A dynamic multi-objective optimization method based on double space knowledge transfer and fusion

Abstract

The application relates to the technical field of human-robot collaborative assembly task planning, and discloses a dynamic multi-objective optimization method based on double-space knowledge transfer and fusion. The method aims at the problem that existing dynamic multi-objective optimization methods can only transfer knowledge in a single space and cannot fully utilize complementary information in different spaces, constructs a decision space knowledge base and a target space knowledge base, searches for historical samples similar to the current environment through KD Tree retrieval, generates candidate solutions through knowledge transfer in the double spaces respectively, calculates a self-fusion weight based on population quality to linearly fuse the candidate solutions, combines multiple source populations and selects optimal individuals to form a new initial population. The application can improve the response speed of the algorithm to the dynamic environment, improve the convergence and diversity of the solution, and is suitable for complex dynamic multi-objective optimization scenarios such as human-robot collaborative assembly dynamic task planning.

Description

Technical Field

[0001] This application relates to the field of human-machine collaborative assembly task planning technology, specifically to a dynamic multi-objective optimization method based on dual-space knowledge transfer and fusion. Background Technology

[0002] Dynamic multi-objective optimization problems are widespread in various fields such as industrial production and resource scheduling. They require simultaneously optimizing multiple conflicting objectives in a time-varying environment. With the development of intelligent manufacturing, human-machine collaborative assembly systems are widely used. Their task allocation process needs to consider both assembly efficiency and operator workload, and factors such as production demand, equipment status, and worker status change dynamically over time, making them typical dynamic multi-objective optimization problems. Most existing dynamic multi-objective optimization methods only construct knowledge models in a single space, either the decision space or the objective space, for knowledge transfer. This fails to fully utilize the complementary information between the two spaces, resulting in slow algorithm response speeds after environmental changes, and the convergence and diversity of solutions are insufficient to meet actual production needs. Summary of the Invention

[0003] To solve, or at least partially solve, the above-mentioned technical problems, this application provides a dynamic multi-objective optimization method based on dual-space knowledge transfer and fusion.

[0004] This application provides a dynamic multi-objective optimization method based on dual-space knowledge transfer and fusion, including the following steps:

[0005] S1. Initialize the initial population of the problem to be optimized, construct the decision space knowledge base and the target space knowledge base, and set the static optimizer to the non-dominated sorting genetic algorithm.

[0006] S2. The initial population is iteratively optimized using the static optimizer, while the environment is checked for changes.

[0007] S3. When an environmental change is detected, the current elite population is obtained by filtering from the initial population it has iterated to the present, and similar historical samples similar to the current environment are retrieved based on the decision space knowledge base and the target space knowledge base, respectively.

[0008] S4. Based on the similar historical samples and the current elite population, knowledge transfer is performed in the decision space using the historical knowledge of the decision space knowledge base and in the target space using the historical knowledge of the target space knowledge base, respectively, to generate candidate solutions for the decision space and candidate solutions for the target space, and the candidate solutions for the target space are mapped back to the decision space.

[0009] S5. Evaluate the population quality of the candidate solutions in the decision space and the candidate solutions in the target space respectively, calculate the fusion weight based on the population quality evaluation results, and perform linear fusion of the candidate solutions in the decision space and the candidate solutions in the target space based on the fusion weight to obtain the fused candidate solutions;

[0010] S6. Merge the current elite population, the decision space candidate solutions, the target space candidate solutions, and the fusion candidate solutions, and select the optimal individual from the merged population to form a new initial population;

[0011] S7. Return to S2 until the optimization termination condition is met, and output the final optimization result.

[0012] Optionally, in S1, the construction of the decision space knowledge base and the target space knowledge base specifically includes:

[0013] Elite individuals are selected from candidate populations in historical environments according to a predetermined ratio to form a historical elite population;

[0014] Calculate the first mean vector and the first covariance matrix of the historical elite population in the decision space under each historical environment, and store them in the decision space knowledge base.

[0015] Calculate the second mean vector and the first standard deviation vector of the historical elite population in the target space under each historical environment, and store them in the target space knowledge base.

[0016] Optionally, in S3, the step of retrieving similar historical samples similar to the current environment based on the decision space knowledge base and the target space knowledge base respectively specifically includes:

[0017] A KD Tree is constructed based on the decision space knowledge base and the target space knowledge base, respectively, and the first mean vector of the current elite population in the decision space and the second mean vector in the target space are calculated in the current environment.

[0018] The KD Tree is used to retrieve a preset number of similar historical samples that are closest to the first mean vector in the decision space and the second mean vector in the target space of the current elite population. Inverse distance weights are calculated based on the distance between the similar historical samples and the current environment.

[0019] Optionally, in S4, knowledge transfer in the decision space specifically includes:

[0020] Based on the inverse distance weight, the first mean vector and the first covariance matrix of the current elite population in the decision space, as well as the first mean vector and the first covariance matrix of the historical elite population corresponding to each similar historical sample in the decision space, are weighted and fused to obtain the fused decision space statistical features.

[0021] The candidate solutions for the decision space are generated based on the statistical features of the fused decision space.

[0022] Optionally, in S4, the knowledge transfer in the target space specifically includes:

[0023] Based on the inverse distance weight, the second mean vector and the first standard deviation vector of the current elite population in the target space, as well as the second mean vector and the first standard deviation vector of the historical elite population corresponding to each similar historical sample in the target space, are weighted and fused to obtain the fused target space statistical features.

[0024] Based on the fused statistical features of the target space, candidate solutions for the target space are generated, and the candidate solutions for the target space are mapped back to the decision space through least squares mapping.

[0025] Optionally, in S5, the step of evaluating the population quality of the candidate solutions in the decision space and the candidate solutions in the target space respectively specifically includes:

[0026] The candidate solutions in the decision space and the candidate solutions in the target space are subjected to non-dominated sorting, and the proportion of individuals with a level of 0 in the non-dominated sort to the total number of corresponding candidate solutions is used as an indicator of population quality.

[0027] Optionally, in S6, the step of selecting the optimal individuals from the merged population to form the new initial population specifically includes:

[0028] The merged population is sorted by non-dominated order and crowding distance is calculated. The optimal number of individuals are selected to form the new initial population in order of non-dominated level from high to low and crowding distance from large to small at the same level.

[0029] Optionally, the problem to be optimized is a dynamic task planning problem for human-machine joint assembly, and the method is used to dynamically optimize the task allocation in the human-machine joint assembly process.

[0030] Optionally, the optimization objective of the human-machine joint assembly dynamic task planning problem includes minimizing the total assembly completion time and minimizing the comprehensive capability loss. The calculation of the total assembly completion time includes worker fatigue penalty and constraint violation penalty, and the comprehensive capability loss is calculated based on the comprehensive capability of resources to perform tasks.

[0031] Optionally, the dynamic task planning problem of human-machine joint assembly also includes consideration of the dynamic changes in worker fatigue, where worker fatigue accumulates during task execution and recovers during idle time, and the fatigue accumulation rate increases with the increase of working time, while the fatigue recovery rate decreases with the increase of working time.

[0032] The method provided in this application has the following beneficial effects:

[0033] This application constructs a decision space knowledge base and a target space knowledge base, respectively storing the statistical characteristics of elite populations in historical environments. By retaining only high-value elite knowledge, it filters out interference from low-quality samples in subsequent knowledge transfer, reduces storage overhead, and improves the efficiency of knowledge retrieval and utilization. The dual-space knowledge base preserves historical optimization experience from both the distribution of decision variables and the distribution of target values, avoiding the information bias problem caused by single-space knowledge modeling.

[0034] Using KD-trees for similar historical sample retrieval enables efficient searching of samples most similar to the current environment from a large number of historical samples, solving the problem of drastic decrease in computational efficiency of traditional linear retrieval methods as the knowledge base grows. Historical samples are weighted based on inverse distance, with higher weights for samples closer to the current environment. This fully utilizes historical knowledge with high similarity to the current environment while reducing the negative transfer risk from significantly different historical knowledge, thus improving the effectiveness of knowledge transfer.

[0035] Independent knowledge transfer is performed in the decision space and the target space. Decision space knowledge transfer directly models and samples the decision variable space, effectively preserving the structural characteristics of the solutions and generating highly feasible candidate solutions. Target space knowledge transfer directly models the Pareto front distribution, generating candidate solutions that more directly point to the optimal target region in the new environment, providing clear directional guidance for the search process. This parallel dual-space knowledge transfer utilizes complementary information from both spaces simultaneously, overcoming the limitations of single-space knowledge transfer and improving the overall quality of candidate solutions.

[0036] Assessing the population quality of two types of candidate solutions based on the proportion of individuals with a rank of 0 in the non-dominated ranking can intuitively and accurately reflect the effectiveness of different spatial knowledge in the current environment. Dynamically calculating the fusion weight based on population quality, with higher-quality candidate solutions receiving greater weight during the fusion process, allows for adjustments to the fusion ratio according to the characteristics of different dynamic environments. This avoids the problem of fixed weights being unable to adapt to complex and changing environments, further reducing the possibility of negative transfer. Individual-level linear fusion can more precisely utilize the information of the two types of candidate solutions, combining the solution structure advantages of the decision space with the directional guidance advantages of the target space to generate fusion candidate solutions with both high feasibility and convergence potential.

[0037] Merging four populations—the current elite population, candidate solutions in the decision space, candidate solutions in the target space, and fusion candidate solutions—combines the advantages of different knowledge sources. It preserves effective information from the end of the old environment while fully utilizing historical transfer knowledge and high-quality solutions generated through fusion, covering all possible high-quality solution regions and avoiding overlooking valuable search directions. Employing an elite selection strategy combining non-dominated ranking with crowding distance to screen the new initial population balances solution convergence and diversity. It prioritizes retaining the best-performing non-dominated solutions and, among solutions of the same level, prioritizes retaining sparser individuals, enabling the new initial population to quickly converge to the Pareto front of the new environment while maintaining sufficient distribution breadth.

[0038] The overall solution proposed in this application can quickly generate a high-quality initial population by utilizing historical optimization experience after environmental changes, significantly shortening the convergence time in new environments while ensuring solution diversity. This effectively solves the problems of slow response speed and unstable solution quality in traditional dynamic multi-objective optimization methods. In the dynamic task planning scenario of human-machine collaborative assembly, it can accurately simulate the dynamic changes in worker fatigue, rationally allocate worker load while ensuring assembly efficiency, generate task allocation schemes that meet actual production needs, and improve the overall operational performance of the human-machine collaborative assembly system. Attached Figure Description

[0039] Figure 1 A schematic diagram of a dynamic multi-objective optimization method based on dual-space knowledge transfer and fusion provided in an embodiment of this application;

[0040] Figure 2 This is a schematic diagram comparing the environmental response performance of a dynamic multi-objective optimization algorithm provided in an embodiment of this application.

[0041] Figure 3 This application provides a task scheduling Gantt chart as an embodiment. Detailed Implementation

[0042] To make the objectives, technical solutions, and advantages of this application clearer, specific embodiments of this application will be described in further detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely for explaining this application and not for limiting it. It should also be noted that, for ease of description, only the parts relevant to this application are shown in the drawings, not all of them. Before discussing exemplary embodiments in more detail, it should be mentioned that some exemplary embodiments are described as processes or methods depicted as flowcharts. Although the flowcharts describe operations (or steps) as sequential processes, many of these operations can be performed in parallel, concurrently, or simultaneously. Furthermore, the order of the operations can be rearranged. The process can be terminated when its operation is completed, but may also have additional steps not included in the drawings. The process can correspond to a method, function, procedure, subroutine, subprogram, etc.

[0043] The technical solutions of the embodiments of this application will be clearly described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application are within the scope of protection of this application.

[0044] See Figures 1 to 2 This application provides a dynamic multi-objective optimization method based on dual-space knowledge transfer and fusion, comprising the following steps:

[0045] S1. Initialize the initial population of the problem to be optimized, construct the decision space knowledge base and the target space knowledge base, and set the static optimizer to a non-dominated sorting genetic algorithm.

[0046] In some implementations, S1 involves constructing a decision space knowledge base and a target space knowledge base, specifically including:

[0047] Elite individuals are selected from candidate populations in historical environments according to a predetermined ratio to form a historical elite population;

[0048] Calculate the first mean vector and first covariance matrix of the historical elite population in the decision space under each historical environment, and store them in the decision space knowledge base.

[0049] Calculate the second mean vector and the first standard deviation vector of the historical elite population in the target space under each historical environment, and store them in the target space knowledge base.

[0050] In some implementations, the problem to be optimized is the dynamic task planning problem for human-machine joint assembly, and the method is used to dynamically optimize the task allocation in the human-machine joint assembly process.

[0051] In some implementations, the optimization objectives of the human-machine collaborative assembly dynamic task planning problem include minimizing the total assembly completion time and minimizing the overall capability loss. The calculation of the total assembly completion time incorporates worker fatigue penalties and constraint violation penalties, and the overall capability loss is calculated based on the overall capability of resources to perform tasks.

[0052] In some implementations, the dynamic task planning problem of human-machine joint assembly also includes consideration of the dynamic changes in worker fatigue, which accumulates during task execution and recovers during idle time. The fatigue accumulation rate increases with the working time, while the fatigue recovery rate decreases with the working time.

[0053] Dynamic multi-objective optimization problems are widely found in fields such as industrial production and resource scheduling. Their core is to continuously track the optimal set of multiple conflicting objectives in a time-varying environment. In flexible manufacturing scenarios such as human-machine collaborative assembly, factors such as production demands, equipment status, and worker status constantly change over time. Task allocation needs to simultaneously consider assembly efficiency and operator workload. Traditional dynamic multi-objective optimization methods mostly perform knowledge modeling and transfer only in a single space, failing to fully utilize complementary information from different spaces. This results in slow algorithm response speeds after environmental changes, and the convergence and diversity of solutions are insufficient to meet practical requirements. This implementation provides a dynamic multi-objective optimization method based on dual-space knowledge transfer and fusion, which can simultaneously utilize historical knowledge from both the decision space and the objective space, improving the algorithm's adaptability to dynamic environments.

[0054] First, the algorithm is initialized to determine the range of decision variables and population size for the problem to be optimized. The static optimizer is set to the Non-Dominated Sorting Genetic Algorithm (NSGA-II). Simultaneously, a decision space knowledge base and a target space knowledge base are constructed. These knowledge bases store effective optimization knowledge from historical environments. During construction, elite individuals are selected from the candidate populations of each historical environment according to a preset ratio to form a historical elite population. Only high-value elite knowledge is retained, while low-quality samples are filtered to avoid interference with subsequent knowledge transfer. For each historical environment, the first mean vector and first covariance matrix of the corresponding historical elite population in the decision space are calculated. These two sets of statistical features are stored in the decision space knowledge base, which is mathematically expressed as follows:

[0055]

[0056] in, Indicates the first The first mean vector of a historical elite population in the decision-making space under a given historical context. Indicates the first The first covariance matrix of a historical elite population in the decision-making space under a given historical context. This represents the capacity of the decision space knowledge base. Simultaneously, the second mean vector and first standard deviation vector of the historical elite population in the target space are calculated for each historical environment. These two sets of statistical features are stored in the target space knowledge base, which is mathematically expressed as:

[0057]

[0058] in, Indicates the first The second mean vector of a historical elite population in the target space under a given historical context. Indicates the first The first standard deviation vector of a historical elite population in the target space under a given historical context. In this implementation, the decision space knowledge base and the target space knowledge base have the same capacity. .

[0059] This method is applicable to dynamic task planning problems in human-machine collaborative assembly, enabling dynamic optimization of task allocation during the assembly process. Human-machine collaborative assembly systems comprise three types of execution resources: humans, robots, and human-machine collaborative teams. These resources exhibit different characteristics in terms of operational precision, flexibility, and stability, requiring rational resource allocation based on task characteristics. First, the comprehensive capability of each resource in performing different tasks is calculated. This comprehensive capability assessment includes four dimensions: safety risk, physical and cognitive load, task physical attributes, and technical requirements. A two-step weighted integration process yields the final resource-task comprehensive capability value. The first step weights and integrates the multi-dimensional evaluation results of a single expert, while the second step weights and integrates the evaluation results of multiple experts, ensuring that the comprehensive capability fully reflects the degree of matching between resources and tasks.

[0060] The dynamic task planning problem for human-machine collaborative assembly sets two core optimization objectives, both of which are minimized. The first objective is the total assembly completion time, which is mathematically expressed as:

[0061]

[0062] in, Indicates the time of completion of final assembly. Indicates the start time of assembly. Indicates the type of execution resource. For binary decision variables, a value of 1 indicates a task. Allocate resources Execution, a value of 0 indicates no allocation. Representing resources Execute the task The basic processing time, Indicates the rate of fatigue increase. This represents the fatigue gain coefficient. express Real-time fatigue levels of workers. This represents the time penalty coefficient for constraint violation. This represents the total constraint violation amount. The total assembly completion time includes worker fatigue penalties and constraint violation penalties, reflecting the impact of worker fatigue on assembly efficiency while ensuring the feasibility of the solution. The second objective is the comprehensive capability loss, mathematically expressed as:

[0063]

[0064] in, This indicates a loss of overall capability. This represents the overall execution capability index, which is the average of the combined capabilities of all task allocation schemes. The smaller the loss in overall capability, the higher the degree of matching between resources and tasks, and the stronger the overall execution capability.

[0065] In the dynamic task planning problem of human-machine collaborative assembly, the dynamic characteristics of worker fatigue need to be considered. Worker fatigue accumulates continuously during task execution, while it recovers to some extent during idle time between consecutive tasks. Furthermore, as working hours increase, the rate of fatigue accumulation gradually rises, while the rate of fatigue recovery gradually decreases. The calculation of the worker's real-time fatigue level considers both the accumulation and recovery processes, and its mathematical expression is as follows:

[0066] When there is idle time between two consecutive tasks assigned to a worker:

[0067]

[0068] When there is no free time:

[0069]

[0070] in, Indicates completion of task Post-worker fatigue levels This indicates the level of fatigue recovery after a period of free time. This indicates the worker's fatigue level after completing the previous task. Indicates task The corresponding fatigue growth rate, Representing resources Execute the task The actual time. The level of fatigue recovery after idle time. ,in This indicates the level of fatigue before free time. Indicates fatigue recovery rate, This indicates the length of idle time. Through the above-mentioned dynamic fatigue calculation method, the changing patterns of worker fatigue in actual production can be accurately simulated, making task allocation schemes more ergonomic and avoiding excessive worker fatigue.

[0071] S2. Use a static optimizer to iteratively optimize the initial population while detecting whether the environment has changed.

[0072] After initialization and problem modeling, a non-dominated sorting genetic algorithm is used to iteratively optimize the initial population, searching for a Pareto optimal solution that satisfies multiple objectives within the current stable environment. During the iterative optimization process, the current population is first non-dominated, dividing individuals into different non-dominated levels, with higher-level individuals being retained preferentially. Next, the crowding distance between individuals of the same level is calculated to distinguish their quality and ensure solution diversity. Then, selection, crossover, and mutation operations are performed sequentially to generate a new offspring population. The parent and offspring populations are merged, and non-dominated sorting and crowding distance calculations are performed again. Individuals of the same size as the initial population are selected as the next generation, completing one iteration.

[0073] Since the objective function, constraints, or problem parameters of dynamic multi-objective optimization problems change over time, the optimal solution in the current environment may no longer be applicable after environmental changes. Therefore, it is necessary to synchronously detect whether the environment has changed during each iteration of optimization to ensure that the algorithm can respond to the dynamic characteristics of the environment in a timely manner. Environmental change detection employs a method of recalculating objective values. After each generation of the population is generated, a subset of individuals is randomly selected, and their objective values ​​are recalculated based on the objective function in the current environment. The calculated objective values ​​are compared with the objective values ​​of the corresponding individuals in the previous generation. If the objective values ​​of the selected individuals change for two consecutive generations, it is determined that the current environment has changed.

[0074] If no environmental change is detected, the next iteration of optimization continues, continuously improving the convergence and diversity of the population, gradually approaching the Pareto front in the current environment. If an environmental change is detected, the current static optimization process is terminated, the search for the optimal solution in the old environment is stopped, and instead, historically accumulated optimization knowledge is used to quickly generate an initial population adapted to the new environment, avoiding the inefficiency caused by re-random initialization in the new environment.

[0075] S3. When an environmental change is detected, the current elite population is selected from the initial population that has been iterated to the present. Similar historical samples with the current environment are retrieved based on the decision space knowledge base and the target space knowledge base, respectively.

[0076] In some implementations, S3 involves retrieving similar historical samples that are similar to the current environment based on the decision space knowledge base and the target space knowledge base, respectively, specifically including:

[0077] KD Trees are constructed based on the decision space knowledge base and the target space knowledge base, respectively, and the first mean vector of the current elite population in the decision space and the second mean vector in the target space are calculated.

[0078] A predetermined number of similar historical samples are retrieved using a KD Tree to find the closest ones to the first mean vector in the decision space and the second mean vector in the target space of the current elite population. The inverse distance weight is calculated based on the distance between the similar historical samples and the current environment.

[0079] When an environmental change is detected, the current elite population is first selected from the initial population iterated to the present. The selection process is consistent with the selection rules of the historical elite population, and the individuals with the best performance are selected from the current population according to a preset ratio to form the current elite population. The current elite population can accurately reflect the distribution characteristics of the optimal solution under the current environment. By selecting elite individuals, low-quality samples in the current population can be filtered out, avoiding invalid information from interfering with the subsequent knowledge retrieval and transfer process.

[0080] KD-trees are constructed based on the decision space knowledge base and the target space knowledge base, respectively. KD-trees are a data structure for fast retrieval of high-dimensional spatial data, capable of efficiently finding the individual closest to the target sample from a large number of historical samples. This solves the problem of the sharp decline in computational efficiency of traditional linear retrieval methods as the knowledge base size increases. Specifically, the decision space KD-tree is constructed based on the first mean vector of all historical elite populations stored in the decision space knowledge base, and the target space KD-tree is constructed based on the second mean vector of all historical elite populations stored in the target space knowledge base.

[0081] The method calculates the first mean vector of the current elite population in the decision space and the second mean vector in the target space. These two vectors fully represent the core characteristics of the current environment from the two dimensions of decision variable distribution and target value distribution, respectively. The first mean vector of the current elite population is input into a KD Tree in the decision space to retrieve a predetermined number of similar historical samples closest to this vector. Simultaneously, the second mean vector of the current elite population is input into a KD Tree in the target space to retrieve the same predetermined number of similar historical samples closest to this vector. Performing independent similarity searches in the decision space and target space fully utilizes the complementary information of the two spaces and avoids the problem of one-sided historical knowledge caused by searching only one space. It should be noted that in this method, the mean vector corresponding to the decision space is uniformly referred to as the first mean vector, and the mean vector corresponding to the target space is uniformly referred to as the second mean vector. Whether corresponding to the current elite population or the historical elite population, this scheme can distinguish them based on preconditions, and such distinctions will be made if there are special requirements.

[0082] Based on the distance between the retrieved similar historical samples and the current environment, the inverse distance weight corresponding to each similar historical sample is calculated. The mathematical expression of the inverse distance weight is:

[0083]

[0084] in, Indicates the first The inverse distance weights corresponding to each similar historical sample Indicates the first Euclidean distance between a number of similar historical samples and the current environment This is a very small constant used to avoid calculation errors where the denominator is zero when the distance is zero. This is a smoothing term used to normalize the weights, ensuring that the sum of all weights is less than or equal to 1. This represents the number of similar historical samples retrieved. The core logic of inverse distance weighting is that the smaller the distance between a similar historical sample and the current environment, the greater its corresponding weight. This indicates that the optimization knowledge accumulated in that historical environment has higher reference value for the current new environment and can play a greater role in subsequent knowledge transfer processes.

[0085] S4. Based on similar historical samples and the current elite population, knowledge transfer is performed in the decision space using historical knowledge from the decision space knowledge base and in the target space using historical knowledge from the target space knowledge base, respectively, to generate candidate solutions in the decision space and the target space, and then the candidate solutions in the target space are mapped back to the decision space.

[0086] In some implementations, in S4, knowledge transfer in the decision space specifically includes:

[0087] Based on the inverse distance weight, the first mean vector and first covariance matrix of the current elite population in the decision space, as well as the first mean vector and first covariance matrix of the historical elite population corresponding to each similar historical sample in the decision space are weighted and fused to obtain the fused statistical features of the decision space.

[0088] Candidate solutions for the decision space are generated based on the statistical features of the fused decision space.

[0089] In some implementations, in S4, knowledge transfer in the target space specifically includes:

[0090] Based on the inverse distance weight, the second mean vector and first standard deviation vector of the current elite population in the target space, as well as the second mean vector and first standard deviation vector of the historical elite population corresponding to each similar historical sample in the target space, are weighted and fused to obtain the fused target space statistical features.

[0091] Based on the fused statistical features of the target space, candidate solutions for the target space are generated, and the candidate solutions for the target space are mapped back to the decision space through least squares mapping.

[0092] After obtaining similar historical samples and their corresponding inverse distance weights, independent knowledge transfer is performed in the decision space and the target space, generating two classes of candidate solutions with potential advantages. This dual-space parallel knowledge transfer can simultaneously utilize the solution structure information of the decision space and the Pareto front distribution information of the target space, overcoming the limitations of single-space knowledge transfer and improving the overall quality of candidate solutions.

[0093] First, knowledge transfer in the decision space is performed. Based on the calculated inverse distance weights, the first mean vector and first covariance matrix of the current elite population in the decision space, as well as the first mean vector and first covariance matrix of the historical elite populations corresponding to each similar historical sample, are weighted and fused to obtain the fused statistical features of the decision space. The mathematical expression of the weighted fusion is:

[0094]

[0095] in, Let represent the first mean vector of the fused decision space. Let represent the first covariance matrix of the fused decision space. Together, these two matrices constitute the statistical characteristics of the fused decision space. This represents the first mean vector of the current elite population in the decision space. This represents the first covariance matrix of the current elite population in the decision space. Indicates the first The first mean vector of the historical elite population corresponding to a number of similar historical samples in the decision space. Indicates the first The first covariance matrix of the historical elite population corresponding to similar historical samples in the decision space. Through this weighted fusion method, the real-time characteristics of the current environment can be organically combined with the accumulated knowledge of similar historical environments. This avoids the negative transfer problem caused by relying entirely on historical knowledge, and makes full use of historical experience to accelerate the search process for new environments.

[0096] Based on the statistical characteristics of the fused decision space, samples are taken from the corresponding multivariate Gaussian distribution to generate candidate solutions for the decision space. The mathematical expression of the sampling process is as follows:

[0097]

[0098] in This represents the set of candidate solutions generated in the decision space. Decision space knowledge transfer directly models and samples within the decision variable space, which can better preserve the structural characteristics of the solutions. The generated candidate solutions have high feasibility and can effectively avoid the solution failure problem that may occur during the inverse mapping of the target space.

[0099] Next, target space knowledge transfer is performed. The statistical feature fusion logic for target space knowledge transfer is consistent with that of the decision space. Based on the inverse distance weight, the second mean vector and first standard deviation vector of the current elite population in the target space, as well as the second mean vector and first standard deviation vector of the historical elite population corresponding to each similar historical sample in the target space, are weighted and fused to obtain the fused target space statistical features. The mathematical expression of the weighted fusion is as follows:

[0100]

[0101] in, Let represent the second mean vector of the fused target space. Let represent the first standard deviation vector of the fused target space. Together, they constitute the statistical features of the fused target space. This represents the second mean vector of the current elite population in the target space. This represents the first standard deviation vector of the current elite population in the target space. Indicates the first The second mean vector of the historical elite population corresponding to each similar historical sample in the target space. Indicates the first The first standard deviation vector of the historical elite population corresponding to each similar historical sample in the target space.

[0102] Based on the statistical features of the fused target space, samples are taken from the corresponding Gaussian distribution to generate candidate solutions for the target space. The mathematical expression of the sampling process is as follows:

[0103]

[0104] in This represents the set of candidate solutions generated in the target space. Target space knowledge transfer directly models the distribution of the Pareto front, and the generated candidate solutions can more directly point to the optimal target region in the new environment, providing clear directional guidance for the search process.

[0105] Since candidate solutions in the objective space are generated in the objective value space, they cannot be directly used as decision variables. They need to be transformed into solutions in the decision space through a mapping relationship. The least squares mapping method is used to construct the mapping matrix from the objective space to the decision space. The process of solving the mapping matrix is ​​as follows:

[0106]

[0107] in Represents the mapping coefficient matrix. This represents the decision variable matrix of the current elite population. This represents the target value matrix corresponding to the current elite population. Let Frobenius norm be denoted. After solving the above least squares problem and obtaining the optimal mapping matrix, the candidate solutions in the target space are mapped back to the decision space to obtain the target space mapped candidate solutions. The mathematical expression of the mapping process is as follows:

[0108]

[0109] in This represents the set of candidate solutions in the target space after mapping. Least squares mapping can quickly establish the transformation relationship between the target space and the decision space based on the correspondence of the current elite population, with high computational efficiency and the ability to ensure the rationality of the mapping results.

[0110] S5. Evaluate the population quality of candidate solutions in the decision space and the target space respectively. Calculate the fusion weight based on the population quality evaluation results. Perform linear fusion of candidate solutions in the decision space and the target space based on the fusion weight to obtain the fused candidate solution.

[0111] In some implementations, S5 involves evaluating the population quality of candidate solutions in the decision space and candidate solutions in the target space, specifically including:

[0112] The candidate solutions in the decision space and the candidate solutions in the target space are subjected to non-dominated ranking, and the proportion of individuals with a rank of 0 in the non-dominated ranking to the total number of corresponding candidate solutions is used as an indicator of population quality.

[0113] After generating candidate solutions in the decision space and the target space, the effectiveness of decision space knowledge and target space knowledge varies under different dynamic environments. Candidate solutions generated in a single space may not simultaneously meet the requirements of convergence and diversity. Therefore, it is necessary to evaluate the population quality of the two types of candidate solutions separately, and then adjust the fusion weight based on the population quality evaluation results to achieve an effective combination of the two types of candidate solutions and give full play to the complementary advantages of dual-space knowledge.

[0114] First, non-dominated ranking is performed on candidate solutions in both the decision space and the target space. Individuals in each candidate solution set are divided into different non-dominated levels, with individuals at level 0 representing the non-dominated solutions in the current candidate solution set. These represent the best-performing individuals in the set, capable of not being dominated by other individuals on multiple optimization objectives simultaneously. The proportion of individuals at level 0 in the non-dominated ranking to the total number of corresponding candidate solutions is used as an indicator of population quality. This indicator directly reflects the proportion of high-value individuals in the candidate solution set; a higher proportion indicates better overall quality of candidate solutions generated in the current environment and stronger adaptability to new environments.

[0115] The mathematical expression for the population quality index of candidate solutions in the decision space is:

[0116]

[0117] in, This represents a population quality index for candidate solutions in the decision space. This represents the number of individuals with a rank of 0 in the candidate solutions of the decision space. This represents the total number of candidate solutions in the decision space. The mathematical expression for the population quality index of candidate solutions in the goal space is:

[0118]

[0119] in This represents the population quality index of candidate solutions in the target space. This represents the number of individuals with a rank of 0 in the candidate solutions of the target space. This represents the total number of candidate solutions in the target space.

[0120] The fusion weight is calculated based on the population quality indices of the two types of candidate solutions. The fusion weight is positively correlated with the population quality index; the higher the quality of the candidate solution set, the greater its weight in the fusion process, ensuring that knowledge more adapted to the current environment is preferentially retained during the fusion process. The mathematical expression of the fusion weight is:

[0121]

[0122]

[0123] in, The weights represent the fusion weights of candidate solutions in the decision space. The weights represent the fusion weights of candidate solutions in the target space. This is a very small constant used to avoid the calculation error of a denominator of zero when the quality indicators of both types of candidate solutions are zero. This weighting method allows for dynamic adjustment of the fusion ratio based on the actual performance of the two types of candidate solutions under different environments, avoiding the problem of fixed weights being unable to adapt to complex dynamic environments and effectively reducing the risk of negative migration.

[0124] Based on the calculated fusion weights, individual-level linear fusion is performed on candidate solutions in the decision space and the target space to generate fused candidate solutions. Individual-level linear fusion can independently weight and combine each candidate solution, making more refined use of the information from both types of candidate solutions than population-level fusion, and fully preserving the advantages of different spatial knowledge. The mathematical expression of individual-level linear fusion is:

[0125]

[0126] in Indicates the first A fusion candidate solution, Indicates the first A number of candidate solutions in the decision space. Indicates the first There are several candidate solutions in the target space. Through the above linear fusion process, the solution structure information retained by the candidate solutions in the decision space can be effectively combined with the optimal target region guidance information provided by the candidate solutions in the target space, generating a fused candidate solution that has both high feasibility and convergence potential, thereby further improving the overall quality of the candidate solutions.

[0127] S6. Merge the current elite population, decision space candidate solutions, target space candidate solutions, and fusion candidate solutions, and select the best individual from the merged population to form a new initial population.

[0128] In some implementations, in S6, selecting the best individuals from the merged population to form a new initial population specifically includes:

[0129] The merged population is sorted by non-dominated order and crowding distance is calculated. The optimal number of individuals are selected to form a new initial population in order of non-dominated level from high to low and crowding distance from large to small at the same level.

[0130] After obtaining the candidate solutions, the candidate populations from multiple sources are merged, and then the best individuals are selected through an elite selection strategy to form a new initial population. Merging multiple populations can combine the advantages of different knowledge sources, retaining effective information from the current environment while making full use of historical transfer knowledge and high-quality solutions generated by fusion, avoiding the limitations of a single-source population, and providing a richer initial search starting point for optimizing the new environment.

[0131] The merged population includes the current elite population, candidate solutions in the decision space, candidate solutions in the goal space, and fusion candidate solutions. The mathematical expression for population merging is:

[0132]

[0133] in This represents the total population after the merger. This represents the current elite population. This represents the population corresponding to the candidate solutions in the decision space. This represents the population corresponding to candidate solutions in the target space. This represents the population corresponding to the fusion candidate solutions. The current elite population retains the individuals with the best performance at the end of the old environment. Although these individuals are no longer fully adapted to the new environment, they usually still have some reference value and can ensure the stability of the algorithm after environmental changes. The decision space candidate solutions and the target space candidate solutions introduce historical knowledge from two different spaces, providing potential high-quality search directions. The fusion candidate solutions combine the advantages of knowledge from both spaces and usually have higher overall quality. By merging these four types of populations, we can comprehensively cover the region of possible high-quality solutions and avoid missing valuable search directions.

[0134] The total population size after merging is larger than the preset size of the initial population, so a preset number of individuals with the best performance need to be selected to form a new initial population. The selection process adopts an elite selection strategy that combines non-dominated ranking with crowding distance. This strategy can simultaneously take into account the convergence and diversity of solutions, so that the generated new initial population can converge quickly to the Pareto front of the new environment while maintaining sufficient distribution breadth.

[0135] First, the merged population is sorted using non-dominated ranking, dividing all individuals into different non-dominated levels, with lower-level individuals exhibiting superior performance. Individuals are selected sequentially from lowest to highest non-dominated level until the number of selected individuals reaches or exceeds the preset population size. If the total number still does not reach the preset size after selecting all individuals of a certain level, individuals from the next level are selected. If selecting only some individuals from a certain level is sufficient to reach the preset size, crowding distance is calculated for all individuals in that level, and individuals are selected in descending order of crowding distance until the total number reaches the preset size.

[0136] Crowding distance measures the distribution density among individuals of the same rank. A larger crowding distance indicates fewer other individuals around that individual, a more unique search area, and better preservation of that individual to maintain population diversity. This elite selection method prioritizes the retention of the best-performing non-dominated solutions while also prioritizing the retention of sparser individuals among solutions of the same rank, avoiding excessive concentration of solutions and achieving a good balance between convergence and diversity in the new initial population.

[0137] After screening, the predetermined number of individuals obtained constitutes the initial population in the new environment. Inputting this initial population into the static optimizer initiates the iterative optimization process in the new environment. This population update method fully utilizes all available effective information, significantly shortens the convergence time in the new environment, and improves the algorithm's response speed and adaptability to dynamic environments.

[0138] S7. Return to S2 until the optimization termination condition is met, and output the final optimization result.

[0139] After obtaining the new initial population, the algorithm returns to the static optimization step, S2, and continues iterative optimization using the non-dominated sorting genetic algorithm, while continuously monitoring for changes in the environment, forming a complete dynamic optimization loop. Throughout the optimization process, whenever an environmental change is detected, the processes of similar historical sample retrieval, dual-space knowledge transfer, weight fusion, and population update are repeatedly executed, ensuring that the algorithm can always track the optimal solution set under the current environment.

[0140] When the preset optimization termination conditions are met, the iteration stops and the final optimization result is output. The optimization termination conditions include reaching the preset maximum number of iterations, or the convergence and diversity of the population meeting the preset requirements, that is, the Pareto front of the population has not changed significantly over several generations, and the fluctuation of the objective value of all non-dominated solutions is within the allowable range.

[0141] The final output is the Pareto optimal solution set under the current environment. This set contains multiple non-dominated optimal solutions, each corresponding to a different set of objective trade-offs. In the dynamic task planning scenario of human-machine collaborative assembly, each solution in the Pareto optimal solution set corresponds to a task allocation scheme. Some schemes focus more on shortening the overall assembly completion time, while others focus more on improving resource matching and reducing worker workload. Decision-makers can select the most suitable task allocation scheme from the solution set for execution based on actual production needs and priorities.

[0142] This method utilizes dual-space knowledge transfer and fusion to fully leverage historical optimization experience and accelerate the search process in new environments. It can quickly generate a high-quality initial population after environmental changes, significantly shortening the convergence time while ensuring solution diversity. This effectively solves the problems of slow response speed and unstable solution quality in traditional dynamic multi-objective optimization methods, and can adapt well to the complex and ever-changing dynamic environment in industrial production.

[0143] To verify the response performance of the method proposed in this embodiment under dynamic environments, the method was compared with various dynamic multi-objective optimization algorithms on standard test problems. Figure 2As shown in the figure, the log(MIGD) value varies with the number of environmental changes for different algorithms (DNSGA2A, DNSGA2B, NSGA2PPS, NSGA2AE, NSGA2KGB, NSGA2KTMM, NSGA2IMKT, and NSGA2DSKTF; all algorithms are dynamic multi-objective optimization variants of NSGA-II, with NSGA2DSKTF representing this method) on six typical test problems: DF1, DF3, DF5, DF7, DF9, and DF12. These problems are all from the CEC2018 dynamic multi-objective optimization benchmark set, which is a standard test problem commonly used in the field of dynamic multi-objective optimization. It includes different types of dynamic changes, objective dimensions, and Pareto front forms, comprehensively verifying the performance of algorithms in various dynamic environments. DF1 is a bi-objective test problem where both the Pareto optimal solution set and the Pareto optimal front shift linearly over time, representing a basic positional asymptotic dynamic change. It is used to verify the algorithm's basic tracking ability for changes in a stable environment. DF3 is a bi-objective test problem where the position and shape of both the Pareto optimal solution set and the Pareto optimal front change over time, while the coupling relationships between decision variables change dynamically over time. It is used to verify the algorithm's adaptability to changes in variable coupling relationships. DF5 is a bi-objective test problem where both the Pareto optimal solution set and the Pareto optimal front change dynamically over time, while the feasible region boundary of the decision variables shrinks periodically over time, exhibiting dynamic constraint change characteristics. It is used to verify the algorithm's search performance in scenarios with fluctuating feasible regions. Problem 7 is a bi-objective test problem where both the Pareto optimal solution set and the Pareto optimal front change over time. The search space contains multiple local optima and multimodal concave regions, making it highly deceptive. It is used to verify the algorithm's ability to avoid getting trapped in local optima and maintain population diversity. Problem 9 is a bi-objective test problem where the Pareto optimal front consists of multiple discrete segments, and the number and position of these segments change dynamically over time, exhibiting discontinuous dynamic changes. It is used to verify the algorithm's ability to track discrete, discontinuous Pareto fronts. Problem 12 is a bi-objective test problem where the position of the Pareto optimal front changes over time, and multiple isolated hole structures exist within the feasible solution region. The disconnected regions change dynamically over time, used to verify the algorithm's ability to dynamically adapt to disconnected feasible regions. The horizontal axis represents the number of environmental changes, and the vertical axis represents the logarithm of the average backward generation distance (log(MIGD)). The smaller this value, the closer the solution set obtained by the algorithm is to the true Pareto front, the faster the convergence speed, and the stronger the tracking ability of the dynamic environment.

[0144] As shown in the figure, for all the test problems presented, the curve of the proposed method remained below the curves of other algorithms during most environmental changes. Algorithms such as DNSGA2A, DNSGA2B, and DNSGA2PPS showed significant increases in log(MIGD) values ​​after each environmental change, with large fluctuations. This indicates that the applicability of these algorithms' original population decreased drastically after a sudden environmental change, requiring multiple iterations to converge to the new Pareto front. In contrast, the proposed method showed a significantly smaller increase in log(MIGD) values ​​after environmental changes, and the values ​​quickly decreased to a lower level. This is because the proposed method can utilize historical optimization experience stored in a dual-space knowledge base to quickly retrieve historical samples similar to the current environment. Through knowledge transfer, it generates candidate solutions with potential advantages, avoiding a search from scratch in the new environment and significantly shortening the convergence time after environmental changes.

[0145] Meanwhile, it can be observed that as the number of environmental changes increases, the performance fluctuations of other algorithms become more pronounced, while the performance of our method remains relatively stable. This indicates that our method can continuously accumulate effective optimization knowledge during multiple environmental changes, thereby constantly improving its adaptability to different dynamic environments.

[0146] To further verify the effectiveness of this method in actual industrial scenarios, this implementation constructs a dynamic task planning example for human-machine collaborative assembly. An assembly task is used as a test case, which includes 25 assembly tasks with sequential constraints, involving three types of execution resources: humans, robots, and human-machine collaborative teams. At the same time, the dynamic accumulation and recovery characteristics of worker fatigue with working hours are considered, which can comprehensively simulate the dynamic task planning scenario in actual flexible manufacturing.

[0147] In this example, this method generated multiple Pareto optimal assembly schemes, and representative schemes are shown in Table 1.

[0148] Table Indicates the time of completion of final assembly. The index represents the overall execution capability, and "Solution" represents the proposed solution. The assembly tasks are numbered; this is the only requirement in this implementation, without needing to specify further details. H represents a task performed by a human alone, R represents a task performed by a robot alone, and T represents a task performed by a human-robot collaborative team. The two sets of values ​​intuitively illustrate the relationship between the two optimization objectives. The RAS1 scheme has the shortest total assembly completion time, maximizing production efficiency, but its overall execution capability index is relatively low. The RAS5 scheme has the highest overall execution capability index, with the best resource-task matching, minimizing worker workload, but its total assembly completion time is relatively long. The RAS2, RAS3, and RAS4 schemes fall between these two, offering different levels of objective trade-offs. Decision-makers can select the most suitable assembly scheme from the Pareto solution set based on actual production priorities; for example, choosing the RAS1 scheme when orders are urgent, and choosing the RAS5 scheme when worker health and reduced labor intensity are required.

[0149] Table 1

[0150] Figure 3 The task scheduling Gantt chart for the RAS3 scheme is shown in Table 1. Green blocks represent the time spent by humans performing tasks alone, blue blocks represent the time spent by robots performing tasks alone, purple blocks represent the time spent by the human-robot collaborative team performing tasks, light gray blocks represent resources in a occupied state, and light yellow blocks represent resources in an idle state. As can be seen from the chart, this scheme first has the human-robot collaborative team complete basic tasks such as system motherboard installation. Then, humans and robots perform subsequent tasks in parallel, each performing tasks they are better at. The overall task arrangement is compact, with minimal resource idle time, and all tasks meet the pre-set sequence constraints. At the same time, this scheme reasonably allocates the workload of humans, keeping the real-time fatigue level of workers within a safe threshold, avoiding operational errors and efficiency decline caused by excessive fatigue.

[0151] The experimental results show that this method not only demonstrates excellent convergence and diversity in the standard dynamic multi-objective optimization benchmark problem, but also effectively solves the dynamic task planning problem in the actual human-machine joint assembly scenario, generates a feasible scheduling scheme that takes into account both production efficiency and worker workload, realizes efficient collaboration of human and machine resources, and improves the overall operation effect and humanization level of the human-machine joint assembly system.

[0152] The aforementioned dynamic multi-objective optimization method based on dual-space knowledge transfer and fusion can effectively solve optimization problems in most dynamic environments, demonstrating good convergence and versatility in industrial scenarios such as human-machine collaborative assembly. In practical applications, considering the differentiated characteristics of different dynamic environments, further improvements can be made in the accuracy of knowledge transfer and the adaptability of population updates to enhance the robustness and adaptability of this method in complex and ever-changing scenarios.

[0153] First, existing methods for similarity retrieval in the target space calculate the distance using the mean vector of all targets, assuming that changes in all targets are equally important. However, in real-world dynamic environments, the magnitude and frequency of changes in different targets often vary significantly. For example, in a human-machine collaborative assembly scenario, when a worker suddenly experiences a brief increase in fatigue, the overall assembly completion time target changes significantly, while the overall capability loss target changes relatively little. Using the overall mean vector for similarity retrieval weakens the characteristics of the dominant changing targets, leading to a decrease in the matching degree between retrieved historical samples and the actual needs of the current environment. To address this issue, we can consider splitting the similarity retrieval in the target space into individual target dimensions. For each target, we independently calculate the distance and inverse distance weights between the current environment and historical samples, and then assign global weights based on the real-time change magnitude of each target, ultimately obtaining the fused statistical features of the target space. Specifically, we first calculate the mean change rate of each target before and after environmental changes, assigning higher global weights to targets with larger change rates; then, we perform historical sample retrieval and statistical feature fusion for each target separately; finally, we weight the fusion results of each target according to the global weights to obtain the final statistical features of the target space. This approach highlights the impact of the dominant changing target, making the transfer of target space knowledge more aligned with the actual changing characteristics of the current environment, and further improving the convergence speed of candidate solutions.

[0154] Secondly, in existing methods, the selection ratio between historical and current elite populations is fixed. However, when environmental changes are minor, most individuals in the current elite population still have high reference value, and a fixed selection ratio will lose some high-quality current solutions. Conversely, when environmental changes are significant, the reference value of the current elite population drops sharply, and an excessively high elite ratio can cause the algorithm to get stuck in local optima of the old environment, failing to adapt quickly to the new environment. To address this issue, a quantitative index of environmental change intensity can be introduced, dynamically adjusting the elite selection ratio based on the severity of the environmental change. Specifically, after detecting an environmental change, the average change in the target value of the current elite population under the old and new environments is calculated, and this change is used as the quantitative value of the environmental change intensity. Then, a mapping relationship is established between the environmental change intensity and the elite selection ratio: the smaller the environmental change intensity, the higher the elite selection ratio, retaining more high-quality individuals in the current environment; the greater the environmental change intensity, the lower the elite selection ratio, incorporating more knowledge from the historical environment. Simultaneously, to avoid a decrease in population diversity due to an excessively high elite ratio or insufficient stability due to an excessively low elite ratio, upper and lower limits are set for the elite ratio, ensuring that the ratio always fluctuates within a reasonable range. This adjustment method can find the optimal balance between current knowledge and historical knowledge based on the actual situation of environmental changes, which ensures the stability of the algorithm when the environmental changes are small, and improves the response speed of the algorithm when the environmental changes are large.

[0155] The above approach improves the accuracy of knowledge transfer by weighting different objectives and enhances the adaptability of population updates by adjusting the proportion of elites. This can further enhance the method's adaptability in complex and dynamic environments and expand its application scope in more industrial scenarios.

[0156] The above description is merely a preferred embodiment and the technical principles employed in this application. This application is not limited to the specific embodiments described herein, and various obvious changes, readjustments, and substitutions that can be made by those skilled in the art will not depart from the scope of protection of this application. Therefore, although this application has been described in detail through the above embodiments, this application is not limited to the above embodiments, and may include many other equivalent embodiments without departing from the concept of this application.

Claims

1. A dynamic multi-objective optimization method based on dual-space knowledge transfer and fusion, characterized in that, The problem to be optimized is the dynamic task planning problem for human-machine joint assembly. The method is used to dynamically optimize the task allocation in the human-machine joint assembly process. The human-machine joint assembly process includes three types of execution resources: humans, robots, and human-machine joint teams. The optimization objectives of the dynamic task planning problem for human-machine joint assembly include minimizing the total assembly completion time and minimizing the comprehensive capability loss. The calculation of the total assembly completion time includes worker fatigue penalties and constraint violation penalties. The comprehensive capability loss is calculated based on the comprehensive capability of the resources to perform the tasks. The method for calculating the total assembly completion time is as follows: in, Indicates the time of completion of final assembly. Indicates the start time of the assembly. Indicates the type of execution resource. For binary decision variables, a value of 1 indicates a task. Allocate resources Execution, a value of 0 indicates no allocation. Representing resources Execute the task The basic processing time, Indicates the rate of fatigue increase. This represents the fatigue gain coefficient. express Real-time worker fatigue levels This represents the time penalty coefficient for constraint violation. Indicates the total number of constraint violations; The method for calculating the overall capability loss is as follows: in, This indicates a loss of overall capability. This represents the overall execution capability index, which is the average comprehensive capability of all task allocation schemes; Worker fatigue accumulates during task execution and recovers during idle time; the rate of fatigue accumulation increases with working hours, while the rate of fatigue recovery decreases with working hours. This applies when there is idle time between two consecutive tasks assigned to a worker. When there is no free time: in, Indicates completion of task Post-worker fatigue levels This indicates the level of fatigue recovery after a period of free time. This indicates the worker's fatigue level after completing the previous task. Indicates task The corresponding fatigue growth rate, Representing resources Execute the task Actual time; fatigue recovery level after idle time ,in This indicates the level of fatigue before free time. Indicates fatigue recovery rate, Indicates the length of idle time; In this method, the decision space is the space composed of decision variables of the human-machine joint assembly dynamic task planning problem, where the decision variables represent the allocation relationship between assembly tasks and execution resources; the target space is the target value space composed of the total assembly completion time and the comprehensive capability loss; the historical environment is the environment of the human-machine joint assembly dynamic task planning problem under different production demands, equipment states, and worker states; the current environment is the current production demands, equipment states, and worker states of the human-machine joint assembly dynamic task planning problem. The method includes the following steps: S1. Initialize the initial population of the problem to be optimized, construct the decision space knowledge base and the target space knowledge base, and set the static optimizer to the non-dominated sorting genetic algorithm. In S1, the construction of the decision space knowledge base and the target space knowledge base specifically includes: Elite individuals are selected from the candidate population in the historical environment according to a preset ratio to form a historical elite population. The historical elite population is a set of elite task allocation schemes obtained by optimizing the human-machine joint assembly dynamic task planning problem in the historical environment. Calculate the first mean vector and the first covariance matrix of the historical elite population in the decision space under each historical environment, and store them in the decision space knowledge base. Calculate the second mean vector and the first standard deviation vector of the historical elite population in the target space under each historical environment, and store them in the target space knowledge base; S2. The initial population is iteratively optimized using the static optimizer, while the environment is checked for changes. S3. When an environmental change is detected, a current elite population is obtained by filtering from the initial population iterated to the present. The current elite population is a set of elite task allocation schemes obtained by optimizing the human-machine joint assembly dynamic task planning problem under the current environment. Similar historical samples similar to the current environment are retrieved based on the decision space knowledge base and the target space knowledge base, respectively. The similar historical samples are statistical feature samples of historical elite populations corresponding to historical environments similar to the current environment stored in the decision space knowledge base and the target space knowledge base. In S3, the step of retrieving similar historical samples to the current environment based on the decision space knowledge base and the target space knowledge base respectively includes: A KD Tree is constructed based on the decision space knowledge base and the target space knowledge base, respectively, and the first mean vector of the current elite population in the decision space and the second mean vector in the target space are calculated in the current environment. The KD Tree is used to retrieve a preset number of similar historical samples that are closest to the first mean vector in the decision space and the second mean vector in the target space of the current elite population. Inverse distance weights are calculated based on the distance between the similar historical samples and the current environment. S4. Based on the similar historical samples and the current elite population, knowledge transfer is performed in the decision space using the historical knowledge of the decision space knowledge base and in the target space using the historical knowledge of the target space knowledge base, respectively, to generate candidate solutions for the decision space and candidate solutions for the target space, and the candidate solutions for the target space are mapped back to the decision space. In S4, knowledge transfer in the decision space specifically includes: Based on the inverse distance weight, the first mean vector and the first covariance matrix of the current elite population in the decision space, as well as the first mean vector and the first covariance matrix of the historical elite population corresponding to each similar historical sample in the decision space, are weighted and fused to obtain the fused decision space statistical features. The candidate solutions for the decision space are generated based on the fused statistical features of the decision space. In S4, the knowledge transfer in the target space specifically includes: Based on the inverse distance weight, the second mean vector and the first standard deviation vector of the current elite population in the target space, as well as the second mean vector and the first standard deviation vector of the historical elite population corresponding to each similar historical sample in the target space, are weighted and fused to obtain the fused target space statistical features. Based on the fused statistical features of the target space, the candidate solutions of the target space are generated, and the candidate solutions of the target space are mapped back to the decision space through least squares mapping. S5. Evaluate the population quality of the candidate solutions in the decision space and the candidate solutions in the target space respectively, calculate the fusion weight based on the population quality evaluation results, and perform linear fusion of the candidate solutions in the decision space and the candidate solutions in the target space based on the fusion weight to obtain the fused candidate solutions; S6. Merge the current elite population, the decision space candidate solutions, the target space candidate solutions, and the fusion candidate solutions, and select the optimal individual from the merged population to form a new initial population; S7. Return to S2 until the optimization termination condition is met, and output the final optimization result.

2. The dynamic multi-objective optimization method based on dual-space knowledge transfer and fusion according to claim 1, characterized in that, In S5, the evaluation of the population quality of the candidate solutions in the decision space and the candidate solutions in the target space specifically includes: The candidate solutions in the decision space and the candidate solutions in the target space are subjected to non-dominated sorting, and the proportion of individuals with a level of 0 in the non-dominated sort to the total number of corresponding candidate solutions is used as an indicator of population quality.

3. The dynamic multi-objective optimization method based on dual-space knowledge transfer and fusion according to claim 1, characterized in that, In S6, the step of selecting the optimal individuals from the merged population to form the new initial population specifically includes: The merged population is sorted by non-dominated order and crowding distance is calculated. The optimal number of individuals are selected to form the new initial population in order of non-dominated level from high to low and crowding distance from large to small at the same level.

4. The dynamic multi-objective optimization method based on dual-space knowledge transfer and fusion according to claim 1, characterized in that, The dynamic task planning problem of human-machine joint assembly also includes consideration of the dynamic changes in worker fatigue. Worker fatigue accumulates during task execution and recovers during idle time. The fatigue accumulation rate increases with the working time, while the fatigue recovery rate decreases with the working time.

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