Multi-operation-area collaborative pre-scheduling method for wafer manufacturing system

Abstract

The invention relates to a multi-operation-area collaborative pre-scheduling method for a wafer manufacturing system, and the method comprises the following steps: constructing a constrained multi-target mathematical model, taking the minimization of total tardiness and total production cost as a target function, and fully considering the influence of multi-time-window constraints; and designing a double-population evolutionary algorithm, wherein the double-population evolutionary algorithm comprises a normal population responsible for exploring diversity of a solution space and a convergence population of a solution space. In the evolutionary process, the two populations dynamically cooperate with each other. And designing a mixed agent auxiliary model based on the RBF and the SVM. An agent model is updated through an online learning strategy, the prediction precision of the model is improved, and it is ensured that the algorithm can explore more feasible regions; and the multi-operation-area pre-scheduling controller of the wafer manufacturing system receives the new order information, triggers algorithm execution and generates a scheduling scheme. The problem of low scheduling efficiency and solution quality in multi-target pre-scheduling of the wafer manufacturing system is solved, the convergence and uniformity of a population and the number of feasible solutions are enhanced, and the total tardiness and the total production cost are effectively balanced.

Description

Technical Field

[0001] The present invention relates to a scheduling optimization technology for a wafer manufacturing system, and in particular to a collaborative pre-scheduling method for multiple operation areas of a wafer manufacturing system. Background Art

[0002] With the rapid development of artificial intelligence technology, market demand for chips continues to rise. As a core component of the semiconductor industry, wafer manufacturing is playing an increasingly important role. The production line of a wafer manufacturing system typically includes the following work areas: oxidation, deposition, and diffusion; photolithography; etching; ion implantation; and polishing. This process is extremely complex and time-consuming, characterized by diverse product routes, hundreds of process steps, non-equivalent parallel machines, and re-entrant processing. Furthermore, the multiple time window constraints imposed by the dwell time and cleaning processes when scheduling wafers across work areas complicate scheduling solutions, often requiring frequent manual intervention, which in turn leads to extended lead times and increased production costs. Therefore, researching effective collaborative pre-scheduling methods for multiple wafer work areas is crucial for improving the stability of wafer manufacturing systems, increasing production efficiency, reducing production costs, and enhancing the market competitiveness of wafer fabs.

[0003] The wafer cross-region manufacturing scheduling problem can be viewed as a constrained multi-objective optimization problem (CMOP). Its complexity leads to a large number of infeasible regions in the solution space. In recent years, evolutionary algorithms have been widely used to solve such problems, but balancing convergence and diversity while ensuring the feasibility of the solution set remains a challenge. Effective constraint handling techniques (CHTs) are key, and current approaches mainly include feasibility methods, penalty function methods, multi-objective methods, and collaborative optimization methods. Collaborative optimization methods, by decomposing the CMOP into subproblems and collaboratively solving them using multiple CHTs, have demonstrated advantages in balancing population feasibility, convergence, and diversity. However, these methods are limited in exploiting infeasible solutions with good objective values, potentially causing the population to become trapped in local infeasible regions. Furthermore, agent-assisted evolutionary algorithms (SAEAs) can obtain a more optimal Pareto solution set within a limited time by replacing expensive fitness evaluations. However, these methods are difficult to effectively screen using single regression or classification models. Summary of the Invention

[0004] In view of the problem that existing research and methods are difficult to balance the convergence and diversity of solution sets while ensuring the feasibility of solution sets in multi-objective pre-scheduling of wafer manufacturing systems, resulting in low scheduling efficiency and solution quality, a multi-operation zone collaborative pre-scheduling method for wafer manufacturing systems is proposed. A hybrid agent-assisted dual-population evolutionary algorithm is used to solve the cross-zone scheduling problem of wafer manufacturing, aiming to overcome the shortcomings of existing methods and improve scheduling efficiency and solution quality.

[0005] The technical solution of the present invention is:

[0006] A method for collaborative pre-scheduling of multiple work areas in a wafer manufacturing system comprises the following steps:

[0007] Step S1, wafer multi-operation area pre-scheduling model construction and data processing: the wafer multi-operation area pre-scheduling production process is modeled as a hybrid flow shop multi-objective scheduling problem with complex constraints;

[0008] Step S2, dual-population co-evolution algorithm encoding, decoding and evolution operator: the first chromosome segment: uses a process-based integer encoding method to represent the process priority of the wafer batch Lot; the second chromosome segment: uses a real number encoding method for the machine selection part; for the integer-coded chromosomes in the first part, a sequence-based crossover operator OX4 is used; for the real-coded chromosomes in the second part, a multi-point crossover operator is used to perform crossover operations at multiple positions; for the process priority chromosomes, a random point exchange mutation operator is used; for the machine selection chromosomes, a non-uniform mutation operator is used;

[0009] Step S3, hybrid agent-assisted model construction and data preprocessing: Before model construction, the coded data of the population individuals are preprocessed; by combining the RBF and SVM models, the RBF predicts the CV value and objective function in the early stage of algorithm evolution, and the SVM directly determines the feasibility of the individual in the later stage of algorithm evolution;

[0010] Step S4, dual-population algorithm framework construction and individual constraint processing method: construct two populations with different constraint processing methods for co-evolution, the two populations are a normal population and a convergent population, the normal population uses the constraint dominance criterion CDP method to process constrained individuals, and the convergent population uses an adaptive penalty function method to add a penalty term to the objective function; during the algorithm evolution process, when the proportion of non-dominated solutions in the convergent population exceeds a certain proportion, the normal population and the convergent population are merged for co-evolution;

[0011] Step S5: Hybrid agent-assisted model prediction and online learning during algorithm evolution: The hybrid agent-assisted model gradually receives and processes training samples, i.e., individuals in the population, and updates the model based on these samples. The model is updated using online learning, and convergence and diversity indicators are introduced to measure the convergence and distribution benefits of candidate individuals, respectively.

[0012] S6. Deployment and execution of the wafer multi-operation area pre-scheduling algorithm: In the dual-population co-evolutionary algorithm module based on the hybrid agent-assisted model, key algorithm parameters are set, and the agent model-assisted algorithm is used to generate a scheduling plan. During the algorithm execution process, its operating status is monitored in real time, and relevant data and scheduling results are recorded; the results of the algorithm execution are collected and analyzed, and its scheduling effect in different operation areas is evaluated; based on the analysis results, the algorithm parameters or strategies are adjusted; the wafer manufacturing system multi-operation area pre-scheduling controller receives new order information, triggers the algorithm execution, and generates a scheduling plan;

[0013] Furthermore, step S1 is specifically as follows:

[0014] The wafer multi-operation area pre-scheduling production process is modeled as a hybrid flow shop multi-objective scheduling problem with complex constraints. It applies to I wafer lots of K products, which are processed in W operation areas with a total number of machines, M. Each operation area contains several non-equivalent parallel machines, each capable of processing a predetermined number of processes. By assigning processing machines to each process in different operation areas for each wafer lot and determining the start time, the objective function, including total tardiness and total production cost, is optimized.

[0015] Data processing: Collect relevant data from machines in each operating area, including the machine's processing capacity, process type, production preparation time, and historical production records; clean and organize the collected data, remove redundant and erroneous data, ensure data accuracy and consistency, and perform outlier detection and missing data filling.

[0016] Furthermore, step S2 is specifically as follows:

[0017] The decision variables describing the processing priority order and processing machine selection for each process in different work areas are encoded and decoded into a specific scheduling plan using a dual-population co-evolutionary algorithm for wafer multi-work area pre-scheduling. The dual-population co-evolutionary algorithm uses a two-stage encoding and decoding scheme.

[0018] The encoding is as follows: The first chromosome: based on process O i,w Integer encoding method, where i represents wafer batch, w represents work area, O i,w Represents the processing steps of batch i in work area w, and represents the process priority of wafer batch Lot; the value of each gene bit corresponds to the priority order of each process that needs to be sorted in the pre-scheduling process, and its length is equal to the total number of processes, which is N1; the second chromosome: uses real number encoding, the range of real numbers is 0 to 1, accurate to one decimal place, and is used to represent process O i,w The length of the processing machines allocated in the work area w is also equal to the length of the process O i,w Total quantity N1;

[0019] Decoding: The first - segment chromosome decoding: Each gene bit represents the priority of the process. By reading the value of each gene bit, the execution order of each process is determined; The second - segment chromosome decoding: First, according to the alternative machine set M i,w for process O Oi,w , M Oi,w is the set of all machines that can be selected for process O i,w in work area w. The interval [0, 1] is evenly split into |M Oi,w | sub - intervals, where |M Oi,w | represents the number of the alternative machine set M i,w for process O Oi,w . Each sub - interval corresponds to a machine m. Then, according to the value of the gene bit in the second - segment chromosome, determine the sub - interval it falls into, and then select the corresponding machine m from the alternative machine set M Oi,w ;

[0020]

[0021] The evolutionary operators include a crossover operator and a mutation operator, which perform crossover and mutation operations on the chromosomes:

[0022] Crossover operator: For the chromosome representing the process priority in the first segment, the order - based crossover operator OX4 is adopted; The specific operation process is as follows: First, input the first - segment chromosomes of two parent chromosomes, randomly select two crossover positions on the chromosome, denoted as positions p1 and p2, and satisfy p1 < p2; Then, directly copy the gene segment between p1 and p2 in the first parent chromosome to the corresponding position of the offspring chromosome; Next, select the genes that have not been included in the offspring chromosome in turn from the second parent chromosome according to the order of gene appearance, and fill them into the vacant positions of the offspring chromosome, ensuring that the genes are not repeated and maintaining the relative order of the processes; Finally, output two new offspring chromosomes;

[0023] Mutation operator: For the process - priority chromosome, the random - point exchange mutation operator is adopted; The specific operation is as follows: First, input the first - part chromosomes of two parent chromosomes, randomly select two exchange positions on the chromosome, denoted as positions z1 and z2; Then, exchange the positions of the two parent chromosomes at z1 and z2; Finally, output two new offspring chromosomes.

[0024] Furthermore, step S3 is specifically as follows:

[0025] Predict the fitness value or feasibility of the population individuals by constructing a hybrid surrogate - assisted model; Adopt a hybrid surrogate - assisted model that combines a radial basis function (RBF) network and a support vector machine (SVM); The specific construction process of the surrogate - assisted model is as follows:

[0026] Step 3.1) Initialize the population at the beginning of the algorithm and collect the decision variables, objective function values, and constraint violation degrees (CV values) of the individuals in the initial population;

[0027] Step 3.2) Preprocess the collected data and organize them into a training data set for constructing the initial RBF regression model; Data preprocessing: Before model construction, the chromosome gene sequences of the population individuals are preprocessed; the preprocessing steps include data standardization and feature extraction;

[0028] Step 3.3) In the early stage of evolution, construct the RBF evaluation individual CV value and objective function value; first use the radial basis function in RBF where r = ‖x i -c i ‖, x i is the input sample, c i is the center of the basis function; then according to the N sample training set, use the formula Solve the weight λ, F=[f1,f2,...,f N ] T is the actual fitness vector of the training set, T is the transpose; finally, select As a polynomial model, where h T is the weighting coefficient, x is the input sample; using the basis function The weight λ and polynomial p(x) are used to construct the RBF regression model to predict the individual CV value and objective function value; the prediction formula is as follows: Indicates the CV value and objective function value of the predicted individual;

[0029] Step 3.4) Construct an SVM model to directly classify whether an individual is feasible. The classification formula is: c(x) = sgn(W T φ(x)+w0), where φ(x) is the mapping function from the input space to the high-dimensional feature space, W∈R^D represents the weight vector, w0∈R is the bias, W and w0 are two parameters to be optimized, where R is a set of real numbers and D is the feature dimension; the sign function sgn(x) will return +1 or -1 respectively; first extract the evaluated individuals from the database, including their decision variables and feasibility labels; then select the RBF kernel function K(x) of the SVM i ,x)=exp(-γ‖x i -x‖), γ is the kernel parameter, where x i Represents the training sample and establishes the SVM optimization problem to minimize the objective function where ξ iis a slack variable, C is a hyperparameter; finally, the training data set is used to solve the optimal weight vector W and bias w0;

[0030] Step 3.5) During the evolution process, the proportion of feasible solutions in the converged population is monitored in real time; when the proportion of feasible solutions exceeds a set threshold, the agent-assisted model switches from using only the RBF model to using the RBF and SVM classification model.

[0031] Furthermore, step S4 is specifically as follows:

[0032] Step 4.1) Initialize the algorithm parameters and generate the initial population;

[0033] Step 4.2) Perform crossover and mutation on the population Pop1 selected using the CDP method to produce offspring Off1; perform crossover and mutation on the offspring population Pop2 selected using the adaptive penalty function method to produce offspring Off2;

[0034] Step 4.3) Merge Pop1, Off1, and Off2 to update the population Pop1; merge Pop2 and Off2 to update the population Pop2;

[0035] Step 4.4) Use the RBF+SVM proxy-assisted model to predict the individual CV value, objective function, and feasibility; determine the proportion of non-dominated individuals in Pop2. If it exceeds the set proportion, merge Pop1 and Pop2 to generate the offspring Off3;

[0036] Step 4.5) Use the CDP method to select Pop1 and update the population Pop1; use the adaptive penalty function method to select Pop2 and update the population Pop2;

[0037] Step 4.6) If the termination condition is met, output the population Pop1; otherwise, return to step 4.2 to continue iteration.

[0038] Furthermore, step S5 is specifically as follows:

[0039] In the initial exploration phase, the offspring selection criteria include first evaluating its constraint violation value (CV) and then evaluating its objective function value; constructing an RBF model to predict the performance of individuals; selectively extracting a subset of individuals for functional evaluation through the RBF model, and storing these individuals in the database; in the late convergence phase, when the proportion of non-dominant solutions in the converged population reaches a high level, constructing an SVM model to directly classify the viability of individuals; the SVM model identifies individuals with high viability through classification operations; at the same time, the RBF model further evaluates individuals predicted to be viable; all sampled individuals are subject to true function evaluation to update the surrogate model; this process continues until all evaluations are completed;

[0040] The model is updated using online learning. First, the population evaluated by the agent-assisted model is normalized, and the optimal value of each objective function of the parent and child generations in the population is used as the ideal point x ideal ; For individual x in the offspring, calculate its difference from all individuals x in the parent population p The maximum value of these distances is used as the diversity index of the individual x* and added to the diversity solution set S div , x* satisfies dus(x*); calculate the individual x* and the ideal point x ideal The Euclidean distance is used as the convergence index of the individual, and the convergence solution set S is added cov , and finally merge S div and S cov , perform non-dominated sorting on all individuals based on diversity and convergence indicators, and add the optimal solution set to the solution set to be evaluated S pop ; According to the original objective function, S pop The individuals in are evaluated for true fitness to update the proxy model; where dus(x*) is as follows:

[0041]

[0042] Where p is the number of individuals in the population and N is the number of population.

[0043] Furthermore, the objective function in step 1 is as follows:

[0044] Min f1=TT;Min f2=TPC (1)

[0045]

[0046] Formula (1) indicates that the objective function is to minimize the total batch delay (TT) and total production cost (TPC); Formulas (2) and (3) indicate the specific calculation steps of TT and TPC; where C i represents the completion time of Lot i; d i Indicates the delivery time of the i-th Lot; I indicates the total number of Lots; CT w,m represents the unit time processing cost of machine m in workspace w; X i,w,m Is a decision variable, indicating that if process O i,w If it is arranged to be processed on machine m, it is 1, otherwise it is 0; i,w,m Indicates process O i,w Processing time; SE m Y represents the unit time cost of machine m when switching the processing route Route; k,g.m It is an auxiliary variable, indicating that if the processing route k on machine m is changed to g; ST k,g,mrepresents the setup time of machine m switching between production routes k and g; ET i,t Indicates the portion of the processing time of the i-th Lot that exceeds the time window constraint t; V i,t It is an auxiliary variable, indicating that if the i-th Lot violates the time window constraint t, it is 1; otherwise, it is 0; RC i,t represents the unit time rework cost of Lot i that violates the time window constraint t.

[0047] Furthermore, when selecting offspring in step 4, the normal population and the convergent population give priority to feasible individuals, followed by individuals with lower CV values, and finally individuals with better objective function values; when the proportion of non-dominated solutions in the convergent population exceeds 50%, the normal population and the convergent population can be merged for co-evolution; in the adaptive penalty function method, the penalty term Pe is initialized to the individual with the largest constraint violation in the population, and Pe is updated to Pe×β during the evolution process.

[0048] Furthermore, in step 5, the surrogate model RBF receives individuals in the unfused stage of the two populations to predict their constraint violation values, i.e., CV values ​​and objective function values. When feasible individuals in the population accumulate to a certain level, i.e., after the two populations are fused, the surrogate model SVM is trained to directly predict the feasibility of the individuals. When the model is updated using online learning, continuous optimization and accuracy of the model are ensured.

[0049] Furthermore, the deployment of the pre-scheduling algorithm in step 6 involves setting the parameters of the dual-population collaborative algorithm; these parameters include: population size Popsize, crossover probability Pc, mutation probability Pm and attenuation factor β; the orthogonal experimental method is used to conduct parameter experiments, and the setting range of each parameter is: Popsize∈{100,120,150}, Pc∈{0.75,0.8,0.85}, Pm∈{0.2,0.25,0.3}, β∈{0.8,0.7,0.6}; the average value of the comprehensive indicator HV is used as the final response size, and the final determined parameters are: Popsize=150, Pc=0.8, Pm=0.25, β=0.2; the termination condition of the algorithm is set to the number of real evaluations of the agent-assisted model exceeding 500 times.

[0050] The beneficial effects of the present invention are:

[0051] This paper abstracts the multi-objective scheduling problem of wafer manufacturing across multiple regions under multiple time window constraints into a hybrid flow shop scheduling optimization problem under complex constraints. To this end, a constrained multi-objective mathematical model is established with the optimization objectives of minimizing total tardiness and total production cost. A dual-population evolutionary algorithm based on a hybrid agent model is designed to solve the problem. First, a constrained multi-objective mathematical model is constructed with the objectives of minimizing total tardiness and total production cost, fully accounting for the impact of multiple time window constraints. Second, a dual-population evolutionary algorithm is designed, consisting of a normal population and a convergent population. The normal population is responsible for exploring the diversity of the solution space, while the convergent population focuses on the convergence of solutions. During the evolutionary process, these two populations dynamically collaborate to balance convergence, diversity, and feasibility. To avoid multiple, costly evaluations of infeasible solutions and accelerate the algorithmic evolutionary process, a hybrid agent-assisted model based on RBF and SVM is designed. An online learning strategy is used to update the agent model, improving its prediction accuracy and ensuring that the algorithm explores a wider range of feasible regions. The designed algorithm enhances the convergence, uniformity and number of feasible solutions of the population, and effectively balances the total delay and total production cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 This is a flow chart of a multi-operation area collaborative pre-scheduling method for a wafer manufacturing system based on an agent-assisted model dual-population evolutionary algorithm of the present invention;

[0053] Figure 2 It is the chromosome encoding and decoding diagram of the dual-population co-evolutionary algorithm of the present invention;

[0054] Figure 3 It is the chromosome crossover variation graph of the dual-population co-evolution algorithm of the present invention;

[0055] Figure 4 This is a framework diagram of the hybrid agent-assisted model of the present invention;

[0056] Figure 5 It is a flow chart of the dual-population co-evolution algorithm of the present invention;

[0057] Figure 6 This is a flow chart of online learning of the hybrid agent-assisted model of the present invention;

[0058] Figure 7 This is a structural block diagram of the deployment and implementation of a multi-operation area collaborative pre-scheduling method for a wafer manufacturing system based on an agent-assisted model dual-population evolutionary algorithm of the present invention. DETAILED DESCRIPTION

[0059] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0060] The present invention aims at the problem of collaborative pre-scheduling of multiple work areas in semiconductor wafer manufacturing systems under complex production processes and multiple time window constraints, and designs a scheduling algorithm based on a hybrid agent model and a dual-population evolutionary algorithm to solve the problem that feasible scheduling solutions are difficult to generate and have long calculation time. The main steps included are as follows: establishing a mathematical model for collaborative pre-scheduling of multiple work areas in wafer manufacturing with the goal of minimizing total delay and total production cost; designing a dual-population co-evolutionary framework, which effectively balances the feasibility, convergence and diversity of the solution set by co-evolving normal populations and convergent populations using different constraint processing techniques; designing the chromosome encoding and decoding method and evolutionary operator of the dual-population co-evolutionary algorithm for crossover mutation; designing a support vector regression (SVM) and radial basis function (RBF) agent model based on online learning, where the SVM agent is used to distinguish the feasibility of individuals in the population, and the RBF agent is used to predict the adaptability of individuals, thereby efficiently exploring the optimal solution set within the feasible region. Through the above steps, the present invention provides an efficient multi-work area collaborative pre-scheduling solution, which significantly improves the scheduling efficiency and economic benefits of the wafer manufacturing system.

[0061] A method for collaborative pre-scheduling of multiple work areas in a wafer manufacturing system, such as Figure 1 As shown, the following steps are included:

[0062] Step S1: Build a wafer multi-operation area pre-scheduling model and process data: The wafer multi-operation area pre-scheduling production process can be modeled as a multi-objective scheduling problem for a hybrid flow shop with complex constraints. By rationally assigning processing machines to each process in different operation areas for each wafer batch and determining their start times, the goal is to achieve multi-objective optimization of total tardiness and total production cost.

[0063] Step S2, dual population co-evolution algorithm encoding and decoding and evolution operator: Figure 2 ,3, the first chromosome: uses the process-based integer encoding method to represent the process priority of the wafer lot (Lot). The second chromosome: for the machine selection part, uses the real number encoding method. The real number range is 0 to 1, accurate to one decimal place, and is used to represent process O i,w The length of the assigned processing machine is equal to the number of possible machine selections, N1. For the integer-coded chromosomes in the first part, the order-based crossover operator OX4 is used; for the real-coded chromosomes in the second part, the multi-point crossover operator is used, performing crossover operations at multiple locations. For the process priority chromosomes, the random point exchange mutation operator is used; for the machine selection chromosomes, the non-uniform mutation operator is used.

[0064] Step S3: Hybrid agent assisted model building and data preprocessing: Figure 4As shown in the figure, before model construction, the encoded data of the population individuals is preprocessed. This preprocessing step includes data standardization and feature extraction to ensure input data quality and model training efficiency. By combining the RBF and SVM models, the RBF predicts the CV value and objective function in the early stages of algorithm evolution, while the SVM directly determines the feasibility of individuals in the later stages of algorithm evolution.

[0065] Step S4, dual population algorithm framework construction and individual constraint processing method: Figure 5 As shown in the figure, two populations with different constraint handling methods are constructed for co-evolution: a normal population and a convergent population. The normal population uses the CDP (Constraint Domination Principle) to handle constrained individuals, while the convergent population uses an adaptive penalty function method, adding a penalty term to the objective function. During the algorithm evolution process, when the proportion of non-dominated solutions in the convergent population exceeds a certain ratio, the normal and convergent populations are merged for co-evolution.

[0066] S5. Hybrid agent model prediction and online learning in algorithm evolution: Figure 6 As shown in the figure: The agent model gradually receives and processes training samples (population individuals) and updates the model based on these samples. The model is updated using online learning, taking into account the population convergence and diversity. Convergence and diversity indicators are introduced to measure the convergence and distribution benefits of candidate individuals respectively. First, the population evaluated by the agent-assisted model is normalized, and the optimal value of each objective function of the parent and offspring in the population is taken as the ideal point x ideal ; For individual x in the offspring, calculate its difference from all individuals x in the parent population p The maximum value of these distances is used as the diversity index of the individual x*, and is added to the diversity solution set D, x* satisfies Dus(x*); calculate the individual x* and the ideal point x ideal The Euclidean distance is used as the convergence indicator of the individual and added to the convergence solution set C. Finally, all individuals are non-dominated and sorted, and the optimal solution set is added to the solution set to be evaluated E. The individuals in E are evaluated for their true fitness according to the original objective function to update the proxy model.

[0067]

[0068] S6. Deployment and execution of wafer multi-operation area pre-scheduling algorithm: Figure 7As shown in the figure: In the dual-population co-evolution algorithm module based on the hybrid agent-assisted model, the key algorithm parameters are first set to ensure the effectiveness and stability of the algorithm. The algorithm is assisted by the agent model to generate a scheduling plan to improve the adaptability and response speed of the algorithm. During the execution of the algorithm, its operating status is monitored in real time, and relevant data and scheduling results are recorded for subsequent analysis and optimization. The execution of the algorithm is terminated when the number of real evaluations exceeds 500 times to ensure sufficient scheduling optimization. The results of the algorithm execution are collected and analyzed to evaluate its scheduling effect in different work areas. Based on the analysis results, the algorithm parameters or strategies are adjusted to further improve scheduling efficiency and production benefits. In terms of system interaction, the multi-work area pre-scheduling controller of the wafer manufacturing system receives new order information (such as Lot, machine, route, etc.), triggers the algorithm execution and generates a scheduling plan.

[0069] The specific process is as follows:

[0070] Step S1 is specifically as follows:

[0071] The wafer multi-operation zone pre-scheduling production process is modeled as a multi-objective scheduling problem for a hybrid flow shop with complex constraints. It applies to I wafer batches (Lots) of K products, which are processed in W operation zones with a total number of machines, M. Each operation zone contains several non-equivalent parallel machines (referred to as "machines"), each of which can process a predetermined number of processes. Machine processing is non-preemptive, meaning that once a machine begins processing a batch of wafers, the entire process cannot be interrupted. Furthermore, when a machine switches to processing different process types, production preparation time is incurred, the length of which depends on the required process type. To optimize the production process, the present invention aims to achieve multi-objective optimization of total delay and total production cost by rationally allocating processing machines and determining their start times for each process in different operation zones for each wafer batch. At the same time, wafer batches must avoid violating multiple time window constraints during processing to ensure the efficiency and economy of the production process.

[0072] Data processing: Relevant data is collected from machines in each operation area, including machine processing capabilities, process types, production preparation times, and historical production records. The collected data is cleaned and organized to remove redundant and erroneous data, ensuring accuracy and consistency. Outlier detection and missing data filling are also performed.

[0073] Step S2 is specifically as follows:

[0074] The decision variables (i.e., variables used to describe the processing priority order and processing machine selection of each process in different work areas) are encoded for the dual-population co-evolutionary algorithm for wafer multi-work area pre-scheduling and decoded into specific scheduling plans, such as Figure 2The core of the process is to determine the processing priority order in different work areas for each process and to select the appropriate processing machine for each process.

[0075] The dual-population co-evolutionary algorithm adopts a two-stage encoding and decoding scheme;

[0076] The encoding is as follows: The first chromosome: based on process O i,w Integer encoding method (where i represents wafer batch, w represents operation area, O i,w represents the processing steps of batch i in work area w), and represents the process priority of wafer batch (Lot). The value of each gene bit corresponds to the priority order of each process that needs to be sorted in the pre-scheduling process. Its length is equal to the total number of processes, which is N1. The second chromosome: uses real number encoding, the range of real numbers is 0 to 1, accurate to one decimal place, and is used to represent process O. i,w The length of the processing machines allocated in the work area w is also equal to the length of the process O i,w Total quantity N1.

[0077] Decoding: First segment chromosome decoding: Each gene bit represents the priority of the process. By reading the value of each gene bit, the execution order of each process is determined. Second segment chromosome decoding: First, according to process O in the first segment chromosome, i,w The set of candidate machines M Oi,w , M Oi,w For process O i,w The set of all machines that can be selected in the work area w splits the interval [0,1] equally into |M Oi,w | subintervals, where |M Oi,w | indicates process O i,w The set of candidate machines M Oi,w Each subinterval corresponds to a machine m. Then, according to the value of the gene bit in the second segment of the chromosome, determine the subinterval it falls into, and then select the candidate machine set M Oi,w Select the corresponding machine m.

[0078]

[0079] In the present invention, the evolution operator (including the crossover operator and the mutation operator) is the key mechanism for performing crossover and mutation operations on chromosomes. Selecting a suitable evolution operator is crucial to the evolution process of the population.

[0080] Crossover operator: For the chromosome representing the operation priority in the first segment, the order-based crossover operator OX4 is adopted. This crossover operator can effectively retain the excellent characteristics of the parental chromosomes while introducing new gene combinations to promote the diversity of the population. The specific operation process is as follows: First, input the first segments of two parental chromosomes, randomly select two crossover positions on the chromosome, denoted as positions p1 and p2, and satisfy p1 < p2. Then, directly copy the gene segment between p1 and p2 in the first parental chromosome to the corresponding position of the offspring chromosome. Next, sequentially select the genes not included in the offspring chromosome from the second parental chromosome according to the order of gene appearance, and fill them into the vacant positions of the offspring chromosome, ensuring that the genes are not repeated and maintaining the relative order of the operations. Finally, output two new offspring chromosomes. As Figure 3 shown, for the operation priority chromosome part, the segments intercepted from the two parental chromosomes are (1,1); (3,2,1) respectively, which are directly inherited to the same positions of the offspring chromosomes. The genes at the remaining positions of Offspring 1 (offspring 1) are filled in sequence from (2,3,3,2) after removing the segment (1,1) from Parent 2 (parent 2). The genes at the remaining positions of Offspring 2 (offspring 2) are filled in sequence from (3,2,1) after removing the segment (3,2,1) from Parent 1 (parent 1). For the second part of the real-number encoded chromosome, a multi-point crossover operator is adopted. This operator further increases the diversity and adaptability of the chromosome by performing crossover operations at multiple positions. The specific operation process is as follows: First, input the second segments of two parental chromosomes, and select a positive integer n (n = L / 3) less than the chromosome length L as the number of crossover points. Then, randomly select n non-repeating crossover point positions [p1, p2,..., p n within the chromosome position range (1 to L), and sort these positions in ascending order. Next, for each crossover point position, exchange the gene values of the parental chromosomes at this position to generate two offspring chromosomes. Finally, output two new offspring chromosomes. As Figure 3 shown, for the machine selection chromosome part, randomly select the 2nd and 5th genes, and directly inherit the gene values (0.7, 0.6); (0.5, 0.3) to the offspring, and the genes at the remaining positions are filled in by the genes of the other parent at the same positions.

[0081] Mutation operator: For the operation priority chromosome, a random point exchange mutation operator is adopted. This operator introduces new priority combinations by randomly exchanging the gene positions in the chromosome. The specific operation is as follows: First, input the first parts of two parental chromosomes, randomly select two exchange positions on the chromosome, denoted as positions z1 and z2. Then, exchange the positions of the two parental chromosomes at z1 and z2. Finally, output two new offspring chromosomes. As Figure 3As shown: The 3rd and 6th positions of the chromosome of Parent3 (parent 3) are randomly selected for exchange. For machine selection of chromosomes, a non-uniform mutation operator is used. This operator introduces a certain degree of randomness in the mutation process, and gradually adjusts the gene value to explore a better solution space. The specific operation is as follows: First, input the second part of the chromosomes of the two parent chromosomes, and randomly select n positions on the chromosome (n=L / 2). Then, for the gene position that needs to be mutated, a number is randomly generated in the interval [0,1] to replace the original gene value. Finally, two new offspring chromosomes are output. As shown Figure 3 As shown, the genes at positions 1, 2, and 6 of Parent 3 (offspring 3) (0.4, 0.7, 0.2) were randomly selected and replaced with (0.9, 0.2, 0.8).

[0082] Step S3 is specifically as follows:

[0083] By constructing a hybrid agent-assisted model to predict the fitness value or feasibility of individuals in the population, the number of expensive evaluations can be reduced, thereby exploring a wider range of solution spaces within a limited time. The present invention adopts a hybrid agent-assisted model, such as Figure 4 As shown in Figure 1, the advantages of radial basis function (RBF) networks and support vector machines (SVM) are combined. By combining RBF and SVM, the hybrid agent-assisted model can provide more accurate prediction results when dealing with complex multi-objective optimization problems. The specific construction process of the agent-assisted model is as follows:

[0084] 1) At the beginning of the algorithm, the population is initialized and the decision variables, objective function values ​​and constraint violation degrees (CV values) of individuals in the initial population are collected.

[0085] 2) Preprocess the collected data and organize it into a training dataset for constructing the initial RBF regression model. Data preprocessing: Before model construction, the chromosomal gene sequences of the population individuals are preprocessed. The preprocessing steps include data standardization and feature extraction to ensure the quality of the input data and the efficiency of model training. Data standardization: Normalize the input data to a uniform scale to eliminate dimensional differences between different features. Feature extraction: By analyzing the encoded features of the population individuals, the most critical features for predicting fitness values ​​are extracted.

[0086] 3) In the early stage of evolution, construct the RBF evaluation individual CV value and objective function value. First, the radial basis function in RBF is selected where r = ‖x i -c i ‖, x i is the input sample, c i is the center of the basis function. Then, based on the N sample training set, use the formula Solve the weight λ, F=[f1,f2,...,f N ] T is the actual fitness vector of the training set, and T is the transpose. As a polynomial model, where h T is the weighting coefficient, and x is the input sample. Using the basis function The weight λ and polynomial p(x) are used to construct the RBF regression model to predict the individual CV value and the objective function value. The prediction formula is as follows: Represents the CV value and objective function value of the predicted individual.

[0087] 4) As the evolution process progresses, the number of feasible solutions increases. The SVM model is constructed to directly classify whether the individual is feasible. The classification formula is: c(x) = sgn(W T φ(x)+w0), where φ(x) is the mapping function from the input space to the high-dimensional feature space, W∈R^D represents the weight vector, w0∈R is the bias, W and w0 are two parameters to be optimized, where R is a set of real numbers and D is the feature dimension. The symbolic function sgn(x) will return +1 or -1 respectively. First, the evaluated individuals are extracted from the database, including their decision variables and feasibility labels (+1 means feasible, -1 means infeasible). Then the RBF kernel function K(x) of the SVM is selected. i ,x)=exp(-γ‖x i -x‖), γ is the kernel parameter, where x i Represents the training sample and establishes the SVM optimization problem to minimize the objective function where ξ i is a slack variable and C is a hyperparameter. Finally, the optimal weight vector W and bias w0 are solved using the training data set.

[0088] 5) During the evolution process, the proportion of feasible solutions in the converged population is monitored in real time. When the proportion of feasible solutions exceeds 50%, the agent-assisted model switches from using only the RBF model to using the RBF and SVM classification model.

[0089] Step S4 is specifically as follows:

[0090] like Figure 5As shown, two populations with different constraint handling methods are constructed for coevolution: a normal population and a convergent population. The normal population uses the Constraint Domination Principle (CDP) to handle constrained individuals, while the convergent population uses an adaptive penalty function method. During the algorithm evolution, when the proportion of non-dominated solutions in the convergent population exceeds a certain percentage, the normal and convergent populations are merged for coevolution. The specific steps are as follows: 1) Initialize the algorithm parameters to generate the initial population. 2) Perform crossover and mutation on the population Pop1, which uses the CDP method to select offspring, to produce offspring Off1. Perform crossover and mutation on the population Pop2, which uses the adaptive penalty function method to select offspring, to produce offspring Off2. 3) Merge Pop1, Off1, and Off2 to update Pop1. Merge Pop2 and Off2 to update Pop2. 4) Use the RBF+SVM surrogate-assisted model to predict individual CV values, objective functions, and feasibility. Determine the proportion of non-dominated individuals in Pop2. If it exceeds 50%, merge Pop1 and Pop2 to generate offspring Off3. 5) Use the CDP method to select Pop1 and update Pop1. Use the adaptive penalty function method to select Pop2 and update Pop2. 6) If the termination condition is met, output Pop1; otherwise, return to step 2 and continue iteration.

[0091] In step 4, when selecting offspring, the normal and convergent populations prioritize feasible individuals, followed by individuals with lower CV values, and finally individuals with better objective function values. When the proportion of non-dominated solutions in the convergent population exceeds 50%, the normal and convergent populations can be merged for coevolution. In the adaptive penalty function method, the penalty term Pe is initialized to the individual with the largest constraint violation in the population and is updated during evolution to Pe × β.

[0092] Step S5 is specifically as follows:

[0093] The surrogate model gradually receives and processes training samples (population individuals) and updates the model based on these samples. During the initial exploration phase, the normal and convergent populations are prone to producing infeasible solutions. The offspring selection criteria in this phase include first evaluating their constraint violation values ​​(CV values) and then evaluating their objective function values. An RBF model is constructed to predict individual performance. Using the RBF model, a subset of individuals is selectively sampled for functional evaluation and stored in a database for future reference. In the late convergence phase, when the proportion of non-dominated solutions in the convergent population reaches a high level, a large number of feasible individuals accumulate in the database. An SVM model is constructed to directly classify individuals by their viability. The SVM model identifies individuals with high viability through classification. Simultaneously, the RBF model further evaluates individuals predicted to be feasible to determine their quality. All sampled individuals undergo true function evaluation to update the surrogate model. This process continues until all evaluations are complete.

[0094] like Figure 6 As shown, the model is updated using online learning. Considering the balance between the convergence and diversity of the final normal population, convergence and diversity indicators are introduced to measure the convergence and distribution benefits of candidate individuals respectively. First, the population evaluated by the agent-assisted model is normalized, and the optimal value of each objective function of the parent and offspring in the population is taken as the ideal point x ideal ; For individual x in the offspring, calculate its difference from all individuals x in the parent population p The maximum value of these distances is used as the diversity index of the individual x* and added to the diversity solution set S div , x* satisfies dus(x*); calculate the individual x* and the ideal point x ideal The Euclidean distance is used as the convergence index of the individual, and the convergence solution set S is added cov , and finally merge S div and S cov , perform non-dominated sorting on all individuals based on diversity and convergence indicators, and add the optimal solution set to the solution set to be evaluated S pop After the above steps, S is pop The individuals in are evaluated for their true fitness to update the proxy model. Where dus(x*) is as follows:

[0095]

[0096] Among them, p is the number of individuals in the population and N is the number of populations.

[0097] In step 5, the surrogate RBF model receives individuals before the two populations converge and predicts their constraint violation values ​​(CVs) and objective function values. Once the number of feasible individuals in the population reaches a certain level, i.e., after the two populations converge, the surrogate SVM model is trained to directly predict individual feasibility. This ensures continuous optimization and accuracy when the model is updated using online learning.

[0098] Step S6 is specifically as follows:

[0099] Key algorithm parameters were set: population size (Popsize), crossover probability (Pc), mutation probability (Pm), and decay factor (β). The agent-assisted model update strategy was set to online learning. After the algorithm was deployed, its operational status was monitored in real time. Algorithm execution was terminated when the number of real evaluations exceeded 500. During execution, the algorithm's operational data and scheduling results were recorded in real time to facilitate subsequent analysis and optimization. The algorithm's execution results were collected and analyzed to evaluate its scheduling effectiveness in different work areas. Based on the analysis, the algorithm parameters or strategies were adjusted to further improve scheduling efficiency and production benefits.

[0100] Among them, the objective function of step 1 is as follows:

[0101] Min f1=TT;Min f2=TPC (1)

[0102]

[0103] Formula (1) indicates that the objective function is to minimize the total batch delay (TT) and total production cost (TPC). Formulas (2) and (3) indicate the specific calculation steps of TT and TPC. i represents the completion time of Lot i; d i Indicates the delivery time of the i-th Lot; I indicates the total number of Lots; CT w,m represents the unit time processing cost of machine m in workspace w; X i,w,m Is a decision variable, indicating that if process O i,w If it is arranged to be processed on machine m, it is 1, otherwise it is 0; i,w,m Indicates process O i,w Processing time; SE m Y represents the unit time cost of machine m when switching the processing route (Route); k,g.m It is an auxiliary variable, indicating that if the processing route k on machine m is changed to g; ST k,g,m represents the setup time of machine m switching between production routes k and g; ET i,t Indicates the portion of the processing time of the i-th Lot that exceeds the time window constraint t; V i,tIt is an auxiliary variable, indicating that if the i-th Lot violates the time window constraint t, it is 1; otherwise, it is 0; RC i,t represents the unit time rework cost of Lot i that violates the time window constraint t.

[0104] The deployment of the pre-scheduling algorithm in step 6 primarily involves setting the parameters of the dual-population collaborative algorithm. These key parameters include: population size (Popsize), crossover probability (Pc), mutation probability (Pm), and decay factor (β). Orthogonal experimental methods were used for parameter experiments, with the parameter settings ranging from: Popsize∈{100,120,150}, Pc∈{0.75,0.8,0.85}, Pm∈{0.2,0.25,0.3}, and β∈{0.8,0.7,0.6}. The average value of the comprehensive indicator HV was used as the final response size, and the final parameters were determined to be: Popsize=150, Pc=0.8, Pm=0.25, and β=0.2. The algorithm's termination condition was set to require more than 500 true evaluations of the agent-assisted model to ensure the algorithm's efficiency and accuracy within a limited timeframe.

[0105] The above-described embodiment merely represents one embodiment of the present invention. While the description is relatively specific and detailed, it should not be construed as limiting the scope of the patent. It should be noted that a person skilled in the art would be able to make various modifications and improvements without departing from the spirit of the present invention, and these modifications and improvements fall within the scope of protection of the present invention. Therefore, the scope of protection of the patent for this invention shall be determined by the appended claims.

Claims

1. A method for collaborative pre-scheduling of multiple work areas in a wafer manufacturing system, characterized in that: The following steps are involved: Step S1, wafer multi-operation area pre-scheduling model construction and data processing: the wafer multi-operation area pre-scheduling production process is modeled as a hybrid flow shop multi-objective scheduling problem with complex constraints; Step S2, dual-population co-evolution algorithm encoding, decoding and evolution operator: the first chromosome segment: uses a process-based integer encoding method to represent the process priority of the wafer batch Lot; the second chromosome segment: uses a real number encoding method for the machine selection part; for the integer-coded chromosomes in the first part, a sequence-based crossover operator OX4 is used; for the real-coded chromosomes in the second part, a multi-point crossover operator is used to perform crossover operations at multiple positions; for the process priority chromosomes, a random point exchange mutation operator is used; for the machine selection chromosomes, a non-uniform mutation operator is used; Step S3, hybrid agent-assisted model construction and data preprocessing: Before model construction, the coded data of the population individuals are preprocessed; by combining the RBF and SVM models, the RBF predicts the CV value and objective function in the early stage of algorithm evolution, and the SVM directly determines the feasibility of the individual in the later stage of algorithm evolution; Step S4, dual-population algorithm framework construction and individual constraint processing method: construct two populations with different constraint processing methods for co-evolution, the two populations are a normal population and a convergent population. The normal population uses the constraint dominance criterion CDP method to process constrained individuals, and the convergent population uses an adaptive penalty function method to add a penalty term to the objective function; During the algorithm evolution process, when the proportion of non-dominated solutions in the convergent population exceeds a certain proportion, the normal population and the convergent population are merged for co-evolution; Step S5: Hybrid agent-assisted model prediction and online learning during algorithm evolution: The hybrid agent-assisted model gradually receives and processes training samples, i.e., individuals in the population, and updates the model based on these samples. The model is updated using online learning, and convergence and diversity indicators are introduced to measure the convergence and distribution benefits of candidate individuals, respectively. S6. Deployment and execution of the wafer multi-operation zone pre-scheduling algorithm: In the dual-population co-evolutionary algorithm module based on the hybrid agent-assisted model, set key algorithm parameters, generate scheduling solutions through the agent-assisted algorithm, monitor the algorithm's operating status in real time during execution, and record relevant data and scheduling results; collect and analyze the results of the algorithm execution, and evaluate its scheduling effect in different operation zones; adjust the algorithm parameters or strategies based on the analysis results; The multi-operation area pre-scheduling controller of the wafer manufacturing system receives new order information, triggers algorithm execution and generates a scheduling plan.

2. The method for collaborative pre-scheduling of multiple work areas in a wafer manufacturing system according to claim 1, wherein: Step S1 is specifically as follows: Model the pre-scheduling production process of wafers with multiple working areas as a multi-objective scheduling problem of a hybrid flow shop with complex constraints; applicable to I wafer lots of K products, these lots are processed in W working areas, and the total number of machines is M; each working area contains several non-equivalent parallel machines, and the process types that each machine can process are pre-determined. By allocating processing machines and determining the start time for each process of each wafer lot in different working areas, the objective functions, including the total tardiness and the total production cost, are optimized. Data processing: Collect relevant data from the machines in each working area, including the processing capacity, process type, production preparation time, and historical production records of the machines; clean and sort the collected data, remove redundant and incorrect data, ensure the accuracy and consistency of the data, and also perform outlier detection and missing data filling.

3. The method for collaborative pre-scheduling of multiple work areas in a wafer manufacturing system according to claim 1, wherein: Step S2 is specifically as follows: Encode the decision variables used to describe the processing priority order and processing machine selection of each process in different working areas, and use a two-population co-evolution algorithm for pre-scheduling of wafers with multiple working areas, and decode it into a specific scheduling plan; the two-population co-evolution algorithm adopts a two-stage encoding and decoding scheme. The encoding is as follows: The first chromosome: based on process O i,w Integer encoding method, where i represents wafer batch, w represents work area, O i,w Represents the processing steps of batch i in work area w, and represents the process priority of wafer batch Lot; the value of each gene bit corresponds to the priority order of each process that needs to be sorted in the pre-scheduling process, and its length is equal to the total number of processes, which is N1; the second chromosome: uses real number encoding, the range of real numbers is 0 to 1, accurate to one decimal place, and is used to represent process O i,w The length of the processing machines allocated in the work area w is also equal to the length of the process O i,w Total quantity N1; Decoding: The first chromosome decoding: Each gene bit represents the priority of the process. By reading the value of each gene bit, the execution order of each process is determined; The second chromosome decoding: First, according to the process O in the first chromosome i,w The set of candidate machines M Oi,w , M Oi,w For process O i,w The set of all machines that can be selected in the work area w splits the interval [0,1] equally into |M Oi,w | subintervals, where |M Oi,w | indicates process O i,w The set of candidate machines M Oi,w Each subinterval corresponds to a machine m; then, according to the value of the gene bit in the second segment of the chromosome, determine the subinterval it falls into, and then select the candidate machine set M Oi,w Select the corresponding machine m; The evolutionary operators include a crossover operator and a mutation operator, which perform crossover and mutation operations on the chromosomes: Crossover operator: For the first segment of the chromosome representing the process priority, use the order-based crossover operator OX4; the specific operation process is as follows: First, input the first segments of the chromosomes of two parent chromosomes, randomly select two crossover positions on the chromosome, denoted as positions p1 and p2, and satisfy p1 < p2; then directly copy the gene segment between p1 and p2 in the first parent chromosome to the corresponding position of the offspring chromosome; then, in the order of gene appearance, sequentially select the genes not included in the offspring chromosome from the second parent chromosome and fill them into the vacant positions of the offspring chromosome, ensuring that the genes are not repeated and the relative order of the processes is maintained; finally, output two new offspring chromosomes. Mutation operator: For the process priority chromosome, use the random point exchange mutation operator; the specific operation is as follows: First, input the first parts of the chromosomes of two parent chromosomes, randomly select two exchange positions on the chromosome, denoted as positions z1 and z2; then exchange the positions of the two parent chromosomes at z1 and z2; finally, output two new offspring chromosomes.

4. The method for collaborative pre-scheduling of multiple work areas in a wafer manufacturing system according to claim 1, wherein: Step S3 is specifically as follows: Predict the fitness value or feasibility of the population individuals by constructing a hybrid surrogate-assisted model; use a hybrid surrogate-assisted model that combines a radial basis function (RBF) network and a support vector machine (SVM); the specific construction process of the surrogate-assisted model is as follows: Step 3.1) At the beginning of the algorithm, initialize the population, and collect the decision variables, objective function values, and constraint violation degrees (i.e., CV values) of the individuals in the initial population. Step 3.2) Preprocess the collected data and organize it into a training data set for constructing an initial RBF regression model; data preprocessing: Before model construction, preprocess the chromosome gene sequences of the population individuals. The preprocessing steps include data normalization and feature extraction. Step 3.3) In the early stage of evolution, construct the RBF evaluation individual CV value and objective function value; first use the radial basis function in RBF where r = ‖x i -c i ‖,x i is the input sample, c i is the center of the basis function; then according to the N sample training set, use the formula (i,j=1,2…,N) solve the weight λ, F=[f1,f2,...,f N ] T is the actual fitness vector of the training set, T is the transpose; finally, select As a polynomial model, where h T is the weighting coefficient, x is the input sample; using the basis function The weight λ and polynomial p(x) are used to construct the RBF regression model to predict the individual CV value and objective function value; the prediction formula is as follows: Represents the CV value and objective function value of the predicted individual; Step 3.4) Construct an SVM model to directly classify whether an individual is feasible. The classification formula is: c(x) = sgn(W T φ(x)+w0), where φ(x) is the mapping function from the input space to the high-dimensional feature space, W∈R^D represents the weight vector, w0∈R is the bias, W and w0 are two parameters to be optimized, where R is a set of real numbers and D is the feature dimension; the sign function sgn(x) will return +1 or -1 respectively; first extract the evaluated individuals from the database, including their decision variables and feasibility labels; then select the RBF kernel function K(x) of the SVM i ,x)=exp(-γ‖x i -x‖), γ is the kernel parameter, where x i Represents the training sample and establishes the SVM optimization problem to minimize the objective function where ξ i is a slack variable, C is a hyperparameter; finally, the training data set is used to solve the optimal weight vector W and bias w0; Step 3.5) During the evolution process, the proportion of feasible solutions in the converged population is monitored in real time; when the proportion of feasible solutions exceeds a set threshold, the agent-assisted model switches from using only the RBF model to using the RBF and SVM classification model.

5. The method for collaborative pre-scheduling of multiple work areas in a wafer manufacturing system according to claim 1, wherein: Step S4 is specifically as follows: Step 4.1) Initialize the algorithm parameters and generate the initial population; Step 4.2) Perform crossover and mutation on the population Pop1 selected using the CDP method to produce offspring Off1; perform crossover and mutation on the offspring population Pop2 selected using the adaptive penalty function method to produce offspring Off2; Step 4.3) Merge Pop1, Off1, and Off2 to update the population Pop1; merge Pop2 and Off2 to update the population Pop2; Step 4.4) Use the RBF+SVM proxy-assisted model to predict the individual CV value, objective function, and feasibility; determine the proportion of non-dominated individuals in Pop2. If it exceeds the set proportion, merge Pop1 and Pop2 to generate the offspring Off3; Step 4.5) Use the CDP method to select Pop1 and update the population Pop1; use the adaptive penalty function method to select Pop2 and update the population Pop2; Step 4.6) If the termination condition is met, output the population Pop1; otherwise, return to step 4.2 to continue iteration.

6. The method for collaborative pre-scheduling of multiple work areas in a wafer manufacturing system according to claim 1, wherein: Step S5 is specifically as follows: In the initial exploration phase, the offspring selection criteria include first evaluating its constraint violation value (CV) and then evaluating its objective function value; constructing an RBF model to predict the performance of individuals; selectively extracting a subset of individuals for functional evaluation through the RBF model, and storing these individuals in the database; in the late convergence phase, when the proportion of non-dominant solutions in the converged population reaches a high level, constructing an SVM model to directly classify the viability of individuals; the SVM model identifies individuals with high viability through classification operations; at the same time, the RBF model further evaluates individuals predicted to be viable; all sampled individuals are subject to true function evaluation to update the surrogate model; this process continues until all evaluations are completed; The model is updated using online learning. First, the population evaluated by the agent-assisted model is normalized, and the optimal value of each objective function of the parent and child generations in the population is used as the ideal point x ideal ; For individual x in the offspring, calculate its difference from all individuals x in the parent population p The maximum value of these distances is used as the diversity index of the individual x* and added to the diversity solution set S div , x* satisfies dus(x*); calculate the individual x* and the ideal point x ideal The Euclidean distance is used as the convergence index of the individual, and the convergence solution set S is added cov , and finally merge S div and S cov , perform non-dominated sorting on all individuals based on diversity and convergence indicators, and add the optimal solution set to the solution set to be evaluated S pop ; According to the original objective function, S pop The individuals in are evaluated for true fitness to update the proxy model; where dus(x*) is as follows: Among them, p is the number of individuals in the population and N is the population size.

7. The method for collaborative pre-scheduling of multiple work areas in a wafer manufacturing system according to claim 2, wherein: The objective function in step 1 is as follows: Min f1=TT;Min f2=TPC (1) Formula (1) indicates that the objective function is to minimize the total batch delay TT and the total production cost TPC; Formulas (2) and (3) indicate the specific calculation steps of TT and TPC; where C i represents the completion time of Lot i; d i Indicates the delivery time of the i-th Lot; I indicates the total number of Lots; CT w,m represents the unit time processing cost of machine m in workspace w; X i,w,m Is a decision variable, indicating that if process O i,w If it is arranged to be processed on machine m, it is 1, otherwise it is 0; i,w,m Indicates process O i,w Processing time; SE m Y represents the unit time cost of machine m when switching the processing route Route; k,g.m It is an auxiliary variable, indicating that if the processing route k on machine m is changed to g; ST k,g,m represents the setup time of machine m switching between production routes k and g; ET i,t Indicates the portion of the processing time of the i-th Lot that exceeds the time window constraint t; V i,t It is an auxiliary variable, indicating that if the i-th Lot violates the time window constraint t, it is 1; otherwise, it is 0; RC i,t represents the unit time rework cost of Lot i that violates the time window constraint t.

8. The method for collaborative pre-scheduling of multiple work areas in a wafer manufacturing system according to claim 1, wherein: When selecting offspring, the normal population and the convergent population in step 4 give priority to feasible individuals, followed by individuals with lower CV values, and finally individuals with better objective function values. When the proportion of non-dominated solutions in the convergent population exceeds 50%, the normal population and the convergent population can be merged for co-evolution. In the adaptive penalty function method, the penalty term Pe is initialized to the individual with the largest constraint violation in the population, and Pe is updated to Pe×β during the evolution process.

9. The method for collaborative pre-scheduling of multiple work areas in a wafer manufacturing system according to claim 1, wherein: In step 5, the surrogate model RBF receives individuals in the unfused stage of the two populations to predict their constraint violation values, i.e., CV values, and objective function values. When feasible individuals in the population accumulate to a certain level, i.e., after the two populations are fused, the surrogate model SVM is trained to directly predict the feasibility of individuals. When the model is updated using online learning, continuous optimization and accuracy of the model are ensured.

10. The method for collaborative pre-scheduling of multiple work areas in a wafer manufacturing system according to claim 1, wherein: The deployment of the pre-scheduling algorithm in step 6 involves setting the parameters of the dual-population collaborative algorithm; these parameters include: population size Popsize, crossover probability Pc, mutation probability Pm, and attenuation factor β; the orthogonal experimental method is used to conduct parameter experiments, and the setting range of each parameter is: Popsize∈{100,120,150}, Pc∈{0.75,0.8,0.85}, Pm∈{0.2,0.25,0.3}, β∈{0.8,0.7,0.6}; the average value of the comprehensive indicator HV is used as the final response size, and the final parameters are determined as: Popsize=150, Pc=0.8, Pm=0.25, β=0.2; the termination condition of the algorithm is set to the number of real evaluations of the agent-assisted model exceeding 500 times.

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