Robust scheduling optimization method for hybrid flow shop under uncertain demand

Abstract

The invention provides a robust scheduling optimization method for a hybrid flow shop under an uncertain demand. The method comprises the following steps: firstly, generating a plurality of possible demand scenes through a multi-scene generation technology; then, a Kriging model is adopted to construct a proxy model used for evaluating the performance of different scheduling schemes in multiple scenes; and then, optimizing the proxy model by using a non-dominated sorting genetic algorithm II (NSGAII), and searching a scheduling scheme which is good in performance on a plurality of scenes. In the optimization process, points which are far away from existing sample points and are not dominated by the existing sample points in a Pareto solution set are selected to update the proxy model, so that the details and accuracy of the model are increased, and the global description capability of the model is improved. And finally, judging whether the global and local errors of the agent model meet preset error requirements or not through an error judgment mechanism. Through an efficient calculation model and an intelligent optimization algorithm, intelligent decision making of hybrid process workshop scheduling in an environment with uncertain requirements is realized, and scheduling efficiency and robustness are improved.

Description

Technical Field

[0001] The present invention relates to the field of information and control technology, and in particular to a hybrid flow shop robustness scheduling method under demand uncertainty. Background Art

[0002] With the rapid development of social economy and the increasing diversification of consumer preferences, the market demand for products is characterized by high uncertainty and rapid changes. This market dynamics has brought great challenges to the production scheduling of manufacturing workshops. Traditional static scheduling methods are often based on fixed production plans and stable market demand, which makes it difficult to effectively respond to frequent demand changes in actual production. Therefore, how to achieve flexibility and efficiency in production scheduling under such an uncertain demand environment has become an urgent problem to be solved in the current manufacturing industry. Manufacturing workshops need a scheduling method that can adapt to changes in market demand and quickly adjust production plans to ensure maximum production efficiency and resource utilization. .

[0003] In recent years, the rapid development of Industrial Internet of Things (IIoT) and artificial intelligence technology (AI) has provided new opportunities for intelligent decision-making in the production and processing of manufacturing workshops. Industrial Internet of Things technology realizes real-time monitoring and precise control of the production process through sensors, smart devices and big data analysis, providing rich real-time data support for the scheduling system. At the same time, artificial intelligence algorithms can mine potential rules in large amounts of data and optimize scheduling strategies. The combination of these technologies enables manufacturing workshops to respond to changes in market demand more intelligently, realize automation and intelligence of production scheduling, and improve production efficiency and product quality.

[0004] However, traditional dynamic scheduling methods still face the problems of high computational cost and insufficient robustness when dealing with mixed process shop scheduling problems under uncertain demand environments. Mixed process shop scheduling problems involve multiple processes, multiple resources, and complex production constraints. The complexity makes it difficult for traditional scheduling methods to find the optimal solution in a short time. In addition, the uncertainty of demand further increases the difficulty of scheduling. Traditional dynamic scheduling methods often find it difficult to balance scheduling robustness and adaptability while ensuring scheduling efficiency. Summary of the invention

[0005] To solve the above problems, the present invention proposes a hybrid flow shop robust scheduling method that integrates an agent model and multi-objective optimization technology, aiming to achieve intelligent decision-making on hybrid flow shop scheduling under an uncertain demand environment through an efficient computing model and intelligent optimization algorithm, thereby improving the efficiency and robustness of scheduling.

[0006] The technical solution adopted by the present invention to achieve the above-mentioned purpose is:

[0007] A hybrid flow shop robust scheduling optimization method under demand uncertainty includes the following steps:

[0008] 1) Generate multiple possible demand scenarios based on the uncertainty of different demands;

[0009] 2) Based on different demand scenarios, the Kriging model is used to build a proxy model;

[0010] 3) Solve the agent model using the non-dominated sorting genetic algorithm II, and take the obtained non-dominated solution set as the optimal solution set;

[0011] 4) From the optimal solution set, sort the distance between each point and the existing sample points from large to small, select the top N points with the closest distance and the points that are not dominated by the existing sample points, and update the optimal solution set;

[0012] 5) The proxy model is used to output a set of hybrid flow shop scheduling solutions that can maintain a high on-time delivery rate under the conditions of uncertainty in the number of workpieces, delivery dates, and arrival times.

[0013] The step 1) comprises the following steps:

[0014] 1.1) Construct uncertainty demand hypothesis;

[0015] 1.2) Generate scenarios based on demand assumptions;

[0016] 1.3) Repeat step 1.2) to generate multiple different demand scenarios and construct an input set for the hybrid flow shop scheduling problem considering demand uncertainty.

[0017] The step 1.1) comprises the following steps:

[0018] 1.1.1) Assume that the number of workpieces follows a normal distribution, and its mean and standard deviation are set based on historical data or expert experience;

[0019] 1.1.2) Assume that the arrival time follows an exponential distribution, and its parameters are set based on historical data or expert experience;

[0020] 1.1.3) The delivery date d is determined by the arrival time and the delivery urgency coefficient, specifically:

[0021] d=T+f3(k)P

[0022] Where T is the order arrival time, f3(k) is the delivery urgency coefficient that follows the Poisson distribution, and P is the total processing time of all workpiece processes.

[0023] The step 1.2) comprises the following steps:

[0024] 1.2.1) Randomly generate a specific number of workpieces according to the normal distribution of the number of workpieces;

[0025] 1.2.2) Randomly assign an arrival time to each generated workpiece according to the exponential distribution of arrival time;

[0026] 1.2.3) According to the Poisson distribution of the delivery time urgency coefficient, a urgency coefficient is randomly generated for each workpiece;

[0027] 1.2.4) Calculate the delivery date for each workpiece using the urgency factor and the total processing time of all steps of the workpiece.

[0028] The step 2) comprises the following steps:

[0029] 2.1) Define the scheduling scheme encoding format;

[0030] 2.2) Construct a proxy model based on the Kriging model, take the coded form of the scheduling plan as the input of the model, and the on-time delivery rate of orders under each demand scenario as the output of the model. Use the input and output data of known sample points to train the Kriging model, establish a mapping relationship between the scheduling plan and the on-time delivery rate, and realize rapid prediction of the performance of unknown scheduling plans.

[0031] The scheduling scheme coding form includes order code and machine code, where:

[0032] The order code is an ordered sequence, which is used to define the execution order of each order in the current scheduling plan. Each element in the sequence represents a unique identifier of an order, which is used to distinguish different orders during the scheduling process. When an order is not included in a specific scenario, the corresponding position of the order in the code sequence will be automatically skipped, and the system will then continue to execute the next order in the sequence;

[0033] The machine encoding is a two-dimensional matrix, which is used to define which machine should process each process of each order. Each row of the matrix represents an order, and each column represents a process of the order. Each element in the matrix specifies a unique identifier of the processing machine corresponding to the order and process.

[0034] In step 4), the distance between each point in the optimal solution set and the current sample set is calculated as follows:

[0035] Calculate the Euclidean distance between the current point and each sample point in the sample set;

[0036] The minimum value of all calculated distances is taken as the distance from the point to the sample set.

[0037] The step 5) is specifically as follows:

[0038] Determine whether both the global error and the local error meet the preset error requirements. If so, stop adding new data points to the sample set used to train the proxy model, and output the optimization result of the proxy model at this time as the final robust scheduling solution set; otherwise, continue to add new data points to the sample set until the error requirements are met.

[0039] The determination coefficient is used to determine the global error of the surrogate model, and the maximum relative error is used to determine the local error of the surrogate model.

[0040] The present invention has the following beneficial effects and advantages:

[0041] 1. By constructing a multi-scenario model, the present invention can fully consider the uncertainty of demand and ensure that the output scheduling solution performs well in a variety of scenarios, thereby improving the robustness of scheduling.

[0042] 2. By using the Kriging model and the NSGAII algorithm, the present invention realizes rapid prediction and optimization of the scheduling scheme, significantly improving the computational efficiency of the scheduling.

[0043] 3. By continuously updating the proxy model, the prediction accuracy of the present invention is gradually improved, ensuring that the output scheduling solution is more reliable and practical.

[0044] 4. The robust scheduling solution set proposed in the present invention can flexibly adapt to specific needs in practical applications and provide strong support for intelligent production in the manufacturing industry. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a schematic diagram of the coding form of the scheduling scheme in the present invention;

[0046] Figure 2 is a flow chart of updating a sample set in the present invention;

[0047] Figure 3 It is a flow chart of the robust scheduling optimization method in the present invention. DETAILED DESCRIPTION

[0048] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0049] like Figure 3 As shown, the specific steps of the present invention are:

[0050] Step 1: Multi-scenario generation: Set the parameters of the probability distribution of the corresponding demand based on historical data or expert experience, and then randomly generate multiple possible demand scenarios based on these distributions.

[0051] First, build scenarios based on uncertainty demand assumptions. These assumptions include:

[0052] Assuming that the number of workpieces follows a normal distribution, its mean and standard deviation are set based on historical data or expert experience. The specific probability density function is as follows:

[0053]

[0054] in:

[0055] x is a random variable;

[0056] μ is the mean number of workpieces;

[0057] σ is the standard deviation of the number of pieces.

[0058] Assuming that the arrival time follows an exponential distribution, its parameter (the order arrival rate per unit time λ) is also based on historical data or expert estimation. The specific formula is as follows:

[0059]

[0060] in:

[0061] t is a random variable;

[0062] λ is the order arrival rate per unit time;

[0063] The delivery date is determined by the arrival time and the delivery urgency coefficient. The specific formula is as follows:

[0064] d=T+f3(k)P

[0065] in:

[0066] T is the order arrival time;

[0067] f3(k) is the delivery deadline urgency coefficient (subject to Poisson distribution), and its parameters reflect the urgency of the delivery deadline;

[0068] P is the total processing time of all processes of the workpiece;

[0069] The delivery urgency coefficient f3(k) follows a Poisson distribution, with the parameter μ based on historical data or expert estimates, and its probability density function is:

[0070]

[0071] in:

[0072] k is a random variable;

[0073] μ is the coefficient.

[0074] Next, based on these assumptions, the scene is generated. The specific generation steps are as follows:

[0075] a. Randomly generate a specific number of workpieces based on the normal distribution of the number of workpieces;

[0076] b. Randomly assign an arrival time to each generated workpiece based on the exponential distribution of arrival time;

[0077] c. According to the Poisson distribution of the delivery urgency coefficient, a random urgency coefficient is generated for each workpiece;

[0078] d. Using the above urgency coefficient and the total processing time of all processes of the workpiece, a specific delivery date is generated for each workpiece through the delivery date calculation formula.

[0079] Finally, in order to more comprehensively consider the uncertainty of demand, it is necessary to repeatedly perform the above scenario generation process to generate multiple different demand scenarios. These scenarios together constitute the input set of the hybrid flow shop scheduling problem considering demand uncertainty.

[0080] Step 2: Proxy model construction: The Kriging model is used as the proxy model. By defining the scheduling scheme coding form including order coding and machine coding, a proxy model is constructed that can predict the on-time delivery rate of orders under different demand scenarios.

[0081] In order to fully describe the specific content of the scheduling scheme and provide accurate input for the subsequent agent model, a unique scheduling scheme encoding form is defined. Figure 1 As shown, the coding form consists of two parts: order code and machine code:

[0082] a. Order code: This is an ordered sequence that defines the execution order of each order in the current scheduling plan. Each element in the sequence represents a unique identifier for an order, ensuring that different orders can be accurately distinguished during the scheduling process. When an order is not included in a specific scenario, the corresponding position of the order in the coding sequence will be automatically skipped, and then the next order in the sequence will be executed.

[0083] b. Machine code: This is a two-dimensional matrix that defines in detail which machine should handle each process of each order. Each row of the matrix represents an order, and each column represents a process of the order. Each element in the matrix specifies the unique identifier of the processing machine for the corresponding order and process, thus ensuring the accuracy and executability of the scheduling plan.

[0084] After defining the encoding form of the scheduling scheme, the Kriging model is used as the proxy model. The Kriging model is an approximate model based on statistical methods, which can efficiently represent the objective function and constraints of the original scheduling optimization problem.

[0085] a. Model input: The input of the Kriging model is the scheduling scheme coding form defined above, including order coding and machine coding. This coding form fully and accurately describes the specific content of the scheduling scheme and provides the necessary input information for the model.

[0086] b. Model output: The output of the Kriging model is the on-time delivery rate of orders placed under each demand scenario. This indicator is a key indicator for measuring the performance of the scheduling solution and can intuitively reflect the performance of the scheduling solution under different demand uncertainties.

[0087] c. Model training: The Kriging model is trained by using the input and output data of known sample points. These sample points contain different scheduling schemes and their corresponding on-time delivery rates. Through the training process, a mapping relationship between scheduling schemes and on-time delivery rates is established, thereby achieving rapid prediction of the performance of unknown scheduling schemes.

[0088] Step 3 Multi-objective optimization based on agent model: The agent model is optimized using the non-dominated sorting genetic algorithm II (NSGAII) to find a scheduling solution that performs well in multiple scenarios.

[0089] The NSGAII algorithm searches for the optimal solution in the solution space by simulating natural selection and genetic mechanisms. In this invention, the coding form of the scheduling scheme (including order coding and machine coding) is used as the coding of the individual in the algorithm, and the fitness of each individual, that is, the on-time delivery rate of orders under different demand scenarios, is evaluated through the agent model. The specific optimization process is as follows:

[0090] a. Initialize the population: Generate an initial population containing multiple random scheduling schemes. These schemes are represented in coded form.

[0091] b. Fitness evaluation: Use the proxy model to evaluate the fitness of each scheduling solution. Specifically, the encoding of the scheduling solution is input into the proxy model, and its on-time delivery rate of orders under multiple demand scenarios is obtained. These on-time delivery rates will be used as the fitness value of the scheduling solution for subsequent genetic operations.

[0092] c. Genetic operations: Genetic operations are performed based on the fitness values ​​of individuals, including selection, crossover, and mutation. These operations are designed to generate new and potentially better solutions by combining and modifying existing solutions.

[0093] Selection: Non-dominated sorting and crowding comparison are used to select excellent individuals to ensure that there are both excellent solutions and diversity in the population.

[0094] Crossover: exchanging part of the coded information of two parent individuals to generate new offspring individuals.

[0095] Mutation: Used to randomly modify the encoding of individuals to increase the scope of exploration of the solution space.

[0096] d. Iterative update: Repeat the above fitness evaluation and genetic operation process until the preset number of iterations is reached or other stopping conditions are met. In each iteration, the population is updated and the best individuals in the current generation are retained as candidate solutions.

[0097] e. Output the optimal solution set: Select the non-dominated solution set (i.e. Pareto solution set) from the final population as the optimal solution set. These solutions are represented by coding and can be directly applied to the actual hybrid flow shop scheduling problem.

[0098] Step 4 Agent model update: Figure 2 As shown in FIG. 1 , during the optimization process, points that are far away from existing sample points and points that are not dominated by existing sample points are selected from the Pareto solution set of NSGAII to update the proxy model.

[0099] Using the optimization results of the non-dominated sorting genetic algorithm II (NSGAII), specific points are selected from the Pareto solution set to update the sample set, thereby further improving the performance of the proxy model. The specific process is as follows:

[0100] a. Screening specific points in the Pareto solution set: Screen specific points from the Pareto solution set for updating the sample set based on two key criteria.

[0101] Distance criterion: Select those points that are far away from the current sample set. Calculate the Euclidean distance from each Pareto point to all points in the sample set, and take the minimum value as the distance from the Pareto point to the sample set. Add the Pareto points with larger distances to the sample set. Their addition can increase the details and accuracy of the proxy model.

[0102] Non-dominated criterion: select points that are not dominated by existing sample points. This means that these points have better or at least non-inferior performance on the Pareto frontier relative to existing sample points. By introducing these points, it can ensure that the proxy model can cover the problem space more comprehensively and improve its prediction ability in different scenarios.

[0103] b. Update the sample set: After filtering out specific points, add these points to the current sample set to form an updated sample set. To ensure the stability of the model, the number of points added to the sample set needs to be controlled. The updated sample set will be used to retrain the proxy model to further improve its prediction accuracy and global description capabilities.

[0104] c. Retrain the proxy model: Use the updated sample set to retrain the Kriging model. Refit the model parameters based on the new input and output data to ensure that the model can accurately reflect the mapping relationship between the scheduling plan and the on-time delivery rate.

[0105] Step 5: Output robust scheduling plan: Use the error judgment mechanism to evaluate the prediction accuracy of the proxy model. If the preset error requirements are met, a set of hybrid flow shop scheduling plans that maintain a high on-time delivery rate under uncertainty conditions is output. The specific process is as follows:

[0106] a. Set preset error requirements based on the accuracy requirements of the robust scheduling solution in actual application scenarios.

[0107] b. Using the coefficient of determination (R 2 ) measures the prediction accuracy of the proxy model in the entire input space, that is, the global error. The specific formula is as follows:

[0108]

[0109] Among them, m is the number of sample points, y i is the true value of the i-th sample point, is the model prediction value of the i-th sample point, is the mean of the true values ​​of the m sample points.

[0110] c. The maximum relative error (MRE) is used to evaluate the prediction accuracy of the proxy model near the newly added sample points, that is, the local error. The specific formula is as follows:

[0111]

[0112] Among them, N is the number of new sample points, y i is the true value of the i-th sample point, is the model prediction value of the i-th sample point.

[0113] d. If both the global error and the local error meet the preset error requirements, stop adding new data points to the sample set used to train the proxy model, and output the optimization result of the proxy model at this time as the final robust scheduling solution set.

[0114] e. If either the global error or the local error does not meet the preset error requirements, continue to add new data points to the sample set and repeat the evaluation process until both the global error and the local error meet the preset requirements.

[0115] Example

[0116] First, multiple scenarios are generated. According to historical data or expert experience, the mean μ and standard deviation σ of the number of workpieces, as well as the order arrival rate λ per unit time and the Poisson distribution parameter μ of the delivery deadline urgency coefficient are set.

[0117] The probability density function f1(x) is used to generate the number of workpieces in this demand scenario. According to the exponential distribution of arrival time f2(t), an arrival time is randomly assigned to each generated workpiece. In addition, a urgency coefficient is randomly generated for each workpiece using the Poisson distribution of the delivery urgency coefficient f3(k). Combining the order arrival time T, the urgency coefficient f3(k) and the total processing time P of all workpiece processes, a specific delivery date is generated for each workpiece using the formula d=T+f3(k)P.

[0118] In order to fully consider the uncertainty of demand, the above scenario generation process is repeatedly executed to generate multiple different demand scenarios, which constitute the input set of the scheduling problem.

[0119] Next, build a proxy model. The Kriging model is used as the proxy model. The input is the scheduling scheme code, and the output is the on-time delivery rate of orders placed for each demand scenario. The scheduling scheme code consists of an order code and a machine code. The order code is an ordered sequence that defines the execution order of each order; the machine code is a two-dimensional matrix that is used to define in detail the processing machine for each process of each order. By training the Kriging model with the input and output data of known sample points, the mapping relationship between the scheduling scheme and the on-time delivery rate is established.

[0120] Then, multi-objective optimization is performed based on the agent model. The agent model is optimized using the non-dominated sorting genetic algorithm II (NSGAII) to find scheduling solutions that perform well in multiple scenarios. Initialize the population and generate an initial population containing multiple random scheduling solutions. Use the agent model to evaluate the fitness of each scheduling solution and obtain its on-time delivery rate of orders under multiple demand scenarios. According to the fitness value of the individual, that is, the on-time delivery rate of the individual orders under multiple demand scenarios, genetic operations, including selection, crossover and mutation, are performed to generate new scheduling solutions. Repeat the fitness evaluation and genetic operation process until the preset number of iterations is reached or other stopping conditions are met. Select the non-dominated solution set (Pareto solution set) from the final population as the optimal solution set.

[0121] During the optimization process, the proxy model is updated. Points that are far away from existing sample points and points that are not dominated by existing sample points are selected from the Pareto solution set of NSGAII, and these points are added to the current sample set to form an updated sample set. The Kriging model is retrained using the updated sample set to improve the prediction accuracy and global description ability of the model.

[0122] Finally, the robust scheduling solution is output. Set the preset error requirements, and use the coefficient of determination (R2) and the maximum relative error (MRE) to measure the global error and local error of the proxy model respectively. If both the global error and the local error meet the preset error requirements, stop adding new data points, and output the optimization results of the proxy model at this time as the final robust scheduling solution set. If either the global error or the local error does not meet the preset error requirements, continue to add new data points to the sample set and repeat the evaluation process until both the global error and the local error meet the preset requirements.

[0123] Through the above-mentioned specific implementation methods, the present invention can fully consider the uncertainty of demand and output a hybrid assembly line workshop scheduling solution that performs well in a variety of scenarios, thereby improving the robustness and computational efficiency of scheduling and providing strong support for intelligent production in the manufacturing industry.

Claims

1. A hybrid flow shop robust scheduling optimization method under demand uncertainty, characterized in that: The following steps are involved: 1) Generate multiple possible demand scenarios based on the uncertainty of different demands; 2) Based on different demand scenarios, the Kriging model is used to build a proxy model; 3) Solve the agent model using the non-dominated sorting genetic algorithm II, and take the obtained non-dominated solution set as the optimal solution set; 4) From the optimal solution set, sort the distance between each point and the existing sample points from large to small, select the top N points with the closest distance and the points that are not dominated by the existing sample points, and update the optimal solution set; 5) The proxy model is used to output a set of hybrid flow shop scheduling solutions that can maintain a high on-time delivery rate under the conditions of uncertainty in the number of workpieces, delivery dates, and arrival times.

2. The method for optimizing robust scheduling of a hybrid flow shop under demand uncertainty according to claim 1 is characterized in that: The step 1) comprises the following steps: 1.1) Construct uncertainty demand hypothesis; 1.2) Generate scenarios based on demand assumptions; 1.3) Repeat step 1.2) to generate multiple different demand scenarios and construct an input set for the hybrid flow shop scheduling problem considering demand uncertainty.

3. The method for optimizing robust scheduling of a hybrid flow shop under demand uncertainty according to claim 2 is characterized in that: Step 1.1) The following steps are involved: 1.1.1) Assume that the number of workpieces follows a normal distribution, and its mean and standard deviation are set based on historical data or expert experience; 1.1.2) Assume that the arrival time follows an exponential distribution, and its parameters are set based on historical data or expert experience; 1.1.3) The delivery date d is determined by the arrival time and the delivery urgency coefficient, specifically: d=T+f3(k)P Where T is the order arrival time, f3(k) is the delivery urgency coefficient that follows the Poisson distribution, and P is the total processing time of all workpiece processes.

4. The method for optimizing robust scheduling of a hybrid flow shop under demand uncertainty according to claim 2 is characterized in that: Step 1.2) The following steps are involved: 1.2.1) Randomly generate a specific number of workpieces according to the normal distribution of the number of workpieces; 1.2.2) Randomly assign an arrival time to each generated workpiece according to the exponential distribution of arrival time; 1.2.3) According to the Poisson distribution of the delivery time urgency coefficient, a urgency coefficient is randomly generated for each workpiece; 1.2.4) Calculate the delivery date for each workpiece using the urgency factor and the total processing time of all steps of the workpiece.

5. The method for optimizing robust scheduling of a hybrid flow shop under demand uncertainty according to claim 1 is characterized in that: The step 2) comprises the following steps: 2.1) Define the scheduling scheme encoding format; 2.2) Construct a proxy model based on the Kriging model, take the coded form of the scheduling plan as the input of the model, and the on-time delivery rate of orders under each demand scenario as the output of the model. Use the input and output data of known sample points to train the Kriging model, establish a mapping relationship between the scheduling plan and the on-time delivery rate, and realize rapid prediction of the performance of unknown scheduling plans.

6. The method for optimizing robust scheduling of a hybrid flow shop under demand uncertainty according to claim 5 is characterized in that: The scheduling scheme coding form includes order code and machine code, where: The order code is an ordered sequence, which is used to define the execution order of each order in the current scheduling plan. Each element in the sequence represents a unique identifier of an order, which is used to distinguish different orders during the scheduling process. When an order is not included in a specific scenario, the corresponding position of the order in the code sequence will be automatically skipped, and the system will then continue to execute the next order in the sequence; The machine encoding is a two-dimensional matrix, which is used to define which machine should process each process of each order. Each row of the matrix represents an order, and each column represents a process of the order. Each element in the matrix specifies a unique identifier of the processing machine corresponding to the order and process.

7. The method for optimizing robust scheduling of a hybrid flow shop under demand uncertainty according to claim 1 is characterized in that: In step 4), the distance between each point in the optimal solution set and the current sample set is calculated as follows: Calculate the Euclidean distance between the current point and each sample point in the sample set; The minimum value of all calculated distances is taken as the distance from the point to the sample set.

8. The method for optimizing robust scheduling of a hybrid flow shop under demand uncertainty according to claim 1 is characterized in that: The step 5) is specifically as follows: Determine whether both the global error and the local error meet the preset error requirements. If so, stop adding new data points to the sample set used to train the proxy model, and output the optimization result of the proxy model at this time as the final robust scheduling solution set; otherwise, continue to add new data points to the sample set until the error requirements are met.

9. The method for optimizing robust scheduling of a hybrid flow shop under demand uncertainty according to claim 8 is characterized in that: The determination coefficient is used to determine the global error of the surrogate model, and the maximum relative error is used to determine the local error of the surrogate model.

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