Flexible manufacturing structured process multi-objective optimization method based on evolutionary computation

Abstract

The invention discloses a flexible manufacturing structured process multi-objective optimization method based on evolutionary computation, and belongs to the technical field of intelligent manufacturing and production scheduling. The method comprises the following steps: modeling a production problem, and taking the workload balance degree of each vehicle type as an independent objective function; performing parallel optimization on process allocation by adopting a multi-objective evolutionary algorithm to generate a Pareto optimal solution set; and visualizing the Pareto frontier through an interactive decision support module, and carrying out multi-criterion decision recommendation based on the user preference weight. According to the method, the defects that a traditional single-target optimization method cannot reflect a multi-target tradeoff relation and depends on prior weight setting are overcome, a series of high-quality scheduling schemes can be provided for multi-variety mixed-line production, and the flexibility, transparency and overall efficiency of a production system are remarkably improved.

Description

Technical Field

[0001] This invention belongs to the field of intelligent manufacturing systems and production engineering technology. More specifically, this invention relates to a multi-objective optimization method for flexible manufacturing structured processes based on evolutionary computation, particularly in mixed-line production modes with multiple product types and variable batch sizes, utilizing a multi-objective evolutionary algorithm to optimize resource allocation and load balancing of assembly tasks. Background Technology

[0002] The modern automotive manufacturing industry is facing the dual challenges of product diversification and production agility. Traditional dedicated production lines (DMLs) with large volumes and few varieties are gradually being replaced by flexible manufacturing systems (FMS) and reconfigurable manufacturing systems (RMS) due to their rigid structure and inability to adapt to market changes. These systems have a certain degree of process and structural flexibility, and can cope with the production needs of multiple varieties and variable batches through software and hardware adjustments. However, their core problem—the assembly line balancing problem (ALBP)—evolves into the more complex mixed-model assembly line balancing problem (MMALBP) in the mixed-model assembly line production environment, which requires the simultaneous coordination of processes, time, and resource allocation for multiple vehicle models.

[0003] To solve MMALBP, existing technologies generally employ metaheuristic algorithms such as genetic algorithms, particle swarm optimization, and simulated annealing. Since this problem is NP-hard, exact algorithms are computationally infeasible, making these methods the mainstream approach. However, existing methods often follow a single-objective optimization paradigm, typically aggregating multiple performance metrics (such as number of workstations, production cycle time, idle time, and cost) into a single objective function through weighted summation, aiming to find an "optimal solution" under predefined evaluation criteria.

[0004] Such single-objective optimization methods have significant limitations: First, they lack strategic flexibility, providing only an isolated optimal solution that fails to reflect the inherent trade-offs between multiple objectives, making it difficult for decision-makers to make dynamic adjustments based on the actual production environment (such as market demand fluctuations, supply chain changes, and vehicle model priority adjustments); Second, they require decision-makers to pre-set the weights of each objective before optimization, i.e., to express "prior preferences." However, in reality, decision-makers find it difficult to accurately quantify preferences when they have not seen all possible trade-off solutions, which can easily lead to decision bias and suboptimal solutions.

[0005] Therefore, there is an urgent need for an intelligent optimization method that can simultaneously optimize multiple conflicting objectives and output a set of Pareto optimal solutions. This would support decision-makers in making flexible and adaptive production scheduling decisions based on a comprehensive understanding of the trade-offs, thereby improving the overall efficiency and responsiveness of the production system. Summary of the Invention

[0006] To address the above technical problems, this invention proposes a multi-objective optimization method for structured processes in flexible manufacturing based on evolutionary computation, comprising the following steps: Step S1, Production Problem Modeling: Obtain production data, including process lists, process hours, and sequential dependencies for various vehicle models. Assign all types of processes for all vehicle models to n workstations to obtain a process allocation scheme. Encode the process allocation scheme into individuals, which are one-dimensional integer arrays. The array index represents a unique process number, and the value at the corresponding index position represents the workstation number to which the process is assigned. Define an independent workstation load balancing objective function for each vehicle model and merge them into an objective vector. Each component in the objective vector corresponds to the workstation load balancing objective function for each vehicle model. Step S2, Multi-objective optimization solution: With the goal of minimizing all components in the objective vector, a multi-objective evolutionary algorithm is used to iteratively optimize the population, generating a Pareto optimal solution set. The multi-objective evolutionary algorithm employs the non-dominated sorting genetic algorithm NSGA-II. Its process includes calculating the objective values ​​for each vehicle model corresponding to all components of each individual; obtaining a fast non-dominated sort and diversity preservation based on crowding distance based on the multi-objective values ​​of each individual; selecting individuals from the population using rank priority followed by crowding distance as comparators to construct a mating pool; generating offspring through crossover and mutation; merging offspring with their parents; comparing the merged individuals with those in the previous generation for non-dominated sorting; and selecting individuals from the sorted individuals using rank priority followed by crowding distance as comparators to fill the new generation population. This process is repeated iteratively until the required number of iterations or convergence conditions are met, at which point the Pareto optimal solution set is output. Step S3, Interactive Decision Support: Visualize the Pareto optimal solution set; receive user input of preference weights for load balancing of different vehicle models, calculate the weighted total score of each Pareto optimal solution based on the weights, and output a recommended solution based on the weighted total score.

[0007] Furthermore, the objective function for workstation load balancing is quantified using mean squared error (MSE). For a single vehicle model, the MSE calculation formula is as follows: in, This model is the first The total working hours on each workstation (obtained by summing the working hours of all relevant processes allocated to that workstation). It is the average working hours of this model across all n workstations, where n is the total number of workstations.

[0008] Furthermore, in steps S1 and S2, a detection and repair mechanism is introduced to handle individuals that may violate process dependency constraints in all individuals, crossovers, and offspring generated by mutations, in order to ensure that all solutions meet the feasibility requirements.

[0009] Furthermore, the detection and repair mechanism includes: defining a list of sequential dependencies between processes; traversing individual coding sequences to verify the pre-order constraints of each process; if the current process is found to violate its pre-order constraints, then re-inserting it into the first legal position after the last process executed among all its pre-order processes.

[0010] Furthermore, the specific steps for selecting individuals from the population or non-dominated ranking using rank as the first criterion and crowding distance as the second criterion include: Step S2.1: Evaluate the target values ​​of each vehicle model for all components of each individual in the population, and screen feasible solutions that satisfy all constraints; Step S2.2: Perform non-dominated comparisons on feasible solutions and classify individuals that are not dominated by any other solutions into the first non-dominated level; Step S2.3: Sequentially identify subsequent non-dominated levels until all feasible solutions are layered; Step S2.4: Rank the non-dominated levels from highest to lowest. Select all individuals in the first i-1 non-dominated levels in turn. If the i-th non-dominated level is overcrowded, truncate them in descending order of crowding distance. The truncating steps based on crowding distance from largest to smallest include: Based on the number of target values ​​N for each individual in the i-th non-dominated level, sort all individuals in the i-th non-dominated level in ascending order according to each target value, and obtain the sorted sequence of all N target values. Set the crowding distance between the best and worst performing individuals in each sorted sequence for the corresponding target value to infinity; Calculate the crowding distance for the remaining individuals j in each sorting sequence. The formula for calculating the crowding distance is: In the formula, This represents the target value of the next neighboring individual of individual j in the target vector, based on the target value of the z-component. This represents the target value of the previous neighboring individual of individual j in the target vector z-component. This represents the maximum value of the z-component of the i-th non-dominated level in the target vector; Let Z represent the minimum value of the z-component of the target vector for the i-th non-dominated level, where Z = 1, 2, ..., N-1, N; Sort the calculated crowding distances of each individual from largest to smallest. From this sorted list, select individuals one by one, starting with the individual with the largest crowding distance, and truncate them.

[0011] Furthermore, the generation of offspring through crossover and mutation includes the following steps: For any selected pair of parent generations, determine whether the processes in the pair of parent generations are crossover based on the crossover probability. If crossover occurs, create an empty offspring individual and exchange the corresponding processes of the workshops in the pair of parent generations to generate a new offspring individual; if the same process is inherited by two workshops, randomly select only one workshop that inherits the process and retain the duplicate process in the selected workshop; finally, trigger a mutation operation for each selected individual with a set probability, randomly select two processes from the individual, and swap the workshops to which they are assigned.

[0012] Furthermore, the visualization uses a three-dimensional scatter plot, with the three coordinate axes representing the MSE values ​​of three different vehicle models, and each data point representing a feasible production line allocation scheme.

[0013] Furthermore, the weighted score is calculated using the following formula: in, , , It is a weight set by the user; , , These are the mean square error values ​​for the corresponding vehicle models.

[0014] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the method when executing the program.

[0015] A computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the method.

[0016] Compared with the prior art, the beneficial effects of the present invention are: 1. This invention constructs a Pareto solution set that truly reflects the conflict relationship between multiple objectives by taking the workload balance of each vehicle model as an independent optimization objective. This breaks through the limitation of traditional single-objective optimization, which can only provide a single solution. It provides a rich and diverse set of preferred solutions for production decision-making, and significantly enhances the strategic flexibility and adaptability of the production scheduling system.

[0017] 2. This invention adopts an "optimization before decision-making" mechanism, which allows decision-makers to apply preferences based on actual production needs after fully grasping all the trade-off information in the Pareto front. This effectively avoids decision-making bias caused by requiring users to pre-set weights in traditional methods, and improves the scientific nature and transparency of decision-making.

[0018] 3. This invention achieves global parallel search based on a multi-objective evolutionary algorithm, which can efficiently and stably approximate the real Pareto front in a complex combinatorial optimization space. Compared with traditional heuristic algorithms that are prone to getting trapped in local optima, it has stronger global exploration capabilities and higher optimization quality assurance.

[0019] 4. This invention integrates optimization calculation with interactive decision support, providing visualized Pareto front analysis and multi-criteria decision recommendation mechanism, which significantly improves the interpretability and operability of optimization results in actual production environments, and supports enterprises in achieving dynamic and precise allocation of production resources. Attached Figure Description

[0020] Figure 1 Flowchart of intelligent optimization method for structured processes in flexible automotive manufacturing; Figure 2 Explanation diagram for the definition of solution A dominating solution B; Figure 3 Interpretive diagram of the definition of mutual non-dominance between solution A and solution B; Figure 4 Map showing the distribution of the Pareto front; Figure 5 A time distribution chart for each vehicle model after allocating the processes to each workstation; Figure 6 A schematic diagram illustrating the effect of selecting cross-processes between parent individuals. Detailed Implementation

[0021] The following detailed description, in conjunction with the accompanying drawings, illustrates a specific implementation of the multi-objective optimization method for flexible manufacturing structured processes based on evolutionary computation according to the present invention.

[0022] Example: A Multi-Objective Optimization Method for Structured Processes in Flexible Manufacturing Based on Evolutionary Computation The method involved in this embodiment mainly consists of three cooperative functional modules: (1) a production problem modeling module; (2) a multi-objective optimization engine; and (3) an interactive decision support module. The algorithm's workflow begins with inputting raw production data (such as the process list, working hours, and sequential dependencies between processes for each vehicle model), undergoes mathematical transformation by the modeling module, iterative solution by the optimization engine, and finally outputs a set of visualized production solutions for decision-makers by the decision support module. The detailed process of this method is as follows: Figure 1 As shown, the connections between various modules, such as the production problem modeling module, the multi-objective optimization engine, and the interactive decision support module, are clearly demonstrated.

[0023] 1. Production Problem Modeling Module This module is responsible for abstracting the complex production scheduling problem in the physical world into a structured mathematical model that can be processed by algorithms.

[0024] 1.1 Obtaining Production Data The production data includes process lists for various vehicle models. Each process list for a particular vehicle model records the sequential dependencies of various processes and the time required for each process.

[0025] 1.2 Encoding of decision variables (genotype) The total number of process types m for all vehicle models is allocated to n workstations (or assembly islands) to obtain a workshop process allocation scheme. For ease of algorithm processing, the workshop process allocation scheme is encoded as a one-dimensional integer array, also known as a "chromosome" or "genotype", with each process being a gene segment.

[0026] In this process, if a certain vehicle model only involves some of the processes, then when calculating its own load, although the combined scheme includes processes that it does not involve, its time consumption will not be calculated. Therefore, the balancing of this algorithm can also take into account the impact of the designed process combination on the different processes required by different vehicle models.

[0027] Encoding structure: The index of each one-dimensional integer array represents a unique process number (e.g., from 0 to m - 1). The value at that index position represents the workstation number to which the process is assigned, i.e., the workshop number (e.g., from 0 to n - 1).

[0028] This direct and compact encoding method has high computational efficiency and can be seamlessly integrated with standard operators such as crossover and mutation in genetic algorithms, laying the foundation for subsequent global search.

[0029] Table 1. Indices and values ​​at the indexes of the one-dimensional integer arrays formed in practical applications. Individual definition: A complete one-dimensional integer array of length m (e.g., [0,6,8,...,11]) constitutes a complete process allocation scheme and is the basic unit for evolutionary algorithms to operate and optimize, i.e., an individual.

[0030] Since m represents the total number of processes for all vehicle models, there may be cases where a certain vehicle model lacks process i. Because the goal of this invention is to design a single solution that can cover load balancing for all vehicle models, all m processes will be included in the calculation. Taking vehicle model A as an example, processes 5 and 20 in Table 1 are jointly assigned to workshop 9. If a certain process is missing for a particular vehicle model, the time consumed for that process is set to 0.

[0031] Table 2 Time consumed by each vehicle model Reference Figure 5 Tables 1 and 2 show the different time consumption of different car models in different workshops (workstations) under the same design scheme, due to the different time consumption of the processes involved. The scheme designed by the method of this invention can balance the workshop time for each car model. In addition, the first column of Table 2 is the allocation result of the processes in different workshops (workstations) in the index table shown in Table 1.

[0032] 1.3. Construction of Multi-Objective Functions (Representational) This step transforms the macro-level business objective of "workload balancing" into a precise, quantifiable mathematical function.

[0033] Load balancing quantification: For a single vehicle model, its load balancing across all n workstations is quantified using the mean squared error (MSE). The calculation formula is as follows: (1) in, This model is the first The total working hours on each workstation (obtained by summing the working hours of all relevant processes allocated to that workstation). This is the average working hours of this vehicle model across all n workstations. The smaller the MSE value, the closer the load of each workstation is to the average level, meaning the load is more balanced.

[0034] Unlike existing technologies that weight and sum or select one of the load balancing indices for different vehicle models, this invention defines the load balancing degree (MSE) of each vehicle model (e.g., CarA, CarB, CarC) as an independent objective function that needs to be minimized simultaneously. Therefore, for a given allocation scheme (an individual entity), its performance is no longer evaluated by a scalar value, but by an objective vector. To evaluate, for example: (2) The goal of optimization is to simultaneously minimize all components of this vector. This fundamental shift in problem modeling expands the solution space of the optimization problem from one dimension to a multidimensional performance surface. This modeling paradigm preserves the inherent complexity and multidimensional trade-offs of the problem, providing a logical prerequisite for discovering Pareto fronts. In short, one of the key innovations of this invention lies not in the specific algorithmic components used, but in constructing the mathematical problem itself in a completely new way, thereby enabling known algorithmic components to produce strategically valuable outputs.

[0035] 1.3. Constraint Handling To explore the algorithmic mechanisms in subsequent chapters in a concrete and in-depth manner, an illustrative case study is constructed that runs throughout the entire text. Suppose an assembly line needs to produce three different configurations of car models in a single production batch, with their specific attributes and assembly processes as follows: Model A (Luxury Sedan): Requires a special feature—a sunroof. It is painted blue, and the overall assembly time is longer.

[0036] Model B (Standard SUV): No special optional parts. It is painted red, and the overall assembly time is moderate.

[0037] Model C (Basic Sedan): No sunroof. It is painted blue and has a shorter overall assembly time.

[0038] Table 3 Vehicle Assembly Process and Constraint Definitions Table 3 clearly illustrates the complexity of the problem. First, there are strict precedence constraints. For example, engine installation (Op2) for all models must follow chassis preparation (Op1). More importantly, model A has a longer constraint chain: its roof liner installation (Op4a) must follow sunroof installation (Op3a), which in turn depends on engine installation (Op2). This dependency is a "hard constraint" that genetic algorithms are prone to violating during crossover and mutation operations. Second, the attributes of different models are directly related to the optimization objective. Models A and C share "blue" paint, while model B is "red," which forms the basis of color switching costs. Furthermore, due to the additional sunroof installation process (Op3a), model A's total task time at a specific workstation is significantly higher than that of models B and C, posing a challenge to workload balancing.

[0039] In the population initialization phase of the algorithm, this invention ensures that the generated initial solutions satisfy these dependencies through methods such as topological sorting. After crossover and mutation operations, a "detection and repair" mechanism is introduced: First, the program needs to access a clearly defined list of constraints, such as the (Op3a, Op4a) pair extracted from Table 1, indicating that Op3a must precede Op4a. Then, starting from the first position of the sequence, the algorithm checks each task one by one, verifying the constraints of its predecessor tasks. Once a conflict is detected, the violating task is removed from its current position and inserted into the first valid position in the sequence, typically defined as immediately following the last task among all its predecessor tasks, thus ensuring the feasibility of all solutions throughout the evolutionary process.

[0040] 2. Multi-objective optimization engine This module is the core computational unit of the algorithm, responsible for solving the multi-objective optimization problem defined by the modeling module. This invention preferably employs an efficient multi-objective evolutionary algorithm, such as the Non-dominated Sorting Genetic Algorithm II (NSGA-II). This algorithm works collaboratively through two core mechanisms to balance the convergence (approaching the true Pareto front) and diversity (uniform distribution on the front) of the solution set.

[0041] The model is solved using a genetic algorithm based on constrained multi-objective optimization, including the following steps: S101, initialize the maximum number of iterations Gmax, the population size P, the current iteration number t, and the solution set Pt; The maximum number of iterations is set to 1000, the population size is set to 100, the current number of iterations is set to 1, and the solution set P1 is initialized. S102, if the current iteration number t is less than Gmax, proceed to S103; otherwise, proceed to S104; S103, search to find the non-dominated set FNDS of all feasible solutions in solution set Pt; for all individuals in solution set Pt, sort the feasible solutions by non-dominated order according to the evaluation function, and find the non-dominated individuals in all feasible solutions in solution set; Among them, a feasible solution refers to an individual in the solution set that satisfies all constraints; Core Mechanism 1: Fast Non-Dominated Sort In multi-objective optimization, it is not possible to simply compare a single numerical value to determine the superiority of two solutions. Therefore, Pareto dominance is used to determine the dominance relationship between two solutions.

[0042] Domination means that if all the objective solutions of a feasible individual are not inferior to all the objective solutions of another individual, and the feasible individual is superior to the other individual in at least one objective, then the individual dominates the other individual. Non-dominance means that if there is no situation where one individual dominates another individual, and one individual is inferior to another individual in at least one objective and the other individual is inferior to one individual in at least one objective, then the relationship between the two individuals is said to be non-dominant. like Figure 2 As shown. If there is no dominance relationship between solution A and solution B (for example, A is superior to B in objective 1, but B is superior to A in objective 2), then they are said to be mutually non-dominant, as... Figure 3 As shown.

[0043] The specific steps are as follows: Step 1.1. Generate the t-th generation population with a population size of M; Step 1.2. Evaluate individuals, calculate the objective value of the objective function for each individual, and check whether they meet all constraints; Step 1.3. Determine feasibility: Select individuals from the t-th generation population that satisfy all constraints; these individuals are called feasible solutions. Step 1.4. Perform feasible solution selection, crossover, and mutation; The process includes: selecting parent individuals of size M from the current population using a binary tournament selection method to construct a mating pool. For any selected parent pair, a crossover probability of 90% determines whether the processes within the parent pair cross over. If crossover occurs, an empty offspring individual is created, and the corresponding gene segments (coding fragments) of the respective workshops from the parent pair are exchanged to generate a new offspring individual. For processes that fail to be inherited during crossover, they are randomly assigned to any workshop in the offspring. Each selected individual has a 10% probability of triggering a mutation operation, randomly selecting two processes from that individual and swapping their assigned workshops. After crossover and mutation, the offspring population is obtained. The detection and repair mechanism in step 1.3 above is used to verify the offspring population to ensure the feasibility of solutions within the offspring population.

[0044] like Figure 6 As shown, from a pair of parent workshop process allocation schemes, randomly select identical workshops and swap processes (the selected parent fragments are highlighted in red) to obtain the resulting child workshop process combination scheme, as shown in the third column box. If the same process is inherited by both workshops, as shown... Figure 6 Processes 4, 15, and 18 are marked as duplicate processes. These processes are recorded as duplicate tasks, and in subsequent processing, only one workshop inheriting these processes is randomly selected. The duplicate processes are then retained in the selected workshop. Processes 2, 12, and 14 failed to complete inheritance during parent generation crossover because they were not selected. After a repair mechanism, one allocation scheme containing the duplicate processes is retained, and the missing processes are randomly assigned to workshops 2, 8, and 10, resulting in the crossover offspring.

[0045] This crossover strategy is designed because MSE and the time consumption of each workshop are strongly correlated. Therefore, when crossovering parent encoding segments, all processes contained in each workshop are selected for crossover, which can largely preserve the good workshop process allocation scheme. At the same time, the random handling of duplicate and missing processes after crossover also allows the algorithm to effectively escape local optima.

[0046] Step 1.5. Merge the parent population and the newly generated offspring population.

[0047] Step 1.6. Perform non-dominated sorting of feasible solutions: Compare each feasible individual in the feasible solution population with all other feasible individuals in the t-th generation population; Step 1.7. Identify non-dominated individuals: During the comparison process, record the number of times each feasible individual is dominated by other individuals in the t-th generation population; those individuals with no domination counts are considered non-dominated. Step 1.8. Construct the Pareto front: Form a set of all non-dominated feasible individuals, which represents the Pareto front of the current population.

[0048] In multi-objective optimization, the quality of a solution cannot be simply compared using a single numerical value as in single-objective optimization. Therefore, a mechanism is needed to "rank" all solutions in the population. Fast non-dominated sorting efficiently divides the entire population into different ranks or fronts. Front 1: The best solutions in the population, not dominated by any other solutions. In this problem, non-domination manifests as the MSE values ​​of the three vehicle types being mutually non-dominated. Because in multi-objective optimization, there are many solutions, each with MSE values ​​for the three vehicle types, and these solutions are mutually non-dominated due to the varying quality of their three objective values. These solutions constitute the current Pareto optimal solution set. Front 2: Solutions second only to the first front, dominated only by solutions in the first front. Front 3, 4, ...: and so on. This ranking result is the primary basis for subsequent selection operations; solutions with higher ranks (lower rank values) are given priority for retention.

[0049] In step 1.4, a binary tournament selection method is used to select parent individuals of population size M from the current population. Specifically, rank is prioritized, followed by crowding distance, as a comparator to select the mating pool from the population. Similarly, in step 1.1, the parent population of generation t+1... (Size N) is also obtained using a binary tournament selection method, t>1. Rank priority means selecting individuals sequentially from the ranked frontiers. This includes: fully accepting all individuals from Front 1, then all individuals from Front 2, and so on. Assuming the algorithm has already placed all individuals from the first i-1 frontiers into the new parent population, there are still vacancies not enough to fully place them into the next frontier. The number of individuals needs to be determined from this non-dominant frontier. Selecting a subset of individuals. Crowding distance is then used as the selection criterion. Crowding distance measures the "sparseness" around a solution within the same frontier, serving as a diversity preservation mechanism.

[0050] Objective: Solutions with large crowding distances are located in a relatively "open" region on the Pareto front, representing a unique trade-off strategy. To maintain the diversity of the solution set, the algorithm prioritizes these "isolated" solutions.

[0051] Based on the crowding distance from the non-dominant frontier Select a subset of individuals as the parent population for generation t+1. The process for individuals includes: Each solution in the current frontier has three objective values ​​(MSE_A, MSE_B, MSE_C). Perform the following operations on each objective value: ① Sorting: Based on the number N of objective values ​​for each solution in the current frontier, sort the non-dominated frontiers sequentially according to each objective value (such as one of MSE_A, MSE_B, MSE_C). All solutions are sorted in ascending order to obtain the MSE sorting sequence of all N objective values ​​(vehicle models). Consider the following two different process allocation schemes: F(Solution 1) = (MSE_A = 0.3), F(Solution 2) = (MSE_A = 0.6), F(Solution 3) = (MSE_A = 0.5), F(Solution 4) = (MSE_A = 0.8). The objective function values ​​of these solutions are compared, and the solutions are sorted in ascending order, resulting in F(Solution 1), F(Solution 3), F(Solution 2), and F(Solution 4).

[0052] ② Boundary point handling: Set the crowding distance between the first and last solutions after sorting (i.e. the best and worst performing solutions on the objective) to infinity (∞) to ensure that they are preferentially retained in the selection, thereby maintaining the extensibility of the Pareto front.

[0053] ③ Intermediate point calculation: For the remaining solutions j in each sorted sequence, the crowding distance is calculated and accumulated by the difference between its left and right neighbors on the objective function, and then normalized.

[0054] The specific formula for calculating congestion distance is as follows: (3) In the formula, This represents the target value of the next adjacent solution of solution j in the sorted sequence on this target; This represents the objective value of the previous adjacent solution of solution j on this objective; This represents the maximum value of the frontier on the target z; This represents the minimum value of the frontier on the target z, where Z = 1, 2, ..., N-1, N, and in this embodiment, N = 3.

[0055] In the summation formula, the congestion distance for the first target MSE_A is calculated when Z=1, the congestion distance for the second target MSE_B is calculated when Z=2, and the congestion distance for the third target MSE_C is calculated when Z=3. Finally, the total congestion distance is summed to obtain the total congestion distance for this solution, which is then used for selection.

[0056] ④ Selection: Sort the calculated crowding distances of each individual from largest to smallest. From this sorted list, select individuals one by one from front to back (i.e., starting with the individual with the largest crowding distance) and fill them into the new population until the number of individuals in the new population reaches the preset size.

[0057] S104. The loop terminates after reaching the preset maximum number of iterations, and selects all individuals with the first frontier (Rank 1) from the final population to form the final Pareto front solution set.

[0058] 3. Interactive Decision Support Module This module serves as a bridge connecting algorithm output with actual business decisions, transforming the abstract data generated by the optimization engine into actionable business intelligence that is meaningful to decision-makers.

[0059] 3.1 Output Generation and Visualization The algorithm's final output is not a single solution, but a set containing dozens or even hundreds of Pareto optimal solutions. To facilitate understanding, the algorithm presents this solution set to the user in a graphical format, such as... Figure 4 As shown in the diagram, in a three-dimensional scatter plot, each point represents a feasible production line allocation scheme, with its coordinate axes corresponding to the MSE values ​​of the three vehicle models. Decision-makers can intuitively understand the trade-offs between the load balance of different vehicle models by observing the shape and distribution of this Pareto front.

[0060] 3.2 Pareto Front Shape and Characteristic Analysis Because this is a combinatorial optimization problem, its decision variables are discrete, not continuous. Its mapping in the objective space—the Pareto front—will also consist of a series of isolated points, rather than a smooth, continuous curve. The structure of the entire surface is typical of the Pareto front in multi-objective minimization problems. This shape intuitively reveals the profound trade-offs between the three objectives. Any attempt to achieve better performance on one objective (i.e., moving towards one coordinate plane) inevitably leads to performance degradation on at least one other objective (i.e., moving away from another coordinate plane). For example, to find a solution with extremely low MSE_A, one must accept higher values ​​for MSE_B or MSE_C. Thus, it establishes a crucial bridge connecting optimization algorithms with practical production decisions.

[0061] 3.3. Multi-criteria decision making (MCDM) Faced with numerous Pareto optimal solutions, decision-makers need a method to select the most suitable one or more solutions based on current specific business needs. This invention integrates a multi-criteria decision-making module to achieve this function.

[0062] Decision-making mechanism: After the optimization calculation is completed, this module allows users to input their preferred weights for the balance of different vehicle models based on the actual production priority. For example, when pursuing balanced development, the weight can be set to 1:1:1; when prioritizing the smooth production of a new model, a personalized weight such as 5:4:1 can be set.

[0063] Recommended solution: After receiving the weights input by the user, the algorithm will iterate through every solution on the Pareto front and calculate its weighted total score according to the following formula: (4) in, , , These are the weights set by the user. The algorithm then sorts all solutions by their scores and presents the solution with the lowest score (i.e., the smallest weighted MSE) as the optimal recommendation to the user, while also providing several alternative solutions with the highest scores. This feature greatly improves the practicality and operability of the optimization results.

[0064] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of this invention. It should be understood that the above descriptions are merely specific embodiments of this invention and are not intended to limit the scope of protection of this invention. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. An evolutionary computation-based flexible manufacturing process structuring procedure multi-objective optimization method, characterized by, The method comprises the following steps: Step S1, production problem modeling: obtaining production data, the production data comprising process lists, process man-hours and sequence dependency relationships among processes of multiple vehicle models, distributing all types of processes of all vehicle models to n workstations to obtain a process distribution scheme; encoding the process distribution scheme into an individual, the individual being a one-dimensional integer array, wherein the array index represents a unique process number, and the value of the array at the corresponding index position represents the workstation number to which the process is distributed; defining an independent workstation load balancing degree objective function for each vehicle model to calculate a target value, and merging into a target vector, each component in the target vector corresponding to the target value of each vehicle model; Step S2, multi-objective optimization solving: minimizing all components in the target vector as the objective, using a multi-objective evolutionary algorithm to iteratively optimize the population, and generating a Pareto optimal solution set; the multi-objective evolutionary algorithm uses a non-dominated sorting genetic algorithm NSGA-II, the process of which comprises calculating the target value of each individual for each vehicle model based on the multi-objective value of each individual, obtaining fast non-dominated sorting and diversity preservation based on crowding distance, selecting individuals from the population to construct a mating pool in the order of rank priority and crowding distance, generating offspring through crossover and mutation, merging the offspring with the parent generation, comparing the merged individuals with the individuals in the last generation population to perform non-dominated sorting, and selecting individuals from the sorted individuals in the order of rank priority and crowding distance to fill the new generation population; repeating the iteration until the number of iterations or the convergence condition is reached, and outputting the Pareto optimal solution set; Step S3, interactive decision support: visualizing the Pareto optimal solution set; receiving user input of preference weights for load balancing degrees of different vehicle models, calculating a weighted total score of each Pareto optimal solution based on the weights, and outputting a recommended scheme according to the weighted total score.

2. The method of claim 1, wherein, The workstation load balancing degree objective function is quantified by using mean square error MSE, and for a single vehicle model, the MSE calculation formula is: in, This model is the first The total working hours on each workstation (obtained by summing the working hours of all relevant processes allocated to that workstation). It is the average working hours of this model across all n workstations, where n is the total number of workstations.

3. The method of claim 1, wherein, In steps S1 and S2, a detection and repair mechanism is introduced to process individuals that may violate process dependency constraints in all individuals and offspring generated by crossover and mutation, to ensure that all solutions meet the feasibility.

4. The method of claim 3, wherein, The detection and repair mechanism comprises: defining a list of sequence dependency relationships among processes; traversing the individual code sequence to verify the antecedent constraints of each process; if it is found that the current process violates its antecedent constraints, it is reinserted into the first legal position after the last executed process of all its antecedent processes.

5. The method of claim 1, wherein, The specific steps of selecting individuals from the population or non-dominated sorting in the order of rank priority and crowding distance comprise: Step S2.1, evaluating the target value of each individual in the population for each vehicle model based on all components, and screening feasible solutions that meet all constraint conditions; Step S2.2, performing non-dominated comparison on the feasible solutions, and dividing the individuals that are not dominated by any other solution into the first non-dominated level; Step S2.3, sequentially identifying subsequent non-dominated levels until all feasible solutions are layered. Step S2.4, selecting all individuals in the first i-1 non-dominated levels in order from high to low according to the non-dominated level, if the i-th non-dominated level is overstaffed, truncating by crowding distance from large to small; The truncating by crowding distance from large to small comprises the following steps: According to the number N of objective values of each individual in the i-th non-dominated level, the all individuals in the i-th non-dominated level are arranged in ascending order according to each objective value respectively, and N sorting sequences of the objective values are obtained respectively; The crowding distance of the individual that performs best and worst in each sorting sequence is set to infinity. The crowding distance of the rest of the individuals j in each sorting sequence is calculated, and the formula of the crowding distance is: wherein denotes the target value of the next neighboring individual of the target value of the z-component of individual j in the target vector; denotes the target value of the previous neighboring individual of the target value of the z-component of individual j in the target vector; denotes the maximum value of the z-component of the i-th non-dominated level in the target vector; denotes the minimum value of the z-component of the i-th non-dominated level in the target vector, Z = 1, 2,..., N-1, N; The calculated crowding distance of each individual is sorted from large to small, and the individuals are selected from the largest crowding distance of the individual in the sorted list.

6. The method of claim 1, wherein, The generating offspring through crossover and mutation comprises the following steps: for any pair of parents selected, a crossover probability is determined to determine whether the processes in the pair of parents are crossed, if the crossover is performed, an empty offspring individual is created, the processes corresponding to the respective workshops of the pair of parents are exchanged to generate a new offspring individual; if the same process is inherited by two workshops, only one of the two workshops that inherits the process is randomly selected, and the repeated process is retained in the selected workshop; finally, each selected individual triggers a mutation operation with a set probability, two processes are randomly selected from the individual, and the allocated workshops are exchanged.

7. The method of claim 1, wherein, The visualization adopts a three-dimensional scatter plot, three coordinate axes represent the MSE values of three different vehicle models respectively, and each data point represents a feasible production line allocation scheme.

8. The method of claim 1, wherein, The weighted score is calculated by the following formula: wherein, , , is a user-set weight; 、 、 are mean square error values for the corresponding vehicle model, respectively.

9. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor implements the method of any one of claims 1-8 when executing the program.

10. A computer-readable storage medium having stored thereon a computer program, characterized in that, The program is executed by the processor to implement the method of any one of claims 1-8. The program is executed by the processor to implement the method of any one of claims 1-8.

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