Scheduling and nesting method, device and equipment for additive manufacturing and storage medium

Abstract

This invention discloses a scheduling and nesting method, apparatus, device, and storage medium for additive manufacturing. The method jointly generates part selection, machine allocation, batch formation, orientation selection, and 2D placement decisions within a sequential decision-making process. This directly couples the spatial nesting results with the temporal scheduling objective, effectively reducing the overall completion time of heterogeneous additive manufacturing (AM) systems while ensuring geometric constraints, and simultaneously improving the real-time reasoning capability of the software system. Compared to MILP, it has better computational efficiency for medium-to-large-scale problems; compared to genetic algorithms, it eliminates the need for long-term population searches on each instance, effectively reducing computation time; and compared to manual heuristic methods, it reduces reliance on fixed part sorting rules and manual parameters.

Description

Technical Field

[0001] The embodiments of the present invention relate to the field of production scheduling technology, and in particular to a scheduling and nesting method, apparatus, equipment and storage medium for additive manufacturing. Background Technology

[0002] Additive manufacturing (AM) is a technology that manufactures solid parts layer by layer based on a 3D digital model, suitable for small-batch, customized, and on-demand production. Taking metal additive manufacturing processes such as selective laser melting and direct laser sintering as examples, parts undergo laser scanning and powder spreading or recoating processes in each layer. Multiple parts can be processed simultaneously in a batch on the same build platform, with batches executed sequentially on the same machine. In this type of production system, batch processing time is usually not the sum of the pre-fixed processing times of individual parts, but is closely related to the geometric placement of parts within the batch. Scanning time is related to the sum of the volume of all parts and their supports within the batch, while powder spreading or recoating time is related to the maximum print height of the batch. Parts have different widths, lengths, heights, and support volumes in different printing orientations; therefore, orientation selection simultaneously affects the 2D footprint, batch height, support requirements, and processing time. Furthermore, parts on the build platform must satisfy 2D boundary constraints, non-overlapping constraints within the same batch, minimum spacing constraints between parts, and machine build height constraints. Therefore, AM scheduling decisions and geometric nesting decisions are strongly coupled: part selection, machine allocation, batch formation, orientation selection, and two-dimensional placement will jointly determine batch processing time, machine completion time, and overall system completion time.

[0003] Existing solutions typically employ Mixed Integer Linear Programming (MILP) to describe AM scheduling and nested problems. These solutions usually define a set of parts, a set of candidate directions, a set of AM machines, and a set of batches. Binary variables represent whether a part is assigned to a particular batch on a particular machine, whether the batch is empty, and whether a part has selected a particular direction. Continuous coordinate variables represent the part's two-dimensional position on the build platform. When considering heterogeneous machines, multiple candidate directions, two-dimensional non-overlapping constraints, batch order, and batch processing time, the allocation variables, direction variables, relative position variables, and coordinate constraints in MILP grow rapidly, leading to excessively high computational complexity and making it difficult to meet real-time production planning requirements. Other solutions employ heuristic, metaheuristic, or rule-driven methods. These methods typically sort parts and machines based on part area, height, volume, or the machine's current load, then select candidate directions and attempt to place the part in the current batch. Metaheuristic methods can also use genetic algorithms to search for part sequences, direction combinations, and machine priorities. However, heuristic methods rely on manually designed area, height, volume, or load sorting rules, and their performance is significantly affected by part geometry, machine build dimensions, and process parameters. While metaheuristic methods such as genetic algorithms can explore a larger space, they typically require instance-level search and parameter setting, and computation time increases significantly with problem size, making them difficult to use stably in real-time inference scenarios. Furthermore, if part sorting, machine allocation, or batch composition is determined first, and then two-dimensional nesting is performed separately, the previous stage may create batches that are difficult to place later. Conversely, if only local geometric compactness is pursued, machine load balancing and batch processing time variations may be ignored. Therefore, separating scheduling and nesting can easily lead to local optima and is unlikely to effectively reduce the overall system completion time. Summary of the Invention

[0004] This invention provides a scheduling and nesting method, apparatus, device, and storage medium for additive manufacturing, overcoming the problems of existing technologies such as separation of scheduling and nesting, long computation time of mathematical programming methods, and reliance on manual rules and insufficient generalization ability of heuristic methods.

[0005] In a first aspect, embodiments of the present invention provide a scheduling and nesting method for additive manufacturing, the method comprising: Step 1: Obtain information about the parts to be processed and the machine configuration parameters; Step 2: Based on the information of the part to be processed and the machine configuration parameters, determine the current part status, machine status, and system status; Step 3: Based on the status of the parts, the status of the machines, and the status of the systems, select the scheduling action for the parts to be assigned or the batch shutdown action; Step 4: If the scheduled action for the part to be assigned is selected, the placement direction and coordinates of the target part in the target machine are determined, and a geometric feasibility verification is performed. Step 5: If the batch shutdown action is selected, the current batch of the target machine is shut down, the processing time of the current batch and the completion time of the current machine are calculated, and the next batch of the target machine is started. Step 6: Repeat steps 2 through 5 until all parts have been assigned and all non-empty batches have been closed; Step 7: Output the batch sequence of each machine, the composition of each batch, the placement direction and coordinates of each part, the processing time of each batch, the completion time of each machine, and the overall completion time of the system.

[0006] Optionally, the part status includes part volume, length, width and height of each candidate direction and support volume of each candidate direction, as well as area pressure relative to the machine in each candidate direction, local matching degree, height utilization rate, height deviation, support volume ratio and incremental processing time caused by inserting the current batch. The machine status includes the length, width and height of the construction platform, as well as the area utilization rate of the current batch, the maximum proportion of free rectangles, the number of available free rectangles, the height utilization rate, the part height variance, the volume utilization rate, the support volume ratio, the estimated processing time of the current batch and the estimated machine completion time. The system status includes the proportion of remaining unallocated parts, the proportion of remaining parts volume, the current overall system completion time, and the variance of the completion time of each machine. It also includes the average area utilization rate, average height utilization rate, average volume utilization rate, and average batch processing time of completed batches.

[0007] Optionally, the method further includes: The scheduling and nesting integration problem on heterogeneous additive manufacturing machines is modeled as a combinatorial optimization problem with the objective of minimizing the overall system completion time. The overall system completion time is calculated as follows: ; ; ; Wherein, C_max represents the overall completion time of the system, T_{b,m} represents the processing time of batch b in batch set B_m on machine m in machine set M, VT_m represents the unit volume scanning time of machine m, v_i represents the body volume of part i in batch b, s_{i,o_i} represents the support volume of part i under the selected placement direction o_i, HT_m represents the unit height powder spreading or recoating time of machine m, H_{b,m} represents the maximum height of batch b, C_m represents the machine completion time of machine m, and SET_m represents the batch setting time of machine m.

[0008] Optionally, the scheduling and nesting integrated problem is specifically modeled as a Markov decision process, with states including the part state, the machine state, and the system state, actions including the scheduling action of the part to be allocated and the batch closing action, rewards including part insertion rewards and batch closing rewards, and termination conditions being that all parts have been allocated and all non-empty batches have been closed.

[0009] Optionally, the scheduling and nesting integration problem is solved using a deep reinforcement learning network. This deep reinforcement learning network includes a part state encoder, a machine state encoder, a system state encoder, a scheduling decoder, a nesting decoder, a value decoder, and an experience cache. The part state encoder encodes the part state, the machine state encoder encodes the machine state, the system state encoder encodes the system state, the scheduling decoder evaluates feasible part-machine combinations based on part embeddings and machine embeddings to determine the scheduling action for the part to be assigned, the nesting decoder evaluates feasible part placement directions based on the scheduling action for the part to be assigned and generates part placement coordinates, the value decoder estimates the long-term value of the current state, and the experience cache stores the state, action, reward, next state, action probability, and value estimate.

[0010] Optionally, the nested decoder is specifically used for: Query the feasible placement directions of the target part in the current batch of the target machine during the scheduling action of the part to be assigned; Evaluate the incremental batch processing time caused by each of the aforementioned feasible placement orientations, and preferentially select the feasible placement orientation with the smaller incremental batch processing time as the part placement orientation; The maximum rectangle algorithm is invoked to place the part in the lower left corner. The placement coordinates of the part are determined according to the placement direction of the part, and a geometric feasibility check is performed.

[0011] Secondly, embodiments of the present invention also provide a scheduling and nesting apparatus for additive manufacturing, the apparatus comprising: The processing information acquisition module is used to execute step one: acquire information about the parts to be processed and machine configuration parameters; The scheduling status update module is used to execute step two: based on the information of the part to be processed and the machine configuration parameters, determine the current part status, machine status and system status; The scheduling action selection module is used to execute step three: select the scheduling action for the part to be assigned or the batch shutdown action based on the part status, the machine status and the system status. The parts placement module is used to execute step four: if the part scheduling action to be assigned is selected, the placement direction and coordinates of the target part in the target machine are determined, and a geometric feasibility verification is performed. The batch shutdown module is used to execute step five: if the batch shutdown action is selected, the current batch of the target machine is shut down, the processing time of the current batch of the target machine and the completion time of the current machine are calculated, and the next batch of the target machine is started. The repeat execution module is used to repeatedly execute steps two through five until all parts have been assigned and all non-empty batches have been closed. The results output module is used to output the batch sequence of each machine, the composition of the parts in each batch, the placement direction and coordinates of each part, the processing time of each batch, the completion time of each machine, and the overall completion time of the system.

[0012] Thirdly, embodiments of the present invention also provide a computer device, the computer device comprising: One or more processors; Memory, used to store one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the scheduling and nesting method for additive manufacturing provided in any embodiment of the present invention.

[0013] Fourthly, embodiments of the present invention also provide a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the scheduling and nesting method for additive manufacturing provided in any embodiment of the present invention.

[0014] Fifthly, embodiments of the present invention also provide a computer program product, which includes a computer program that, when executed by a processor, implements the scheduling and nesting method for additive manufacturing provided in any embodiment of the present invention.

[0015] This invention provides a scheduling and nesting method for additive manufacturing (AM). By jointly generating part selection, machine allocation, batch formation, orientation selection, and 2D placement decisions in a sequential decision-making process, the spatial nesting results are directly coupled with the time scheduling objective. While ensuring geometric constraints, this effectively reduces the overall completion time of heterogeneous AM systems and improves the real-time inference capability of the software system. Compared to MILP, it has better computational efficiency for medium-to-large-scale problems. Compared to genetic algorithms, it eliminates the need for long-term population searches on each instance, effectively reducing computation time. Compared to manual heuristic methods, it reduces reliance on fixed part sorting rules and manual parameters. Attached Figure Description

[0016] Figure 1 A flowchart of a scheduling and nesting method for additive manufacturing provided in Embodiment 1 of the present invention; Figure 2 This is a flowchart of the overall scheduling and nested reasoning execution provided in Embodiment 1 of the present invention; Figure 3 This is a schematic diagram illustrating the integrated problem of additive manufacturing scheduling and nesting provided in Embodiment 1 of the present invention; Figure 4 This is a schematic diagram of the deep reinforcement learning network structure provided in Embodiment 1 of the present invention; Figure 5 This is a flowchart of the deep reinforcement learning network training process provided in Embodiment 1 of the present invention; Figure 6 This is a schematic diagram of the scheduling and nesting device for additive manufacturing provided in Embodiment 2 of the present invention. Figure 7 This is a schematic diagram of the structure of a computer device provided in Embodiment 3 of the present invention. Detailed Implementation

[0017] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present invention, and not all of the structures.

[0018] Before discussing the exemplary embodiments in more detail, it should be noted that some exemplary embodiments are described as processes or methods depicted as flowcharts. Although the flowcharts describe the steps as sequential processes, many of these steps can be performed in parallel, concurrently, or simultaneously. Furthermore, the order of the steps can be rearranged. The process can be terminated when its operation is complete, but may also have additional steps not included in the figures. The process can correspond to a method, function, procedure, subroutine, subroutine, etc.

[0019] Example 1 Figure 1 This is a flowchart of a scheduling and nesting method for additive manufacturing provided in Embodiment 1 of the present invention. This embodiment is applicable to additive manufacturing production planning and scheduling scenarios, where there are multiple parts, multiple candidate printing directions, multiple heterogeneous additive manufacturing machines, and two-dimensional nesting constraints, generating geometrically feasible scheduling and nesting schemes with short overall completion times. This method can be executed by the scheduling and nesting device for additive manufacturing provided in this embodiment of the present invention. This device can be implemented in hardware and / or software, and is generally integrated into a computer device. Figure 1 As shown, the method specifically includes the following steps: S11. Obtain information on the parts to be processed and machine configuration parameters.

[0020] S12. Based on the information of the part to be processed and the machine configuration parameters, determine the current part status, machine status and system status.

[0021] S13. Based on the part status, the machine status, and the system status, select the part scheduling action or batch shutdown action to be assigned.

[0022] S14. If the scheduled action for the part to be assigned is selected, the placement direction and coordinates of the target part in the target machine are determined, and a geometric feasibility check is performed.

[0023] S15. If the batch closing action is selected, the current batch of the target machine is closed, the processing time of the current batch of the target machine and the completion time of the current machine are calculated, and the next batch of the target machine is started.

[0024] S16. Repeat S12-S15 until all parts are assigned and all non-empty batches are closed.

[0025] S17. Output the batch sequence of each machine, the composition of each batch, the placement direction and coordinates of each part, the processing time of each batch, the completion time of each machine, and the overall completion time of the system.

[0026] Specifically, the information on parts to be processed can include the set of parts, the volume and candidate orientation of each part, the width, length, and height of each part in different candidate orientations, and the support volume of each part in different candidate orientations. Machine configuration parameters can include the AM machine set, the width, length, and height of the build platform for each machine, the batch setup time for each machine, the unit volume scanning time for each machine, and the unit height powder application or recoating time for each machine. After inputting the information on parts to be processed and the machine configuration parameters, the current batch for each machine can be initialized to empty. Simultaneously, unassigned parts can be managed through an unassigned parts set, which can be initialized to the input parts set.

[0027] Scheduling and nested processes can then be initiated, determining the current part status, machine status, and system status based on the information of the parts to be processed and machine configuration parameters. The part status describes the geometric and temporal impacts of the parts being inserted into the current batch on different machines and in different orientations. The machine status describes the geometric utilization and temporal load of each machine in the current batch. The system status describes the global production progress and load balancing status. By designing these three types of states, both local executability and global completion time and load balancing are characterized.

[0028] In an optional implementation, the part status includes part volume, length, width, and height of each candidate direction, and support volume of each candidate direction, as well as area pressure relative to the machine in each candidate direction, local matching degree, height utilization rate, height deviation, support volume ratio, and incremental processing time caused by inserting the current batch; the machine status includes the length, width, and height of the construction platform, as well as the area utilization rate of the current batch, maximum free rectangle ratio, number of available free rectangles, height utilization rate, part height variance, volume utilization rate, support volume ratio, estimated processing time of the current batch, and estimated machine completion time; the system status includes the proportion of remaining unassigned parts, the proportion of remaining part volumes, the overall completion time of the current system, and the variance of completion time of each machine, as well as the average area utilization rate, average height utilization rate, average volume utilization rate, and average batch processing time of completed batches.

[0029] Among them, in the part status, the area pressure can be calculated based on the ratio of the projected area of ​​the part in the selected direction to the current remaining area of ​​the selected machine; the local matching degree can be calculated based on the matching degree of the projected area of ​​the part in the selected direction to the currently available free rectangular area of ​​the selected machine; the height utilization rate can be calculated based on the ratio of the height of the part in the selected direction to the construction height of the selected machine; the height deviation can be calculated based on the difference between the height of the part in the selected direction and the maximum height of the current batch of the selected machine; the support volume ratio can be calculated based on the ratio of the support volume of the part in the selected direction to the volume of the part; and the incremental processing time can be calculated based on the difference between the estimated processing time of the current batch before and after the part in the selected direction is inserted into the current batch of the selected machine. In machine status, area utilization can be calculated based on the ratio of the area occupied by inserted parts in the current batch of the corresponding machine to the area of ​​the building platform. The free rectangle refers to the rectangular area that can be planned in the current remaining space of the building platform, which can be determined using the maximum rectangle algorithm MaxRects. The maximum free rectangle ratio can be calculated based on the ratio of the maximum free rectangle to the area of ​​the building platform. Height utilization can be calculated based on the ratio of the height occupied by inserted parts in the current batch of the corresponding machine to the building height. Part height variance is the height variance among inserted parts in the current batch of the corresponding machine. Volume utilization can be calculated based on the ratio of the volume occupied by inserted parts and their supports in the current batch of the corresponding machine to the volume of the building platform. Support volume ratio can be calculated based on the ratio of the volume of all supports of inserted parts in the current batch of the corresponding machine to the volume of all parts. The estimated processing time of the current batch is the estimated processing time required for inserted parts in the current batch of the corresponding machine. The estimated machine completion time is the sum of the batch processing time required for the current batch to be completed and the estimated processing time of the current batch. In the system status, the proportion of remaining unassigned parts is the proportion of parts to be assigned to all parts, the proportion of remaining parts volume is the volume ratio among the remaining parts, and the current overall system completion time can be the maximum value among the current estimated machine completion times of all machines.

[0030] After obtaining the current part status, machine status, and system status, either a part scheduling action or a batch closing action can be selected based on the current status. The part scheduling action can involve selecting a target part from the pending parts and simultaneously selecting a target machine, then attempting to insert the target part into the target machine's current batch. The batch closing action can involve selecting a target machine, closing its current batch, and releasing it as a batch to be processed. To facilitate the implementation of the batch closing action, a batch closing virtual token can be appended to the part status sequence. This token's characteristics can be set to zero or a dedicated embedding to represent a candidate action for "closing the target machine's current batch," thus allowing proactive decision-making on when to end a batch and avoiding fixed batch sizes.

[0031] If the assigned part scheduling action is selected, the placement direction and coordinates of the target part on the target machine can be further determined. Specifically, the feasible placement directions of the target part on the current batch of the target machine can be queried first, and the incremental batch processing time caused by each feasible placement direction can be evaluated. The smaller feasible placement direction is selected as the part placement coordinate. Then, the two-dimensional occupied area of ​​the target part can be represented by a rectangular envelope under the part placement direction. For the current batch of the target machine, the software can maintain a set of available rectangles and use the maximum rectangle algorithm with a bottom-left placement strategy to try to place the target part on the build platform of the target machine to determine the part placement coordinate.

[0032] A geometric feasibility check can be performed on the determined part placement direction and coordinates. If the check passes, the target part can be added to the current batch of the target machine; otherwise, the part placement direction and coordinates can be redefined. If all feasible placement directions fail, the scheduling action for the part to be assigned can be reselected. Failed feasible placement directions or scheduling actions for the part to be assigned can be masked to avoid reselection. By embedding the geometric feasibility check into the action execution flow, it can be ensured that the output scheduling action can ultimately form a geometrically feasible batch layout. Specifically, the geometric feasibility check can include: checking whether the placed part exceeds the width and length of the machine platform; checking whether the target part overlaps with already placed parts in the same batch; checking whether the minimum spacing between parts is met; and checking whether the maximum height of the batch after placement exceeds the machine's build height.

[0033] If the batch close action is selected, the current batch of the target machine can be closed, and the processing time of the current batch of the target machine can be calculated based on the parts already added in the current batch. Then the completion time of the current machine is updated, which is the sum of the processing times of all completed batches, and then the next batch of the target machine is started.

[0034] After completing the geometric feasibility verification and obtaining the placement direction and coordinates of feasible target parts, the target parts can be removed from the unassigned parts set. Then, based on the information of the parts to be processed and the machine configuration parameters, the current part status, machine status, and system status are redefined. Alternatively, after completing the batch closing action, the current part status, machine status, and system status are redefined based on the information of the parts to be processed and the machine configuration parameters. This process of selecting and executing actions can be repeated until all parts are assigned and all non-empty batches are closed. Ultimately, within the same software flow, the batch sequence for each machine, the part composition within each batch, the placement direction and coordinates of each part, the processing time for each batch, the completion time for each machine, and the overall system completion time (makespan) can be output simultaneously, directly coupling the spatial nesting results with the time scheduling objective. Furthermore, the area utilization rate, height utilization rate, and volume utilization rate for each batch can be output, allowing users to more intuitively understand the scheduling effect. Batch nesting diagrams, machine scheduling diagrams, and statistical reports can also be output for manual verification. The overall scheduling and nested reasoning execution flow is as follows: Figure 2 As shown.

[0035] Based on the above technical solution, optionally, the method further includes: modeling the scheduling and nesting integration problem on the heterogeneous additive manufacturing machine as a combinatorial optimization problem with the objective of minimizing the overall system completion time, wherein the overall system completion time is calculated as follows: ; ; ; Wherein, C_max represents the overall completion time of the system, T_{b,m} represents the processing time of batch b in batch set B_m on machine m in machine set M, VT_m represents the unit volume scanning time of machine m, v_i represents the body volume of part i in batch b, s_{i,o_i} represents the support volume of part i under the selected placement direction o_i, HT_m represents the unit height powder spreading or recoating time of machine m, H_{b,m} represents the maximum height of batch b, C_m represents the machine completion time of machine m, and SET_m represents the batch setting time of machine m.

[0036] Specifically, the model can satisfy the following rules: each part can only be assigned to one batch on one machine; each part can only select one printing orientation; each part must be within the target machine's build platform boundary after selecting an orientation; no two parts in the same batch can overlap on the build platform; parts in the same batch must meet a minimum spacing requirement; the batch height is equal to the maximum height of the parts in the batch; the batch height must not exceed the machine's build height; batch processing time consists of scanning time and powder application or recoating time; batches on each machine are processed sequentially, with batch setup time included between batches; the overall system completion time is the maximum of all machine completion times; the optimization objective is to minimize the overall system completion time, etc. The batch processing time consists of two parts: the first part is the scanning time, which is related to the sum of the body volume of all parts in the batch and the support volume under the selected orientation; the second part is the powder application or recoating time, which is related to the height of the tallest part in the batch. Therefore, batch processing time can be expressed as: machine unit volume scanning time multiplied by total batch scanning volume, plus machine unit height powder application or recoating time multiplied by maximum batch height. The total batch scanning volume includes the part body volume and the support volume under the selected orientation. This calculation method integrates orientation selection, support volume, 2D nesting, and batch height into scheduling decisions. The problem of integrating additive manufacturing scheduling and nesting is as follows... Figure 3 As shown, this illustrates the process of starting from parts and candidate directions, forming batches through two-dimensional nesting, and then allocating them to heterogeneous AM machines to form a batch sequence.

[0037] In an optional implementation, the scheduling and nesting integration problem is specifically modeled as a Markov decision process, with states including the part state, the machine state, and the system state, actions including the scheduling action of the part to be allocated and the batch closing action, rewards including part insertion rewards and batch closing rewards, and termination conditions being that all parts have been allocated and all non-empty batches have been closed.

[0038] Specifically, at each decision step, an action can be selected based on the current part state, machine state, and system state. After the action is executed, the states and rewards are updated until a complete schedule is formed. The reward function can employ potential-based reward shaping to provide dense feedback during training without altering the original goal of minimizing the makespan. For the part insertion reward, when a target part is inserted into the current batch of the target machine, the reward can be calculated based on the change in the expected processing time of the batch before and after insertion. ; Here, TP_before represents the estimated processing time of the current batch before insertion, and TP_after represents the estimated processing time of the current batch after insertion. Since inserting parts typically increases batch processing time, this reward can be understood as a penalty for the incremental processing time, used to guide the strategy to form batches with shorter processing times and tighter geometry. For batch closure rewards, when a batch is explicitly closed or implicitly closed at the end of the episode, the reward can be calculated based on the change in makespan before and after closure, and a batch processing time offset term is added: ; Here, Cmax_before represents the system makespan before the batch is closed, Cmax_after represents the system makespan after the batch is closed, and TP_b represents the processing time of the closed batch. This offsetting term is used to offset the part-related rewards accumulated during the part insertion phase of the batch, ensuring that the local reward is consistent with the global objective. Additionally, the total reward for an episode can be set. The cumulative reward for a complete scheduled episode satisfies: R_episode = -Cmax, meaning that maximizing the cumulative reward is strictly equivalent to minimizing the final system makespan. This reward design provides intermediate decision feedback while maintaining consistency with the original optimization objective. Furthermore, the reward function can also incorporate auxiliary terms such as material utilization and machine load balancing while maintaining consistency with the makespan objective.

[0039] Optionally, the scheduling and nesting integration problem is solved using a deep reinforcement learning network. This deep reinforcement learning network includes a part state encoder, a machine state encoder, a system state encoder, a scheduling decoder, a nested decoder, a value decoder, and an experience cache. The part state encoder encodes the part state, the machine state encoder encodes the machine state, the system state encoder encodes the system state, the scheduling decoder evaluates feasible part-machine combinations based on part embeddings and machine embeddings to determine the scheduling action for the part to be assigned, the nested decoder evaluates feasible part placement directions based on the scheduling action for the part to be assigned and generates part placement coordinates, the value decoder estimates the long-term value of the current state, and the experience cache stores the state, action, reward, next state, action probability, and value estimate.

[0040] Specifically, this deep reinforcement learning network can employ a PPO-based geometric perception end-to-end deep reinforcement learning network to directly map states to scheduled actions from the policy network. The part state encoder can use a Transformer to encode part state features to capture the contextual competition between candidate parts; alternatively, it can be replaced with other sequence models or graph neural networks. The machine state encoder can use a multilayer perceptron to encode machine state features, and the system state encoder can use a multilayer perceptron to encode system state features. The network can employ an asymmetric actor-critic structure. The actor primarily generates locally executable actions based on part and machine states, while the critic additionally uses system states for value estimation. This design allows the value network to obtain global long-term information while enabling the policy network to focus on executable part-machine-batch operations. This improves the accuracy of value estimation while maintaining controllable policy action space. Furthermore, through machine states, the policy network can simultaneously compare the spatial availability, batch compactness, batch height variation, and machine load levels of different machines, thus balancing geometric feasibility and scheduling time objectives during part allocation. The actor includes a scheduling decoder and a nested decoder. The scheduling decoder evaluates feasible part-machine combinations based on part embeddings and machine embeddings, and outputs an action probability distribution with action masks. The nested decoder evaluates feasible directions after a given part-machine action and uses the maximum rectangle algorithm's bottom-left placement strategy to generate part placement coordinates. The critic aggregates part, machine, and system embeddings through a value decoder to estimate the long-term value of the current state. The experience cache stores the state, action, reward, next state, action probability, and value estimate, which can be used for subsequent PPO updates. The deep reinforcement learning network structure is as follows: Figure 4 The diagram illustrates the data flow relationships between the part status encoder, machine status encoder, system status encoder, policy network, value network, nested decoder, environment, and experience cache.

[0041] In an optional implementation, the nested decoder is specifically used to: query the feasible placement directions of the target part in the current batch of the target machine in the part scheduling action to be assigned; evaluate the incremental batch processing time caused by each feasible placement direction, and preferentially select the feasible placement direction with the smaller incremental batch processing time as the part placement direction; call the maximum rectangle algorithm bottom left placement strategy, determine the part placement coordinates according to the part placement direction, and perform geometric feasibility verification.

[0042] Specifically, the action space can be designed as a hierarchical structure to avoid directly enumerating the huge combination space of "part-machine-direction-x-y coordinate". At each decision step, the scheduling decoder can select the part scheduling action to be assigned or the batch shutdown action. For the part scheduling action to be assigned between the target part and the target machine, the above direction and coordinate generation process can continue to be executed through the nested decoder. This action design allows each action output by the actor to be transformed into an executable scheduling and nested operation, while preserving the end-to-end learning framework.

[0043] Before applying a deep reinforcement learning network to solve the problem, the network can be trained first. The training process may include: initializing the part state encoder, machine state encoder, system state encoder, actor decoder, and critic decoder; constructing training instances containing different part geometries, candidate orientations, and AM machine configurations; resetting the environment in each training episode, initializing the unassigned part set, the current machine batch, and the machine completion time; calculating the current part state, machine state, and system state; obtaining the part embedding, machine embedding, and system embedding through the state encoder; sampling or selecting actions through the scheduling decoder; if the action is a part-machine action, calling the nested decoder for orientation selection and 2D placement; if the action is a batch closing action, closing the corresponding current machine batch; updating the batch layout, machine state, system state, and unassigned part set after executing the action; calculating the reward based on part insertion or batch closing; writing the state, action, reward, action probability, and value estimate into the experience cache; calculating the advantage function and objective reward after collecting several episodes; updating the actor and critic parameters based on the PPO clipped objective, value loss, and entropy regularization; repeating training until the preset number of updates is reached, and saving the trained policy network parameters. After training, it can output complete scheduling and nested solutions within seconds of inference time, making it suitable for medium to large-scale AM ​​production planning scenarios. The deep reinforcement learning network training process is as follows: Figure 5 As shown.

[0044] The method provided in this embodiment was further tested. On small-scale instances, the average deviation from the optimal solution of MILP was 5.3%, while reducing the computation time from approximately 1200 seconds to 1-3 seconds. As the problem size increased, MILP could not obtain a feasible solution within 1200 seconds in some instances, while this method still maintained second-level inference. Simultaneously, the average makespan was reduced by 22.5% compared to the best geometric heuristic and by 3.9% compared to the average makespan of GA, with a computation time of approximately 1% of GA. Furthermore, ablation experiments showed that the lowest average makespan was achieved under different numbers of machines and part sizes. Removing geometric features caused the most significant performance degradation, indicating that geometry-aware state representation plays a crucial role in AM scheduling and nested integration. Generalization experiments showed that, without retraining or parameter tuning, this method can be transferred to real industrial part geometry and unseen machine configurations, consistently outperforming the heuristic baseline.

[0045] The technical solution provided by this invention, by jointly generating part selection, machine allocation, batch formation, orientation selection, and two-dimensional placement decisions in a sequential decision-making process, directly couples the spatially nested results with the time scheduling objective. While ensuring geometric constraints, this effectively reduces the overall completion time of the heterogeneous AM system and improves the real-time inference capability of the software system. Compared to MILP, it has better computational efficiency for medium-to-large-scale problems; compared to genetic algorithms, it eliminates the need for long-term population searches on each instance, effectively reducing computation time; and compared to manual heuristic methods, it reduces reliance on fixed part sorting rules and manual parameters.

[0046] Example 2 Figure 6 This is a schematic diagram of the scheduling and nesting device for additive manufacturing provided in Embodiment 2 of the present invention. This device can be implemented in hardware and / or software, and is generally integrated into a computer device to execute the scheduling and nesting method for additive manufacturing provided in any embodiment of the present invention. Figure 6 As shown, the device includes: The processing information acquisition module 21 is used to perform step one: acquiring information about the part to be processed and machine configuration parameters; The scheduling status update module 22 is used to execute step two, which determines the current part status, machine status and system status based on the information of the part to be processed and the machine configuration parameters. The scheduling action selection module 23 is used to execute step three: select the scheduling action of the part to be assigned or the batch shutdown action according to the part status, the machine status and the system status. The parts placement module 24 is used to execute step four: if the part scheduling action to be assigned is selected, the placement direction and coordinates of the target part in the target machine are determined, and a geometric feasibility verification is performed. Batch shutdown module 25 is used to execute step five: if the batch shutdown action is selected, the current batch of the target machine is shut down, the processing time of the current batch of the target machine and the completion time of the current machine are calculated, and the next batch of the target machine is started. Repeat execution module 26 is used to repeatedly execute steps two through five until all parts are assigned and all non-empty batches are closed. The output module 27 is used to output the batch sequence of each machine, the composition of the parts in each batch, the placement direction and coordinates of each part, the processing time of each batch, the completion time of each machine, and the overall completion time of the system.

[0047] The technical solution provided by this invention, by jointly generating part selection, machine allocation, batch formation, orientation selection, and two-dimensional placement decisions in a sequential decision-making process, directly couples the spatially nested results with the time scheduling objective. While ensuring geometric constraints, this effectively reduces the overall completion time of the heterogeneous AM system and improves the real-time inference capability of the software system. Compared to MILP, it has better computational efficiency for medium-to-large-scale problems; compared to genetic algorithms, it eliminates the need for long-term population searches on each instance, effectively reducing computation time; and compared to manual heuristic methods, it reduces reliance on fixed part sorting rules and manual parameters.

[0048] Based on the above technical solution, optionally, the part status includes part volume, length, width and height of each candidate direction and support volume of each candidate direction, as well as area pressure relative to the machine in each candidate direction, local matching degree, height utilization rate, height deviation, support volume ratio and incremental processing time caused by inserting the current batch. The machine status includes the length, width and height of the construction platform, as well as the area utilization rate of the current batch, the maximum proportion of free rectangles, the number of available free rectangles, the height utilization rate, the part height variance, the volume utilization rate, the support volume ratio, the estimated processing time of the current batch and the estimated machine completion time. The system status includes the proportion of remaining unallocated parts, the proportion of remaining parts volume, the current overall system completion time, and the variance of the completion time of each machine. It also includes the average area utilization rate, average height utilization rate, average volume utilization rate, and average batch processing time of completed batches.

[0049] Based on the above technical solution, optionally, the device further includes: The problem modeling module is used to model the scheduling and nested integrated problem on heterogeneous additive manufacturing machines as a combinatorial optimization problem with the objective of minimizing the overall system completion time. The overall system completion time is calculated as follows: ; ; ; Wherein, C_max represents the overall completion time of the system, T_{b,m} represents the processing time of batch b in batch set B_m on machine m in machine set M, VT_m represents the unit volume scanning time of machine m, v_i represents the body volume of part i in batch b, s_{i,o_i} represents the support volume of part i under the selected placement direction o_i, HT_m represents the unit height powder spreading or recoating time of machine m, H_{b,m} represents the maximum height of batch b, C_m represents the machine completion time of machine m, and SET_m represents the batch setting time of machine m.

[0050] Based on the above technical solution, optionally, the scheduling and nesting integrated problem is specifically modeled as a Markov decision process, the state includes the part state, the machine state and the system state, the action includes the scheduling action of the part to be allocated and the batch closing action, the reward includes the part insertion reward and the batch closing reward, and the termination condition is that all parts are allocated and all non-empty batches are closed.

[0051] Based on the above technical solution, optionally, the scheduling and nesting integration problem is solved using a deep reinforcement learning network. This deep reinforcement learning network includes a part state encoder, a machine state encoder, a system state encoder, a scheduling decoder, a nesting decoder, a value decoder, and an experience cache. The part state encoder encodes the part state, the machine state encoder encodes the machine state, the system state encoder encodes the system state, the scheduling decoder evaluates feasible part-machine combinations based on part embeddings and machine embeddings to determine the scheduling action for the part to be assigned, the nesting decoder evaluates feasible part placement directions based on the scheduling action for the part to be assigned and generates part placement coordinates, the value decoder estimates the long-term value of the current state, and the experience cache stores the state, action, reward, next state, action probability, and value estimate.

[0052] Based on the above technical solution, optionally, the nested decoder is specifically used for: Query the feasible placement directions of the target part in the current batch of the target machine during the scheduling action of the part to be assigned; Evaluate the incremental batch processing time caused by each of the aforementioned feasible placement orientations, and preferentially select the feasible placement orientation with the smaller incremental batch processing time as the part placement orientation; The maximum rectangle algorithm is invoked to place the part in the lower left corner. The placement coordinates of the part are determined according to the placement direction of the part, and a geometric feasibility check is performed.

[0053] The scheduling and nesting apparatus for additive manufacturing provided in the embodiments of the present invention can execute the scheduling and nesting method for additive manufacturing provided in any embodiment of the present invention, and has the corresponding functional modules and beneficial effects of the execution method.

[0054] It is worth noting that in the above embodiments of the scheduling and nesting device for additive manufacturing, the various units and modules included are only divided according to functional logic, but are not limited to the above division, as long as the corresponding functions can be achieved; in addition, the specific names of each functional unit are only for easy differentiation and are not used to limit the scope of protection of the present invention.

[0055] Example 3 Figure 7 This is a schematic diagram of the structure of a computer device provided in Embodiment 3 of the present invention, showing a block diagram of an exemplary computer device suitable for implementing the embodiments of the present invention. Figure 7 The computer device shown is merely an example and should not be construed as limiting the functionality or scope of the embodiments of the present invention. Figure 7 As shown, the computer device includes a processor 31, a memory 32, an input device 33, and an output device 34; the number of processors 31 in the computer device can be one or more. Figure 7 Taking a processor 31 as an example, the processor 31, memory 32, input device 33, and output device 34 in a computer device can be connected via a bus or other means. Figure 7 Taking the example of a connection between China and Israel via a bus.

[0056] The memory 32, as a computer-readable storage medium, can be used to store software programs, computer-executable programs, and modules, such as the program instructions / modules corresponding to the scheduling and nesting method for additive manufacturing in this embodiment of the invention (e.g., the processing information acquisition module 21, scheduling status update module 22, scheduling action selection module 23, part placement module 24, batch closing module 25, repetitive execution module 26, and result output module 27 in the scheduling and nesting device for additive manufacturing). The processor 31 executes various functional applications and data processing of the computer device by running the software programs, instructions, and modules stored in the memory 32, thereby realizing the aforementioned scheduling and nesting method for additive manufacturing.

[0057] The memory 32 may primarily include a program storage area and a data storage area. The program storage area may store the operating system and at least one application program required for a given function; the data storage area may store data created based on the use of the computer device. Furthermore, the memory 32 may include high-speed random access memory and non-volatile memory, such as at least one disk storage device, flash memory, or other non-volatile solid-state storage device. In some instances, the memory 32 may further include memory remotely located relative to the processor 31, which can be connected to the computer device via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0058] Input device 33 can be used to acquire information about the parts to be processed and machine configuration parameters, as well as to generate key signal inputs related to user settings and function control of the computer equipment. Output device 34 can be used to display visual scheduling and nesting results to the user, etc.

[0059] Example 4 Embodiment 4 of the present invention also provides a storage medium containing computer-executable instructions, which, when executed by a computer processor, are used to perform a scheduling and nesting method for additive manufacturing, the method comprising: Step 1: Obtain information about the parts to be processed and the machine configuration parameters; Step 2: Based on the information of the part to be processed and the machine configuration parameters, determine the current part status, machine status, and system status; Step 3: Based on the status of the parts, the status of the machines, and the status of the systems, select the scheduling action for the parts to be assigned or the batch shutdown action; Step 4: If the scheduled action for the part to be assigned is selected, the placement direction and coordinates of the target part in the target machine are determined, and a geometric feasibility verification is performed. Step 5: If the batch shutdown action is selected, the current batch of the target machine is shut down, the processing time of the current batch and the completion time of the current machine are calculated, and the next batch of the target machine is started. Step 6: Repeat steps 2 through 5 until all parts have been assigned and all non-empty batches have been closed; Step 7: Output the batch sequence of each machine, the composition of each batch, the placement direction and coordinates of each part, the processing time of each batch, the completion time of each machine, and the overall completion time of the system.

[0060] Storage media can be any type of memory device or storage device. The term "storage media" is intended to include: mounting media, such as CD-ROMs, floppy disks, or magnetic tape devices; computer system memory or random access memory, such as DRAM, DDR RAM, SRAM, EDO RAM, Rambus RAM, etc.; non-volatile memory, such as flash memory, magnetic media (e.g., hard disks or optical storage); registers or other similar types of memory elements. Storage media may also include other types of memory or combinations thereof. Furthermore, storage media may reside in a computer system in which the program is executed, or may reside in a different second computer system connected to the computer system via a network (such as the Internet). The second computer system can provide program instructions to the computer for execution. The term "storage media" can include two or more storage media that may reside in different locations (e.g., in different computer systems connected via a network). Storage media may store program instructions (e.g., specifically implemented as a computer program) that can be executed by one or more processors.

[0061] Of course, the computer-executable instructions provided in the embodiments of the present invention are not limited to the method operations described above, but can also execute related operations in the scheduling and nesting methods for additive manufacturing provided in any embodiment of the present invention.

[0062] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. Computer-readable signal media may also be any computer-readable medium other than computer-readable storage media, capable of sending, propagating, or transmitting programs for use by or in connection with an instruction execution system, apparatus, or device.

[0063] Program code contained on a computer-readable medium may be transmitted using any suitable medium, including but not limited to wireless, wire, optical fiber, RF, etc., or any suitable combination thereof.

[0064] Based on the above description of the implementation methods, those skilled in the art can clearly understand that the present invention can be implemented using software and necessary general-purpose hardware, and of course, it can also be implemented using hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as a computer floppy disk, read-only memory (ROM), random access memory (RAM), flash memory, hard disk, or optical disk, etc., including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments of the present invention.

[0065] Example 5 Embodiment 5 of the present invention also provides a computer program product, which includes a computer program (also referred to as code or instructions). The computer program can be stored in a computer-readable storage medium. When the computer program is executed by a processor, it is used to execute the scheduling and nesting method for additive manufacturing provided in any of the above embodiments, and has the corresponding beneficial effects of the execution method.

[0066] Note that the above description is merely a preferred embodiment of the present invention and the technical principles employed. Those skilled in the art will understand that the present invention is not limited to the specific embodiments described herein, and various obvious changes, readjustments, and substitutions can be made without departing from the scope of protection of the present invention. Therefore, although the present invention has been described in detail through the above embodiments, the present invention is not limited to the above embodiments, and may include many other equivalent embodiments without departing from the concept of the present invention, the scope of which is determined by the scope of the appended claims.

Claims

1. A scheduling and nesting method for additive manufacturing, characterized in that, include: Step 1: Obtain information about the parts to be processed and the machine configuration parameters; Step 2: Based on the information of the part to be processed and the machine configuration parameters, determine the current part status, machine status, and system status; Step 3: Based on the status of the parts, the status of the machines, and the status of the systems, select the scheduling action for the parts to be assigned or the batch shutdown action; Step 4: If the scheduled action for the part to be assigned is selected, the placement direction and coordinates of the target part in the target machine are determined, and a geometric feasibility verification is performed. Step 5: If the batch shutdown action is selected, the current batch of the target machine is shut down, the processing time of the current batch and the completion time of the current machine are calculated, and the next batch of the target machine is started. Step 6: Repeat steps 2 through 5 until all parts have been assigned and all non-empty batches have been closed; Step 7: Output the batch sequence of each machine, the composition of each batch, the placement direction and coordinates of each part, the processing time of each batch, the completion time of each machine, and the overall completion time of the system.

2. The scheduling and nesting method for additive manufacturing according to claim 1, characterized in that, The part status includes part volume, length, width and height of each candidate direction and support volume of each candidate direction, as well as area pressure relative to the machine in each candidate direction, local matching degree, height utilization rate, height deviation, support volume ratio and incremental processing time caused by inserting the current batch. The machine status includes the length, width and height of the construction platform, as well as the area utilization rate of the current batch, the maximum proportion of free rectangles, the number of available free rectangles, the height utilization rate, the part height variance, the volume utilization rate, the support volume ratio, the estimated processing time of the current batch and the estimated machine completion time. The system status includes the proportion of remaining unallocated parts, the proportion of remaining parts volume, the current overall system completion time, and the variance of the completion time of each machine. It also includes the average area utilization rate, average height utilization rate, average volume utilization rate, and average batch processing time of completed batches.

3. The scheduling and nesting method for additive manufacturing according to claim 1, characterized in that, The method further includes: The scheduling and nesting integration problem on heterogeneous additive manufacturing machines is modeled as a combinatorial optimization problem with the objective of minimizing the overall system completion time. The overall system completion time is calculated as follows: ； ； ； Wherein, C_max represents the overall completion time of the system, T_{b,m} represents the processing time of batch b in batch set B_m on machine m in machine set M, VT_m represents the unit volume scanning time of machine m, v_i represents the body volume of part i in batch b, s_{i,o_i} represents the support volume of part i under the selected placement direction o_i, HT_m represents the unit height powder spreading or recoating time of machine m, H_{b,m} represents the maximum height of batch b, C_m represents the machine completion time of machine m, and SET_m represents the batch setting time of machine m.

4. The scheduling and nesting method for additive manufacturing according to claim 3, characterized in that, The scheduling and nesting integrated problem is specifically modeled as a Markov decision process. The states include the part state, the machine state, and the system state. The actions include the scheduling action of the part to be allocated and the batch closing action. The rewards include the part insertion reward and the batch closing reward. The termination condition is that all parts have been allocated and all non-empty batches have been closed.

5. The scheduling and nesting method for additive manufacturing according to claim 4, characterized in that, The scheduling and nesting integration problem is solved by a deep reinforcement learning network, which includes a part state encoder, a machine state encoder, a system state encoder, a scheduling decoder, a nesting decoder, a value decoder, and an experience cache. The part state encoder is used to encode the part state, the machine state encoder is used to encode the machine state, the system state encoder is used to encode the system state, the scheduling decoder is used to evaluate feasible part-machine combinations based on part embedding and machine embedding to determine the scheduling action of the part to be assigned, the nested decoder is used to evaluate feasible part placement directions based on the scheduling action of the part to be assigned and generate part placement coordinates, the value decoder is used to estimate the long-term value of the current state, and the experience cache is used to store the state, action, reward, next state, action probability, and value estimate.

6. The scheduling and nesting method for additive manufacturing according to claim 5, characterized in that, The nested decoder is specifically used for: Query the feasible placement directions of the target part in the current batch of the target machine during the scheduling action of the part to be assigned; Evaluate the incremental batch processing time caused by each of the aforementioned feasible placement orientations, and preferentially select the feasible placement orientation with the smaller incremental batch processing time as the part placement orientation; The maximum rectangle algorithm is invoked to place the part in the lower left corner. The placement coordinates of the part are determined according to the placement direction of the part, and a geometric feasibility check is performed.

7. A scheduling and nesting apparatus for additive manufacturing, characterized in that, include: The processing information acquisition module is used to execute step one: acquire information about the parts to be processed and machine configuration parameters; The scheduling status update module is used to execute step two: based on the information of the part to be processed and the machine configuration parameters, determine the current part status, machine status and system status; The scheduling action selection module is used to execute step three: select the scheduling action for the part to be assigned or the batch shutdown action based on the part status, the machine status and the system status. The parts placement module is used to execute step four: if the part scheduling action to be assigned is selected, the placement direction and coordinates of the target part in the target machine are determined, and a geometric feasibility verification is performed. The batch shutdown module is used to execute step five: if the batch shutdown action is selected, the current batch of the target machine is shut down, the processing time of the current batch of the target machine and the completion time of the current machine are calculated, and the next batch of the target machine is started. The repeat execution module is used to repeatedly execute steps two through five until all parts have been assigned and all non-empty batches have been closed. The results output module is used to output the batch sequence of each machine, the composition of the parts in each batch, the placement direction and coordinates of each part, the processing time of each batch, the completion time of each machine, and the overall completion time of the system.

8. A computer device, characterized in that, include: One or more processors; Memory, used to store one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the scheduling and nesting method for additive manufacturing as described in any one of claims 1-6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the program implements the scheduling and nesting method for additive manufacturing as described in any one of claims 1-6.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the scheduling and nesting method for additive manufacturing as described in any one of claims 1-6.

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