3D printing scheduling method considering workpiece rotation arrangement

Abstract

The invention provides a 3D printing scheduling method considering workpiece rotation arrangement, and belongs to the field of intelligent manufacturing. The minimum total completion time is used as an optimization target, and the constraint of the printing problem considers the working space size constraint of the printing equipment; a plurality of workpieces with different geometrical shapes are distributed to a plurality of 3D printing devices to be manufactured, and a plurality of same or different workpieces are arranged in a working space of each 3D printing device; workpieces can rotate around the x axis, the y axis and the z axis of a standard Cartesian space coordinate system when being placed into a working space of 3D printing equipment, all feasible rotation angle combinations around the x axis and the y axis are listed according to the technological requirements of all the workpieces during printing and serve as an xy rotation combination set of the workpieces, and in addition, the workpieces are allowed to rotate around the z axis at any angle; in order to completely describe problem attributes of a printing task, a coding structure of individuals in a population is a four-layer integer code composed of a workpiece sequence, an equipment sequence, an xy rotation sequence and a z rotation sequence; the arrangement angles of the workpieces are preliminarily selected according to the features of the workpieces, optimization is carried out according to the arrangement compactness, and then the quality of the arrangement result of each generation of population is improved; and constructing a mathematical model in combination with a swarm intelligence algorithm, carrying out solving, and outputting a final arrangement optimization result.

Description

Technical Field

[0001] The present invention relates to the field of intelligent manufacturing, and in particular to a 3D printing scheduling method that takes into account the rotational arrangement of workpieces. Background Art

[0002] At present, as 3D printing technology gradually matures, the demand for high-performance 3D printing products and workpieces is increasing. However, high-performance 3D printing equipment is expensive, and customer needs are personalized and small batches. Therefore, high-performance 3D printing mainly adopts the production and operation model of 3DPaas (3D Printing as a Service): according to customers' personalized customized orders, based on existing equipment, the 3D printing service in the order is completed within the delivery period.

[0003] Printing efficiency is crucial for 3DPaaS. Photocuring printing technologies such as digital light processing (DLP) and liquid-crystal display (LCD) and multi-nozzle powder sintering (Power Bed Fusion, PBF) printing technology can realize the simultaneous processing of multiple workpieces in one production batch, and have the characteristics of basically equal printing time for each layer. Therefore, the single printing time of such equipment mainly depends on the height of the workpiece. For such 3D printing tasks, if the utilization rate of the equipment printing workspace can be fully utilized, and multiple workpieces can be printed in the same printing equipment in the same production, the printing efficiency will be greatly improved because the printing time of each layer is relatively fixed. However, the arrangement of workpieces with different geometric shapes and the batch processing machine problems in printing production affect each other, jointly affect production efficiency, and directly affect production costs. Differences in arrangement strategies will affect the utilization rate of printing space and placement strategies, and then affect the batch division results and production time; differences in equipment allocation results will also change the batch division results due to the difference in the size of the printing space of different workbenches, and then cause changes in printing production time. In order to make full use of current production resources, reduce workpiece production time, improve production efficiency and capacity, and optimize equipment utilization in batch printing production, it is urgently necessary to propose a more reasonable scheduling optimization solution. Summary of the invention

[0004] The object of the present invention is to provide a 3D printing scheduling method taking into account the rotational arrangement of workpieces.

[0005] A definition of a 3D printing scheduling problem that takes into account the rotational arrangement of workpieces can be described as follows: multiple workpieces of different geometric shapes are assigned to multiple 3D printing devices for manufacturing, and multiple identical or different workpieces are arranged in the workspace of each 3D printing device to optimize the overall completion time; the workpiece can be rotated when placed in the workspace of the 3D printing device; wherein the rotation can be performed around the x, y, and z axes of the standard Cartesian space coordinate system, and according to the process requirements of each workpiece when printing, all feasible rotation angle combinations around the x and y axes are listed as the xy rotation combination set of the workpiece, In addition, the workpiece is allowed to rotate around the z-axis at any angle; the arrangement angle of the workpiece is preliminarily selected according to the workpiece characteristics and optimized according to the arrangement compactness, where the arrangement compactness is the ratio of the projected area of ​​all arranged workpieces to the area of ​​the minimum enveloping rectangle of the workpiece, which is used to reflect the compactness of the workpiece arrangement; given the workpieces assigned to each 3D printing device, the workspace size of each device, and the rotation angle of each workpiece placement, a printing plan is constructed; minimizing the total completion time is taken as the optimization goal, and a mathematical model is constructed in combination with the swarm intelligence algorithm, and the constraints of the model take into account the workspace size constraints of the printing device;

[0006] The problem model must meet the following constraints:

[0007] 1) During the arrangement process, the workpieces are not stacked or nested with each other;

[0008] 2) The rotation directions in the xy rotation combination set all meet the process requirements and production requirements;

[0009] 3) During the printing process, all printing devices have the same printing speed, and the printing time is positively correlated with the maximum height of all workpieces in the printing plan;

[0010] 4) All workpieces can be processed at time zero;

[0011] The objective function of the problem model is as follows:

[0012] Total processing time: In the formula is the time required for the bth printing plan of the mth device, n b is the total printing plan quantity, T ms The processing time before and after the production of 3D printing equipment, is the maximum workpiece printing height of the bth printing plan of the mth device, n is the total number of workpieces, a ik The projection area when selecting the kth xy rotation combination for the i-th workpiece, x imb Indicates whether the i-th workpiece is arranged in the b-th printing plan of the m-th device.

[0013] To solve the above problems, the present invention aims to disclose a 3D printing scheduling method considering the rotation arrangement of workpieces, which mainly includes the following steps:

[0014] Step 1: Generate an initial population; the population consists of multiple individuals, each of which has a four-layer coding structure, which includes a workpiece sequence, a device sequence, an xy rotation sequence, and a z rotation sequence; each individual corresponds to a feasible solution for a printing task, and is generated according to different xy rotation combinations and different workpiece placement sequences, with different workpiece placement positions and rotation angles around the z axis;

[0015] 1a: The workpieces in the printing task are randomly shuffled to form a workpiece sequence; the numbering order of the workpiece sequence is the current workpiece placement order; according to the order of the workpiece sequence, the xy rotation combination is randomly selected from the xy rotation combination set of each workpiece in turn, and the final sequence generated is the xy rotation sequence;

[0016] 1b: Combine the workpiece sequence and the xy rotation sequence to obtain the initial height of each device in the 3D printing workspace. The specific steps are as follows:

[0017] 1b-1: According to the workpiece sequence and combined with the xy rotation sequence, obtain the printing height sequence and projection area sequence corresponding to all workpieces;

[0018] 1b-2: Sort the print height sequence from small to large to obtain a new print height sequence;

[0019] 1b-3: According to the discrete degree of the height values ​​in the newly sorted new printing height sequence, the new sequence is divided into several height intervals; if the number of intervals is less than the number of devices, the interval with a larger number of individuals in the interval is copied; if the number of intervals is more than the number of devices, the adjacent intervals with a smaller number of individuals in the interval are merged; the final number of intervals is equal to the number of devices in the 3D printing workspace;

[0020] 1b-4: Obtain the total projection area corresponding to each height interval according to the projection area sequence and the printing height sequence before sorting;

[0021] 1b-5: Determine the initial height of each device based on the total projection area and the specifications of each 3D printing device; if the total projection area is larger, try to choose a device with larger specifications;

[0022] 1c: According to the order of the workpiece sequence, the difference between each workpiece and the initial height of each device in the 3D printing workspace is calculated in turn, and the device number with the smallest difference is put into the same sequence. The final generated sequence is the device sequence;

[0023] 1d: According to the xy rotation sequence and the workpiece features, the initial rotation angles of each workpiece are determined and put into the same sequence. The final generated sequence is the z rotation sequence; the z rotation sequence of all individuals is automatically optimized according to a critical polygon arrangement method that takes rotation into account;

[0024] The specific steps of the critical polygon arrangement method considering rotation are:

[0025] 1d-1: Fix the filled figure and mark it as the original figure A, mark the figure to be filled as B, draw the envelope rectangle E of the figure B when it is not rotated, mark the center point of the envelope rectangle E as O, and execute 1d-2;

[0026] 1d-2: Rotate figure B around point O by an angle of β, and execute 1d-3;

[0027] 1d-3: Select a vertex from shape B as the moving reference point C, move shape B close to a vertex of the filled pattern A, and execute 1d-4;

[0028] 1d-4: Translate the graphic B close to the graphic A until B cannot move or is about to leave A, then change the angle so that the graphic B continues to be closely translated, and record the movement trajectory. Repeat the above operation until the graphic B circles around A. The graphic constructed by the trajectory of point C is the workpiece constraint graphic; Translate the graphic B within the boundary of the workbench of the 3D printing device according to the above method. The graphic constructed by the trajectory of point C is the workbench constraint graphic; Combine the workpiece constraint graphic and the workbench constraint graphic, and use all the vertices of the workpiece constraint graphic within the workbench constraint graphic as optional placement points, and execute 1d-5;

[0029] 1d-5: Place the graphic B into each optional placement point in turn, draw the envelope rectangle F of the entire graphic on the workbench after placement, calculate the ratio γ of the current workbench image area to the envelope rectangle F area, and the ratio γ is used to reflect the arrangement compactness of the graphic. Select the placement point with the lowest arrangement compactness as the optimal placement position at the current angle, record the arrangement compactness, placement coordinates and current rotation angle of the optimal placement position, and execute 1d-6;

[0030] 1d-6: If the current rotation angle of shape B is greater than or equal to 360°, execute 1d-7; otherwise, return to execute 1d-2;

[0031] 1d-7: Determine the final placement coordinates and rotation angle of shape B based on the lowest value of the arrangement compactness of all optimal placement positions;

[0032] Step 2: According to the equipment allocation, printing plan division and workpiece arrangement results of the current printing task, the xy rotation sequence and z rotation sequence within all individuals are automatically optimized through the xy rotation combination reconstruction optimization method, so as to change the final placement coordinates of the workpiece and the rotation angles around the x, y, and z axes, thereby shortening the time consumption of each printing plan, reducing the number of printing plans, and reducing the total production time;

[0033] The specific steps of the xy rotation combined reconstruction optimization method are as follows:

[0034] 2a: If there is a printing plan that has not been optimized among all the printing plans, a printing plan is randomly selected for optimization, and the selected printing plan is used as the printing plan to be optimized, and step 2b is executed; otherwise, step 2f is executed;

[0035] 2b: If the workpieces in the print plan to be optimized have not been traversed completely, then select the workpieces from the plan in order according to the workpiece sequence, and use the workpieces as the workpieces to be optimized; take out all the xy rotation combinations of the workpieces to be optimized whose printing height is not greater than the maximum printing height of the print plan to be optimized, put them into the xy rotation combination set to be selected, and execute 2c; otherwise, the print plan is optimized, and execute 2a;

[0036] 2c: Determine whether the set of xy rotation combinations to be selected has been traversed. If not, select the xy rotation combinations to be selected in sequence, take the selected combinations as the pending xy rotation combinations, and execute 2d; otherwise, take the xy rotation combination solution selected when the arrangement compactness is the lowest among all the results as the optimal solution, replace the xy rotation sequence and the z rotation sequence according to the optimal solution, and execute 2b;

[0037] 2d: Replace the xy rotation combination of the workpiece with the undetermined xy rotation combination, and re-complete the layout of the printing plan through a critical polygon layout method that takes rotation into account. When the printing plan is replaced so that all workpieces are placed, record the xy rotation combination, rotation angle around the z axis and layout compactness of the current plan, and execute 2c; otherwise, execute 2e;

[0038] 2e: First, among the xy rotation combinations of all remaining workpieces except the workpiece to be optimized, all xy rotation combinations that are not greater than the maximum printing height of the print plan to be optimized are taken out and put into the xy rotation candidate set. The replacement combination solution set is obtained through the xy rotation candidate set to determine whether there is at least one feasible replacement combination solution in the replacement combination solution set:

[0039] If there is at least one feasible replacement combination scheme in the replacement combination scheme set, then all feasible replacement combination schemes are replaced in turn, and all replacement results are compared. The scheme with the lowest arrangement compactness is taken as the current optimal scheme, and the xy rotation combination, rotation angle around the z axis and arrangement compactness of all workpieces in the scheme are recorded, and 2c is executed;

[0040] If there is no feasible replacement combination solution in the replacement combination solution set, the pending xy rotation combination is deleted from the candidate xy rotation combination set, and 2c is executed;

[0041] The replacement combination solution set contains multiple replacement combination solutions; the replacement combination solution refers to the remaining workpieces except the workpiece to be optimized, and the xy rotation combination corresponding to the workpiece is selected from the xy rotation candidate set in turn, and the solution is finally formed; all permutation and combination solutions are traversed and put into the same set, and the set finally formed is the replacement combination solution set;

[0042] The feasibility of the replacement combination scheme means that if the printing plan is replaced according to the replacement combination scheme, all workpieces can be arranged in the working space of the printing device, then the replacement combination scheme is feasible, otherwise it is an infeasible scheme;

[0043] 2f: All printing plans have been optimized, and the xy rotation combination reconstruction optimization is finished;

[0044] Step 3: Calculate the population objective function value; decode the four-layer structure code of each individual in the current population, and calculate the objective function value and fitness of each individual in combination with the attribute information of the printing task; perform corresponding operations on the parent population according to the characteristics of the selected swarm intelligence algorithm to obtain the child population;

[0045] Step 4: Generate a new population; mix the parent population with the child population, perform multi-objective evaluation on the mixed population, and use the first half of the mixed population with better individuals as the new population according to the evaluation results. If the iteration end condition is not met, return to step 3; if the iteration end condition is met, terminate the loop and output the current optimal population as the optimal arrangement result. DETAILED DESCRIPTION

[0046] The following describes the specific implementation of the present invention in detail using the whale group algorithm as an example:

[0047] A definition of a 3D printing scheduling problem that takes into account the rotational arrangement of workpieces can be described as follows: multiple workpieces of different geometric shapes are assigned to multiple 3D printing devices for manufacturing, and multiple identical or different workpieces are arranged in the workspace of each 3D printing device to optimize the overall completion time; the workpiece can be rotated when placed in the workspace of the 3D printing device; wherein the rotation can be performed around the x, y, and z axes of the standard Cartesian space coordinate system, and according to the process requirements of each workpiece when printing, all feasible rotation angle combinations around the x and y axes are listed as the xy rotation combination set of the workpiece, In addition, the workpiece is allowed to rotate around the z-axis at any angle; the arrangement angle of the workpiece is preliminarily selected according to the workpiece characteristics and optimized according to the arrangement compactness, where the arrangement compactness is the ratio of the projected area of ​​all arranged workpieces to the area of ​​the minimum enveloping rectangle of the workpiece, which is used to reflect the compactness of the workpiece arrangement; given the workpieces assigned to each 3D printing device, the workspace size of each device, and the rotation angle of each workpiece placement, a printing plan is constructed; minimizing the total completion time is taken as the optimization goal, and a mathematical model is constructed in combination with the swarm intelligence algorithm, and the constraints of the model take into account the workspace size constraints of the printing device;

[0048] The problem model must meet the following constraints:

[0049] 1) During the arrangement process, the workpieces are not stacked or nested with each other;

[0050] 2) The rotation directions in the xy rotation combination set all meet the process requirements and production requirements;

[0051] 3) During the printing process, all printing devices have the same printing speed, and the printing time is positively correlated with the maximum height of all workpieces in the printing plan;

[0052] 4) All workpieces can be processed at time zero;

[0053] The objective function of the problem model is as follows:

[0054] Total processing time: In the formula is the time required for the bth printing plan of the mth device, n b is the total printing plan quantity, T ms The processing time before and after the production of 3D printing equipment, is the maximum workpiece printing height of the bth printing plan of the mth device, n is the total number of workpieces, a ik The projection area when selecting the kth xy rotation combination for the i-th workpiece, x imb Indicates whether the i-th workpiece is arranged in the b-th printing plan of the m-th device.

[0055] In order to solve the above problems, the present invention adopts a 3D printing scheduling method considering the rotation arrangement of workpieces, which mainly includes the following steps:

[0056] Step 1: Generate an initial population; the population consists of multiple individuals, each of which has a four-layer coding structure, which includes a workpiece sequence, a device sequence, an xy rotation sequence, and a z rotation sequence; each individual corresponds to a feasible solution for a printing task, and is generated according to different xy rotation combinations and different workpiece placement sequences, with different workpiece placement positions and rotation angles around the z axis;

[0057] 1a: The workpieces in the printing task are randomly shuffled to form a workpiece sequence; the numbering order of the workpiece sequence is the current workpiece placement order; according to the order of the workpiece sequence, the xy rotation combination is randomly selected from the xy rotation combination set of each workpiece in turn, and the final sequence generated is the xy rotation sequence;

[0058] 1b: Combine the workpiece sequence and the xy rotation sequence to obtain the initial height of each device in the 3D printing workspace. The specific steps are as follows:

[0059] 1b-1: According to the workpiece sequence and combined with the xy rotation sequence, obtain the printing height sequence and projection area sequence corresponding to all workpieces;

[0060] 1b-2: Sort the print height sequence from small to large to obtain a new print height sequence;

[0061] 1b-3: According to the discrete degree of the height values ​​in the newly sorted new printing height sequence, the new sequence is divided into several height intervals; if the number of intervals is less than the number of devices, the interval with a larger number of individuals in the interval is copied; if the number of intervals is more than the number of devices, the adjacent intervals with a smaller number of individuals in the interval are merged; the final number of intervals is equal to the number of devices in the 3D printing workspace;

[0062] 1b-4: Obtain the total projection area corresponding to each height interval according to the projection area sequence and the printing height sequence before sorting;

[0063] 1b-5: Determine the initial height of each device based on the total projection area and the specifications of each 3D printing device; if the total projection area is larger, try to choose a device with larger specifications;

[0064] 1c: According to the order of the workpiece sequence, the difference between each workpiece and the initial height of each device in the 3D printing workspace is calculated in turn, and the device number with the smallest difference is put into the same sequence. The final generated sequence is the device sequence;

[0065] 1d: According to the xy rotation sequence and the workpiece features, the initial rotation angles of each workpiece are determined and put into the same sequence. The final generated sequence is the z rotation sequence; the z rotation sequence of all individuals is automatically optimized according to a critical polygon arrangement method that takes rotation into account;

[0066] The specific steps of the critical polygon arrangement method considering rotation are:

[0067] 1d-1: Fix the filled figure and mark it as the original figure A, mark the figure to be filled as B, draw the envelope rectangle E of the figure B when it is not rotated, mark the center point of the envelope rectangle E as O, and execute 1d-2;

[0068] 1d-2: Rotate figure B around point O by an angle of β, and execute 1d-3;

[0069] 1d-3: Select a vertex from shape B as the moving reference point C, move shape B close to a vertex of the filled pattern A, and execute 1d-4;

[0070] 1d-4: Translate the graphic B close to the graphic A until B cannot move or is about to leave A, then change the angle so that the graphic B continues to be closely translated, and record the movement trajectory. Repeat the above operation until the graphic B circles around A. The graphic constructed by the trajectory of point C is the workpiece constraint graphic; Translate the graphic B within the boundary of the workbench of the 3D printing device according to the above method. The graphic constructed by the trajectory of point C is the workbench constraint graphic; Combine the workpiece constraint graphic and the workbench constraint graphic, and use all the vertices of the workpiece constraint graphic within the workbench constraint graphic as optional placement points, and execute 1d-5;

[0071] 1d-5: Place the graphic B into each optional placement point in turn, draw the envelope rectangle F of the entire graphic on the workbench after placement, calculate the ratio γ of the current workbench image area to the envelope rectangle F area, and the ratio γ is used to reflect the arrangement compactness of the graphic. Select the placement point with the lowest arrangement compactness as the optimal placement position at the current angle, record the arrangement compactness, placement coordinates and current rotation angle of the optimal placement position, and execute 1d-6;

[0072] 1d-6: If the current rotation angle of shape B is greater than or equal to 360°, execute 1d-7; otherwise, return to execute 1d-2;

[0073] 1d-7: Determine the final placement coordinates and rotation angle of shape B based on the lowest value of the arrangement compactness of all optimal placement positions;

[0074] Step 2: According to the equipment allocation, printing plan division and workpiece arrangement results of the current printing task, the xy rotation sequence and z rotation sequence within all individuals are automatically optimized through the xy rotation combination reconstruction optimization method, so as to change the final placement coordinates of the workpiece and the rotation angles around the x, y, and z axes, thereby shortening the time consumption of each printing plan, reducing the number of printing plans, and reducing the total production time;

[0075] The specific steps of the xy rotation combined reconstruction optimization method are as follows:

[0076] 2a: If there is a printing plan that has not been optimized among all the printing plans, a printing plan is randomly selected for optimization, and the selected printing plan is used as the printing plan to be optimized, and step 2b is executed; otherwise, step 2f is executed;

[0077] 2b: If the workpieces in the print plan to be optimized have not been traversed completely, then select the workpieces from the plan in order according to the workpiece sequence, and use the workpieces as the workpieces to be optimized; take out all the xy rotation combinations of the workpieces to be optimized whose printing height is not greater than the maximum printing height of the print plan to be optimized, put them into the xy rotation combination set to be selected, and execute 2c; otherwise, the print plan is optimized, and execute 2a;

[0078] 2c: Determine whether the set of xy rotation combinations to be selected has been traversed. If not, select the xy rotation combinations to be selected in sequence, take the selected combinations as the pending xy rotation combinations, and execute 2d; otherwise, take the xy rotation combination solution selected when the arrangement compactness is the lowest among all the results as the optimal solution, replace the xy rotation sequence and the z rotation sequence according to the optimal solution, and execute 2b;

[0079] 2d: Replace the xy rotation combination of the workpiece with the undetermined xy rotation combination, and re-complete the layout of the printing plan through a critical polygon layout method that takes rotation into account. When the printing plan is replaced so that all workpieces are placed, record the xy rotation combination, rotation angle around the z axis and layout compactness of the current plan, and execute 2c; otherwise, execute 2e;

[0080] 2e: First, among the xy rotation combinations of all remaining workpieces except the workpiece to be optimized, all xy rotation combinations that are not greater than the maximum printing height of the print plan to be optimized are taken out and put into the xy rotation candidate set. The replacement combination solution set is obtained through the xy rotation candidate set to determine whether there is at least one feasible replacement combination solution in the replacement combination solution set:

[0081] If there is at least one feasible replacement combination scheme in the replacement combination scheme set, then all feasible replacement combination schemes are replaced in turn, and all replacement results are compared. The scheme with the lowest arrangement compactness is taken as the current optimal scheme, and the xy rotation combination, rotation angle around the z axis and arrangement compactness of all workpieces in the scheme are recorded, and 2c is executed;

[0082] If there is no feasible replacement combination solution in the replacement combination solution set, the pending xy rotation combination is deleted from the candidate xy rotation combination set, and 2c is executed;

[0083] The replacement combination solution set contains multiple replacement combination solutions; the replacement combination solution refers to the remaining workpieces except the workpiece to be optimized, and the xy rotation combination corresponding to the workpiece is selected from the xy rotation candidate set in turn, and the solution is finally formed; all permutation and combination solutions are traversed and put into the same set, and the set finally formed is the replacement combination solution set;

[0084] The feasibility of the replacement combination scheme means that if the printing plan is replaced according to the replacement combination scheme, all workpieces can be arranged in the working space of the printing device, then the replacement combination scheme is feasible, otherwise it is an infeasible scheme;

[0085] 2f: All printing plans have been optimized, and the xy rotation combination reconstruction optimization is finished;

[0086] Step 3: Calculate the population objective function value; decode the four-layer structure code of each individual in the current population, and calculate the objective function value and fitness of each individual in combination with the attribute information of the printing task; perform corresponding operations on the parent population according to the characteristics of the selected swarm intelligence algorithm to obtain the child population;

[0087] Step 4: Generate a new population; mix the parent population with the child population, perform multi-objective evaluation on the mixed population, and use the first half of the mixed population with better individuals as the new population according to the evaluation results. If the iteration end condition is not met, return to step 3; if the iteration end condition is met, terminate the loop and output the current optimal population as the optimal arrangement result.

[0088] The specific process of the whale group algorithm is as follows:

[0089] S1. Initialize the parameters of the whale group algorithm: population size N, problem size, maximum number of iterations G, stability threshold Ts, random move probability g_pMove;

[0090] S2, population initialization: Initialize the population and evaluate all individuals, then perform a non-dominant sort on the initialized population and initialize the Pareto external archive;

[0091] S3, individual position update: find the "better and closest" guide individual for each individual. If the guide individual exists, then establish the individual movement rule according to the movement rule 2d of the xy rotation combination reconstruction optimization method to generate a copy of the individual; if it does not exist, then perform a neighborhood search for the individual according to the search rule 2e of the xy rotation combination reconstruction optimization method to generate a copy of the individual;

[0092] S4, dominance relationship judgment whether to keep the new copy: judge the dominance relationship between the old individual and its copy individual. If the old individual dominates its copy individual, increase the count value of the old individual and discard the copy individual; otherwise, add the copy individual to the offspring population;

[0093] S5, stability threshold detection: determine whether the count of each individual exceeds the stability threshold Ts. If so, reinitialize the corresponding individual;

[0094] S6, update the population and Pareto external archive: first merge the offspring population with the original parent population, then perform fast non-dominant sorting on the merged population, and finally update the population, keeping the original size P unchanged, and update the Pareto external archive;

[0095] S7, iteration number t++, determine whether the termination condition of the algorithm is met, if so, output the Pareto external archive, otherwise return to S3.

Claims

1. A 3D printing scheduling method considering the rotation arrangement of workpieces, characterized in that: Assign multiple workpieces of different geometric shapes to multiple 3D printing devices for manufacturing, and arrange multiple identical or different workpieces in the workspace of each 3D printing device to optimize the overall completion time; the workpiece can be rotated when placed in the workspace of the 3D printing device; wherein the rotation can be performed around the x, y, and z axes of the standard Cartesian space coordinate system, and according to the process requirements of each workpiece when printing, all feasible rotation angle combinations around the x-axis and the y-axis are listed as the xy rotation combination set of the workpiece, and the workpiece is allowed to rotate around the z-axis at any angle; the arrangement angle of the workpiece is preliminarily selected according to the characteristics of the workpiece, and is optimized according to the arrangement compactness, wherein the arrangement compactness is the ratio of the projected area of ​​all arranged workpieces to the area of ​​the minimum enveloping rectangle of the workpiece, which is used to reflect the compactness of the workpiece arrangement; Given the workpieces assigned to each 3D printing device, the workspace size of each device, and the rotation angle of each workpiece, a printing plan is constructed; minimizing the total completion time is used as the optimization goal, and a mathematical model is constructed in combination with the swarm intelligence algorithm. The constraints of the model take into account the workspace size constraints of the printing device; The specific steps include: Step 1: Generate an initial population; the population consists of multiple individuals, each of which has a four-layer coding structure, which includes a workpiece sequence, a device sequence, an xy rotation sequence, and a z rotation sequence; each individual corresponds to a feasible solution for a printing task, and is generated according to different xy rotation combinations and different workpiece placement sequences, with different workpiece placement positions and rotation angles around the z axis; 1a: The workpieces in the printing task are randomly shuffled to form a workpiece sequence; the numbering order of the workpiece sequence is the current workpiece placement order; according to the order of the workpiece sequence, the xy rotation combination is randomly selected from the xy rotation combination set of each workpiece in turn, and the final sequence generated is the xy rotation sequence; 1b: Combine the workpiece sequence and the xy rotation sequence to obtain the initial height of each device in the 3D printing workspace. The specific steps are as follows: 1b-1: According to the workpiece sequence and combined with the xy rotation sequence, obtain the printing height sequence and projection area sequence corresponding to all workpieces; 1b-2: Sort the print height sequence from small to large to obtain a new print height sequence; 1b-3: According to the discrete degree of the height values ​​in the newly sorted new printing height sequence, the new sequence is divided into several height intervals; if the number of intervals is less than the number of devices, the interval with a larger number of individuals in the interval is copied; if the number of intervals is more than the number of devices, the adjacent intervals with a smaller number of individuals in the interval are merged; the final number of intervals is equal to the number of devices in the 3D printing workspace; 1b-4: Obtain the total projection area corresponding to each height interval according to the projection area sequence and the printing height sequence before sorting; 1b-5: Determine the initial height of each device based on the total projection area and the specifications of each 3D printing device; if the total projection area is larger, try to choose a device with larger specifications; 1c: According to the order of the workpiece sequence, the difference between each workpiece and the initial height of each device in the 3D printing workspace is calculated in turn, and the device number with the smallest difference is put into the same sequence. The final generated sequence is the device sequence; 1d: According to the xy rotation sequence and the workpiece features, the initial rotation angles of each workpiece are determined and put into the same sequence. The final generated sequence is the z rotation sequence; the z rotation sequence of all individuals is automatically optimized according to a critical polygon arrangement method that takes rotation into account; Step 2: According to the equipment allocation, printing plan division and workpiece arrangement results of the current printing task, the xy rotation sequence and z rotation sequence within all individuals are automatically optimized through the xy rotation combination reconstruction optimization method, so as to change the final placement coordinates of the workpiece and the rotation angles around the x, y, and z axes, thereby shortening the time consumption of each printing plan, reducing the number of printing plans, and reducing the total production time; The specific steps of the xy rotation combined reconstruction optimization method are as follows: 2a: If there is a printing plan that has not been optimized among all the printing plans, a printing plan is randomly selected for optimization, and the selected printing plan is used as the printing plan to be optimized, and step 2b is executed; otherwise, step 2f is executed; 2b: If the workpieces in the print plan to be optimized have not been traversed completely, then select the workpieces from the plan in order according to the workpiece sequence, and use the workpieces as the workpieces to be optimized; take out all the xy rotation combinations of the workpieces to be optimized whose printing height is not greater than the maximum printing height of the print plan to be optimized, put them into the xy rotation combination set to be selected, and execute 2c; otherwise, the print plan is optimized, and execute 2a; 2c: Determine whether the set of xy rotation combinations to be selected has been traversed. If not, select the xy rotation combinations to be selected in sequence, take the selected combinations as the pending xy rotation combinations, and execute 2d; otherwise, take the xy rotation combination solution selected when the arrangement compactness is the lowest among all the results as the optimal solution, replace the xy rotation sequence and the z rotation sequence according to the optimal solution, and execute 2b; 2d: Replace the xy rotation combination of the workpiece with the undetermined xy rotation combination, and re-complete the layout of the printing plan through a critical polygon layout method that takes rotation into account. When the printing plan is replaced so that all workpieces are placed, record the xy rotation combination, rotation angle around the z axis and layout compactness of the current plan, and execute 2c; otherwise, execute 2e; 2e: First, among the xy rotation combinations of all remaining workpieces except the workpiece to be optimized, all xy rotation combinations that are not greater than the maximum printing height of the print plan to be optimized are taken out and put into the xy rotation candidate set. The replacement combination solution set is obtained through the xy rotation candidate set to determine whether there is at least one feasible replacement combination solution in the replacement combination solution set: If there is at least one feasible replacement combination scheme in the replacement combination scheme set, then all feasible replacement combination schemes are replaced in turn, and all replacement results are compared. The scheme with the lowest arrangement compactness is taken as the current optimal scheme, and the xy rotation combination, rotation angle around the z axis and arrangement compactness of all workpieces in the scheme are recorded, and 2c is executed; If there is no feasible replacement combination solution in the replacement combination solution set, the pending xy rotation combination is deleted from the candidate xy rotation combination set, and 2c is executed; The replacement combination solution set contains multiple replacement combination solutions; the replacement combination solution refers to the remaining workpieces except the workpiece to be optimized, and the xy rotation combination corresponding to the workpiece is selected from the xy rotation candidate set in turn, and the solution is finally formed; all permutation and combination solutions are traversed and put into the same set, and the set finally formed is the replacement combination solution set; The feasibility of the replacement combination scheme means that if the printing plan is replaced according to the replacement combination scheme, all workpieces can be arranged in the working space of the printing device, then the replacement combination scheme is feasible, otherwise it is an infeasible scheme; 2f: All printing plans have been optimized, and the xy rotation combination reconstruction optimization is finished; Step 3: Calculate the population objective function value; decode the four-layer structure code of each individual in the current population, and calculate the objective function value and fitness of each individual in combination with the attribute information of the printing task; perform corresponding operations on the parent population according to the characteristics of the selected swarm intelligence algorithm to obtain the child population; Step 4: Generate a new population; mix the parent population with the child population, perform multi-objective evaluation on the mixed population, and use the first half of the mixed population with better individuals as the new population according to the evaluation results. If the iteration end condition is not met, return to step 3; if the iteration end condition is met, terminate the loop and output the current optimal population as the optimal arrangement result.

2. A 3D printing scheduling method considering the rotation arrangement of workpieces according to claim 1, characterized in that: The specific steps of the critical polygon arrangement method considering rotation described in step 1d are: Step 1: Fix the filled figure and mark it as the original figure A, mark the figure to be filled as B, draw the envelope rectangle E of the figure B when it is not rotated, mark the center point of the envelope rectangle E as O, and execute step 2; Step 2: Rotate figure B around point O by an angle of β, and then proceed to step 3; Step 3: Select a vertex from shape B as the moving reference point C, move shape B close to a vertex of the filled pattern A, and execute step 4; Step 4: Translate the figure B close to the figure A until B cannot move or is about to leave A, then change the angle so that the figure B continues to be close to the translation operation, and record the movement trajectory. Repeat the above operation until the figure B goes around A for one circle, and the figure constructed by the point C trajectory is the workpiece constraint figure; Translate the figure B within the worktable boundary of the 3D printing device according to the above method, and the figure constructed by the point C trajectory is the worktable constraint figure; Combine the workpiece constraint figure and the worktable constraint figure, and use all the vertices of the workpiece constraint figure inside the worktable constraint figure as optional placement points, and execute step 5; Step 5: Place the figure B into each optional placement point in turn, draw the envelope rectangle F of the entire workbench figure after placement, calculate the ratio γ of the current workbench image area to the envelope rectangle F area, and the ratio γ is used to reflect the arrangement compactness of the figure. Select the placement point with the lowest arrangement compactness as the optimal placement position at the current angle, record the arrangement compactness, placement coordinates and current rotation angle of the optimal placement position, and execute step 6; Step 6: If the current rotation angle of figure B is greater than or equal to 360°, execute step 7; otherwise, return to step 2; Step 7: Determine the final placement coordinates and rotation angle of shape B based on the lowest value of the arrangement compactness of all optimal placement positions.