Multi-objective parallel waste product disassembly line optimization method based on number of skills of workers

Abstract

The invention discloses a multi-objective parallel waste product disassembly line optimization method based on the number of skills of workers, and relates to a waste product disassembly line optimization method, which comprises the following steps of: constructing a disassembly line balance model according to product information of a product to be disassembled, disassembly line information and disassembly skill information of the workers; constructing a target function by taking the minimum skill number of chemical workers and the maximum net profit of product disassembly as targets; setting constraint conditions of the disassembly line balance optimization model; encoding the disassembly task based on an encoding mechanism of a priority relation matrix, generating a feasible solution, and decoding; obtaining a task allocation scheme of the to-be-disassembled product; in an actual case, the IDBA is compared with five algorithms including NSGA-II, NSGA-III, SPEA-II, ESPEA, MOEA / D and the like. The improved discrete bat algorithm is provided according to the actual case of the disassembly line, the multi-target parallel disassembly line balance problem is optimized, and the task and skill distribution efficiency is remarkably improved.

Description

Technical Field

[0001] The invention relates to a method for optimizing a waste product disassembly line, in particular to a method for optimizing a waste product disassembly line based on multi-objective parallelism of worker skill numbers. Background Art

[0002] The rapid development of information technology has profoundly changed the daily life of modern society. At the same time, the vigorous development of modern manufacturing has led to a decrease in product costs and a surge in market demand, which has not only accelerated the pace of product replacement, but also significantly increased the rate of waste product generation. Faced with the dual pressures of resource waste and environmental pollution, the recycling and reprocessing of waste products is particularly urgent. In this process, the disassembly link plays a vital role, which involves separating useful parts and potentially harmful substances from waste products. Through meticulous disassembly, these parts can be recycled, and after rigorous testing, repair and upgrading, they will re-enter the remanufacturing process, thereby maximizing the value of waste products and minimizing their impact on the environment and human health.

[0003] The disassembly of waste products requires extremely high standardization and specialization of the industry. In order to ensure the efficiency and environmental protection of the disassembly process, disassembly companies need to formulate detailed disassembly strategies for various products. In the disassembly operation, it is necessary not only to maintain the balance of the production line, but also to fully consider the actual operation of the workers, including the number of skills mastered by the workers, the applicability of the disassembly tools, the rationality of the disassembly sequence, and the disassembly priority of the parts. Summary of the invention

[0004] The purpose of the present invention is to provide a multi-objective parallel optimization method for waste product disassembly lines based on the number of workers' skills. The method improves the overall efficiency of the disassembly line by considering the number of skills mastered by the workers, focuses on optimizing the skill distribution of the workers, so that each worker can give full play to his or her maximum potential during the disassembly process, and can achieve balanced operation of the disassembly line, improve disassembly efficiency, and reduce the risk of operational errors and work-related injuries.

[0005] The present invention provides the following technical solutions:

[0006] A method for optimizing a waste product disassembly line based on worker skill number and multi-objective parallelism, the method comprising the following steps:

[0007] S1 builds a disassembly line balance model based on the product information and disassembly line information of the product to be disassembled and the disassembly skill information of the workers;

[0008] S2 constructs the objective function with the goal of minimizing the number of skills that workers need to master and maximizing the net profit of product disassembly;

[0009] S3 sets the constraint conditions of the disassembly line balance optimization model;

[0010] S4 encodes the disassembly task, generates feasible solutions, and decodes it based on the encoding mechanism of the priority relation matrix;

[0011] S5 uses the improved discrete bat algorithm (IDBA) to solve the multi-objective disassembly line balance optimization model and obtain the task allocation plan for the products to be disassembled;

[0012] S6 compares the improved IDBA with five algorithms including NSGA-II, NSGA-III, SPEA-II, ESPEA, and MOEA / D in actual cases.

[0013] The method for optimizing the disassembly line of used products based on multi-objective parallelism of the number of worker skills, wherein the information of the products to be disassembled includes the number of disassembly tasks, the number of components, the number of parts of the products to be disassembled, the unit time disassembly cost and recycling cost of the product components, the priority relationship between the disassembly tasks of the products, the disassembly relationship between tasks and components, and the disassembly time of each task on the disassembly line; the disassembly line information includes the cycle period of the disassembly line; and all the disassembly skill information of the workers includes the number of disassembly skills mastered by the workers in the process of product disassembly.

[0014] The method for optimizing the waste product disassembly line based on the number of worker skills and multiple objectives is characterized in that the method aims to minimize the number of skills required by workers and maximize the net profit of product disassembly, and constructing the objective function includes:

[0015] max f 1

[0016] min f 2

[0017]

[0018] Among them, f 1 represents the net profit from product disassembly, f 2 represents the number of skills mastered by the worker; k∈K represents the skill set of the worker; m∈M represents the set of disassembly workstations; R km indicates that the worker in workstation m uses skill k, otherwise R km =0; l∈L, (L=2) represents the assembly line set of disassembly lines; i∈N l represents the task number of the disassembled product on the disassembly line l; s∈S represents the component set of the product to be disassembled; d si =1 means that the product disassembly task i can disassemble component s; if component s is disassembled by task i, then d si = -1, otherwise d si =0;vs represents the revenue cost of product component s; x ilm =1 means that disassembly task i is executed in workstation m of disassembly line l, otherwise it is 0; c il represents the unit time disassembly cost of product components; t il It represents the disassembly time of disassembly task i on disassembly line l.

[0019] The above-mentioned method for optimizing the disassembly line of used products based on multi-objective parallelism of worker skill number includes the following constraints for setting the disassembly line balance optimization model: task allocation constraints, workstation time constraints, task priority constraints, and workstation activation constraints:

[0020] S41. Task allocation constraints:

[0021]

[0022] Among them, T k represents the set of disassembly tasks using skill k;

[0023] S42. Workstation time constraints:

[0024]

[0025] Where C represents the cycle of the disassembly line;

[0026] S43. Task priority constraints:

[0027]

[0028]

[0029]

[0030] Among them, p i,j Represents the priority relationship between disassembly tasks;

[0031] S44. Activation constraints for workstations:

[0032]

[0033] Among them, z m =1 means the workstation is open, otherwise z m =0.

[0034] The method for optimizing the disassembly line of used products based on the multi-objective parallelization of the number of worker skills, wherein the encoding mechanism based on the priority relationship matrix encodes the disassembly task, generates a feasible solution, and decodes the solution, comprises:

[0035] S51, obtaining a priority relationship matrix of tasks according to an AND / OR graph of the execution order of tasks in the product;

[0036] S52. According to the priority relationship matrix of tasks, vector π is introduced to represent a disassembly task sequence of a product. Each element in π corresponds to a task number and is arranged in order. This vector π is a task encoding method. By introducing vector π, the system can digitally represent the disassembly sequence. For some complex disassembly tasks, vector π ensures that each task can follow the rules of the priority relationship matrix, thereby maintaining the logical order of the tasks.

[0037] S53, generate feasible solutions through sequential insertion method; insert the disassembly task sequence of one product into the task sequence of another product to ensure that the disassembly tasks are allocated in sequence and meet the priority and time requirements of the tasks;

[0038] S54, distribute the generated task disassembly sequence to different workstations to ensure that the task time of the workstation does not exceed its cycle time; in this decoding process, not only the task disassembly sequence must be considered, but also the task time constraint must be met.

[0039] The method for optimizing the disassembly line of used products based on multi-objective parallelism of worker skill number, using an improved discrete bat optimization algorithm to solve the multi-objective disassembly line balance optimization model and obtain a task allocation plan for the products to be disassembled includes:

[0040] S61, population initialization and adjustment;

[0041] S62, updating the individuals through a crossover operation based on priority-preserving crossover (PPX) and a mutation operation based on the immediate predecessor task sequence;

[0042] S63, update the population by non-dominated sorting and other methods, select the Pareto optimal solution set, and iterate step by step until the stopping condition is met;

[0043] S64: Obtain a disassembly line balancing strategy that satisfies the balancing constraint condition.

[0044] In the above-mentioned method for optimizing waste product disassembly line based on multi-objective parallelism of worker skill number, the initialization and adjustment of the population in S61 includes:

[0045] S611. Each individual in the population represents a feasible disassembly sequence. The population is generated by random insertion to ensure the randomness and diversity of each individual. Specifically, the disassembly task sequence of product II is randomly inserted into the disassembly task sequence of product I.

[0046] S612. When generating a feasible disassembly sequence for a parallel disassembly line, it is necessary to ensure that the disassembly task of each product follows its priority relationship; however, a randomly generated sequence may not necessarily satisfy these constraints, so further adjustments must be made;

[0047] S613. The adjustment process is divided into three stages: adding operation, adding the omitted tasks to the existing infeasible sequence according to the priority relationship; removing operation, removing conflicting tasks in the task sequence (conflicting tasks refer to tasks that cannot exist in the same disassembly sequence at the same time); swapping operation, after the first two stages are completed, if some tasks still do not meet the priority relationship, adjust the task order.

[0048] In the method for optimizing the disassembly line of used products based on the multi-objective parallelization of the number of worker skills, the method for updating individuals in S62 through a crossover operation (PPX) based on priority-preserving crossover and a mutation operation based on a direct predecessor task sequence includes:

[0049] S621. Priority-preserving crossover operation aims to inherit the good genes in the parent generation when updating individuals and ensure that the priority relationship of the disassembly tasks is not destroyed.

[0050] S622: The process of the crossover operation based on priority retention is as follows: First, two individuals are input, namely, the current best individual π f and an individual π randomly selected from the current Pareto solution set m , and a randomly generated mask sequence MASK; if the mask bit is 1, the corresponding parent individual π m The elements of new If the mask bit is 0, the corresponding parent individual π f The elements of new In; Final output: The generated new individual π new ;

[0051] S623, mutation operation based on the immediate predecessor task sequence, which can make local adjustments to individuals while maintaining their basic structure, thereby improving the diversity of solutions and helping the algorithm to jump out of the local optimum; in this optimization method, the mutation operation is based on the immediate predecessor task sequence, that is, each task must satisfy the priority relationship of its predecessor task to ensure that the disassembly tasks are performed in the correct order;

[0052] S624. The process of mutation operation based on the direct predecessor task sequence is as follows: determine the mutated individual, randomly select an individual π from the population, and the individual represents a feasible sequence of disassembly tasks; randomly select a task, and in the task sequence of the individual, randomly select a task i, which will become the object of mutation; select the predecessor task, and find the immediate predecessor task of task i, that is, task j that task i directly depends on in the disassembly sequence (task j must be completed before task i), otherwise it will cause the task sequence to not comply with the priority relationship; adjust the task sequence, and in order to perform the mutation operation, reinsert task i in front of or behind the predecessor task j, thereby generating a new task sequence.

[0053] The method for optimizing the disassembly line of used products based on the multi-objective parallelization of worker skill number, in which the population is updated by non-dominated sorting or the like, the Pareto optimal solution set is selected, and the stepwise iteration is performed until the stopping condition is met, comprises:

[0054] S631, in the population update process, individuals are first selected by non-dominated sorting; according to the domination rule, the algorithm divides the solutions into multiple levels, and the solutions that are not dominated by other solutions are called Pareto optimal solutions, which form the first layer; for the remaining solutions, they are allocated to the next layer in turn according to the domination situation;

[0055] Assume there are U objective functions, if the solution x 0 Can dominate the solution x 1 , the following conditions must be met:

[0056]

[0057] In this way, non-dominated sorting classifies the population hierarchically to ensure that individuals in each generation have certain superiority. At the same time, in order to ensure the diversity of solutions, the concept of crowding distance is introduced. Crowding distance selects more sparse solutions by calculating the density of individuals in the solution space. Sparse individuals dominate in the crowding distance, avoiding the population from being concentrated in a certain area, thereby achieving a wide distribution of solutions.

[0058] S632. On this basis, the article combines these sorted individuals with the current population to form the next generation population; when updating, the algorithm gives priority to those sparse individuals based on the crowding distance, thereby maintaining the diversity of the population; in multi-objective optimization, the fitness of an individual is determined by multiple objective functions, and the combination of non-dominated sorting and crowding distance enables each individual to comprehensively consider various objectives, thereby avoiding the limitations of single-objective optimization; this method not only retains excellent individuals, but also ensures the coverage of the understanding space through diversified updates;

[0059] S633. After multiple rounds of iterations, the algorithm will gradually approach the optimal solution set, namely the Pareto optimal solution. In each iteration, the current Pareto solution set will be found through non-dominated sorting, and the diversity of solutions will be ensured by combining the crowding distance. As the iterations proceed, the Pareto solution set is continuously updated until the predetermined stopping conditions are met, such as when the maximum number of iterations is reached or the solution set converges, and finally a balanced multi-objective optimization solution set is obtained. This process ensures the efficiency and accuracy of the optimization.

[0060] The method for optimizing the disassembly line of scrap products based on the multi-objective parallelization of worker skill number, and the comparison of the improved IDBA with five algorithms including NSGA-II, NSGA-III, SPEA-II, ESPEA, and MOEA / D in actual cases include:

[0061] S10.1. Select five products with different numbers of tasks and randomly combine them into three different product combinations;

[0062] S10.2. For all algorithms, set the population size to 100, the number of iterations to 100, the crossover probability to 0.7, the mutation probability to 0.5 times the inverse of the task sequence length, and the cycle time of the workstation to 50;

[0063] S10.3, using the first product combination as an experimental case, the IDBA algorithm is compared with five algorithms, namely NSGA-II, NSGA-III, SPEA-II, ESPEA, and MOEA / D, from the perspectives of IGD metric, HV metric, and Epsilon-metric metric. The results show that the IDBA algorithm has more advantages than other algorithms in dealing with multi-objective parallel disassembly line problems;

[0064] S10.4. Next, the IDBA algorithm is compared with five algorithms, namely, NSGA-II, NSGA-III, SPEA-II, ESPEA, and MOEA / D, in terms of the changes in three different evaluation indicators when dealing with practical problems as the iteration time and population size change.

[0065] S10.5. In order to further prove the superiority of evaluating IDBA in dealing with practical problems, three box plots are used to record the values ​​of IGD metric, HV metric and Epsilon metric;

[0066] S10.6. The final output is the distribution of skilled workers and disassembly tasks in the disassembly line workstations of the experimental case of the first product combination.

[0067] The beneficial effects of the present invention are:

[0068] 1. The present invention can optimize the profit and skill requirements of the disassembly line: The present invention proposes an improved discrete bat algorithm, which is applicable to the multi-objective parallel disassembly line balancing problem. The method optimizes the performance of the disassembly line by maximizing the disassembly profit and minimizing the number of worker skills required, thereby achieving an efficient disassembly process.

[0069] 2. The present invention provides a variety of solution options: The improved discrete bat algorithm (IDBA) in the present invention is based on the Pareto dominance relationship, selects the best solution through non-dominated sorting, and guides the algorithm towards the optimal solution. It combines two main operators: the order-preserving crossover (PPX) operator and the position-based mutation operator to ensure that excellent genes are retained in multi-objective optimization, and local optimality can be jumped out to improve global optimization performance. Through these optimization strategies, the best solution can be flexibly selected from a series of balanced solutions in the Pareto front according to different disassembly requirements, production constraints, and resource allocation.

[0070] 3. The IDBA algorithm of the present invention can find an appropriate balance between multiple objectives such as disassembly rhythm, profit maximization and worker skill minimization. Experimental results show that IDBA performs well in a variety of industrial disassembly scenarios, the generated Pareto solution set is more evenly distributed and more convergent, and the solution set shows high flexibility and practicality in multi-objective optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 It is a flow chart of a parallel disassembly line balancing optimization method considering the number of worker skills in an embodiment of the present invention;

[0072] Figure 2 is an AND / OR diagram of a product to be disassembled in an embodiment of the present invention;

[0073] Figure 3 A skill allocation diagram in an embodiment of the present invention;

[0074] Figure 4 A schematic diagram of a coding strategy in an embodiment of the present invention;

[0075] Figure 5 A schematic diagram of a decoding strategy flow in an embodiment of the present invention;

[0076] Figure 6 Schematic diagram of the initialization process in an embodiment of the present invention;

[0077] Figure 7 Schematic diagram of three stages of the adjustment process in an embodiment of the present invention;

[0078] Figure 8 Schematic diagram of the process of the improved discrete bat optimization algorithm in the embodiment of the present invention;

[0079] Fig. 9 Schematic diagram of the Pareto front comparison between the IDBA algorithm and the other five algorithms in the embodiment of the present invention DETAILED DESCRIPTION

[0080] In order to make the technical problems, technical solutions and advantages to be solved by the present invention more clear, a detailed description will be given below with reference to the accompanying drawings and specific embodiments.

[0081] The embodiment of the present invention provides an optimization method for the parallel disassembly line balance problem taking into account the number of skills mastered by workers, and the method can be implemented by an electronic device. Figure 1 The flowchart of the optimization method for the parallel disassembly line balancing problem considering the number of worker skills is shown in the figure. The processing flow of the method of the invention of the present application includes the following steps:

[0082] S1. Construct a disassembly line balance model based on the product information and disassembly line information of the product to be disassembled and the disassembly skill information of the workers;

[0083] S2. Construct an objective function with the goal of minimizing the number of skills that workers need to master and maximizing the net profit of product disassembly;

[0084] S3, setting the constraint conditions of the disassembly line balance optimization model;

[0085] S4, encoding the disassembly task based on the encoding mechanism of the priority relation matrix, generating feasible solutions, and decoding;

[0086] S5. Use the improved discrete bat algorithm (IDBA) to solve the multi-objective disassembly line balance optimization model and obtain the task allocation plan for the products to be disassembled;

[0087] S6. In actual cases, the improved IDBA is compared with five algorithms, including NSGA-II, NSGA-III, SPEA-II, ESPEA, and MOEA / D.

[0088] The above steps S1 to S6 are described in detail below:

[0089] First, step S1 is introduced in detail:

[0090] S11. Information on the product to be disassembled includes the number of disassembly tasks, the number of components, the number of parts, the unit time disassembly cost and recycling cost of the product components, the priority relationship between the product disassembly tasks, the disassembly relationship between tasks and components, and the disassembly time of each task on the disassembly line;

[0091] Among them, for example Figure 2is the AND / OR diagram of the product information to be disassembled described in S11, and is the AND / OR diagram of the disassembly process of an actual product, a ballpoint pen. Through the AND / OR diagram of the product, the disassembly relationship between the tasks in the product can be understood;

[0092] S12, disassembly line information includes the cycle period of the disassembly line, which is a parameter. In a specific actual case, it can be appropriately set according to the actual disassembly situation;

[0093] S13. All disassembly skill information of workers includes the number of disassembly skills mastered by workers during the product disassembly process;

[0094] Among them, for example Figure 3 The disassembly skill information of the workers in the disassembly line described in S13, the boxes of the same color represent the same product disassembly skills, and the numbers in the boxes represent the disassembly task sequence numbers of the products;

[0095] Similarly, for example Figure 3 The left half of the figure represents that the workers at the first workstation W1 need two disassembly skills, and W2 also needs two disassembly skills. This task distribution requires the workers at these two workstations to master a total of four skills. Figure 3 The right half of the represents that the workers in the W1 workstation only need to master one skill, and the workers in W2 also only need to master one skill. Then such a task distribution only requires the workers in these two workstations to master a total of two skills. It is proposed to construct an objective function that minimizes the number of skills that workers need to master and maximizes the net profit of product disassembly, aiming to improve enterprise efficiency.

[0096] Next, step S2 is described in detail:

[0097] Among them, the objective function in S2 is as follows:

[0098] maxf 1 , minf 2 ;

[0099]

[0100] Among them, f 1 Net profit from dismantling products;

[0101] f 2 The number of skills required for workers;

[0102] Among them, k∈K represents the worker skill set; m∈M represents the disassembly workstation set; R km indicates that the worker in workstation m uses skill k, otherwise R km =0; l∈L, (L=2) represents the assembly line set of disassembly lines; i∈N lrepresents the task number of the disassembled product on the disassembly line l; s∈S represents the component set of the product to be disassembled; d si =1 means that the product disassembly task i can disassemble component s; if component s is disassembled by task i, then d si = -1, otherwise d si =0;v s represents the revenue cost of product component s; x ilm =1 means that disassembly task i is executed in workstation m of disassembly line l, otherwise it is 0; c il represents the unit time disassembly cost of product components; t il It represents the disassembly time of disassembly task i on disassembly line l.

[0103] Next, step S3 is described in detail:

[0104] The constraint conditions for setting the disassembly line balance optimization model described in S3 include: task allocation constraint, workstation time constraint, task priority constraint and workstation activation constraint;

[0105] S31, where the task allocation constraints include that each task can only be assigned to one workstation at most; workers at the workstation need to use corresponding disassembly skills to perform the task, which is specifically expressed as follows:

[0106]

[0107] Among them, T k represents the set of disassembly tasks using skill k;

[0108] S32, wherein the workstation time constraint includes the cycle time of each workstation, which is specifically expressed as follows:

[0109]

[0110] Where C represents the cycle of the disassembly line;

[0111] S33, where the task priority constraints include that task i must be executed immediately before task j; if task j is executed, it must be ensured that task i immediately following task j has been executed; and that the conflict relationship of tasks must be satisfied; specifically expressed as follows:

[0112]

[0113]

[0114]

[0115] Among them, p i,j Represents the priority relationship between disassembly tasks;

[0116] S34, wherein the activation constraint of the workstation includes enabling the workstation in sequence, which is specifically expressed as follows:

[0117]

[0118] Among them, z m =1 means the workstation is open, otherwise z m =0.

[0119] Next, step S4 is described in detail:

[0120] The encoding mechanism based on the priority relation matrix encodes the disassembly task, generates feasible solutions, and decodes them;

[0121] The encoding mechanism based on the priority relationship matrix described in S4 encodes the disassembly task including:

[0122] S411, obtaining a priority relationship matrix of tasks according to an AND / OR graph of the execution order of product disassembly tasks in the product;

[0123] S412, according to the priority relationship matrix of the tasks, introduce a vector π to represent a disassembly task sequence of the product, each element in π corresponds to a task number and is arranged in order;

[0124] S413, this vector π is a task encoding method. By introducing vector π, the system can digitally represent the disassembly order. For some complex disassembly tasks, vector π ensures that each task can follow the rules of the priority relationship matrix, thereby maintaining the logical order of the tasks;

[0125] example Figure 4 Real number coding diagram for the task;

[0126] The generation of a feasible solution to the disassembly task described in S4 includes:

[0127] S421. In the balancing problem of parallel disassembly lines, consider two linear disassembly lines, each of which is assigned a single product type;

[0128] S422, generating non-repeating random numbers according to the number of disassembly tasks of the product, and inserting them in sequence to generate feasible solutions, which greatly ensures the randomness and integrity of the disassembly sequence;

[0129] The decoding of the disassembly task in S4 includes:

[0130] S431. Allocate the generated task disassembly sequence to different workstations to ensure that the task time of the workstation does not exceed its cycle time.

[0131] In this decoding process, not only the disassembly order of the tasks must be considered, but also the task time constraints must be met;

[0132] example Figure 5 Decode the process diagram for the complete task.

[0133] Next, step S5 is described in detail:

[0134] S51, population initialization and adjustment;

[0135] S52, updating the individuals through a crossover operation based on priority-preserving crossover (PPX) and a mutation operation based on the immediate predecessor task sequence;

[0136] S53, update the population by non-dominated sorting and other methods, select the Pareto optimal solution set, and iterate step by step until the stopping conditions are met;

[0137] S54, obtaining a disassembly line balancing strategy that satisfies the balancing constraint condition;

[0138] The initialization and adjustment of the population in S51 includes:

[0139] S511. Each individual in the population represents a feasible disassembly sequence. The population initialization process is generated by random insertion method as described in the encoding process to ensure the randomness and diversity of each individual.

[0140] S512: The specific method is to randomly insert the disassembly task sequence of product II into the disassembly task sequence of product I;

[0141] example Figure 6 The process of initializing the population;

[0142] S513. When generating a feasible disassembly sequence for a parallel disassembly line, the disassembly priority relationship between the disassembled products on the parallel disassembly line must be ensured;

[0143] Taking the parallel disassembly line of a simple product with two products as an example, the disassembly sequence generated for each product using the random integer method may not be guaranteed to be feasible. Therefore, it is necessary to adjust the generated sequence to make it a feasible disassembly sequence;

[0144] S514, the adjustment process is divided into three stages: adding operation, adding the missing tasks to the existing infeasible sequence according to the priority relationship; removing operation, removing conflicting tasks in the task sequence (conflicting tasks refer to tasks that cannot exist in the same disassembly sequence at the same time); swapping operation, after the first two stages are completed, if some tasks still do not meet the priority relationship, adjust the task order;

[0145] example Figure 7To initialize the three stages of the adjustment process;

[0146] Among them, the updating of individuals according to the crossover operation (PPX) based on the priority preserving crossover operator and the mutation operation based on the direct preceding task sequence described in S2 includes:

[0147] S521, a crossover operation based on a priority-preserving crossover operator, the purpose of which is to inherit the good genes in the parent generation when updating individuals and to ensure that the priority relationship of the disassembly tasks is not destroyed;

[0148] S522, the process of the crossover operation based on priority retention is as follows: first, two individuals are input, namely, the current best individual π f and an individual π randomly selected from the current Pareto solution set m , and a randomly generated mask sequence MASK; if the mask bit is 1, the corresponding parent individual π m The elements of new If the mask bit is 0, the corresponding parent individual π f The elements of new In; Final output: The generated new individual π new ;

[0149] S523, mutation operation based on the immediate predecessor task sequence, which can make local adjustments to individuals while maintaining their basic structure, thereby improving the diversity of solutions and helping the algorithm to escape from the local optimum. In the optimization method, the mutation operation is based on the immediate predecessor task sequence, that is, each task must satisfy the priority relationship of its predecessor task to ensure that the disassembly tasks are carried out in the correct order;

[0150] S524, the process of mutation operation based on the direct predecessor task sequence is as follows: determine the mutation individual, randomly select an individual π from the population, the individual represents a feasible sequence of disassembly tasks; randomly select tasks, in the task sequence of the individual, randomly select a task i, this task will become the object of mutation; select the predecessor task, find the immediate predecessor task of task i, that is, task j that task i directly depends on in the disassembly sequence (task j must be completed before task i), otherwise it will cause the task sequence to not comply with the priority relationship; adjust the task sequence, in order to perform the mutation operation, reinsert task i in front of or behind the predecessor task j, thereby generating a new task sequence;

[0151] Among them, updating the population by non-dominated sorting and other methods described in S3, selecting the Pareto optimal solution set, and gradually iterating until the stopping condition is met includes:

[0152] S531. In the population update process, individuals are first selected through non-dominated sorting. According to the domination rule, the algorithm divides the solutions into multiple levels. Solutions that are not dominated by other solutions are called Pareto optimal solutions, which form the first layer. For the remaining solutions, they are allocated to the next layer in turn according to the domination situation;

[0153] Assume there are U objective functions, if the solution x 0 Can dominate the solution x 1 , the following conditions must be met:

[0154]

[0155] In this way, non-dominated sorting hierarchically sorts the population, ensuring that individuals in each generation have a certain superiority;

[0156] At the same time, in order to ensure the diversity of solutions, the concept of crowding distance is also introduced. Crowding distance selects more sparse solutions by calculating the density of individuals in the solution space. Sparse individuals dominate in the crowding distance, avoiding the concentration of the population in a certain area, thereby achieving a wide distribution of solutions;

[0157] S532. On this basis, the article combines these sorted individuals with the current population to form the next generation population. When updating, the algorithm gives priority to those sparser individuals based on the crowding distance, thereby maintaining the diversity of the population. In multi-objective optimization, the fitness of an individual is determined by multiple objective functions. The combination of non-dominated sorting and crowding distance enables each individual to comprehensively consider various objectives, thereby avoiding the limitations of single-objective optimization. This method not only retains excellent individuals, but also ensures the coverage of the understanding space through diversified updates;

[0158] S533. After multiple rounds of iterations, the algorithm will gradually approach the optimal solution set, namely the Pareto optimal solution. In each iteration, the current Pareto solution set will be found through non-dominated sorting, and the diversity of solutions will be ensured by combining the crowding distance. As the iteration proceeds, the Pareto solution set is continuously updated until the predetermined stopping condition is met, such as reaching the maximum number of iterations or the solution set converges, and finally a balanced multi-objective optimization solution set is obtained; for example Figure 8 Flowchart of IDBA algorithm.

[0159] Next, step S6 is described in detail:

[0160] The comparison of the improved IDBA with five algorithms including NSGA-II, NSGA-III, SPEA-II, ESPEA, and MOEA / D in actual cases described in S6 includes:

[0161] S61, select five products with different numbers of tasks, and randomly combine them into three different forms of product combinations;

[0162] S62. For all algorithms, set the population size to 100, the number of iterations to 100, the crossover probability to 0.7, the mutation probability to 0.5 times the inverse of the task sequence length, and the cycle time of the workstation to 50;

[0163] S63. Using one of the product combinations as an experimental case, the IDBA algorithm is compared with five algorithms, namely, NSGA-II, NSGA-III, SPEA-II, ESPEA, and MOEA / D, from the perspectives of IGD metric, HV metric, and Epsilon-metric.

[0164] S64. In multi-objective optimization problems, the Pareto front can intuitively show the distribution of the objective values ​​obtained by the algorithm. Fig. 9 The Pareto frontier data graph obtained for each algorithm. The X-axis (f1) represents the objective function disassembly profit, and the Y-axis (f2) represents the objective function skill number;

[0165] S65, example Fig. 9 It can be observed that high-quality solution sets are distributed in the lower right part of the figure, which shows that the Pareto solution set obtained by IDBA has better convergence and uniformity;

[0166] S66. The final output is the allocation of skilled workers and disassembly tasks in the disassembly line workstations based on the product combination case applied in the experiment.

[0167] In an exemplary embodiment, a computer-readable storage medium is also provided, such as a memory including instructions, which can be executed by a processor in a terminal to implement an optimization method for a multi-objective parallel disassembly line balancing problem. The optimization method described in the present invention, including the steps of task allocation, skill minimization, and profit maximization, can be implemented by a computer program.

[0168] For example, the computer-readable storage medium may be a ROM, a random access memory (RAM), a CD-ROM, a magnetic tape, a floppy disk, or an optical data storage device, etc. A person skilled in the art will appreciate that all or part of the steps to implement the above embodiments may be completed by hardware, or may be completed by instructing related hardware through software programs, and these programs may be stored in a computer-readable storage medium. The above storage medium may be a read-only memory, a magnetic disk, or an optical disk, etc.

[0169] The above contents are only preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Within the spirit and principle of the present invention, any modification, equivalent replacement or improvement shall be included in the protection scope of the present invention.

Claims

1. A multi-objective parallel optimization method for waste product disassembly lines based on worker skill number, characterized in that: The method The process includes: S1 builds a disassembly line balance model based on the product information and disassembly line information of the product to be disassembled and the disassembly skill information of the workers; S2 constructs the objective function with the goal of minimizing the number of skills that workers need to master and maximizing the net profit of product disassembly; S3 sets the constraint conditions of the disassembly line balance optimization model; S4 encodes the disassembly task, generates feasible solutions, and decodes it based on the encoding mechanism of the priority relation matrix; S5 uses the improved discrete bat algorithm (IDBA) to solve the multi-objective disassembly line balance optimization model and obtain the task allocation plan for the products to be disassembled; S6 compares the improved IDBA with five algorithms including NSGA-II, NSGA-III, SPEA-II, ESPEA, and MOEA / D in actual cases.

2. The method for optimizing waste product disassembly lines based on worker skill number and multi-objective parallelism according to claim 1 is characterized in that: The information of the product to be disassembled includes the number of disassembly tasks, the number of components, the number of parts of the product to be disassembled, the unit time disassembly cost and recycling cost of the product components, the priority relationship between the product disassembly tasks, the disassembly relationship between tasks and components, and the disassembly time of each task on the disassembly line; The disassembly line information includes the cycle period of the disassembly line; the worker's all disassembly skill information includes the number of disassembly skills mastered by the worker during the product disassembly process.

3. The method for optimizing waste product disassembly lines based on worker skill number and multi-objective parallelism according to claim 1 is characterized in that: The method aims to minimize the number of skills that workers need to master and maximize the net profit of product disassembly. The objective function is constructed as follows: max f1 min f2 Where f1 represents the net profit of product disassembly, f2 represents the number of skills mastered by workers; k∈K represents the skill set of workers; m∈M represents the set of disassembly workstations; R km indicates that the worker in workstation m uses skill k, otherwise R km =0; l∈L, (L=2) represents the assembly line set of disassembly lines; i∈N l represents the task number of the disassembled product on the disassembly line l; s∈S represents the component set of the product to be disassembled; d si =1 means that the product disassembly task i can disassemble component s; if component s is disassembled by task i, then d si = -1, otherwise d si =0;v s represents the revenue cost of product component s; x ilm =1 means that disassembly task i is executed in workstation m of disassembly line l, otherwise it is 0; c il represents the unit time disassembly cost of product components; t il It represents the disassembly time of disassembly task i on disassembly line l.

4. The method for optimizing waste product disassembly lines based on worker skill number and multi-objective parallelism according to claim 1 is characterized in that: The constraint conditions for setting the disassembly line balance optimization model include task allocation constraints, workstation time constraints, task priority constraints and workstation activation constraints: S41. Task allocation constraints: Among them, T k represents the set of disassembly tasks using skill k; S42. Workstation time constraints: Where C represents the cycle of the disassembly line; S43. Task priority constraints: Among them, p i，j Represents the priority relationship between disassembly tasks; S44. Activation constraints for workstations: Among them, z m =1 means the workstation is open, otherwise z m =0.

5. The method for optimizing waste product disassembly lines based on worker skill number and multi-objective parallelism according to claim 1 is characterized in that: The encoding mechanism based on the priority relation matrix encodes the disassembly task, generates feasible solutions, and decodes the disassembly task, including: S51, obtaining a priority relationship matrix of tasks according to an AND / OR graph of the execution order of tasks in the product; S52. According to the priority relationship matrix of tasks, vector π is introduced to represent a disassembly task sequence of a product. Each element in π corresponds to a task number and is arranged in order. This vector π is a task encoding method. By introducing vector π, the system can digitally represent the disassembly sequence. For some complex disassembly tasks, vector π ensures that each task can follow the rules of the priority relationship matrix, thereby maintaining the logical order of the tasks. S53, generate feasible solutions through sequential insertion method; insert the disassembly task sequence of one product into the task sequence of another product to ensure that the disassembly tasks are allocated in sequence and meet the priority and time requirements of the tasks; S54, distribute the generated task disassembly sequence to different workstations to ensure that the task time of the workstation does not exceed its cycle time; in this decoding process, not only the task disassembly sequence must be considered, but also the task time constraint must be met.

6. The method for optimizing waste product disassembly lines based on worker skill number and multi-objective parallelism according to claim 1 is characterized in that: The improved discrete bat optimization algorithm is used to solve the multi-objective disassembly line balance optimization model, and the task allocation scheme of the products to be disassembled is obtained, including: S61, population initialization and adjustment; S62, updating the individuals through a crossover operation based on priority-preserving crossover (PPX) and a mutation operation based on the immediate predecessor task sequence; S63, update the population by non-dominated sorting and other methods, select the Pareto optimal solution set, and iterate step by step until the stopping condition is met; S64: Obtain a disassembly line balancing strategy that satisfies the balancing constraint condition.

7. The method for optimizing waste product disassembly lines based on worker skill number and multi-objective parallelism according to claim 6 is characterized in that: The initialization and adjustment of the population in S61 includes: S611. Each individual in the population represents a feasible disassembly sequence. The population is generated by random insertion to ensure the randomness and diversity of each individual. Specifically, the disassembly task sequence of product II is randomly inserted into the disassembly task sequence of product I. S612. When generating a feasible disassembly sequence for a parallel disassembly line, it is necessary to ensure that the disassembly task of each product follows its priority relationship; however, a randomly generated sequence may not necessarily satisfy these constraints, so further adjustments must be made; S613. The adjustment process is divided into three stages: adding operation, adding the omitted tasks to the existing infeasible sequence according to the priority relationship; removing operation, removing conflicting tasks in the task sequence (conflicting tasks refer to tasks that cannot exist in the same disassembly sequence at the same time); swapping operation, after the first two stages are completed, if some tasks still do not meet the priority relationship, adjust the task order.

8. The method for optimizing waste product disassembly lines based on worker skill number and multi-objective parallelism according to claim 6 is characterized in that: The method of updating the individuals by a crossover operation (PPX) based on priority-preserving crossover and a mutation operation based on a direct predecessor task sequence in S62 includes: S621. Priority-preserving crossover operation aims to inherit the good genes in the parent generation when updating individuals and ensure that the priority relationship of the disassembly tasks is not destroyed. S622: The process of the crossover operation based on priority retention is as follows: First, two individuals are input, namely, the current best individual π f and an individual π randomly selected from the current Pareto solution set m , and a randomly generated mask sequence MASK; if the mask bit is 1, the corresponding parent individual π m The elements of new If the mask bit is 0, the corresponding parent individual π f The elements of new In; Final output: The generated new individual π new ; S623, mutation operation based on the immediate predecessor task sequence, which can make local adjustments to individuals while maintaining their basic structure, thereby improving the diversity of solutions and helping the algorithm to jump out of the local optimum; in this optimization method, the mutation operation is based on the immediate predecessor task sequence, that is, each task must satisfy the priority relationship of its predecessor task to ensure that the disassembly tasks are performed in the correct order; S624. The process of mutation operation based on the direct predecessor task sequence is as follows: determine the mutated individual, randomly select an individual π from the population, and the individual represents a feasible sequence of disassembly tasks; randomly select a task, and in the task sequence of the individual, randomly select a task i, which will become the object of mutation; select the predecessor task, and find the immediate predecessor task of task i, that is, task j that task i directly depends on in the disassembly sequence (task j must be completed before task i), otherwise the task sequence will not comply with the priority relationship; adjust the task sequence, in order to perform the mutation operation, reinsert task i into the front or back of the predecessor task, thereby generating a new task sequence.

9. A method for optimizing waste product disassembly lines based on worker skill number and multi-objective parallelism according to claim 6, characterized in that: In S63, the population is updated by non-dominated sorting or the like, a Pareto optimal solution set is selected, and the iteration is performed step by step until the stopping condition is satisfied, including: S631, in the population update process, individuals are first selected by non-dominated sorting; according to the domination rule, the algorithm divides the solutions into multiple levels, and the solutions that are not dominated by other solutions are called Pareto optimal solutions, which form the first layer; for the remaining solutions, they are allocated to the next layer in turn according to the domination situation; Assuming there are U objective functions, if the solution x0 can dominate the solution x1, the following conditions need to be met: In this way, non-dominated sorting classifies the population hierarchically to ensure that individuals in each generation have certain superiority. At the same time, in order to ensure the diversity of solutions, the concept of crowding distance is introduced. Crowding distance selects more sparse solutions by calculating the density of individuals in the solution space. Sparse individuals dominate in the crowding distance, avoiding the population from being concentrated in a certain area, thereby achieving a wide distribution of solutions. S632. On this basis, the article combines these sorted individuals with the current population to form the next generation population; when updating, the algorithm gives priority to those sparse individuals based on the crowding distance, thereby maintaining the diversity of the population; in multi-objective optimization, the fitness of an individual is determined by multiple objective functions, and the combination of non-dominated sorting and crowding distance enables each individual to comprehensively consider various objectives, thereby avoiding the limitations of single-objective optimization; this method not only retains excellent individuals, but also ensures the coverage of the understanding space through diversified updates; S633. After multiple rounds of iterations, the algorithm will gradually approach the optimal solution set, namely the Pareto optimal solution. In each iteration, the current Pareto solution set will be found through non-dominated sorting, and the diversity of solutions will be ensured by combining the crowding distance. As the iterations proceed, the Pareto solution set is continuously updated until the predetermined stopping conditions are met, such as when the maximum number of iterations is reached or the solution set converges, and finally a balanced multi-objective optimization solution set is obtained. This process ensures the efficiency and accuracy of the optimization.

10. The method for optimizing waste product disassembly lines based on worker skill number and multi-objective parallelism according to claim 1, characterized in that: The comparison of the improved IDBA with five algorithms, namely NSGA-II, NSGA-III, SPEA-II, ESPEA, and MOEA / D, in actual cases includes: S10.

1. Select five products with different numbers of tasks and randomly combine them into three different product combinations; S10.

2. For all algorithms, set the population size to 100, the number of iterations to 100, the crossover probability to 0.7, the mutation probability to 0.5 times the inverse of the task sequence length, and the cycle time of the workstation to 50; S10.3, using the first product combination as an experimental case, the IDBA algorithm is compared with five algorithms, namely NSGA-II, NSGA-III, SPEA-II, ESPEA, and MOEA / D, from the perspectives of IGD metric, HV metric, and Epsilon-metric metric. The results show that the IDBA algorithm has more advantages than other algorithms in dealing with multi-objective parallel disassembly line problems; S10.

4. Next, the IDBA algorithm is compared with five algorithms, namely, NSGA-II, NSGA-III, SPEA-II, ESPEA, and MOEA / D, in terms of the changes in three different evaluation indicators when dealing with practical problems as the iteration time and population size change. S10.

5. In order to further prove the superiority of evaluating IDBA in dealing with practical problems, three box plots are used to record the values ​​of IGD metric, HV metric and Epsilon metric; S10.

6. The final output is the distribution of skilled workers and disassembly tasks in the disassembly line workstations of the experimental case of the first product combination.

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