Scheduling method for aviation composite manufacturing hybrid flow shop containing batch processor

Abstract

The invention discloses a batch processor-containing aviation composite material manufacturing hybrid flow shop scheduling method, which comprises the following steps of: carrying out characteristic analysis on two key processes of laying and hot press molding in aviation composite material manufacturing, and determining related parameters; non-equal parallel processing equipment and a non-equal parallel batch processor are respectively arranged for the two working procedures; workpiece family compatibility, time window constraint and resource limitation are comprehensively considered, and a scheduling model with the purpose of minimizing completion time is constructed. And solving an optimal scheduling scheme by adopting an extended particle swarm optimization algorithm introducing a hybrid population initialization strategy, a self-adaptive parameter control mechanism and a local search strategy. The optimal scheduling scheme is applied to the actual manufacturing process, and the production efficiency and the scheduling level are improved. According to the method, the machining sequence and batch composition of the workpieces can be reasonably arranged, the manufacturing efficiency is improved while various constraint conditions are met, and powerful decision support is provided for production scheduling in an aviation composite material manufacturing system.

Description

Technical Field

[0001] The present invention belongs to the technical field of production scheduling in the manufacturing process of aviation composite materials, and in particular relates to a scheduling method for a hybrid flow shop containing a batch processing machine for manufacturing aviation composite materials. Background Art

[0002] Composite materials, due to their superior fatigue resistance, corrosion resistance, and lightweight, high-strength properties, have become the material of choice for aerospace equipment structural design. Compared to traditional metal materials, composites offer lower density and higher specific strength, enabling component weight reductions of 30% to 50% while maintaining comparable mechanical properties. With the widespread application of composite materials in aerospace structures, manufacturing efficiency has become a key factor influencing production cycle times and directly determining the market competitiveness of aerospace equipment. Existing scheduling methods often focus on optimizing the hot press forming process alone, neglecting the coordination and interdependence between the hot press forming process and the preceding layup process in terms of process parameters and processing time windows. This severely restricts manufacturing efficiency in actual production. A survey of a composite material aviation manufacturing company in my country revealed that the layup and hot press forming processes are not only closely linked but also play a decisive role in the overall efficiency of the scheduling scheme. These two key processes constitute critical composite material manufacturing processes. Optimizing them in isolation can lead to scheduling bottlenecks and waste resources. To address these issues, this paper proposes a scheduling method for a hybrid flow shop in aerospace composite manufacturing with batch processing machines, comprehensively considering the impact of workpiece family compatibility constraints, time window constraints, and resource limitations on production scheduling. This method has important practical significance and broad application prospects for improving manufacturing efficiency and achieving high-quality and on-time delivery of aviation products. Summary of the Invention

[0003] To address the aforementioned challenges in the existing technology, this paper proposes a scheduling method for hybrid assembly lines in aviation composite manufacturing, including batch processing machines. By comprehensively considering workpiece family compatibility constraints, time window constraints, and resource limitations, a corresponding scheduling model is constructed. An extended particle swarm optimization algorithm is then employed for efficient solution, resulting in an optimal scheduling solution. This method aims to improve the rationality of the scheduling solution and the overall efficiency of the manufacturing process, while also being robustly applicable to the complex production scenarios of aviation composite manufacturing systems.

[0004] To achieve the above technical objectives, this application provides the following technical solutions: A scheduling method for a hybrid flow shop for aviation composite material manufacturing including batch processing machines, specifically comprising: S1. Analyze the characteristics of the workpieces and equipment involved in each of the two key processes of layup and hot pressing in aviation composite material manufacturing, and determine relevant parameters. These parameters include: the processing time of the workpiece on different equipment in each process, the workpiece family affiliation, the release time and cut-off time, the workpiece area, the required number of thermocouples, and the area capacity of the equipment and the number of available thermocouples. S2. Setting up non-equivalent parallel processing equipment in the layup process and setting up non-equivalent parallel batch processing machines with capacity restrictions and thermocouple number constraints in the hot pressing process to complete batch processing of workpieces; S3. Comprehensively consider the impact of workpiece family compatibility, time window constraints, and resource limitations on production scheduling, and construct a hybrid flow shop scheduling model with the goal of minimizing completion time; S4. Solve the hybrid flow shop scheduling model constructed in step S3 using an extended particle swarm optimization algorithm that introduces a hybrid population initialization strategy, an adaptive parameter control mechanism, and a local search strategy to obtain an optimal scheduling solution; S5. Apply the optimal scheduling solution obtained in step S4 to the actual manufacturing process of aviation composite materials to improve production efficiency and scheduling level.

[0005] Furthermore, the hybrid flow shop scheduling model constructed in step S3 is represented by a three-field method, specifically: FFs | p - batch , incompatible , r ij , d ij , A m , TC m | C max ; in, FFs Indicates that s A hybrid flow shop scheduling problem with multiple stages; C max represents the maximum completion time of all workpieces as the optimization goal; p - batch , incompatible , r ij , d ij , A m , TC m The scheduling constraints involved in the scheduling model; i 、 jRepresents the artifact family and artifact index respectively, m Indicates the device number; p - batch Indicates parallel batch processing; incompatible Represents the compatibility constraints of artifact families; r ij 、 d ij Respectively represent the workpiece ( i , j) Release time and cut-off time; A m 、 TC m Respectively represent devices m The upper limit of area capacity and the upper limit of the number of thermocouples; The optimization goal of the scheduling model is to minimize the maximum completion time of all workpieces, that is: ; in, is the objective function of the scheduling model, C ij Represents a workpiece ( i , j) The completion time, F Is a collection of artifact families, indexed by i Represents a single artifact family; J i For workpiece family i The collection of artifacts in , indexed by j Represents a single artifact.

[0006] Furthermore, the scheduling constraints involved in the hybrid flow shop scheduling model specifically include: (1) ; (2) ; in, S For stage collection, index s Represents a single stage, s = 1 represents the laying stage, s = 2 represents the hot pressing stage; M s For the stage s A collection of devices, indexed by m Represents a single device; B is a batch collection, indexed by b 、 b' Represents a single batch; is a 0-1 decision variable. If the workpiece ( i , j) Assigned to batch b During processing, , otherwise 0; (3) ; (4) ; in, r ij 、 d ij Respectively represent the workpiece ( i , j) Release time and deadline, Represents a workpiece ( i , j) In the stage s The actual processing time; (5) ; in, Represents a workpiece ( i , j) In the stage s +1 completion time, Represents a workpiece ( i , j) In the stage s +1 actual processing time; (6) ; (7) ; Among them, index i' represents a single artifact family, and index j' represents a single artifact; Represents a workpiece ( i' , j') In the stage s The completion time, Represents a workpiece ( i' , j') In the stage s The actual processing time, N represents a sufficiently large positive number, is a 0-1 decision variable. If the workpiece ( i , j) and artifacts ( i' , j') On the device m adjacent processing, and the workpiece ( i , j) The processing sequence of the workpiece ( i' , j') Before, , otherwise 0; (8) ; (9) ; in, Indicates batch bThe actual processing time; (10) ; in, is a 0-1 decision variable. If the workpiece ( i , j) Assigned to device m On processing, , otherwise 0; Represents a workpiece ( i , j) In the stage s Zhongyou Equipment m The processing time required for processing; (11) ; (12) ; in, is a 0-1 decision variable. If the batch b Assigned to device m For processing, ; otherwise 0; (13) ; (14) ; (15) ; in, is a 0-1 decision variable. If the workpiece ( i' , j') Assigned to batch b During processing, , otherwise 0; (16) ; in, is a 0-1 decision variable. If the batch b In batches, , otherwise 0; (17) ; (18) ; (19) ; in, Represents a workpiece ( i , j) The area, Represents a workpiece ( i , j) The required number of thermocouples, Representation device m The area capacity, Representation device mThe number of thermocouples available; (20) ; (twenty one), .

[0007] Furthermore, step S4 specifically includes: S41. Initialize parameters, including setting the population size, defining the termination condition based on the maximum running time, and specifying parameters related to the improvement mechanism, including the learning rate α , discount factor γ and greed factor ε ; S42. Generate an initial mixed population using a real number sorting encoding scheme and calculate the fitness function value of each particle in the population; the fitness function value is the objective function value of the scheduling model, that is, the maximum completion time of all workpieces. The lower the fitness value, the better the performance. S43. Update the particle's velocity and position; dynamically adjust the inertia weight using an adaptive parameter control mechanism. w , cognitive coefficient c 1 and social coefficient c 2; S44, implement local search strategy to improve the local development capability of the algorithm and the quality of the solution; S45. Determine whether the iteration stop condition is met. If so, output the optimal scheduling solution; otherwise, return to S43.

[0008] Furthermore, in step S42, generating the initial mixed population using the real number sorting coding scheme specifically includes: P1. Encode particles using real number sorting encoding. Specifically, each workpiece is mapped to a real value in the interval [0, 1] to form a real number encoding vector. The processing order of the workpieces is determined by sorting the real values in the vector in ascending order. P2, first use the random generation rule to generate N / 2 particles, forming subpopulation SP1, where N represents the overall population size; P3, then use the release time segmentation rule to generate N / 4 particles, forming subpopulation SP2; specifically: all artifacts are released according to the release time r ij Sort in ascending order and sort by the maximum release time value max{ r ij} Divide the workpiece into three groups: If r ij <(1 / 3)·max{ r ij}, classified as group 1; if (1 / 3)·max{r ij} ≤ r ij <(2 / 3)·max{ r ij}, classified as Group 2; if r ij ≥(2 / 3)·max{ r ij}, classified as group 3; on this basis, real number coding values are assigned to each group of workpieces to ensure that group 1 is ranked before group 2, and group 2 is ranked before group 3; P4, use the deadline segmentation rule again to generate N / 4 particles, forming subpopulation SP3; specifically: all workpieces are sorted according to the deadline d ij Sort in ascending order and sort by the maximum deadline value max{ d ij} Divide the workpiece into three groups: If d ij <(1 / 3)·max{ d ij}, classified as group 1; if (1 / 3)·max{ d ij} ≤ d ij <(2 / 3)·max{ d ij}, classified as Group 2; if d ij ≥ (2 / 3)·max{ d ij}, classified as group 3; on this basis, real number coding values are assigned to each group of workpieces to ensure that group 1 is ranked before group 2, and group 2 is ranked before group 3; P5. Merge subpopulations SP1, SP2, and SP3 to obtain a complete initial mixed population.

[0009] Furthermore, step S43 is specifically as follows: An adaptive parameter control mechanism based on Q-learning is introduced to achieve dynamic parameter configuration adjustment of particles during the process of velocity and position update. The basic components of the adaptive parameter control mechanism include: intelligent agent, environment, state set, action set and reward function. Set the agent to the particle itself; Set the environment to the optimization process of the scheduling model, which includes the current scheduling results, particle positions, particle fitness function values, particle speeds, and global optimal solution information; The state set is divided into three states according to the fitness function value of the particles, including: state 0: represents the first 1 / 3 particles with the best fitness; state 1: represents the 1 / 3 particles with the middle fitness; state 2: represents the 1 / 3 particles with the worst fitness; Set the action set to three parameter configuration actions, including: Action 1: Configure inertia weight w = 0.9, cognitive coefficient c 1 = 1.0, social coefficient c 2 = 1.0; Action 2: Configuration w = 0.6, c 1 = 1.0, c 2 = 2.0; Action 3: Configuration w =0.6, c 1 = 2.0, c 2 = 1.0; Set the reward function to evaluate the change between the current state and the previous state; if the state improves, the reward is equal to the difference between the state indices; if the state remains unchanged, the reward is 0; otherwise, a negative reward of −1 is given uniformly; at the same time, set the Q table to be reinitialized every third of the total running time, and introduce ε - Greedy strategy, control the agent to 1 - ε The probability of selecting the action with the largest Q value in the current state is ε The probability of choosing a random action is .

[0010] Furthermore, step S44 specifically includes: S441, sorting the current population according to the fitness function values of the particles; S442: Select the top 10% of high-quality particles and execute the exchange operator and the reverse operator with a probability of 50% to explore a better scheduling solution; S443. Select the last 10% of inferior particles and update them using the adversarial learning strategy. The formula for calculating the adversarial solution is: ; in, It is a particle p s In dimension i The value above and in the interval [ lb i , ub i ]Inside, yes The opposite value of lb i and ub i Respectively represent iThe lower and upper bounds of the dimensional search space.

[0011] Based on the above technical solution, the present invention has at least the following beneficial effects: To address the close relationship and resource constraints between the two key processes of layup and hot pressing in aviation composite manufacturing, this paper constructs a hybrid flow shop scheduling model with the goal of minimizing completion time. This model fully considers workpiece family compatibility, time window constraints, and resource limitations, and can more realistically reflect the scheduling characteristics of aviation composite manufacturing systems. By modeling multiple complex scheduling constraint relationships, this paper effectively avoids the bottleneck problems caused by fragmented optimization between processes, improves the rationality of the scheduling solution and the overall efficiency of the manufacturing process, and has good engineering adaptability and application promotion value.

[0012] The present invention further designs an extended particle swarm optimization algorithm, which combines mixed population initialization, adaptive parameter control and local search strategy to enhance the global search capability and local development capability of the algorithm. The mixed population initialization strategy generates multiple subpopulations by combining real number sorting encoding with heuristic rules to improve the diversity of the initial solution. The algorithm introduces an adaptive parameter control mechanism based on Q learning, which enables particles to dynamically adjust algorithm parameters according to the current state during the speed and position update process, effectively improving the search intelligence and reducing the risk of falling into local optimality. The local search strategy enhances search diversity and improves the overall population quality and algorithm convergence speed by exchanging and reversing high-quality individuals and introducing an adversarial learning mechanism for low-quality individuals. The resulting scheduling scheme not only has a better objective function value, but can also be stably applied to complex production scenarios of aviation composite material manufacturing systems, effectively improving production efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 This is a flow chart of a scheduling method for a hybrid flow shop for aviation composite material manufacturing including a batch processing machine proposed by the present invention; Figure 2 Flowchart of the extended particle swarm optimization algorithm implemented in the present invention; Figure 3 This is an example diagram of the real number sorting encoding scheme in the present invention; Figure 3 (a) is a schematic diagram of real number sorting coding. Figure 3 (b) is a Gantt chart; Figure 4 An example graph for executing the exchange and reversal operators in the present invention; Figure 4 (a) in the equation is the commutative operator. Figure 4 (b) in the equation is the inversion operator. DETAILED DESCRIPTION

[0014] In order to make the purpose, technical solutions and advantages of the present invention more clear, the following Figure 1-4 It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0015] Although the steps in the present invention are arranged with numbers, they are not intended to limit the order of the steps. Unless the order of the steps is clearly stated or the execution of a step requires other steps as a basis, the relative order of the steps can be adjusted. It is understood that the term "and / or" used herein refers to and covers any and all possible combinations of one or more of the associated listed items.

[0016] In this embodiment, Figure 1 As shown in FIG, a scheduling method for a hybrid flow shop for aviation composite manufacturing with batch processing machines is proposed, which specifically includes the following steps: S1. Analyze the characteristics of the workpieces and equipment involved in each of the two key processes of layup and hot pressing in aviation composite material manufacturing, and determine relevant parameters. These parameters include: the processing time of the workpiece on different equipment in each process, the workpiece family affiliation, the release time and cut-off time, the workpiece area, the required number of thermocouples, and the area capacity of the equipment and the number of available thermocouples. S2. In the layup process, non-equivalent parallel processing equipment is provided. In this embodiment, non-equivalent parallel processing equipment refers to a parallel structure consisting of multiple devices, where different devices process the same workpiece at different times due to different processing speeds. In the hot pressing process, a non-equivalent parallel batch processor with capacity restrictions and thermocouple quantity constraints is provided to complete batch processing of workpieces. S3. Comprehensively consider the impact of workpiece family compatibility, time window constraints, and resource limitations on production scheduling, and construct a hybrid flow shop scheduling model with the goal of minimizing completion time; In this application, workpiece family compatibility is based on workpiece family affiliation information, which is used to constrain batch processing tasks to only allow combinations of workpieces from the same workpiece family, and prohibit workpieces from different workpiece families from being assigned to the same batch; time window constraints include the release time and deadline of the workpiece, which are used to limit the processable time range of the workpiece; resource constraints include equipment area capacity limitations and thermocouple quantity limitations, which are used to ensure that the equipment's capacity and thermocouple resources meet the workpiece requirements during batch processing.

[0017] In addition, before building the model, the following assumptions must be met: all workpieces follow a fixed processing route and cannot be interrupted during processing; each machine can only process one workpiece or batch of workpieces at a time and remains available at all times; and the transportation time between workpieces is negligible or already included in the processing time. As a preferred implementation, in this embodiment, the hybrid flow shop scheduling model constructed in step S3 is represented using the three-field method, specifically: FFs | p - batch , incompatible , r ij , d ij , A m , TC m | C max ; in, FFs Indicates that s A hybrid flow shop scheduling problem with multiple stages; C max represents the maximum completion time of all workpieces as the optimization goal; p - batch , incompatible , r ij , d ij , A m , TC m The scheduling constraints involved in the scheduling model; i 、 j Represents the artifact family and artifact index respectively, m Indicates the device number; p - batch Indicates parallel batch processing; incompatible Represents the compatibility constraints of artifact families; r ij 、 d ij Respectively represent the workpiece ( i , j) Release time and cut-off time; A m 、 TC m Respectively represent devices m The upper limit of area capacity and the upper limit of the number of thermocouples; The optimization goal of the scheduling model is to minimize the maximum completion time of all workpieces, that is: ; in, is the objective function of the scheduling model, C ij Represents a workpiece ( i , j) The completion time, F Is a collection of artifact families, indexed by i Represents a single artifact family; J i For workpiece family i The collection of artifacts in , indexed by j Represents a single artifact.

[0018] More specifically, in this embodiment, the scheduling constraints involved in the hybrid flow shop scheduling model specifically include: (1) ; (2) ; in, S For stage collection, index s Represents a single stage, s = 1 represents the laying stage, s = 2 represents the hot pressing stage; M s For the stage s A collection of devices, indexed by m Represents a single device; B is a batch collection, indexed by b 、 b' Represents a single batch; is a 0-1 decision variable. If the workpiece ( i , j) Assigned to batch b During processing, , otherwise 0; (3) ; (4) ; in, r ij 、 d ij Respectively represent the workpiece ( i , j) Release time and deadline, Represents a workpiece ( i , j) In the stage s The actual processing time; (5) ; in, Represents a workpiece ( i , j)In the stage s +1 completion time, Represents a workpiece ( i , j) In the stage s +1 actual processing time; (6) ; (7) ; Among them, index i' represents a single artifact family, and index j' represents a single artifact; Represents a workpiece ( i' , j') In the stage s The completion time, Represents a workpiece ( i' , j') In the stage s The actual processing time, N represents a sufficiently large positive number, is a 0-1 decision variable. If the workpiece ( i , j) and artifacts ( i' , j') On the device m adjacent processing, and the workpiece ( i , j) The processing sequence of the workpiece ( i' , j') Before, , otherwise 0; At the same time, it should be noted that i' 、 j' 、 b ' is a differentiated index symbol used to avoid confusion when multiple similar objects (such as two different artifact families, two different artifacts, two different batches) need to be referred to at the same time in the same context. Its essential function is the same as i, j, b Consistent, only used to distinguish different individuals in the same category.

[0019] (8) ; (9) ; in, Indicates batch b The actual processing time; (10) ; in, is a 0-1 decision variable. If the workpiece ( i , j) Assigned to device m On processing, , otherwise 0; Represents a workpiece ( i , j) In the stage s Zhongyou Equipment m The processing time required for processing; (11) ; (12) ; in, is a 0-1 decision variable. If the batch b Assigned to device m For processing, ; otherwise 0; (13) ; (14) ; (15) ; in, is a 0-1 decision variable. If the workpiece ( i' , j') Assigned to batch b During processing, , otherwise 0; (16) ; in, is a 0-1 decision variable. If the batch b In batches (i.e. activated), then , otherwise 0; (17) ; (18) ; (19) ; in, Represents a workpiece ( i , j) The area, Represents a workpiece ( i , j) The required number of thermocouples, Representation device m The area capacity, Representation device m The number of thermocouples available; (20) ; (twenty one), .

[0020] Among the above constraints, constraints (1) and (2) are used to define the workpiece ( i ,j) Completion time C ij , which is not less than the workpiece in stage s Completion time , and the completion time of the batch ; Constraints (3) and (4) are used to ensure that the workpiece ( i , j) The processing at its release time r ij Starts after and ends at its d ij Completed before; Constraint (5) stipulates that for each workpiece ( i , j) , its processing in the first stage must be completed before its processing in the second stage begins; constraints (6) and (7) define the order in which the equipment processes the workpieces and processes the batches respectively; constraints (8) and (9) are used to ensure that the workpiece ( i , j) The completion time is equal to the batch to which it belongs b The completion time of the workpiece ( i , j) The actual processing time in stage 1; constraints (11) and (12) are used to define the workpiece ( i , j) The actual processing time in stage 2; constraints (13) and (14) ensure that each workpiece is processed only once in the first and second stages; constraint (15) is used to restrict workpieces of different workpiece families from being assigned to the same batch to meet the workpiece family compatibility constraint; constraint (16) is used to ensure that the batch processing equipment is allowed to process only when the batch to which it is assigned is activated; constraint (17) is used to ensure that a batch is considered activated only when at least one workpiece is assigned to it; constraints (18) and (19) define the area limit and the number of thermocouples of the batch processing equipment respectively; constraints (20) to (21) ensure that the decision variables are within the feasible range.

[0021] S4. An extended particle swarm optimization algorithm that introduces a hybrid population initialization strategy, an adaptive parameter control mechanism, and a local search strategy is used to solve the hybrid flow shop scheduling model constructed in step S3 to obtain the optimal scheduling solution. This application improves the basic particle swarm optimization algorithm to enhance the global search capability and local development capability, thereby improving the scheduling efficiency and the quality of the solution.

[0022] As a preferred embodiment, Figure 2 As shown, step S4 specifically includes: S41, initialization parameters, including setting the population size, defining the termination condition based on the maximum running time, and specifying the parameters related to the improvement mechanism, including the learning rate α, the discount factor γ, and the greed factor ε; It should be noted that the maximum running time here refers to the longest allowed duration of the algorithm execution process, which is used to control the termination of the algorithm iteration (if the algorithm runs for more than this time, the calculation will stop), and is the time threshold setting for the algorithm iteration.

[0023] S42. Generate an initial mixed population using a real number sorting encoding scheme and calculate the fitness function value of each particle in the population (each particle represents a complete scheduling plan); the fitness function value is the objective function value of the scheduling model, that is, the maximum completion time of all workpieces. The lower the fitness value, the better the performance. As a preferred embodiment, the use of the real number sorting encoding scheme to generate the initial mixed population in step S42 specifically includes: P1. Use real number sorting encoding to encode particles. Specifically, each workpiece is mapped to a real value in the interval [0,1] to form a real number encoding vector. The processing order of the workpieces is determined by sorting the real values in the vector in ascending order. This encoding method can not only effectively represent any feasible workpiece processing sequence, but also facilitates efficient optimization operations in the continuous search space, and is suitable for continuous optimization algorithms such as particle swarm optimization. Figure 3 As shown in (a) in the figure, in this embodiment, for a scheduling problem containing three workpiece families and a total of 9 workpieces, the original sequence [(1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (3,1), (3,2)] is encoded as [0.51, 0.65, 0.19, 0.97, 0.06, 0.25, 0.79, 0.28, 0.95], and then the encoded vector is sorted in ascending order to obtain [0.06, 0.19, 0.25, 0.28, 0.51, 0.65, 0.79, 0.95, 0.97]. The corresponding workpiece processing order is [(2,1), (1,3), (2,2), (3,1), (1,1), (1,2), (2,3), (3,2), (1,4)].

[0024] The workpiece is assigned to each device according to the decoded processing sequence. Figure 3As shown in (b) of the figure, the first workpiece (2,1) is assigned to the idle machine with the smallest index (i.e., machine 1), and its processing start time is the release time of the workpiece. Throughout the workpiece allocation process, the "earliest available machine first" rule is applied, meaning each workpiece is assigned to the machine with the earliest idle time. For example, the fourth workpiece (3,1) is assigned to machine 3 because it is the earliest idle machine at that moment. The start time of a batch is the maximum completion time of the workpieces it contains during the first phase. For example, if batch 1 contains workpieces (2,1), (2,2), and (2,3), its start processing time is equal to the maximum completion time of these three workpieces during the first phase, i.e., the completion time of workpiece (2,3). The actual processing time of a batch is the maximum processing time of all workpieces in the batch. This scheduling process strictly adheres to the constraints of the constructed hybrid flow shop scheduling model for aviation composite manufacturing with batch processing machines, ensuring the rationality of batch generation and the accuracy of completion time calculation.

[0025] Next, we discuss several ways to generate the initial mixed population: P2, first use the random generation rule to generate N / 2 particles, forming subpopulation SP1, where N represents the overall population size; P3, then use the release time segmentation rule to generate N / 4 particles, forming subpopulation SP2; specifically: all artifacts are released according to the release time r ij Sort in ascending order and sort by the maximum release time value max{ r ij} Divide the workpiece into three groups: If r ij <(1 / 3)·max{ r ij}, classified as group 1; if (1 / 3)·max{ r ij} ≤ r ij <(2 / 3)·max{ r ij}, classified as Group 2; if r ij ≥(2 / 3)·max{ r ij}, classified as group 3; on this basis, real number coding values are assigned to each group of workpieces to ensure that group 1 is ranked before group 2, and group 2 is ranked before group 3; P4, use the deadline segmentation rule again to generate N / 4 particles, forming subpopulation SP3; specifically: all workpieces are sorted according to the deadline dij Sort in ascending order and sort by the maximum deadline value max{ d ij} Divide the workpiece into three groups: If d ij <(1 / 3)·max{ d ij}, classified as group 1; if (1 / 3)·max{ d ij} ≤ d ij <(2 / 3)·max{ d ij}, classified as Group 2; if d ij ≥ (2 / 3)·max{ d ij}, classified as group 3; on this basis, real number coding values are assigned to each group of workpieces to ensure that group 1 is ranked before group 2, and group 2 is ranked before group 3; In addition, it should be noted that the groups divided in P3 and P4 only refer to the grouping of workpieces based on release time (or cutoff time) in a single particle code, which is used to constrain the interval allocation of code values and has nothing to do with subpopulations SP1, SP2, and SP3.

[0026] P5. Merge subpopulations SP1, SP2, and SP3 to obtain a complete initial mixed population.

[0027] S43. Update the particle's velocity and position; dynamically adjust the inertia weight using an adaptive parameter control mechanism. w , cognitive coefficient c 1 and social coefficient c 2; As a preferred embodiment, step S43 is specifically as follows: An adaptive parameter control mechanism based on Q-learning is introduced to achieve dynamic parameter configuration adjustment of particles during the process of velocity and position update. The basic components of the adaptive parameter control mechanism include: intelligent agent, environment, state set, action set and reward function. Set the agent to the particle itself; Set the environment to the optimization process of the scheduling model, which includes the current scheduling results, particle positions, particle fitness function values, particle speeds, and global optimal solution information; The state set is divided into three states according to the fitness function value of the particles, including: state 0: represents the first 1 / 3 particles with the best fitness; state 1: represents the 1 / 3 particles with the middle fitness; state 2: represents the 1 / 3 particles with the worst fitness; Set the action set to three parameter configuration actions, including: Action 1: Configure inertia weightw = 0.9, cognitive coefficient c 1 = 1.0, social coefficient c 2 = 1.0; Action 2: Configuration w = 0.6, c 1 = 1.0, c 2 = 2.0; Action 3: Configuration w =0.6, c 1 = 2.0, c 2 = 1.0; Set up a reward function to evaluate the change between the current state and the previous state; if the state improves (i.e., the state index decreases), the reward is equal to the difference between the state indices (e.g., from state 2 to state 0, the reward is +2); if the state does not change, the reward is 0; otherwise (as long as the state decreases), a negative reward of −1 is given; At the same time, the Q table is set to be reinitialized every one-third of the total running time, and the ε - Greedy strategy, control the agent to 1 - ε The probability of selecting the action with the largest Q value in the current state is ε The probability of choosing a random action is .

[0028] S44, implement local search strategy to improve the local development capability of the algorithm and the quality of the solution; As a preferred embodiment, step S44 specifically includes: S441, sorting the current population according to the fitness function values of the particles; S442. Select the top 10% of high-quality particles and execute the exchange operator and the reverse operator with a probability of 50% to explore a better scheduling solution; wherein, the exchange operator refers to randomly selecting two values at different positions in the particle code sequence for exchange. This embodiment provides a schematic diagram of the exchange operator, such as Figure 4 As shown in (a) in the figure, the original particle code is [0.51, 0.65, 0.27, 0.19, 0.97, 0.06, 0.25]. Position 2 and position 5 (i.e., 0.65 and 0.06) are randomly selected and exchanged, and the new particles obtained are [0.51, 0.06, 0.27, 0.19, 0.97, 0.65, 0.25]. The inversion operator randomly selects a continuous subsequence in the particle code sequence and reverses the order of the subsequence. This embodiment provides a schematic diagram of the inversion operator, as shown in FIG. Figure 4As shown in (b), the original particles are [0.51, 0.65, 0.27, 0.19, 0.97, 0.06, 0.25], and the randomly selected continuous subsequence is [0.65, 0.27, 0.19, 0.97]. The new particles obtained after inversion are [0.51, 0.97, 0.19, 0.27, 0.65, 0.06, 0.25]. S443. Select the last 10% of inferior particles and update them using the adversarial learning strategy. The formula for calculating the adversarial solution is: ; in, It is a particle p s In dimension i The value above and in the interval [ lb i , ub i ]Inside, yes The opposite value of lb i and ub i Respectively represent i The lower and upper bounds of the dimensional search space.

[0029] In addition, it should be noted that in this application, intermediate particles are not searched locally in order to balance efficiency and optimization effect: high-quality particles need to be finely optimized, and low-quality particles need to break through limitations. However, the room for improvement of intermediate particles is limited. No additional processing can reduce computing costs, while retaining population diversity and avoiding convergence caused by excessive search.

[0030] S45. Determine whether the iteration stop condition is met. If so, output the optimal scheduling solution; otherwise, return to S43.

[0031] S5. Apply the optimal scheduling solution obtained in step S4 to the actual manufacturing process of aviation composite materials to improve production efficiency and scheduling level.

[0032] In addition, this embodiment further illustrates the effectiveness and feasibility of the scheduling method for a hybrid flow shop for aviation composite material manufacturing including batch processing machines proposed by the present invention through the following example experiments.

[0033] All case studies were implemented using Python programming and conducted on a computer running Microsoft Windows 11, equipped with an Intel (R) Ultra 3800MHz processor and 1TB of RAM. The advantages of the extended particle swarm optimization (EPSO) algorithm for solving this type of scheduling problem were fully verified through comparative analysis with five representative metaheuristic optimization algorithms: genetic algorithm (GA), differential evolution (DE), standard particle swarm optimization (PSO), biogeographic optimization (BBO), and whale optimization algorithm (WOA). Furthermore, a typical scheduling case was constructed for a specific production instance to verify the feasibility and scheduling optimization effectiveness of this method in actual aerospace composite manufacturing scenarios.

[0034] (1) Experimental design and parameter setting In this invention, all workpiece parameters are assumed to follow a uniform distribution. Specifically, the workpiece area ranges from 2 to 30, the required number of thermocouples ranges from 1 to 5, and the release time is set between 0 and 50. The deadline is determined by adding a uniformly distributed offset between 168 and 360 to each workpiece's release time. In the first stage (layup), the workpiece processing time ranges from 2 to 16; in the second stage (hot press forming), the workpiece processing time ranges from 8 to 24. The processing time variation between different machines in the same stage does not exceed 10%. The batch processing equipment in the second stage is configured with an area capacity of 40 or 60 and a thermocouple capacity of 10 or 20. A naming convention is established for benchmark instances of different sizes, reflecting the number of workpiece families, the number of machines in each stage, and the total number of workpieces. For example, an instance labeled "f1-s3'1-j20" indicates one workpiece family, three machines in the first stage, one machine in the second stage, and a total of 20 workpieces.

[0035] After trial running of all algorithms, the present invention sets the termination condition of the algorithm to 0.5× n × m seconds, of which n is the total number of workpieces, m is the total number of devices; the population size of all algorithms is set to 30. In the adaptive parameter control mechanism of the extended particle swarm optimization algorithm, the learning rate α = 0.3, discount factor γ = 0.9, greed factor ε = 0.3.

[0036] (2) Optimization solution The present invention uses the proposed extended particle swarm optimization (EPSO) algorithm to optimize and solve the scheduling model and compares it with five classic metaheuristic optimization algorithms. The experimental results are shown in Tables 1 and 2 below. As can be seen from the results of the nine typical test cases in Table 1, EPSO achieved the best average scheduling results on eight of the cases (better values are indicated in bold). Table 2 further lists the standard deviation results of each algorithm over 30 runs to measure the stability of the solution. The standard deviation results show that EPSO exhibits good stability in most cases. For example, in the cases f3-s3'1-j20 and f5-s2'1-j20, EPSO's standard deviations are 1.78 and 1.74, respectively, significantly lower than those of the other algorithms, demonstrating that it can stably output high-quality scheduling solutions across multiple independent runs. This demonstrates that the proposed extended particle swarm optimization algorithm has significant optimization capabilities and good stability in solving the scheduling problem of hybrid flow shop manufacturing for aviation composites with batch processing machines.

[0037] Table 1 Comparison of average scheduling results of different optimization algorithms

[0038] Table 2 Comparison of standard deviations of scheduling results of different optimization algorithms

[0039] To validate the applicability and superiority of the proposed scheduling method in real-world production environments, two typical production scenarios were selected from the composite material production workshop of a leading Chinese aerospace manufacturer, designated Case 1 (f3-s8'6-j51) and Case 2 (f6-s10'5-j65). The proposed extended particle swarm optimization (EPSO) algorithm was applied to each of these two examples and compared with five typical metaheuristic optimization algorithms. Each algorithm was independently run 30 times on each example. Evaluation metrics included mean, optimal value, worst value, and standard deviation. The results are shown in Tables 3 and 4, respectively, with the optimal result indicated in bold. The experimental results show that the proposed EPSO algorithm outperforms the other compared algorithms in terms of mean, optimal value, and worst value, demonstrating superior scheduling optimization capabilities. Although the DE algorithm performed better in terms of standard deviation, EPSO maintained good stability. Overall, the EPSO algorithm demonstrates good practicality and effectiveness in the aviation composite material manufacturing scheduling problem.

[0040] Table 3 Experimental results of Case 1

[0041] Table 4 Experimental results of Case 2

[0042] In summary, the present invention addresses the close relationship and resource constraints between the two key processes of layup and hot pressing in the manufacturing of aviation composite materials, and proposes a hybrid flow shop scheduling model with the goal of minimizing the completion time. This model fully considers the compatibility constraints of the workpiece family, time window constraints and resource limitations, and can more realistically reflect the scheduling characteristics of the aviation composite material manufacturing system. On this basis, an extended particle swarm optimization algorithm was designed to optimize and solve the model. The results of simulation experiments and actual case verification show that the proposed scheduling method has good effectiveness and practicality. Compared with the five classic metaheuristic algorithms, the extended particle swarm optimization algorithm of the present invention performs well in key indicators, and the resulting scheduling scheme can be stably applied to the complex production scenarios of the aviation composite material manufacturing system, effectively improving production efficiency.

[0043] In the description of this specification, the reference terms "one embodiment," "some embodiments," "example," "specific example," or "some examples" mean that the specific features, structures, materials, or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. Moreover, the specific features, structures, materials, or characteristics described may be combined in any appropriate manner in any one or more embodiments or examples. In addition, those skilled in the art may combine and combine different embodiments or examples described in this specification, as well as features of different embodiments or examples, unless they are mutually inconsistent.

[0044] The logic and / or steps represented in the flowchart or otherwise described herein may be considered, for example, as an ordered list of executable instructions for implementing logical functions, and may be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a system including a processor, or other system that can fetch and execute instructions from an instruction execution system, apparatus, or device).

[0045] The above embodiments provide a detailed introduction to the present invention. Specific examples are used herein to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core ideas. At the same time, for those skilled in the art, according to the ideas of the present invention, there may be changes in the specific implementation methods and application scopes. In summary, the contents of this specification should not be understood as limiting the present invention.

Claims

1. A scheduling method for a hybrid flow shop for aviation composite material manufacturing containing batch processing machines, characterized in that: The specific steps include: S1. Analyze the characteristics of the workpieces and equipment involved in each of the two key processes of layup and hot pressing in aviation composite material manufacturing, and determine relevant parameters. These parameters include: the processing time of the workpiece on different equipment in each process, the workpiece family affiliation, the release time and cut-off time, the workpiece area, the required number of thermocouples, and the area capacity of the equipment and the number of available thermocouples. S2. Setting up non-equivalent parallel processing equipment in the layup process and setting up non-equivalent parallel batch processing machines with capacity restrictions and thermocouple number constraints in the hot pressing process to complete batch processing of workpieces; S3. Comprehensively consider the impact of workpiece family compatibility, time window constraints, and resource limitations on production scheduling, and construct a hybrid flow shop scheduling model with the goal of minimizing completion time; S4. Solve the hybrid flow shop scheduling model constructed in step S3 using an extended particle swarm optimization algorithm that introduces a hybrid population initialization strategy, an adaptive parameter control mechanism, and a local search strategy to obtain an optimal scheduling solution; S5. Apply the optimal scheduling solution obtained in step S4 to the actual manufacturing process of aviation composite materials to improve production efficiency and scheduling level.

2. The scheduling method for a hybrid flow shop for manufacturing aviation composite materials containing a batch processing machine according to claim 1, characterized in that: The hybrid flow shop scheduling model constructed in step S3 is represented by the three-field method, specifically: FFs | p - batch , incompatible , r ij , d ij , A m , TC m | C max ； in, FFs Indicates that s A hybrid flow shop scheduling problem with multiple stages; C max represents the maximum completion time of all workpieces as the optimization goal; p - batch , incompatible , r ij , d ij , A m , TC m The scheduling constraints involved in the scheduling model; i 、 j Represents the artifact family and artifact index respectively, m Indicates the device number; p - batch Indicates parallel batch processing; incompatible Represents the compatibility constraints of artifact families; r ij 、 d ij Respectively represent the workpiece ( i , j) Release time and cut-off time; A m 、 TC m Respectively represent devices m The upper limit of area capacity and the upper limit of the number of thermocouples; The optimization goal of the scheduling model is to minimize the maximum completion time of all workpieces, that is: ； in, is the objective function of the scheduling model, C ij Represents a workpiece ( i , j) The completion time, F Is a collection of artifact families, indexed by i Represents a single artifact family; J i For workpiece family i The collection of artifacts in , indexed by j Represents a single artifact.

3. The scheduling method for a hybrid flow shop for manufacturing aviation composite materials containing a batch processing machine according to claim 2, characterized in that: The scheduling constraints involved in the hybrid flow shop scheduling model include: (1)、 ； (2)、 ； in, S For stage collection, index s Represents a single stage, s = 1 represents the laying stage, s = 2 represents the hot pressing stage; M s For the stage s A collection of devices, indexed by m Represents a single device; B is a batch collection, indexed by b 、 b' Represents a single batch; is a 0-1 decision variable. If the workpiece ( i , j) Assigned to batch b During processing, , otherwise 0; (3)、 ； (4)、 ； in, r ij 、 d ij Respectively represent the workpiece ( i , j) Release time and deadline, Represents a workpiece ( i , j) In the stage s The actual processing time; (5)、 ； in, Represents a workpiece ( i , j) In the stage s +1 completion time, Represents a workpiece ( i , j) In the stage s +1 actual processing time; (6)、 ； (7)、 ； Among them, index i' represents a single artifact family, and index j' represents a single artifact; Represents a workpiece ( i' , j') In the stage s The completion time, Represents a workpiece ( i' , j') In the stage s The actual processing time, N represents a sufficiently large positive number, is a 0-1 decision variable. If the workpiece ( i , j) and artifacts ( i' , j') On the device m adjacent processing, and the workpiece ( i , j) The processing sequence of the workpiece ( i' , j') Before, , otherwise 0; (8)、 ； (9)、 ； in, Indicates batch b The actual processing time; (10)、 ； in, is a 0-1 decision variable. If the workpiece ( i , j) Assigned to device m On processing, , otherwise 0; Represents a workpiece ( i , j) In the stage s Zhongyou Equipment m The processing time required for processing; (11)、 ； (12)、 ； in, is a 0-1 decision variable. If the batch b Assigned to device m For processing, ; otherwise 0; (13)、 ； (14)、 ； (15)、 ； in, is a 0-1 decision variable. If the workpiece ( i' , j') Assigned to batch b During processing, , otherwise 0; (16)、 ； in, is a 0-1 decision variable. If the batch b In batches, , otherwise 0; (17)、 ； (18)、 ； (19)、 ； in, Represents a workpiece ( i , j) The area, Represents a workpiece ( i , j) The required number of thermocouples, Representation device m The area capacity, Representation device m The number of thermocouples available; (20)、 ； (21)、 。 4. The method for scheduling a hybrid flow shop for manufacturing aviation composite materials containing a batch processing machine according to claim 1, characterized in that: Step S4 specifically includes: S41. Initialize parameters, including setting the population size, defining the termination condition based on the maximum running time, and specifying parameters related to the improvement mechanism, including the learning rate α , discount factor γ and greed factor ε ; S42. Generate an initial mixed population using a real number sorting encoding scheme and calculate the fitness function value of each particle in the population; the fitness function value is the objective function value of the scheduling model, that is, the maximum completion time of all workpieces. The lower the fitness value, the better the performance. S43. Update the particle's velocity and position; dynamically adjust the inertia weight using an adaptive parameter control mechanism. w , cognitive coefficient c 1 and social coefficient c 2; S44, implement local search strategy to improve the local development capability of the algorithm and the quality of the solution; S45. Determine whether the iteration stop condition is met. If so, output the optimal scheduling solution; otherwise, return to S43.

5. The method for scheduling a hybrid flow shop for manufacturing aviation composite materials containing a batch processing machine according to claim 4, characterized in that: In step S42, the real number sorting coding scheme is used to generate the initial mixed population, specifically including: P1. Encode particles using real number sorting encoding. Specifically, each workpiece is mapped to a real value in the interval [0, 1] to form a real number encoding vector. The processing order of the workpieces is determined by sorting the real values in the vector in ascending order. P2, first use the random generation rule to generate N / 2 particles, forming subpopulation SP1, where N represents the overall population size; P3, then use the release time segmentation rule to generate N / 4 particles, forming subpopulation SP2; specifically: all artifacts are released according to the release time r ij Sort in ascending order and sort by the maximum release time value max{ r ij } Divide the workpiece into three groups: If r ij < (1 / 3)·max{ r ij }, classified as group 1; if (1 / 3)·max{ r ij } ≤ r ij < (2 / 3)·max{ r ij }, classified as Group 2; if r ij ≥(2 / 3)·max{ r ij }, classified as group 3; on this basis, real number coding values are assigned to each group of workpieces to ensure that group 1 is ranked before group 2, and group 2 is ranked before group 3; P4, use the deadline segmentation rule again to generate N / 4 particles, forming subpopulation SP3; specifically: all workpieces are sorted according to the deadline d ij Sort in ascending order and sort by the maximum deadline value max{ d ij } Divide the workpiece into three groups: If d ij < (1 / 3)·max{ d ij }, classified as group 1; if (1 / 3)·max{ d ij } ≤ d ij < (2 / 3)·max{ d ij }, classified as Group 2; if d ij ≥ (2 / 3)·max{ d ij }, classified as group 3; on this basis, real number coding values are assigned to each group of workpieces to ensure that group 1 is ranked before group 2, and group 2 is ranked before group 3; P5. Merge subpopulations SP1, SP2, and SP3 to obtain a complete initial mixed population.

6. The method for scheduling a hybrid flow shop for manufacturing aviation composite materials containing a batch processing machine according to claim 4, characterized in that: Step S43 is specifically as follows: An adaptive parameter control mechanism based on Q learning is introduced to achieve dynamic parameter configuration adjustment of particles during the process of speed and position update; The basic components of the adaptive parameter control mechanism include: intelligent agent, environment, state set, action set and reward function; Set the agent to the particle itself; Set the environment to the optimization process of the scheduling model, which includes the current scheduling results, particle positions, particle fitness function values, particle speeds, and global optimal solution information; The state set is divided into three states according to the fitness function value of the particles, including: state 0: represents the first 1 / 3 particles with the best fitness; state 1: represents the 1 / 3 particles with the middle fitness; state 2: represents the 1 / 3 particles with the worst fitness; Set the action set to three parameter configuration actions, including: Action 1: Configure inertia weight w = 0.9, cognitive coefficient c 1 = 1.0, social coefficient c 2 = 1.0; Action 2: Configuration w = 0.6, c 1 = 1.0, c 2 = 2.0; Action 3: Configuration w = 0.6, c 1 = 2.0, c 2 = 1.0; Set the reward function to evaluate the change between the current state and the previous state; if the state improves, the reward is equal to the difference between the state indices; if the state remains unchanged, the reward is 0; otherwise, a negative reward of −1 is given uniformly; at the same time, set the Q table to be reinitialized every third of the total running time, and introduce ε - Greedy strategy, control the agent to 1 - ε The probability of selecting the action with the largest Q value in the current state is ε The probability of choosing a random action is .

7. The method for scheduling a hybrid flow shop for manufacturing aviation composite materials containing a batch processing machine according to claim 4, characterized in that: Step S44 specifically includes: S441, sorting the current population according to the fitness function values of the particles; S442: Select the top 10% of high-quality particles and execute the exchange operator and the reverse operator with a probability of 50% to explore a better scheduling solution; S443. Select the last 10% of inferior particles and update them using the adversarial learning strategy. The formula for calculating the adversarial solution is: ； in, It is a particle p s In dimension i The value above and in the interval [ lb i , ub i ]Inside, yes The opposite value of lb i and ub i Respectively represent i The lower and upper bounds of the dimensional search space.

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