Large-scale disassembly line balance optimization system and method based on transfer learning

Abstract

The invention discloses a large-scale disassembly line balance optimization system and method based on transfer learning. The system comprises a single-target optimization module used for correspondingly storing each single-target problem optimization solution to an independent knowledge base; the multi-objective optimization module is used for performing multi-objective problem optimization by using an evolutionary algorithm; the mapping relation building module is used for building an integer type mapping relation from each single-target problem solution set of the current generation to a multi-target problem solution set when transfer learning is triggered; and the transfer learning execution module is used for obtaining a transfer solution on the multi-target problem according to the multiple single-target problem optimization solutions in the independent knowledge base and the integer type mapping relation, and obtaining an initial population of next-generation multi-target problem optimization according to the transfer solution. Based on a transfer learning mechanism and an evolutionary algorithm, the problem of large-scale disassembly line balance optimization under the conditions of discrete decision space, high variable correlation and complex constraint is effectively solved, algorithm convergence is remarkably accelerated, and the solution set quality is improved.

Description

Technical Field

[0001] This invention relates to the field of disassembly line balancing technology, specifically to a large-scale disassembly line balancing optimization system and method based on transfer learning. Background Technology

[0002] With rapid industrialization and the continuous expansion of manufacturing, a large number of waste products have been generated, known as end-of-life (EOL) products. Research indicates that these waste products often contain abundant recyclable resources, and how to properly dispose of them is a major challenge for the manufacturing industry. Disassembly is a key step in the recycling and reuse of EOL products, and disassembly lines are the best option for large-scale disassembly. Therefore, effective design and balancing of disassembly lines are crucial for improving disassembly efficiency. The Disassembly Line Balancing Problem (DLBP) refers to the problem of how to allocate disassembly tasks to corresponding workstations and robots to optimize a specific objective, without violating constraints such as disassembly priority relationships.

[0003] In modern manufacturing environments, disassembly line balancing problems increasingly exhibit large-scale characteristics, such as a wide variety of mixed products and complex disassembly tasks. These types of disassembly line balancing problems are called Large-scale Disassembly Line Balancing Problems (LSDLBP). These large-scale characteristics make LSDLBP essentially a Large-scale Multi-objective Optimization Problem (LSMOP).

[0004] Current research on large-scale multi-objective problems mostly focuses on continuous optimization problems and uses related strategies for grouping decision variables. It cannot solve LSDLBP, which has a discrete decision space, highly correlated decision variables, and complex constraints.

[0005] For large-scale multi-objective optimization problems, researchers have proposed many specialized algorithms. Among them, algorithms based on subgeneration have attracted widespread attention due to their high performance and broad applicability. The basic idea behind subgeneration-based large-scale multi-objective optimization algorithms is to improve the convergence speed and solution set quality by designing efficient subgeneration mechanisms. However, existing subgeneration-based algorithms are designed for continuous decision spaces and do not consider the discrete decision space and complex constraints of the decomposed line equilibrium problem. Therefore, existing subgeneration-based large-scale multi-objective optimization algorithms need to be improved to suit the characteristics of large-scale decomposed line equilibrium problems. Summary of the Invention

[0006] The purpose of this invention is to provide a large-scale decomposition line balance optimization system and method based on transfer learning. This invention solves the problems of large-scale decomposition line balance optimization under conditions of discrete decision space, high variable correlation and complex constraints in existing large-scale decomposition line balance optimization.

[0007] To achieve this objective, the present invention provides a large-scale decomposition line balancing optimization system and method based on transfer learning, comprising: The single-objective optimization module is used to independently optimize multiple single-objective problems obtained by decomposing the large-scale line balance problem using an evolutionary algorithm, and saves the optimized solution set generated in each generation to an independent knowledge base, thus obtaining an independent knowledge base corresponding to each single-objective problem. The multi-objective optimization module is used to optimize multi-objective problems using evolutionary algorithms to obtain optimized solutions to multi-objective problems; The mapping relationship construction module is used to establish an integer mapping relationship between each single-objective problem solution set and the multi-objective problem solution set of the current generation when transfer learning is triggered; The transfer learning execution module is used to obtain the optimized solution in the knowledge base corresponding to each single-objective problem, and to use the integer mapping relationship to map the current generation optimized solution to the transfer solution on the multi-objective problem. The transfer solution is then incorporated into the current generation evolutionary population of the multi-objective problem as the initial population for the next generation of multi-objective problem optimization.

[0008] The beneficial effects of this invention are as follows: 1. This invention decomposes the complex coupled decision problem into three structured discrete subspaces by designing a three-level sequence encoding mechanism (robot-workstation allocation, task-robot allocation, and task execution order). This systematically separates the optimization dimension, enabling the algorithm to accurately handle key decisions such as resource allocation and process scheduling, fundamentally conforming to the discrete characteristics of large-scale decomposition line balancing problems.

[0009] 2. This invention introduces a transfer learning mechanism, utilizing high-quality solutions accumulated during the four single-objective optimization processes as "prior knowledge." During multi-objective optimization, mapped and repaired "transfer solutions" are periodically injected as the initial population for the next generation. This provides high-quality "seed solutions" for multi-objective optimization, significantly shortening the search path and dramatically accelerating the algorithm's convergence process.

[0010] 3. This invention proposes a method for constructing integer mapping relationships for three-level sequences, enabling accurate and operable discrete knowledge transfer from single-objective to multi-objective approaches, thus overcoming the bottleneck of traditional methods being unable to transfer knowledge in discrete spaces.

[0011] 4. A systematic solution repair mechanism was designed, which can automatically detect and repair illegal solutions, ensuring that all solutions entering the population are physically executable and feasible, avoiding invalid searches and improving the efficiency and stability of the algorithm.

[0012] 5. A decoding mechanism based on the earliest possible start time principle was designed. Combined with the priority constraints of the TAOG graph (task AND / OR graph), the earliest start time of each task is dynamically calculated, generating an executable scheduling sequence ordered by time. This mechanism not only ensures the feasibility of decoding but also provides accurate time basis for accurately calculating objective functions such as cycle time and energy consumption.

[0013] 6. The selection, crossover, and mutation operations were designed with specific problems in mind, which effectively improved the algorithm's global search and local optimization capabilities in complex solution spaces.

[0014] 7. In the vast majority of test cases, the present invention (MOTLE) achieved optimal results in both HV and IGD metrics; even in the few cases where it did not achieve optimal results, the performance difference was very small; and as the problem size increased, the performance advantage of the present invention became more significant. This fully demonstrates the effectiveness and practicality of the present invention in solving large-scale disassembly line balancing problems. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating the module workflow of a large-scale decomposition line balancing optimization system based on transfer learning according to the present invention. Figure 2 This is a flowchart illustrating the workflow of a large-scale decomposition line balancing optimization method based on transfer learning according to the present invention. Figure 3 This is a schematic diagram illustrating the encoding and decoding processes of three vectors in an embodiment of the present invention; Figure 4 This is a schematic diagram of the crossover operation process of the first vector in an embodiment of the present invention; Figure 5 This is a schematic diagram of the crossover operation process of the third vector in an embodiment of the present invention; Figure 6 This is a schematic diagram illustrating three vector mutation operations in an embodiment of the present invention; Figure 7 This is a schematic diagram illustrating the HV result variation trend of the algorithm of the present invention and four other algorithms on test cases of different scales in an embodiment of the present invention. Figure 8 This is a schematic diagram illustrating the trend of IGD results of the algorithm of the present invention and four other algorithms on test cases of different scales in an embodiment of the present invention. Detailed Implementation

[0016] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments: Example 1: like Figures 1-8 The above describes a large-scale decomposition line balancing optimization system based on transfer learning, comprising: The single-objective optimization module is used to independently optimize multiple single-objective problems obtained by decomposing the large-scale line balance problem using an evolutionary algorithm, and saves the optimized solution set generated in each generation to an independent knowledge base, thus obtaining an independent knowledge base corresponding to each single-objective problem. The multi-objective optimization module is used to optimize multi-objective problems using evolutionary algorithms to obtain optimized solutions to multi-objective problems; The mapping relationship construction module is used to establish an integer mapping relationship between each single-objective problem solution set and the multi-objective problem solution set of the current generation when transfer learning is triggered; The transfer learning execution module is used to obtain the optimized solution in the knowledge base corresponding to each single-objective problem, and to use the integer mapping relationship to map the current generation optimized solution to the transfer solution on the multi-objective problem. The transfer solution is then incorporated into the current generation evolutionary population of the multi-objective problem as the initial population for the next generation of multi-objective problem optimization.

[0017] This invention constructs a large-scale dismantling line balancing problem. It explicitly defines the allocation between robots and workstations, the allocation between dismantling tasks and robots, and the order of dismantling tasks, encoding these into a three-level sequence. This sequence constrains the input, separates the constraint concerns, and solves complex constraint problems. Combining the three-level sequence, the optimization objectives are to minimize cycle time, minimize the number of robots used, minimize total robot energy consumption, and minimize workstation peak energy consumption. By independently optimizing four single-objective problems, the originally complex coupled space is reduced to three jointly optimized coded subspaces. The correlation between variables is dynamically learned to address the problem of high correlation between decision variables. Optimization information is independently stored in four independent knowledge bases. For the multi-objective problem, the frequency of transfer learning is specified. When transfer learning occurs, an integer mapping from the four single-objective problems to the multi-objective problem is constructed to address the discreteness of the decision space. The transferred solution is injected into the current evolutionary population, participating in the next generation of evolution alongside the original solutions. This invention's large-scale dismantling line balancing optimization method based on transfer learning-assisted evolutionary algorithms can accelerate the convergence process of algorithms solving large-scale dismantling line balancing problems and significantly improve the quality of solutions.

[0018] Preferably, the disassembly line balancing mathematical model used in this invention comes from [YL Fang, Q Liu, MQ Li, YJ Laili, DT Pham. Evolutionary many-objective optimization for mixed-model disassembly line balancing with multi-robotic workstations. European Journal of Operational Research, 2019, 276(1), 160-174.] (Evolutionary multi-objective optimization for mixed-model disassembly line balancing with multi-robotic workstations).

[0019] Encoding and decoding mechanisms are crucial for solving the disassembly line balancing optimization problem. Their core lies in establishing a mapping relationship between individuals in the evolutionary algorithm population and the actual optimization problem. For multi-robot LSDLBP of hybrid products, obtaining a feasible solution requires determining robot task allocation, robot task processing order, and robot-workstation allocation. Three two-dimensional integer vectors are used for solution encoding: Robot-WorkstationAssignment Vector (RW), Task-Robot Assignment Vector (TR), and Disassembly Task Sequence Vector (TS).

[0020] In the above technical solution, in the single-objective optimization module and the multi-objective optimization module, the evolutionary algorithm is used to obtain the optimized solution of the single-objective problem and the optimized solution of the multi-objective problem, and the encoding method of the individual information in the optimized solution is a three-level sequence; The third-level sequence includes: The first vector is used to encode the allocation relationship between the robot and the workstation; The second vector is used to encode the task-robot assignment relationship; The third vector is used to encode the execution order of the task; Wherein, the first vector is represented as: ; in, This is represented as a vector representing the relationship between all robots and workstations. The length is equal to the total number of robots. Represented as a robot The serial number assigned to the workstation. , For workstation index set, For the robot index set, if the robot No workstation was assigned. ; The second vector is represented as: ; in, This is represented as a vector showing the assignment relationships between all tasks and robots. Indicates being responsible for a task The robot's serial number, , For the set of all tasks, When, it indicates a task. No robots were assigned. A second vector that can assign tasks to robots Simplified representation: Selected task and robot assigned vector This is used when optimizing tertiary sequence encoding using evolutionary algorithms in single-objective learning modules and multi-objective evolutionary modules. Represented as: ; in, This is represented as a vector showing the assignment relationship between the selected task and the robot. This represents the selected set of tasks. Indicates being responsible for a task Robot serial number ; The third vector is represented as: ; in, This is represented as the selected disassembly task sequence vector. This represents the selected set of dismantling tasks. , This is indicated as a dismantling task. The serial number, exist The location is for dismantling tasks. The position of the priority level in the sorting.

[0021] The construction of the third vector must not violate the TAOG graph.

[0022] The TAOG graph is a graph structure used to describe the dependencies between tasks. It expresses the sequence of tasks and multiple possible decomposition paths through "AND" and "OR" nodes. Therefore, the task ordering in the TS vector should ensure that all preceding tasks appear before dependent tasks to guarantee the feasibility and rationality of the decomposition process.

[0023] To transform the encoded information into a specific decomposition scheme, ensure the feasibility of the solution, and evaluate the objective function, a decoding scheme was designed. , , Decode the vector.

[0024] The above process defines a structured three-level sequence encoding mechanism for evolutionary algorithms, laying the technical foundation for the entire invention. It transforms the complex decomposition line balancing problem into three distinct discrete decision vectors: robot and workstation allocation (…). ), task and robot matching ( ) and task execution sequences constrained by TAOG graphs ( This structured encoding method systematically separates the problem dimension, enabling the algorithm to accurately handle key decisions such as machine deployment, task allocation, and process scheduling. Furthermore, by forcing task sequences to adhere to the priority constraints of the TAOG graph and designing a corresponding decoding scheme to transform the encoding into feasible scheduling, it fundamentally ensures the physical executability of the generated solution. This effectively solves the core challenges of discrete decision space, strong variable coupling, and complex constraints in large-scale decomposition line balancing problems, providing clear and reliable operational objects for subsequent evolutionary operations (crossover, mutation), thereby significantly improving the algorithm's search efficiency and solution set quality in a vast solution space.

[0025] In the above technical solution, the evolutionary algorithm also includes a decoding mechanism for receiving single-objective optimization solutions or multi-objective optimization solutions and performing the following operations: According to the first vector Determine the workstation to which each robot belongs and its available time window; According to the second vector Each disassembly task is assigned to a corresponding robot; According to the third vector The priority relationship in the algorithm is used to calculate the earliest start time of each task on its bound robot and generate an executable scheduling sequence in ascending order of start time. The set of performance metrics for four single-objective problems is calculated based on the executable scheduling sequence. The four single-objective problems are: cycle time, total robot energy consumption, workstation peak energy consumption, and number of robots used. The set of performance metrics is then output.

[0026] For robots and the tasks assigned to them The scanning robot starts from the initial time. The task allocation status on the robot, and obtain the information already available on the robot. The first available idle time interval between assigned tasks is used to execute the task. It is important to note that robots within the same workstation share the same time "zero," but the time "zero" of one workstation differs from the time "zero" of an adjacent workstation by one cycle. This means that the working time interval of the robot in workstation 1 is... The working time interval of the robot in workstation 2 is And so on.

[0027] For any selected task and corresponding robot in a task sequence TS, the available idle time interval is determined by the following formula: ; in, and These represent the start and end times of the interval, respectively. Represents robots There is an assigned task. Represents robots Processing tasks Time, express The completion time of the direct predecessor task of the middle task. When Tasks in Need to be done in the robot When allocating tasks within the first available time interval, the start time of the task is taken as the start time of that available time interval for the robot. At this point, it must be ensured that the sum of the start time and the task processing time is less than or equal to the end time of that work time interval before allocation. If no such time interval exists, the task is allocated to the end of all allocated tasks. Again, it must be ensured that the sum of the end time of the previous task and the processing time of the current task is less than or equal to the end time of that work time interval before allocation. Once a solution is decoded according to the above process, The tasks are arranged in ascending order according to their start time. The encoding and decoding process is as follows: Figure 3 As shown.

[0028] The above describes the core process and rules of the decoding mechanism, which transforms the three-level sequence encoding in the evolutionary algorithm into a specific decomposition and scheduling scheme that can be quantified and evaluated. It is a key bridge connecting algorithm search and practical problem solving.

[0029] The encoded information is mapped to feasible schedules with explicit temporal attributes. Resource (robot, workstation) ownership is determined based on vector allocation relationships. Then, based on TAOG graph constraints and the "earliest start time" principle, execution time slots are dynamically arranged for each task within the specified robot's working time window—by scanning idle intervals and considering the completion time of predecessor tasks, ensuring that task scheduling satisfies both priority relationships and workstation cycle time constraints. This rigorously guarantees that any solution generated by the algorithm during evolution can be parsed into a feasible split-line schedule, thus avoiding invalid searches. Simultaneously, by generating scheduling sequences with timelines, it provides direct evidence for accurately calculating four key performance indicators, including cycle time and energy consumption, allowing for precise quantification and comparison of optimization objectives. Finally, this decoding mechanism, closely integrated with the aforementioned encoding scheme, ensures that the evolutionary algorithm can efficiently find high-quality, executable balance solutions within a large but well-defined solution space.

[0030] In the above technical solution, the evolutionary algorithm in the single-objective optimization module further includes selection operation, crossover operation, and mutation operation; The selection operation is as follows: using the tournament selection method, two high-quality parents are selected from the parent population in turn based on Pareto dominance, crowding distance, or random selection. The crossover operation is as follows: Corresponding to the first vector The first vector of the first parent in the parent population. Part of the index value is copied to the child generation, and then the first vector of the second parent generation is copied. The remaining index values ​​are added to the corresponding positions of the offspring to obtain the first vector after the crossover. ; conduct Cross operator design. The crossover operator is used to generate new Vector. For A tournament selection method is used to select high-quality individuals from the parent population. Then, a portion of the index value of the first parent individual is directly passed to the offspring, and the remaining index value of the second parent individual is used to supplement the corresponding position in the offspring. Considering the limitations of the maximum robot capacity and the number of fixed workstations, the resulting... The vector may be an infeasible solution. Therefore, a repair mechanism is introduced to handle invalid solutions. The vector mechanism comprises two key steps: detecting the robot configuration of each workstation and randomly selecting idle robots to fill any vacant workstations; and randomly removing excess robots when the number of robots in a workstation exceeds the upper limit until the capacity constraint is met.

[0031] The method for determining the two parents using the tournament selection method is as follows: Four pairs of individuals are randomly selected from the current population. Each pair is then subjected to a "tournament" comparison to determine the winner. The winner from each pair is selected as the parent and participates in subsequent crossover and mutation operations. For the two individuals participating in the comparison... The determination of the winner follows a hierarchical rule: comparing the Pareto dominance of the two individuals, if... Dominate ,but For the winner, or else If neither can dominate the other, proceed to the next judgment condition and compare crowding distances; the one with the larger crowding distance wins. If the outcome is still undecided, a winner is randomly selected with a 50% probability to ensure the algorithm's exploration capability.

[0032] like Figure 4 The first vector generated in the diagram does not meet the constraint on the number of robots in the workstation, so it needs to be corrected. Workstation 1 has already been allocated 6 robots, which exceeds the maximum number, so 1 robot needs to be randomly removed and the corresponding value is set to -1. At the same time, there are no robots in workstation 2, so an idle robot is allocated to workstation 2.

[0033] For the third vector The entire task sequence is considered as consisting of task subsequences of different product models. Each task subsequence of the offspring is selected from the parent sequence according to a preset probability, resulting in a third vector after crossover. ; Preferably, with a preset probability of p (0 ≤ p ≤ 1), the entire decomposition sequence is divided into multiple partial sequences. A partial sequence is selected from parent generation 1 with probability p, and a partial sequence is selected from parent generation 2 with probability 1-p. Assume there exists a decomposition sequence composed of both model 1 and model 2, meaning the decomposition sequence is divided into two parts. Therefore, the offspring needs to select from parent generation 1 and parent generation 2 for these two parts according to probability p. The offspring might select a decomposition sequence belonging to model 1 from parent generation 1 and a decomposition sequence belonging to model 2 from parent generation 2, or it might select both decomposition sequences belonging to models 1 and 2 from parent generation 1. After selection, the third vector after crossover is obtained. The third vector The crossover process is as follows Figure 5 As shown.

[0034] For the second vector Using the third vector after the cross Generate the second vector after the crossover. ; When the third vector after the intersection Once determined, the second vector The allocation process will be triggered, generating the second vector after the crossover. The third vector after the intersection with the vector sorted by task priority .

[0035] The mutation operation is as follows: For the first vector Randomly select an undeployed robot and a deployed robot to swap their positions, generating the mutated first vector. ; For the second vector Randomly select a position in the vector and replace that position with another robot that satisfies the priority relationship constraints between the disassembly tasks, generating a mutated second vector. ; For the third vector Randomly select a task from the TS vector, move it to another feasible position that satisfies the constraints, and swap the original solution at that feasible position with the mutation point to generate the mutated third vector. .

[0036] The first vector Second vector and the third vector Simulating chromosome mutations involves generating new vectors by modifying the values ​​of solutions at specific positions within a vector. For the first vector... The algorithm randomly selects an undeployed robot and a deployed robot to swap their positions, and repairs infeasible solutions to generate the first vector. For the second vector In this vector, a task is randomly selected, and by examining its direct predecessor and successor robots and workstations, that robot is replaced with another available robot. For the third vector... The neighborhood solution is obtained by using an insertion operator, which randomly selects the third vector. One of the tasks is moved to another feasible location that satisfies the constraints, and the original solution at that feasible location is swapped to the mutation point. In the third vector During the mutation process, corresponding solution repair mechanisms are added to determine whether the generated new solution satisfies the constraints, ensuring that the mutation process generates feasible solutions. The mutation process is as follows: Figure 6 As shown.

[0037] The above process illustrates the specific methods of population iteration and new solution generation in single-objective and multi-objective optimization modules of evolutionary algorithms, serving as the driving force for global search and local exploration. Through the systematic design of selection, crossover, and mutation operations, this mechanism ensures that the algorithm can efficiently seek optimization in complex discrete solution spaces.

[0038] Selection, combining Pareto dominance and crowding, effectively filters high-quality genes; crossover, by fusing parental information through vector and sequence partitioning, achieves the combination and inheritance of superior gene modules; mutation, through robot swapping, task redistribution, and sequence position movement, injects new changes while maintaining the structural legitimacy of the solution (e.g., without violating priority relationships), thus escaping local optima. This collaborative mechanism ensures that the evolutionary process effectively utilizes historical knowledge and accelerates convergence while maintaining population diversity and enhancing global exploration capabilities, thereby providing core algorithmic support for ultimately solving high-quality, feasible large-scale decomposition line equilibrium schemes.

[0039] In the above technical solution, the evolutionary algorithm also includes a solution repair mechanism, which is used to repair individuals that violate the constraints after crossover or mutation operations, and generate feasible solutions that satisfy all constraints.

[0040] In the above technical solution, the solution repair mechanism utilizes the following rule-based individual repair methods: Does the number of robots at any workstation exceed the capacity limit? Does the start time of any task violate the completion time of all its predecessor tasks? Whether any task cannot be completed within its workstation time window; if any violation is detected, perform corrective actions such as removing redundant robots, supplementing idle robots, or delaying the task start time, until the executable scheduling sequence satisfies all constraints, and then send the corrected feasible scheduling sequence back to the decoding module to update the performance index set. If any violation is detected, corrective actions such as removing redundant robots, adding idle robots, or delaying the task start time are performed until the executable scheduling three-level sequence satisfies all constraints. Then, the corrected executable scheduling three-level sequence is sent back to the performance metric set and the performance metric set is updated.

[0041] The above process is a solution repair mechanism, providing a key guarantee and correction link for evolutionary algorithms. It ensures that after random operations such as crossover and mutation, all generated solutions can satisfy the complex physical and logical constraints of the problem, thereby maintaining the entire search process within the feasible solution space efficiently.

[0042] This mechanism systematically detects and corrects three typical violations by establishing rules: workstation robot overload, task timing conflicts, and time window out-of-bounds errors. By executing specific corrective actions such as removing redundant robots, replenishing idle resources, or delaying task start times, it can quickly transform infeasible solutions into valid ones. This process significantly improves the algorithm's robustness and search efficiency, avoids wasting computational resources on invalid solutions, and ensures that every individual in the population is correctly decoded and evaluated. Ultimately, the corrective mechanism, in close coordination with encoding, decoding, and evolutionary operations, forms a complete optimization loop, which is a crucial foundation for the invention's ability to reliably and stably solve complex, large-scale disassembly line balancing problems.

[0043] Preferably, the transfer learning is triggered at a frequency of every One substitution, that is, in the process of multi-objective iterative optimization, each One transfer learning is triggered, where It is a positive integer.

[0044] In the above technical solution, the method for constructing the integer mapping relationship set from the solution set of the four single-objective problems to the solution set of the multi-objective problem in the mapping relationship construction module is as follows: First vector Integer mapping relationship with the solution set of multi-objective problems The construction process is as follows: According to the The first in the knowledge base of a single-objective problem By archiving the non-dominated solutions, we can obtain the probability matrix of the robot-workstation allocation relationship; robot Assigned to workstation The probability is expressed as: ; in, Represented as the first Robot in a single-objective problem Assigned to workstation The probability, Represented as the first The first single-objective problem The archive set of non-dominated solutions, Represented as an archive set One of the candidate solutions. Represented as in candidate solutions China Robot Assigned to workstation , This is represented as an indicator function, which is 1 if the condition is true and 0 otherwise. According to the The probability of all robot-workstation assignment relationships in a single-objective problem. The probability matrix can be obtained. ,and , and These represent the total number of robots and the total number of workstations, respectively. The candidate set of all valid robot-workstation assignments is represented as: ; in, Represented as robot Assigned to workstation The probability, For robot index set, For workstation index set; The candidate set of valid robot-workstation assignment relationships. Sort the elements in descending order to obtain a priority queue set containing the probabilities of all valid robot-workstation assignment relationships. , represented as: ; The original solution obtained from single-objective optimization Through integer mapping relationships Transformed into a migration solution, expressed as: ; in, This is represented as the migration solution. Represented as the first An integer mapping relationship between all solutions of the robot-workstation allocation relationship in single-objective optimization and the transition solutions of the robot-workstation allocation relationship in multi-objective optimization; The integer mapping relationship Obtained according to the following rules: Initialize all robots to an unassigned state: ; For the original solution Each robot in Search Chinese correspondence The element with the maximum value Select this workstation As the target workstation If the robot For allocation and target workstation If not full, then perform allocation. ; Third vector Integer mapping relationship with the solution set of multi-objective problems The construction method is as follows: When the population evolves to the... In the past, from single-objective knowledge base Obtain the average position of each task to get the task In the knowledge base Average position in Specifically: ; in, Indicates task In candidate solutions The position in the middle, This indicates the number of solutions in the knowledge base; Utilizing the integer mapping relationship between the original solution of task execution priority relationship in single-objective optimization and the transition solution of task execution priority relationship in multi-objective optimization. The specific transition solution for obtaining the task execution priority relationship in multi-objective optimization is as follows: ; in, The original solution representing the task execution priority relationship; The mapping function will The disassembly task in the knowledge base The average position in the middle is reordered; Second vector Integer mapping relationship with the solution set of multi-objective problems The construction method is as follows: When the population evolves to the... In the past, from single-objective knowledge base Obtain tasks from Assigned to robots frequency Specifically: ; in, Represented as in candidate solutions Medium task Assigned to robots , This is represented as an indicator function, which is 1 if the condition is true and 0 otherwise. for Each task arranged in order ,from Select the robot with the highest assignment frequency from the robots already assigned to workstations. Assigned to task Specifically: ; in, This indicates that the robot is in an assigned state. Represented as a task The robot with the highest allocation frequency; By obtaining the robot with the highest task allocation frequency among all tasks, we can obtain the task and robot allocation relationship in multi-objective optimization corresponding to the original solution of the task and robot allocation relationship in single-objective optimization. Using the above process, we obtain the sets of integer mappings from the solution sets of the four single-objective problems to the solution sets of the multi-objective problems. .

[0045] The integer mapping relationship construction method described in the mapping relationship construction module is a key technical step in solving the large-scale decomposition line balance optimization problem of this invention. It can effectively handle problems such as discrete decision space, high correlation of decision variables, and complex constraints. This method constructs integer mapping relationships from four single-objective problem solution sets to multi-objective problem solution sets, accurately transferring the optimization knowledge accumulated in the single-objective optimization process to the multi-objective optimization framework, thereby significantly improving the convergence efficiency and solution quality of the algorithm. Specifically, this method employs innovative strategies such as probability matrices, average position sorting, and allocation frequency analysis for three dimensions: robot-workstation allocation relationship, task execution order, and task-robot allocation relationship, respectively, to achieve accurate mapping from single-objective to multi-objective. Its advantages are as follows: First, by constructing a probability matrix and a priority queue, the discrete decision space problem is solved, ensuring accurate mapping of discrete decision variables. Second, by utilizing dynamic analysis of average position and allocation frequency, the correlation between decision variables is effectively captured and utilized, avoiding the solution quality degradation caused by ignoring variable correlation in traditional methods. Third, by constructing integer mapping relationships, efficient transfer of knowledge from single-objective optimization is achieved, avoiding the slow convergence problem caused by the lack of an effective initial population in multi-objective optimization. Finally, this method enables the system to effectively transform high-quality solutions obtained from single-objective optimization into an initial population for multi-objective optimization while maintaining the constraints, thereby significantly shortening the number of iterations required for the algorithm to reach a high-quality solution and significantly improving the solution efficiency and solution set quality of large-scale decomposed line balance problems.

[0046] In the above technical solution, the transfer learning execution module utilizes a set of integer mapping relationships. The method for obtaining the initial population for the next generation of population evolution, along with the repair and resolution mechanism, is as follows: When transfer learning is triggered, the first of the four single-objective questions is selected from the independent knowledge bases corresponding to them. Select the first generation from the population. The optimal solution Through integer mapping Multiple target problems The migration solution is as follows: ; in, Represented as a multi-objective problem The migration solution on, and ; Using a solution repair mechanism, the migration solution is... The infeasible solutions in the sequence are repaired to obtain the repaired migration solutions, and the repaired migration solutions are then incorporated into the migration population. The first generation of evolutionary population as the first The initial population of the generation.

[0047] The transfer learning execution module, which constructs a high-quality initial population through an integer mapping set and a solution repair mechanism, is the core component for achieving efficient solutions in multi-objective optimization. This method plays a crucial role in the paper: it accurately transfers optimization knowledge accumulated in single-objective optimization to the multi-objective framework, effectively overcoming the slow convergence problem caused by low-quality initial populations in multi-objective optimization. By selecting high-quality solutions from four independent knowledge bases of single-objective problems and transforming them into multi-objective problem solutions through integer mapping, efficient transfer of optimization knowledge is achieved. The solution repair mechanism ensures the feasibility of the transferred solutions, avoiding interference from infeasible solutions in the optimization process. Using the repaired transferred solutions as the next generation of initial population significantly shortens the number of iterations required for the algorithm to reach a high-quality solution, thus significantly improving solution efficiency. This mechanism enables the system to fully utilize high-quality solutions from single-objective optimization under all constraints, providing effective technical support for solving challenges such as discrete decision spaces, strong variable correlations, and complex constraints in large-scale decomposed line equilibrium problems, achieving dual optimization of convergence speed and solution quality.

[0048] To better demonstrate the effectiveness and practicality of the proposed MOTLE algorithm, the proposed algorithm and four frontier comparison algorithms were applied to 30 LSDLBP test cases of different scales. The specific configuration of the disassembly line was as follows: 10 available workstations, with a maximum robot capacity of 5 per workstation, for a total of 25 available robots. Experiments were conducted on the TAOG dataset, which contains approximately 200, 500, and 1000 disassembly tasks. The energy consumption of each robot and the time consumption of each disassembly task were given in the dataset. Due to the problem characteristics of LSDLBP, four representative large-scale multi-objective optimization algorithms that can solve this specific problem in recent years were selected for comparative experiments. The four algorithms are: Large-scale multi-objective evolutionary optimization algorithm with adaptive progeny generation (DGEA), Fuzzy Decision Variable Frame (FDV) for large-scale multi-objective optimization, Million-Dimensional Multi-Objective Evolutionary Algorithm Based on Fast Sampling (FLEA), and Large-scale multi-objective competitive group optimization algorithm (LMOCSO).

[0049] To analyze the performance of the large-scale decomposition line balance optimization method based on transfer learning and evolutionary computation algorithms of this invention and its comparative algorithms, a specific embodiment uses two metrics to compare their results: hypervolume (HV) and inverse generation distance (IGD). HV primarily calculates the volume comprised of the obtained solutions and reference points containing the two maximum objective values ​​in all solution sets. A larger hypervolume indicates better approximation and distribution. When calculating the hypervolume, the objective function values ​​of all solutions are normalized to [0,1], and the reference points are set to (1.1,1.1,1.1,1.1). IGD is the average distance from the obtained solution to the nearest solution in the optimal solution set. A smaller IGD indicates better approximation and distribution. Note that due to the lack of a unified benchmark set and the unknowable theoretical Pareto front, the experimental section uses the union of the approximate Pareto solutions obtained by the five algorithms as the approximate true front. Five algorithms were applied to LSDLBP test cases of scales of 200, 500, and 1000, respectively. The mean and standard deviation of HV and IGD (in parentheses) after 10 independent runs are shown in Tables 1 to 6. The optimal algorithm result is highlighted in bold. The trends of HV and IGD results for the five algorithms on test cases of different scales are shown below. Figures 7 to 8 As shown.

[0050] Among them, the DGEA algorithm is derived from [Cheng H, et al. Adaptive Offspring Generation for Evolutionary Large-Scale Multiobjective Optimization[J]. IEEE Transactions on Systems, Man & Cybernetics. Systems, 2022, 52: 786-798.] (Adaptive Offspring Generation Algorithm for Evolutionary Large-Scale Multiobjective Optimization).

[0051] The FDV algorithm originates from [Yang X, Zou J, et al. A Fuzzy Decision Variables Framework for Large-Scale Multiobjective Optimization[J]. IEEE Transactions on Evolutionary Computation, 2023, 27: 445-459.] (a fuzzy decision variable framework for large-scale multiobjective optimization).

[0052] The FLEA algorithm originates from [Li LH, He C, et al. A fast sampling based evolutionary algorithm for million-dimensional multiobjective optimization[J]. Swarm and Evolutionary Computation, 2022, 75: 101181.] (a million-dimensional multiobjective evolutionary algorithm based on fast sampling).

[0053] The LMOCSO algorithm originates from [Tian Y, Zheng XT, Zhang XY, et al. Efficient Large-Scale Multiobjective Optimization Based on a Competitive Swarm Optimizer[J]. IEEE transactions on cybernetics, 2020, 50: 3696-3708.] (Efficient large-scale multiobjective optimization based on a competitive swarm optimizer).

[0054] Table 1. HV results of the five algorithms on 200 test cases. Table 2. HV results of the five algorithms on 500 test cases. Table 3. HV results of the five algorithms on 1000 test cases. Table 4. IGD results of the five algorithms on 200 test cases. Table 5. IGD results of the five algorithms on 500 test cases. Table 6. IGD Results of Five Algorithms on 1000 Test Cases As shown in Tables 1 to 3, the HV calculation results reveal that, compared to the other four algorithms, the MOTLE algorithm achieves the best solution performance for the vast majority of problems. Algorithm FLEA achieves the best solution performance for problems L500-1 and L1000-5, while algorithm LMOCSO achieves the best solution performance for problem L200-8. In problems L200-8 and L500-1, the difference between MOTLE and the optimal algorithm is also very small.

[0055] As shown in Tables 4 to 6, the IGD calculation results reveal that, compared with the other four algorithms, the MOTLE algorithm achieves the best solution performance for the vast majority of problems. The FDV algorithm achieves the best solution performance for problems L200-6, L500-2, L500-4, L500-5, L1000-3, and L1000-9. The LMOCSO algorithm achieves the best solution performance for problem L200-8. The FLEA algorithm achieves the best solution performance for problem L500-1.

[0056] In summary, the method proposed in this invention solves the problem that traditional methods struggle to optimize large-scale decomposition line balance problems with discrete decision spaces, high correlation of decision variables, and complex constraints, thereby accelerating the algorithm's convergence process and improving the quality of the solution set.

[0057] Example 2: A large-scale decomposition line balancing optimization method based on transfer learning includes the following steps: Step 1: Decompose the large-scale line balancing problem into multiple single-objective problems and optimize them independently using an evolutionary algorithm. Save the optimized solution set generated in each generation to an independent knowledge base to obtain the independent knowledge base corresponding to each single-objective problem. Step 2: Use evolutionary algorithms to optimize the multi-objective problem and obtain the optimized solution to the multi-objective problem; Step 3: When transfer learning is triggered, establish an integer mapping relationship between each single-objective problem solution set and the multi-objective problem solution set of the current generation; Step 4: Obtain the optimized solution in the knowledge base corresponding to each single-objective problem, and use the integer mapping relationship to map the current generation optimized solution to the transfer solution on the multi-objective problem. Then, merge the transfer solution into the current generation's evolutionary population in the multi-objective problem to serve as the initial population for the next generation's multi-objective problem optimization.

[0058] Example 3: A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the above-described method.

[0059] Example 4: A computer program product includes a computer program that, when executed by a processor, implements the steps of the above-described method.

[0060] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

Claims

1. A large-scale decomposition line balancing optimization system based on transfer learning, characterized in that, include: The single-objective optimization module is used to independently optimize multiple single-objective problems obtained by decomposing the large-scale line balance problem using an evolutionary algorithm, and saves the optimized solution set generated in each generation to an independent knowledge base, thus obtaining an independent knowledge base corresponding to each single-objective problem. The multi-objective optimization module is used to optimize multi-objective problems using evolutionary algorithms to obtain optimized solutions to multi-objective problems; The mapping relationship construction module is used to establish an integer mapping relationship between each single-objective problem solution set and the multi-objective problem solution set of the current generation when transfer learning is triggered; The transfer learning execution module is used to obtain the optimized solution in the knowledge base corresponding to each single-objective problem, and to use the integer mapping relationship to map the current generation optimized solution to the transfer solution on the multi-objective problem. The transfer solution is then incorporated into the current generation evolutionary population of the multi-objective problem as the initial population for the next generation of multi-objective problem optimization.

2. The large-scale decomposition line balancing optimization system based on transfer learning according to claim 1, characterized in that, In the single-objective optimization module and the multi-objective optimization module, the evolutionary algorithm is used to obtain the optimized solution of the single-objective problem and the optimized solution of the multi-objective problem. The encoding method of the individual information in the optimized solution is a three-level sequence. The third-level sequence includes: The first vector is used to encode the allocation relationship between the robot and the workstation; The second vector is used to encode the task-robot assignment relationship; The third vector is used to encode the execution order of the task; Wherein, the first vector is represented as: ； in, This is represented as a vector representing the relationship between all robots and workstations. The length is equal to the total number of robots. Represented as a robot The serial number assigned to the workstation. , For workstation index set, For the robot index set, if the robot No workstation was assigned. ; The second vector is represented as: ； in, This is represented as a vector showing the assignment relationships between all tasks and robots. Indicates being responsible for a task The robot's serial number, , For the set of all tasks, When, it indicates a task. No robots were assigned; A second vector that can assign tasks to robots Simplified representation: Selected task and robot assigned vector This is used when optimizing tertiary sequence encoding using evolutionary algorithms in single-objective learning modules and multi-objective evolutionary modules. Represented as: ； in, This is represented as a vector showing the assignment relationship between the selected task and the robot. This represents the selected set of tasks. Indicates being responsible for a task Robot serial number ; The third vector is represented as: ； in, This is represented as the selected disassembly task sequence vector. This represents the selected set of dismantling tasks. , This is indicated as a dismantling task. The serial number, exist The location is for dismantling tasks. Its position in the priority ranking; The construction of the third vector must not violate the TAOG graph.

3. The large-scale decomposition line balancing optimization system based on transfer learning according to claim 2, characterized in that, The evolutionary algorithm also includes a decoding mechanism for receiving single-objective or multi-objective optimization solutions and performing the following operations: According to the first vector Determine the workstation to which each robot belongs and its available time window; According to the second vector Each disassembly task is assigned to a corresponding robot; According to the third vector The priority relationship in the algorithm is used to calculate the earliest start time of each task on its bound robot and generate an executable scheduling sequence in ascending order of start time. The set of performance metrics for four single-objective problems is calculated based on the executable scheduling sequence. The four single-objective problems are: cycle time, total robot energy consumption, workstation peak energy consumption, and number of robots used. The set of performance metrics is then output.

4. The large-scale decomposition line balancing optimization system based on transfer learning according to claim 3, characterized in that, In the single-objective optimization module, the evolutionary algorithm further includes selection, crossover, and mutation operations; The selection operation is as follows: using the tournament selection method, two high-quality parents are selected from the parent population in turn based on Pareto dominance, crowding distance, or random selection. The crossover operation is as follows: Corresponding to the first vector The first vector of the first parent in the parent population. Part of the index value is copied to the child generation, and then the first vector of the second parent generation is copied. The remaining index values ​​are added to the corresponding positions of the offspring to obtain the first vector after the crossover. ; For the third vector The disassembly sequence of each product in the offspring generation is selected from the parent generation according to a preset probability to obtain the third vector after crossover. ; For the second vector Using the third vector after the cross Generate the second vector after the crossover. ; The mutation operation is as follows: For the first vector Randomly select an undeployed robot and a deployed robot to swap their positions, generating the mutated first vector. ; For the second vector Randomly select a position in the vector and replace that position with another robot that satisfies the priority relationship constraints between the disassembly tasks, generating a mutated second vector. ; For the third vector Randomly select a task from the TS vector, move it to another feasible position that satisfies the constraints, and swap the original solution at that feasible position with the mutation point to generate the mutated third vector. .

5. The large-scale decomposition line balancing optimization system based on transfer learning according to claim 4, characterized in that, The evolutionary algorithm also includes a solution repair mechanism, which is used to repair individuals that violate constraints after crossover or mutation operations, and generate feasible solutions that satisfy all constraints.

6. The large-scale decomposition line balancing optimization system based on transfer learning according to claim 5, characterized in that, The solution repair mechanism utilizes the following rule individuals for repair: Does the number of robots at any workstation exceed the capacity limit? Does the start time of any task violate the completion time of all its predecessor tasks? Whether any task cannot be completed within its workstation time window; if any violation is detected, perform corrective actions such as removing redundant robots, supplementing idle robots, or delaying the task start time, until the executable scheduling sequence satisfies all constraints, and then send the corrected feasible scheduling sequence back to the decoding module to update the performance index set. If any violation is detected, corrective actions such as removing redundant robots, adding idle robots, or delaying the task start time are performed until the executable scheduling three-level sequence satisfies all constraints. Then, the corrected executable scheduling three-level sequence is sent back to the performance metric set and the performance metric set is updated.

7. The large-scale decomposition line balancing optimization system based on transfer learning according to claim 6, characterized in that, In the mapping relationship construction module, the method for constructing the integer mapping relationship set from the solution set of the four single-objective problems to the solution set of the multi-objective problem is as follows: First vector Integer mapping relationship with the solution set of multi-objective problems The construction process is as follows: According to the The first in the knowledge base of a single-objective problem By archiving the non-dominated solutions, we can obtain the probability matrix of the robot-workstation allocation relationship; robot Assigned to workstation The probability is expressed as: ； in, Represented as the first Robot in a single-objective problem Assigned to workstation The probability, Represented as the first The first single-objective problem The archive set of non-dominated solutions, Represented as an archive set One of the candidate solutions. Represented as in candidate solutions China Robot Assigned to workstation , This is represented as an indicator function, which is 1 if the condition is true and 0 otherwise. According to the The probability of all robot-workstation assignment relationships in a single-objective problem. The probability matrix can be obtained. ,and , and These represent the total number of robots and the total number of workstations, respectively. The candidate set of all valid robot-workstation assignments is represented as: ； in, Represented as robot Assigned to workstation The probability, For robot index set, For workstation index set; The candidate set of valid robot-workstation assignment relationships. Sort the elements in descending order to obtain a priority queue set containing the probabilities of all valid robot-workstation assignment relationships. , represented as: ； The original solution obtained from single-objective optimization is used to determine the allocation relationship between the robot and the workstation. Through integer mapping relationships Transformed into a migration solution, expressed as: ； in, This is represented as the migration solution. Represented as the first An integer mapping relationship between all solutions of the robot-workstation allocation relationship in single-objective optimization and the transition solutions of the robot-workstation allocation relationship in multi-objective optimization; The integer mapping relationship Obtained according to the following rules: Initialize all robots to an unassigned state: ; For the original solution Each robot in Search Chinese correspondence The element with the maximum value Select this workstation As the target workstation If the robot For allocation and target workstation If not full, then perform allocation. ; Third vector Integer mapping relationship with the solution set of multi-objective problems The construction method is as follows: When the population evolves to the... In the past, from single-objective knowledge base Obtain the average position of each task to get the task In the knowledge base Average position in Specifically: ； in, Indicates task In candidate solutions The position in the middle, This indicates the number of solutions in the knowledge base; Using the original solution of task execution priority relationship in single-objective optimization Through integer mapping relationships The specific transition solution for obtaining the task execution priority relationship in multi-objective optimization is as follows: ； in, The original solution representing the task execution priority relationship; The mapping function will The disassembly task in the knowledge base The average position in the middle is reordered; Second vector Integer mapping relationship with the solution set of multi-objective problems The construction method is as follows: When the population evolves to the... In the past, from single-objective knowledge base Obtain tasks from Assigned to robots frequency Specifically: ； in, Represented as in candidate solutions Medium task Assigned to robots , This is represented as an indicator function, which is 1 if the condition is true and 0 otherwise. for Each task arranged in order ,from Select the robot with the highest assignment frequency from the robots already assigned to workstations. Assigned to task Specifically: ； in, This indicates that the robot is in an assigned state. Represented as a task The robot with the highest allocation frequency; By identifying the robot with the highest task allocation frequency across all tasks, we obtain the task-robot allocation relationship in multi-objective optimization corresponding to the original solution of the task-robot allocation relationship in single-objective optimization, i.e., the second vector. Integer mapping relationship with the solution set of multi-objective problems ; Using the above process, we obtain the sets of integer mappings from the solution sets of the four single-objective problems to the solution sets of the multi-objective problems. .

8. The large-scale decomposition line balancing optimization system based on transfer learning according to claim 7, characterized in that, In the transfer learning execution module, an integer mapping relationship set is used. The method for obtaining the initial population for the next generation of population evolution, along with the repair and resolution mechanism, is as follows: When transfer learning is triggered, the first of the four single-objective questions is selected from the independent knowledge bases corresponding to them. Select the first generation from the population. The optimal solution Through integer mapping Multiple target problems The migration solution is as follows: ； in, Represented as a multi-objective problem in The migration solution on, and ; Using a solution repair mechanism, the migration solution is... The infeasible solutions in the sequence are repaired to obtain the repaired migration solutions, and the repaired migration solutions are then incorporated into the migration population. The first generation of evolutionary population as the first The initial population of the generation.

9. A large-scale decomposition line balancing optimization method based on transfer learning, characterized in that, Includes the following steps: The large-scale decomposition of the line balance problem is decomposed into multiple single-objective problems, which are then independently optimized using an evolutionary algorithm. The optimized solution set generated in each generation is saved to an independent knowledge base, thus obtaining an independent knowledge base for each single-objective problem. Evolutionary algorithms are used to optimize multi-objective problems and obtain optimized solutions. When transfer learning is triggered, an integer mapping relationship is established between each single-objective problem solution set of the current generation and the multi-objective problem solution set; Obtain the optimized solution from the knowledge base corresponding to each single-objective problem, and use the integer mapping relationship to map the current generation optimized solution to the transfer solution on the multi-objective problem. Then, merge the transfer solution into the current generation's evolutionary population in the multi-objective problem to serve as the initial population for the next generation's multi-objective problem optimization.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method of claim 9.

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