go to S405; otherwise, go to S406.

[0202] S406, Open a new workstation k k=1, s k Operation time T k The execution time t_task_L is set to task_L. k The disassembly task set in the middle is set to ζ k , ζ k ={task_L};

[0203] S407. Determine if the disassembly task Task_L can be performed on the current workstation. k The process is executed, and T is judged. k The relationship between +t_task_L and cycle time CT, if T kIf +t_task_L < CT, go to S407; otherwise, go to S408;

[0204] S408. Set T k = T k + t_task_L, and add the disassembly task Task_L to ζ k ;

[0205] S409. Open a new workstation, set k = k + 1, and set the operation time T k of s k to the execution time t_task_L of task_L, and set the disassembly task set in s k to ζ k , ζ k = {task_L};

[0206] S410. If L ≠ position_max, set L = L + 1, set HI equal to HI plus L multiplied by the hazard attribute of the part corresponding to Task_L, and repeat steps S404 - S408; otherwise, output the disassembly plan, output k as the number of workstations NS turned on, and output HI as the hazard index;

[0207] S411. Select the maximum value in T k as Tc;

[0208] S412. Substitute Tk and Tc into the following formula (8) to calculate the workstation load smoothness SI. <000055%51>

[0210] S5. Use the global multi-level elite strategy to screen the mixed population, generate a new parental population, and output the new parental population to the external archive. The specific process is as follows: Judge whether the number of Pareto-optimal solutions in the mixed population is greater than the population size Pop_m. If the number of Pareto-optimal solutions in the mixed population is greater than the population size Pop_m, calculate the global multi-level crowding distance for the selected Pareto-optimal solutions, then sort them in ascending order according to the global multi-level crowding distance, and select the Pareto-optimal solutions with the population size to form a new parental population; If the number of selected Pareto-optimal solutions is less than the population size, randomly select a certain number of population individuals from the remaining mixed population after screening and combine them with the selected Pareto-optimal solutions to form a new generation of parental population, and output the new parental population to the external archive; <:

[0211] In step S5, the global multi-level crowding distance is involved. The calculation method of the global multi-level crowding distance is as shown in the following formula (9):

[0212]

[0213] In the formula, o is the target number, o=(1,2,3,4), O is the number of targets, O=4, pop and pop´ are both superior individuals in the Pareto population, pop o f is the set of all individuals in the population that achieve the optimal value of the function for the o-th objective. o Let be the o-th objective function.

[0214] S6. Repeat steps S3-S5 according to the predetermined number of iterations.

[0215] S7 outputs the Pareto optimal solutions from the external archive as the dismantling scheme. The specific process is as follows: determine whether the number of Pareto optimal solutions in the external archive is greater than the population size Pop_m. If the number of Pareto optimal solutions in the external archive is greater than the population size Pop_m, calculate the global multi-level congestion distance for the selected Pareto optimal solutions, and then sort them according to the global multi-level congestion distance from smallest to largest. Select the Pareto optimal solutions with the largest population size as the dismantling scheme output. If the number of Pareto optimal solutions selected from the external archive is less than the population size, randomly select a certain number of population individuals from the remaining solutions after selection in the external archive and combine them with the selected Pareto optimal solutions to form the dismantling scheme output.

[0216] Specific experimental examples

[0217] The above describes the entire process of establishing and solving the model. The following section uses the same model and algorithm to perform a mixed disassembly of the surveyed televisions, refrigerators, and printers. To verify the superiority of the NPNSGAⅡ provided in this invention in solving the mixed waste product U-shaped incomplete disassembly line balancing problem (MUPDLBP), NSGAⅡ, HypE, and CS (i.e., fast elite multi-objective genetic algorithm, multi-objective optimization algorithm based on fast hypervolume estimation, and cuckoo search algorithm) are selected as comparative algorithms.

[0218] The information obtained from the survey for the three products is as follows:

[0219] The priority relationship diagram for disassembling the three products is as follows: Figure 2-4 As shown in Table 1-3, the disassembly task data for the three products are as follows.

[0220] Table 1 contains relevant data on various disassembly tasks of the television set surveyed.

[0221]

[0222] Table 2 shows the relevant data for each refrigerator disassembly task surveyed.

[0223]

[0224] Table 3 shows the relevant data information for each printer disassembly task surveyed.

[0225]

[0226] The cycle time CT was set to 800 seconds. To ensure a fair comparison of the results from several algorithms, the computation termination condition was set to the same time t_end, where t_end = 500 seconds. Each algorithm was run independently 30 times. The population size for the algorithms was set to 300. The crossover and mutation probabilities associated with the genetic operations were set to 0.95 and 0.85, respectively. HypE estimated the hypervolume using 10,000 points, and the discovery probability for the CS algorithm was set to 0.3.

[0227] Since hypervolume can effectively evaluate the quality of non-dominated solution sets without requiring a reference set, and provides a relatively objective assessment of the quality of non-dominated solution sets, it is used to evaluate the quality of solutions obtained by each algorithm. The reference points for hypervolume are set to (15, 0, 5000, 108). Table 4 shows the 95% confidence intervals of the mean and standard deviation of various algorithms on the hypervolume metric.

[0228] Table 4. 95% confidence intervals of the mean and standard deviation of various algorithms on the hypervolume index.

[0229]

[0230] As shown in Table 4, the average value range of the hypervolume index of NPNSGAⅡ is significantly larger than that of the other three methods, and the standard deviation range of NPNSGAⅡ is significantly smaller than that of the other three comparison algorithms, indicating that NPNSGAⅡ has obvious advantages in solving MUPDLBP.

[0231] Figure 5 The hypervolume boxplots obtained using different methods are shown. From Figure 5 It can be seen that the INSGAⅡ algorithm proposed in this paper has better stability compared to the other three methods.

[0232] Figure 6 The supervolume iteration curves of NPNSGAⅡ are shown. (By...) Figure 6It can be seen that the hypervolume index improved from 26151.28 to 42129.73. The hypervolume index grew rapidly in the early stages of the algorithm iterations, reaching 38277.12 after 20 iterations, an increase of 46.37% compared to the initial hypervolume value, but 9.14% lower than the final hypervolume value. In the last 97 iterations, the hypervolume index improved from 38277.12 in the 20th iteration to 41890.28, an increase of 9.44%, at which point it was only 0.57% lower than the optimal hypervolume value. Figure 6 It can be seen that NPNSGAⅡ has good convergence.

[0233] Figure 6 The supervolume iteration curves of NPNSGAⅡ are shown. (By...) Figure 6 It can be seen that the hypervolume index improved from 173224.19 to 906849.46. The hypervolume index grew rapidly in the early stages of the algorithm iterations, reaching 785662.88 after 157 iterations, an increase of 353.55% compared to the initial hypervolume value, but 13.36% lower than the final hypervolume value. At the 350th iteration, the hypervolume index improved from 785662.88 in the 157th iteration to 902725.07, an increase of 14.90%, at which point it was only 0.45% lower than the optimal hypervolume value. Figure 6 It can be seen that NPNSGAⅡ has good convergence.

[0234] Depend on Figure 7 It is known that the printer has 21 parts that do not need to be disassembled. The television has 7 parts that do not need to be disassembled. The refrigerator has 1 part that does not need to be disassembled. Searching the solution space using a brute-force method reveals that there are no parts in the printer, television, or refrigerator that do not need to be disassembled. The maximum disassembly time for all workstations is taken as the actual cycle time T. actual The workload rate of each workstation is denoted as Δ, where Δ = T k / T actual ×100%, T k This is the sum of the times for all disassembly tasks performed in workstation k. (By...) Figure 7 As can be seen from this scheme, the actual cycle time is 800s, and the workload rate of each workstation is above 95%. This indicates that NPNSGAⅡ can balance the load of each workstation while ensuring the minimum number of disassembled parts when processing MUPDLBP.

[0235] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, apparatus, article, or method that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, apparatus, article, or method. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, apparatus, article, or method that includes that element.

[0236] The above description is merely a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A U-shaped incomplete disassembly line balancing control method for mixed waste products, characterized by, Includes the following steps: S1. Construct a disassembly line balancing optimization model with the objectives of minimizing the number of workstations, hazard indicators, disassembly depth, and maximizing workstation load smoothness, and establish a priority relationship matrix for each product to be disassembled; wherein, the disassembly line balancing optimization model is: In the above formulas, equations (1)-(4) are objective functions, and equations (5)-(7) are constraints; equation (1) is the function to minimize the number of open workstations; equation (2) is the function to minimize the hazard index; equation (3) is the function to minimize the dismantling depth; equation (4) is the function to maximize the workstation load smoothness; equation (5) is the priority relationship constraint between dismantling tasks; equation (6) is the dismantling necessity constraint; equation (7) is the cycle time constraint; HI is the hazard index; DD is the dismantling depth; SI is the workstation load smoothness; k is the workstation number, k∈{1,2,…,K}, K is the number of workstations; m is the waste product type number; i is the dismantling task number; Nap is the number of waste product types; Nm is the total dismantling task volume of the m-th waste product; Tk is the sum of the times of all dismantling tasks executed in workstation k. Tc is the maximum value among all Tk. ; Let i be the hazard attribute of the part corresponding to disassembly task i in product m. If the part is hazardous, then =1, otherwise =0; Let i be the operation time for disassembly task i in product m; Let i be the set of dismantling tasks immediately preceding dismantling task i in waste product m; Let i be the set of dismantling tasks immediately following dismantling task i in waste product m; Enable state variables for workstations; if workstation k is enabled, then... =1, otherwise =0; To decompose the task execution order variable, , Assign variables to the disassembly tasks. If the i-th disassembly task of the m-th product is assigned to the entrance side of the k-th workstation of the U-shaped disassembly line, then... , ,otherwise , ; S2. Generate a parent population of size Pop_num using the Monte Carlo simulation initialization method; S3. Use a two-stage crossover method and a two-stage mutation method to process individuals in the parent population to generate the offspring population; S4. Merge the parent population and the offspring population to generate a mixed population, and calculate the objective function value of all individuals in the mixed population; S5. A global multi-level elite strategy is used to screen the mixed population, generate a new parent population, and output the new parent population to an external archive. The specific process of the global multi-level elite strategy is as follows: If the number of Pareto better solutions in the mixed population is greater than the population size, the global multi-level crowding distance is calculated for the screened Pareto better solutions. Then, the Pareto better solutions are sorted from smallest to largest according to the global multi-level crowding distance, and the population size is selected to form a new parent population. If the number of screened Pareto better solutions is less than the population size, a certain number of population individuals are randomly selected from the remaining mixed population after screening and combined with the screened Pareto better solutions to form a new generation of parent population. S6. Repeat S3-S5 according to the predetermined number of iterations; S7. Output the Pareto optimal solution from the external file as the disassembly scheme.

2. The U-shaped incomplete disassembly line balancing control method for mixed WOPs according to claim 1, wherein In step S2, the population consists of multiple sets of feasible dismantling task sequences, with each set of feasible dismantling task sequences serving as an individual in the population. Each set of feasible dismantling task sequences is represented by a two-dimensional integer encoding. The absolute value of each integer in the first dimension of each feasible dismantling task sequence represents the number of the waste product to be dismantled. The absolute value of each integer in the second dimension of each feasible dismantling task sequence represents the dismantling task number of the product to be dismantled corresponding to the first dimension. The sign of the integer in the second dimension indicates the position of the corresponding dismantling task in the U-shaped dismantling line. A positive integer in the second dimension indicates that the corresponding dismantling task is assigned to the entrance side of the U-shaped dismantling line for execution, and a negative integer in the second dimension indicates that the corresponding dismantling task is assigned to the exit side of the U-shaped dismantling line for execution.

3. The U-shaped incomplete disassembly line balancing control method for mixed WOPs according to claim 1, characterized in that, The specific process of step S2 is as follows: S201. Determine the set E of the discarded products that need to be dismantled, E={1,2,…Nap}; S202. Select the discarded product m to be dismantled from set E, m=1; S203. For each individual pop_m in the current population, based on the priority relationship matrix between dismantling tasks of the discarded product m. Shadow Priority Relationship Matrix Among all unassigned dismantling tasks, identify the dismantling tasks whose preceding work is empty, forming a set C of unassigned dismantling tasks to be assigned. This is equivalent to identifying the dismantling tasks corresponding to the columns in P where the sum of all column elements is 0, and removing the dismantling tasks already recorded in pop_m. Next, among all unassigned dismantling tasks, identify the dismantling tasks whose succeeding work is empty, forming a shadow set Cs of unassigned dismantling tasks to be assigned. The dismantling tasks corresponding to the columns where the sum of all column elements is 0 are identified, and dismantling tasks already recorded in pop_m are removed. S204. Randomly select a dismantling task i from the set {C, Cs}. If the dismantling task i comes from the set C, first record the number of the dismantling task i as +i, and then record +i in the current position of the current population individual pop_m; if the dismantling task i comes from the set Cs, first record the number of the dismantling task i as -i, and then record -i in the current position of the current population individual pop_m. S205, if the disassembly task i selected in S204 is from the set C, all the immediate-preceding constraints associated with the disassembly task i are released, i.e. the element in the row where the disassembly task i is located in P is set to 0; if the disassembly task i selected in S204 is from the set Cs, all the immediate-following constraints associated with the disassembly task i are released, i.e. the element in the row where the disassembly task i is located in P is set to 0. the element in the row where the disassembly task i is located in P is set to 0. S206. Repeat S203-S205 until all dismantling tasks of the waste product m have been assigned, and a set of feasible dismantling task sequences is obtained, pop_m as a population individual; S207, Repeat S203-S206 until Pop_m individuals are generated for waste product m; S208. Take out the first D elements of the current population individual pop_m, generate an incomplete disassembly sequence icpop_m of depth D, and output icpop_m to the incomplete disassembly sequence set Q; S209, repeat S208, until all population individuals in S207 have generated the corresponding incomplete disassembly sequence; S210. Remove duplicates from Q to generate a set of incompletely disassembled sequences Q_d without repetition. S211. Sequentially extract the element q_d from Q_d; S212. Calculate the frequency of q_d in Q, fq_d; S213. Pop q_d as the current population individual pop_m, and repeat S203-S205 until all dismantling tasks of the waste product m have been assigned. S214. Repeat S213 until Pop_m×fq_d population individuals are generated for waste product m; S215. Repeat S211-S214 until all elements in Q_d have been removed; S216. Repeat S201-S215 until Pop_m individuals are generated for all the waste products that need to be dismantled in set E. S217. Randomly select one individual from the population of each product; S218. While keeping the order of disassembly tasks within each product population unchanged, randomly combine the disassembly tasks of different products to obtain a mixed product population. S219. Repeat S217-S218 until Pop_m mixed product populations are generated; S220. Take the Pop_m mixed product populations obtained in S219 and form a parent population, and output the parent population.

4. The U-shaped incomplete disassembly line balancing control method for mixed WOPs according to claim 1, characterized in that, The specific process of the two-stage crossover method described in step S3 is as follows: S301. Randomly select two individuals from the parent population and define two paired individuals, denoted as Pop_1 and Pop_2 respectively. S302. Randomly select two identical points on the feasible disassembly sequence of the paired individuals, map the elements between the two points on the feasible disassembly sequence to each other and move their positions so that the paired individuals form two new disassembly sequences respectively. The two new disassembly sequences are denoted as Seq_1 and Seq_2 respectively. S303. Select Pop_1 and Seq_1 as the current parent individual NowPop and the current new disassembly sequence NowSeq; S304. Compare NowPop with NowSeq, find the element whose sign has changed in the second dimension of the dismantling sequence as the current element NowEle, and determine the waste product number m and dismantling task number i corresponding to NowEle. S305. Determine the sign of the second dimension of NowEle's code. If it is positive, proceed to S306; otherwise, proceed to S307. S306, Locate all preceding jobs of NowEle and proceed to S308; S307. Locate all of NowEle's immediate successor works and proceed to S309; S308. Determine whether all the codes corresponding to the immediate predecessors of NowEle in NowSeq are positive. If so, go to S314; otherwise, go to S310. S309. Determine whether all the codes corresponding to the immediate successor work of NowEle in NowSeq are negative. If so, go to S315; otherwise, go to S312. S310. Under the condition that the absolute value of the second dimension of NowEle remains unchanged, modify the second dimension of NowEle to a negative integer; S311, Locate all of NowEle's immediate successor works and proceed to S315; S312. Under the condition that the absolute value of the second dimension of NowEle remains unchanged, modify the second dimension of NowEle to a positive integer; S313, Locate all of NowEle's preceding work and proceed to S314; S314. In NowSeq, adjust the position of NowEle to any position after all preceding disassembly tasks to obtain a new feasible disassembly sequence as the child individual Pop_child, and go to S316. S315. In NowSeq, adjust the position of NowEle to any position before all subsequent disassembly tasks to obtain a new feasible disassembly sequence as the child individual Pop_child, and go to S316. S316. Generate a random number α in the interval [0,1). If α>a, go to S317; otherwise, go to S318. S317. Use a two-stage mutation method to process Pop_child and add the processed Pop_child to the offspring population. Proceed to S319. S318. Add Pop_child to the offspring population, then proceed to S319. S319. Select Pop_2 and Seq_2 as the current parent individual NowPop and the current new disassembly sequence NowSeq; S320, Repeat S304-S316 once; S321. Repeat S301-S320 until Pop_m offspring individuals are generated; S322. Form a sub-population from all offspring individuals and output the sub-population. Where a is a real number, and 0 ≤ a < 1.

5. The U-shaped incomplete disassembly line balancing control method for mixed WOPs according to claim 4, wherein, The specific process of the two-stage mutation method described in step S317 is as follows: S31701. Randomly select a position on the feasible disassembly sequence of the individual pop_mutation that is undergoing two-stage mutation, determine the element corresponding to the position as the mutation element MutationEle, and determine the waste product number m and disassembly task number i corresponding to MutationEle. S31702, Find all predecessor and successor activities of MutationEle; S31703. Find all elements in pop_mutation whose second dimension is negative and which are the immediate predecessors of MutationEle. Record the positions of these elements in pop_mutation and take the first position as A. S31704. Find all elements in pop_mutation whose second dimension is negative and which are the next work of MutationEle. Record the position of these elements in pop_mutation and take the last position as B. S31705. Find all elements in pop_mutation whose second dimension is positive and which are the immediate predecessors of MutationEle. Record the positions of these elements in pop_mutation and take the last position as C. S31706. Find all elements in pop_mutation whose second dimension is positive and which are the next work of MutationEle. Record the position of these elements in pop_mutation and take the first position as D. S31707. Determine the sign of the second dimension of MutationEle's encoding. If it is positive, go to S31708; otherwise, go to S31709. S31708. Determine whether all the codes corresponding to the immediate successor work in pop_mutationMutationEle are negative. If so, go to S31710; otherwise, go to S31715. S31709. Determine whether all the codes corresponding to the immediate successor work in pop_mutationMutationEle are positive. If so, go to S31711; otherwise, go to S31714. S31710. Generate a random number β in the interval [0,1). If β>0.5, go to S31712; otherwise, go to S31715. S31711. Generate a random number β in the interval [0,1). If β>0.5, go to S31713; otherwise, go to S31714. S31712. Under the condition that the absolute value of the second dimension of MutationEle remains unchanged, modify the second dimension of MutationEle to a negative integer and go to S31714. S31713. Under the condition that the absolute value of the second dimension of MutationEle remains unchanged, modify the second dimension of MutationEle to a positive integer and go to S31715. S31714. In pop_mutation, adjust the position of MutationEle to any position between B and A to obtain the mutated individual Pop_M; S31715. In pop_mutation, adjust the position of MutationEle to any position between C and D to obtain the mutated individual Pop_M.

6. The U-shaped, semi-disassembly line balancing control method for mixed WIPs according to claim 1, characterized in that, In step S4, the specific steps for calculating the objective function value of all individuals in the mixed population are as follows: S401. Merge the parent population and the offspring population to generate a mixed population, and use the mixed population as the current population; S402. For each current population individual pop_m, determine the corresponding disassembly task sequence, and further determine the position of the disassembly task with the hazardous attribute of the corresponding part in the disassembly sequence, and record the last position position_1; further determine the position of the disassembly task with the demand attribute of the corresponding part in the disassembly sequence, and record the last position position_2; take position_max=max{ position_1, position_2}. S403. Delete the dismantling tasks after position_max in the dismantling task sequence corresponding to pop_m to obtain the current individual pop_m_true. The number of dismantling tasks in the dismantling task sequence corresponding to pop_m_true is the dismantling depth DD of individual pop_m. S404, Set L=1, HI=0; S405. Take out the Lth disassembly task Task_L in pop_m_true, set HI to HI plus L multiplied by the hazard attribute of the part corresponding to Task_L. If L=1, go to S405; otherwise, go to S406. S406, open a new workstation s k , k = 1, s k The operation time T k The execution time t_task_L of task_L is set k The disassembly task set in ζ k , ζ k = { task_L}; S407. Determine whether the disassembly task Task_L can be executed at the current workstation s k and judge T k the relationship between +t_task_L and the cycle time CT. If T k +t_task_L < CT, go to S407; otherwise, go to S408; S408, set T k =T k +t_task_L, and add the disassembly task Task_L to ζ k ; S409, open a new workstation, set k = k + 1, s k the operation time T k the execution time t_task_L, s, of task_L k the disassembly task set ζ k , ζ k = { task_L}; S410. If L ≠ position_max, then set L = L + 1, set HI equal to HI plus L multiplied by the hazard attribute of the part corresponding to Task_L, and repeat steps S404-S408; otherwise, output the disassembly scheme, output k as the number of workstations to be opened NS, and output HI as the hazard index. S411, select the maximum value in Tc as T k ; S412, Substitute Tk and Tc into equation (8) to calculate the workstation load smoothness SI:

7. The U-shaped, semi-disassembly line balancing control method for mixed WIPs according to claim 1, characterized in that, The specific formula for calculating the global multi-level congestion distance is as follows: In the formula, o is the target number, o=(1,2,3,4), O is the number of targets, O=4, pop and pop´ are both population individuals with better Pareto, popo is the set of all population individuals that make the function value of the o-th target obtain the optimal value, and fo is the o-th objective function.

8. The method for balancing a U-shaped incomplete dismantling line for mixed waste products according to claim 1, characterized in that, The specific process of step S7 is as follows: If the number of Pareto better solutions in the external archive is greater than the population size Pop_m, then calculate the global multi-level crowding distance for the selected Pareto better solutions, and then sort them according to the global multi-level crowding distance from smallest to largest, and select the Pareto better solutions with the largest population size as the dismantling scheme output; if the number of Pareto better solutions selected from the external archive is less than the population size, then randomly select a certain number of population individuals from the remaining solutions after screening in the external archive and combine them with the selected Pareto better solutions to form the dismantling scheme output.

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