Robust scheduling method for R&D and trial production of high-end equipment based on buffer time setting

Abstract

The present invention provides a robust scheduling method for high-end equipment R&D and trial production based on buffer time setting, which relates to the technical field of production scheduling. The present invention first sets the input parameters and operating parameters of the variable neighborhood search algorithm, constructs the greedy initial solution x 0 , for the initial solution x 0 Perform the shaking operation and update the solution to x by moving the particles. 1 , select the neighborhood structure pair x 1 Perform local search to obtain the local optimal solution x based on the robustness goal 2 , judge x 2 Is it better than the initial solution x? 1 If so, then x 2 As the initial solution, continue to iterate until the global optimal solution x is found best , according to the optimal solution x best The provided solution assigns R&D personnel and production lines to achieve a linear weighted sum Z of the robustness of the scheduling solution quality and the robustness of the solution min Minimum, that is, the maximum completion time is as short as possible and the R&D process deviation is as small as possible to ensure the robustness of the scheduling plan.

Description

Technical Field

[0001] The present invention relates to the technical field of production scheduling, and in particular to a robust scheduling method for research and development and trial production of high-end equipment based on buffer time setting. Background Art

[0002] High-end equipment manufacturing involves multiple fields, including general aviation equipment, rail transit equipment, intelligent manufacturing equipment, new energy equipment, and automotive manufacturing. High-end equipment, centered around advanced technologies, is typically complex and requires customization. Therefore, the R&D phase for high-end equipment involves complex processes, and strict precedence-follower constraints exist between the R&D processes for each type of high-end equipment. After R&D is complete, product trial production often precedes successful trial production, followed by mass production. In actual high-end equipment manufacturing companies, multiple types of high-end equipment are often developed simultaneously, sharing the same R&D personnel and production lines. To ensure timely delivery of various types of high-end equipment, and considering the potential interruption of R&D processes due to fluctuating demand during the R&D phase, buffer time is inserted after each R&D process to compensate for this uncertainty. By allocating personnel and production lines, the maximum completion time is minimized and the deviation of each R&D process is minimized, ensuring the robustness of the overall scheduling plan.

[0003] Currently, research on robust scheduling for the R&D and trial production phases of high-end equipment typically relies on exact algorithms or proofs based on the insertion of resource and time buffers. However, considering the maximum completion time deviation across a complex multi-product process network and the process deviation of each step in the R&D process requires extensive computation, significantly increasing the complexity of the problem. This makes it difficult to quickly find an optimal solution, making it difficult to quickly respond to personalized user needs during the R&D and trial production of high-end equipment.

[0004] It can be seen from this that the existing robust scheduling technology for the two stages of high-end equipment research and development and trial production cannot quickly and accurately obtain the optimal solution for the robustness index. Summary of the Invention

[0005] (1) Technical problems solved

[0006] In response to the shortcomings of the existing technology, the present invention provides a robust scheduling method for the research and development and trial production of high-end equipment based on buffer time settings, which provides a reference for the technical problem of quickly and accurately finding the optimal solution to the robustness indicators for the simultaneous research and development and trial production of multiple types of high-end equipment while sharing the same R&D personnel and production lines.

[0007] (2) Technical solution

[0008] To achieve the above objectives, the present invention is implemented through the following technical solutions:

[0009] A robust scheduling method for high-end equipment R&D and trial production based on buffer time setting, the method comprising the following steps:

[0010] S1. Setting input parameters for the variable neighborhood search algorithm, wherein the input parameters are combined with the high-end equipment R&D and trial production process, including R&D procedures and R&D personnel data in the R&D stage and production line data in the trial production stage;

[0011] S2. Set the operating parameters for the variable neighborhood search algorithm, including:

[0012] The maximum number of iterations k of the algorithm max ; Neighborhood structure number NS; Iteration count initialization k=0; Neighborhood structure count initialization s=1;

[0013] S3. Encode the R&D stage based on the greedy strategy based on the R&D process and R&D personnel data of the high-end equipment R&D stage, randomly generate the trial production stage code based on the production line data of the high-end equipment trial production stage, and combine the two parts of the code to generate the greedy initial solution x 0 ;

[0014] S4, Particle movement based on particle swarm algorithm for greedy initial solution x 0 Perform Shaking operation to obtain new solution x 1 ;

[0015] S5. New solution x based on the constructed sth neighborhood structure 1 Perform local search to obtain the current local optimal solution x 2 ;

[0016] S6, Comparison of new solutions x 1 The fitness value and local optimal solution x 2 The size of the fitness value, if x 2 The fitness value is less than x 1 The fitness value of x 1 =x 2 , continue to search for the local optimal solution based on the current neighborhood structure; if not, set s = s + 1 and go to S7;

[0017] S7. Determine whether s≤NS holds. If so, return to S5; otherwise, set K=k+1 and proceed to S8.

[0018] S8. Determine k≤k max Is it true? If so, record the optimal solution px for the kth time k And the global optimal solution gx up to the kth iteration k , return to S4; otherwise, go to S9;

[0019] S9, the algorithm terminates and outputs the current global optimal solution xbest , for x best Decode and output set PS p and AS l , P.S. p It represents the process set formed by the R&D processes assigned by the pth R&D personnel and including the sequence of R&D processes, AS l It represents the high-end equipment assigned to the lth production line and the high-end equipment set including the production sequence.

[0020] Preferably, the S3 specifically includes:

[0021] S31. Based on the basic R&D working hours of each R&D process of high-end equipment and the R&D process network, the critical path set of the R&D stage of each high-end equipment product is calculated based on the greedy strategy to meet the capacity coefficient α. p ≥1 R&D personnel are assigned to the R&D processes in the critical path set to obtain the greedy initial solution x 0 coding sequences during the development phase;

[0022] S32. Set the trial production phase to produce only one piece of each high-end equipment. Based on the total number of high-end equipment types and the number of production lines available during the trial production phase, match each high-end equipment with a production line based on a random generation strategy to obtain the greedy initial solution x. 0 Coding sequence in the pilot stage.

[0023] Preferably, the S4 specifically includes:

[0024] Determine whether k=0 is true, if so, set x 1 =x 0 ;

[0025] Otherwise, get the optimal solution px of the kth iteration recorded in the last iteration process k And the global optimal solution gx up to the kth iteration k , for the initial solution x 0 The new solution x is obtained by moving the particles and rounding them up to get the value of Shaking. 1 , the particle movement method is as follows:

[0026] x 1 =x 0 +v k

[0027] v k =ωv k-1 +c1random(0,1)(px k -x 0 )+c2random(0,1)(gx k -x 0 )

[0028] v k represents the velocity of the particle at the kth iteration;

[0029] w represents the inertia weight;

[0030] C1 represents the cognitive coefficient, which is used to adjust the direction of px k Step length of movement;

[0031] c2 represents the social coefficient, which is used to adjust the gx k The step size of the movement.

[0032] Preferably, the fitness value calculation formula of S6 is expressed as follows:

[0033]

[0034] Among them, Z min It represents a weighted combination of quality robustness and solution robustness, and uses minimizing project duration deviation and minimizing expected process deviation to measure the robustness.

[0035] C max Indicates the total time span of R&D and trial production of multiple high-end equipment in actual scheduling;

[0036] Indicates the total time span of R&D and trial production of multiple high-end equipment in forecast scheduling;

[0037] C ij represents the completion time of R&D process j in high-end equipment i during the R&D phase in actual scheduling;

[0038] represents the completion time of R&D process j in high-end equipment i during the R&D phase in the forecast scheduling;

[0039] β1 and β2 are adjustment coefficients of the robustness weight, satisfying β1+β2=1.

[0040] Preferably,

[0041]

[0042]

[0043] Among them, ES il represents the earliest start time of high-end equipment i on production line l during the trial production phase, so min(ES il ) indicates the earliest start time of production line 1;

[0044] represents the actual completion time of high-end equipment i in the R&D stage;

[0045] t i represents the time taken for the production of high - end equipment i, where high - end equipment i is the high - end equipment assigned to be produced at l;

[0046] w il represents the waiting time of high - end equipment i on production line l;

[0047] represents the completion time of high - end equipment u that is arranged in front of high - end equipment i on production line l.

[0048] Preferably, the neighborhood structure set in S5 includes:

[0049] Neighborhood structure 1: Define variables x1, x2, y. For the R & D stage coding, randomly and without replacement draw two integers within the interval [1, n], and assign them to x1 and x2 with x1 < x2. The R & D processes corresponding to the x1 - th and x2 - th positions belong to the critical path set. Mutate the R & D personnel numbers at the x1 - th and x2 - th positions in the coding of the current solution, and randomly draw two R & D personnel with replacement from the set of R & D personnel with ability coefficient α p ≥1 and assign them to the x1 - th and x2 - th positions in the coding; for the trial production stage coding, randomly draw an integer within the interval [n + 1, n + m], assign it to y, and randomly draw an integer within the interval [1, b] for the production line number corresponding to the y - th position in the coding of the current solution and assign it to the y - th position in the coding of the current solution;

[0050] Neighborhood structure 2: Define variables x1, x2, y. For the R & D stage coding, randomly and without replacement draw two integers within the interval [1, n], and assign them to x1 and x2 with x1 < x2. Reverse the R & D personnel numbers between the x1 - th and x2 - th positions in the coding of the current solution; for the trial production stage coding, randomly draw an integer within the interval [n + 1, n + m], assign it to variable y, and randomly draw an integer within the interval [1, b] for the production line number corresponding to the y - th position in the coding of the current solution and assign it to the y - th position; [[ID=2S]]

[0051] Neighborhood structure 3: Define variables x1, x2, y. For the R & D stage coding, randomly and without replacement draw two integers within the interval [1, n], and assign them to x1 and x2 with x1 < x2. Reverse the R & D personnel numbers on both sides of the x1 - th and x2 - th positions in the coding of the current solution respectively; for the trial production stage coding, randomly draw an integer within the interval [n + 1, n + m], assign it to variable y, and randomly draw an integer within the interval [1, b] for the production line number corresponding to the y - th position in the coding of the current solution and assign it to the y - th position;

[0052] Neighborhood Structure 4: Define variables x1, x2, y1, y2. For the R & D stage coding, randomly and without replacement draw two integers from the interval [1, n], assign them to x1 and x2 with x1 < x2, the R & D processes corresponding to the x1-th and x2-th positions do not belong to the critical path set, and swap the R & D personnel numbers at the x1-th and x2-th positions in the current solution's coding; for the trial production stage coding, randomly and without replacement draw two integers from the interval [n + 1, n + m], assign them to y1 and y2 with y1 < y2, and swap the production line numbers at the y1-th and y2-th positions in the current solution's coding.

[0053] Neighborhood Structure 5: Define variables x1, x2, y1, y2. For the R & D stage coding, randomly and without replacement draw two integers from the interval [1, n], assign them to x1 and x2 with x1 < x2, the R & D processes corresponding to the x1-th and x2-th positions belong to the critical path set, and swap the R & D personnel numbers at the x1-th and x2-th positions in the current solution's coding; for the trial production stage coding, randomly and without replacement draw two integers from the interval [n + 1, n + m], assign them to y1 and y2 with y1 < y2, and swap the production line numbers at the y1-th and y2-th positions in the current solution's coding.

[0054] Neighborhood Structure 6: Define variables x1, x2, y1, y2. For the R & D stage coding, randomly and without replacement draw two integers from the interval [1, n], assign them to x1 and x2 with x1 < x2, assign the R & D personnel number at the x1-th position in the current solution's coding to the x2-th position and move the R & D personnel numbers from the (x1 + 1)-th position to the x2-th position one position to the left; for the trial production stage coding, randomly and without replacement draw two integers from the interval [n + 1, n + m], assign them to y1 and y2 with y1 < y2, assign the production line number at the y1-th position in the current solution's coding to the y2-th position and move the production line numbers from the (y1 + 1)-th position to the y2-th position one position to the left.

[0055] Neighborhood Structure 7: Define variables x1, x2, y1, y2. For the R & D stage coding, randomly and without replacement draw two integers from the interval [1, n], assign them to x1 and x2 with x1 < x2, assign the R & D personnel number at the x2-th position in the current solution's coding to the x1-th position and move the R & D personnel numbers from the x1-th position to the (x2 - 1)-th position one position to the right; for the trial production stage coding, randomly and without replacement draw two integers from the interval [n + 1, n + m], assign them to y1 and y2 with y1 < y2, assign the production line number at the y2-th position in the current solution's coding to the y1-th position and move the production line numbers from the y1-th position to the (y2 - 1)-th position one position to the right.

[0056] Neighborhood structure 8: Define variables x1, x2, x3, y. For the R & D stage coding, randomly and without replacement draw three integers within the interval [1, n], and assign them to x1, x2, and x3, and x1 < x2 < x3. The R & D processes corresponding to the x1-th position, the x2-th position, and the x3-th position belong to the critical path set. Assign the R & D personnel number at the x1-th position in the current solution's coding to the x2-th position, the R & D personnel number at the x2-th position to the x3-th position, and the R & D personnel number at the x3-th position to the x1-th position; for the trial production stage coding, randomly draw an integer within [n + 1, n + m], assign it to y, and randomly draw an integer within the interval [1, b] for the production line number corresponding to the y-th position in the current solution's coding and assign it to the y-th position in the current solution's coding.

[0057] (III) Beneficial effects

[0058] The present invention provides a robust scheduling method for high-end equipment R & D and trial production based on buffer time setting. Compared with the prior art, it has the following beneficial effects:

[0059] The present invention first sets the input parameters of the variable neighborhood search algorithm based on the R & D process data, R & D resource data in the high-end equipment R & D and trial production stages, and production resource data in the trial production stage, then sets the operation parameters of the algorithm, and constructs a greedy initial solution x 0 , calculates the actual R & D process duration and process interruption probability based on the initial solution, and then obtains the buffer time of each process. Perform a Shaking operation on the initial solution x 0 to update the solution to x 1 by particle movement, select a neighborhood structure to perform local search on x 1 to obtain a local optimal solution x 2 , judge whether x 2 is better than the initial solution x 1 , if so, use x 2 as the initial solution and continue to iterate until the global optimal solution x best is searched. Assign R & D personnel and production lines according to the solution provided by the optimal solution x best to minimize the linear weighted sum Z min of the quality robustness of the scheduling solution and the robustness of the solution, that is, to make the makespan as short as possible and the deviation of the R & D process as small as possible to ensure the robustness of the scheduling solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0061] Figure 1 A flowchart of a robust scheduling method for high-end equipment R&D and trial production based on buffer time setting provided by an embodiment of the present invention;

[0062] Figure 2 Flowchart of another robust scheduling method for high-end equipment R&D and trial production based on buffer time setting provided by an embodiment of the present invention

[0063] Figure 3 Schematic diagram of coding in an embodiment of the present invention. DETAILED DESCRIPTION

[0064] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention are clearly and completely described. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0065] The embodiments of the present application provide a robust scheduling method for R&D and trial production of high-end equipment based on buffer time settings, thereby providing a reference for the technical problem of quickly and accurately finding the optimal solution for robustness indicators for simultaneous R&D and trial production of multiple types of high-end equipment while sharing the same R&D personnel and production lines.

[0066] The technical solution in the embodiments of the present application is to solve the above technical problems, and the overall idea is as follows:

[0067] In order to develop the optimal robust scheduling plan for the coordinated development and trial production of high-end equipment, this technical solution designs a variable neighborhood search algorithm that integrates the particle movement of the particle swarm algorithm. First, based on the greedy strategy, an initial solution is randomly generated and a shaking operation is performed on it, so that the current initial solution is close to the current optimal solution recorded in the previous iteration and another point in the feasible domain is generated, avoiding falling into too many local optimal points within the current feasible domain and avoiding too many invalid iterations, thereby improving the efficiency of the algorithm's global search for the optimal solution; this technical solution designs eight neighborhood structures based on the actual industrial scenarios of the coordinated development and trial production of high-end equipment and taking into account the critical path, thereby improving the optimal solution search capability of the variable neighborhood search algorithm.

[0068] In order to better understand the above technical solution, the above technical solution will be described in detail below with reference to the accompanying drawings and specific implementation methods.

[0069] Example:

[0070] like Figure 1 As shown, an embodiment of the present invention provides a method for robust scheduling of high-end equipment R&D and trial production based on buffer time setting, the method comprising the following steps:

[0071] S1. Setting input parameters for the variable neighborhood search algorithm, wherein the input parameters are combined with the high-end equipment R&D and trial production process, including R&D procedures and R&D personnel data in the R&D stage and production line data in the trial production stage;

[0072] S2. Set the operating parameters for the variable neighborhood search algorithm, including:

[0073] The maximum number of iterations k of the algorithm max ; Neighborhood structure number NS; Iteration count initialization k=0; Neighborhood structure count initialization s=1;

[0074] S3. Encode the R&D stage based on the greedy strategy based on the R&D process and R&D personnel data of the high-end equipment R&D stage, randomly generate the trial production stage code based on the production line data of the high-end equipment trial production stage, and combine the two parts of the code to generate the greedy initial solution x 0 ;

[0075] S4, Particle movement based on particle swarm algorithm for greedy initial solution x 0 Perform Shaking operation to obtain new solution x 1 ;

[0076] S5. New solution x based on the constructed sth neighborhood structure 1 Perform local search to obtain the current local optimal solution x 2 ;

[0077] S6, Comparison of new solutions x 1 The fitness value and local optimal solution x 2 The size of the fitness value, if x 2 The fitness value is less than x 1 The fitness value of x 1 =x 2 , continue to search for the local optimal solution based on the current neighborhood structure; if not, set s = s + 1 and go to S7;

[0078] S7. Determine whether s≤NS holds. If so, return to S5; otherwise, set k=k+1 and proceed to S8.

[0079] S8. Determine k≤k maxIs it true? If so, record the optimal solution px for the kth time k And the global optimal solution gx up to the kth iteration k , return to S4; otherwise, go to S9;

[0080] S9, the algorithm terminates and outputs the current global optimal solution x best , for x best Decode and output set PS p and AS l , P.S. p It represents the process set formed by the R&D processes assigned by the pth R&D personnel and including the sequence of R&D processes, AS l It represents the high-end equipment assigned to the lth production line and the high-end equipment set including the production sequence.

[0081] The embodiment of the present invention provides the optimal solution x obtained by the above method. best The provided solution assigns R&D personnel and production lines to achieve a linear weighted sum Z of the robustness of the scheduling solution quality and the robustness of the solution min Minimum, that is, the maximum completion time is as short as possible and the R&D process deviation is as small as possible to ensure the robustness of the scheduling plan.

[0082] The following will introduce the steps of the above technical solution in detail with specific content:

[0083] First, it should be noted that the solution provided by the embodiment of the present invention takes into account the following constraints:

[0084] First, during the R&D stage of each high-end equipment, no R&D personnel can carry out the R&D of two R&D processes at the same time. A certain R&D process can only be carried out after all the previous R&D processes are completed; during the trial production stage, no two high-end equipment can be trial-produced on any production line at the same time.

[0085] Second, the R&D process j and its basic R&D working hours in high-end equipment i are respectively represented by symbols O ij and d ij Indicates that there is a tight before-tight after constraint relationship between each R&D process, R&D process O ij All the predecessor tasks are set A ij It means that only when the set A ij All R&D processes have been completed, R&D process O ij The earliest start time is

[0086] Third, the R&D processes between any two high-end equipment are independent of each other, without any constraints on the preceding or following relationship.

[0087] In step S1, input parameters are set for the variable neighborhood search algorithm, and the input parameters are combined with the high-end equipment R&D and trial production process, including R&D procedures, R&D personnel data in the R&D stage, and production line data in the trial production stage.

[0088] like Figure 2 As shown in the figure, the total number of high-end equipment types that need to be developed in the R&D stage is m; the total number of R&D processes corresponding to all types of high-end equipment in the R&D stage is n; the basic R&D working hours of R&D process j in high-end equipment i is d ij ; Production time t of high-end equipment i i ;Total number of R&D personnel in the enterprise R&D departmenta;R&D personnelp p Capacity coefficient α p ;The number of production lines available during the trial phase b;

[0089] A collection of R&D processes for a single high-end equipment Among them O ij represents R&D process j, n in high-end equipment i i represents the number of R&D processes included in the i-th high-end equipment;

[0090] The set of all available R&D personnel in the R&D stage P = {P1, P2, ..., P p ,…,P a};

[0091] The set of all available production lines in the trial production phase M = {M1, M2, ..., M l ,…,M b}.

[0092] In step S2, operating parameters are set for the variable neighborhood search algorithm, including:

[0093] The maximum number of iterations k of the algorithm max ; Neighborhood structure number NS; Iteration count initialized k=0; Community structure count initialized s=1.

[0094] In step S3, the R&D stage is encoded based on the greedy strategy in combination with the R&D process and R&D personnel data of the high-end equipment R&D stage, and the trial production stage code is randomly generated in combination with the production line data of the trial production stage of the high-end equipment. The two parts of the code are combined to generate the greedy initial solution x 0 ;

[0095] The generation of initial solutions is divided into the generation of initial solutions in the R&D stage and the generation of initial solutions in the trial production stage. The assignment in the R&D stage is based on personnel, and the assignment in the trial production stage is based on production lines. That is, in coding, the initial solution x 0 It consists of two parts:

[0096] Each column code in the first part represents the R&D personnel assigned to a R&D process. The order of R&D processes is based on the earliest start time of each process. Sorting; In the second part, each column code represents the production line assigned to a high-end equipment, and its position corresponds to the earliest completion order of its R&D stage.

[0097] Therefore, the initial solution can be expressed as: where x ij represents the personnel assigned to the jth R&D process of the i-th high-end equipment; i Indicates the production line assigned to the i-th high-end equipment.

[0098] In addition, it should be noted that in the R&D process of high-end equipment i, there are multiple paths from the first R&D process to the last R&D process. Select a path that meets the basic working time d of all R&D processes on the path. ij The sum of the maximum and the maximum completion time of the R&D stage of high-end equipment i is the maximum completion time of the R&D project. This path is the critical path of the R&D project, and the critical path set CP is defined. i , represents the set of all R&D processes on the critical path of high-end equipment i sorted by the earliest start time from smallest to largest, and defines the non-critical path set NP i , which represents the set of R&D processes in equipment i except all R&D processes on the critical path.

[0099] like Figure 3 As shown, obtain the greedy initial solution x 0 The specific process includes:

[0100] S31. Based on the basic R&D working hours of each R&D process of high-end equipment and the R&D process network, the critical path set of the R&D stage of each high-end equipment product is calculated based on the greedy strategy to meet the capacity coefficient α. p ≥1 R&D personnel are assigned to the R&D processes in the critical path set to obtain the greedy initial solution x 0 coding sequences during the development phase;

[0101] S32. Set the trial production phase to produce only one piece of each high-end equipment. Based on the total number of high-end equipment types and the number of production lines available during the trial production phase, match each high-end equipment with a production line based on a random generation strategy to obtain the greedy initial solution x. 0 Coding sequence in the pilot stage.

[0102] In step S4, the particle movement based on the particle swarm algorithm is used to calculate the greedy initial solution x 0 Perform Shaking operation to obtain new solution x 1 ; Specifically include:

[0103] Determine whether k=0 is true, if so, set x 1 =x 0 ;

[0104] Otherwise, get the optimal solution px of the kth iteration recorded in the last iteration process k And the global optimal solution gx up to the kth iteration k , for the initial solution x 0 The new solution x is obtained by moving the particles and rounding them up to get the value of Shaking. 1 , the particle movement method is as follows:

[0105] x 1 =x 0 +v k

[0106] v k =ωv k-1 +c1random(0,1)(px k -x 0 )+c2random(0,1)(gx k -x 0 )

[0107] v k represents the velocity of the particle at the kth iteration;

[0108] w represents the inertia weight;

[0109] C1 represents the cognitive coefficient, which is used to adjust the direction of px k Step length of movement;

[0110] c2 represents the social coefficient, which is used to adjust the gx k The step size of the movement.

[0111] The embodiment of the present invention solves the initial solution x 0 The particle movement based on the particle swarm algorithm performs a shaking operation, which makes the current initial solution approach the current optimal solution recorded in the previous iteration and generates another point in the feasible domain. This avoids falling into the local optimum too much in the current feasible domain and avoids too many invalid iterations, thereby improving the efficiency of the algorithm's global search for the optimal solution.

[0112] In step S5, the new solution x is constructed based on the sth neighborhood structure. 1 Perform local search to obtain the current local optimal solution x 2 .

[0113] The neighborhood structure set may include the following situations:

[0114] Neighborhood Structure 1: Define variables x1, x2, y. For the R & D stage coding, randomly and without replacement extract two integers from the interval [1, n], and assign them to x1 and x2 with x < x2. The R & D processes corresponding to the x1 - th and x2 - th positions belong to the critical path set. Mutate the R & D personnel numbers at the x1 - th and x2 - th positions in the current solution's coding, and randomly and with replacement extract two R & D personnel from the set of R & D personnel with the ability coefficient α p ≥ 1 and assign them to the x1 - th and x2 - th positions of the coding; For the trial production stage coding, randomly extract an integer from the interval [n + 1, n + m], assign it to y, and randomly extract an integer from the interval [1, b] for the production line number corresponding to the y - th position in the current solution's coding and assign it to the y - th position of the current solution's coding;

[0115] Neighborhood Structure 2: Define variables x1, x2, y. For the R & D stage coding, randomly and without replacement extract two integers from the interval [1, n], and assign them to x1 and x2 with x < x2. Reverse the R & D personnel numbers between the x1 - th and x2 - th positions in the current solution's coding; For the trial production stage coding, randomly extract an integer from the interval [n + 1, n + m], assign it to the variable y, and randomly extract an integer from the interval [1, b] for the production line number corresponding to the y - th position in the current solution's coding and assign it to the y - th position;

[0116] Neighborhood Structure 3: Define variables x1, x2, y. For the R & D stage coding, randomly and without replacement extract two integers from the interval [1, n], and assign them to x1 and x2 with x < x2. Reverse the R & D personnel numbers on both sides of the x1 - th and x2 - th positions in the current solution's coding respectively; For the trial production stage coding, randomly extract an integer from the interval [n + 1, n + m], assign it to the variable y, and randomly extract an integer from the interval [1, b] for the production line number corresponding to the y - th position in the current solution's coding and assign it to the y - th position;

[0117] Neighborhood Structure 4: Define variables x1, x2, y1, y2. For the R & D stage coding, randomly and without replacement extract two integers from the interval [1, n], and assign them to x1 and x2 with x < x2. The R & D processes corresponding to the x1 - th and x2 - th positions do not belong to the critical path set. Exchange the R & D personnel numbers at the x1 - th and x2 - th positions in the current solution's coding; For the trial production stage coding, randomly and without replacement extract two integers from the interval [n + 1, n + m], and assign them to y1 and y2 with y1 < y2. Exchange the production line numbers corresponding to the y1 - th and y2 - th positions in the current solution's coding;

[0118] Neighborhood Structure 5: Define variables x1, x2, y1, y2. For the R & D stage coding, randomly and without replacement, draw two integers from the interval [1, n], and assign them to x1 and x2 with x1 < x2. The R & D processes corresponding to the x1-th and x2-th positions belong to the critical path set. Swap the R & D personnel numbers at the x1-th and x2-th positions in the coding of the current solution. For the trial production stage coding, randomly and without replacement, draw two integers from the interval [n + 1, n + m], and assign them to y1 and y2 with y1 < y2. Swap the production line numbers at the y1-th and y2-th positions in the coding of the current solution.

[0119] Neighborhood Structure 6: Define variables x1, x2, y1, y2. For the R & D stage coding, randomly and without replacement, draw two integers from the interval [1, n], and assign them to x1 and x2 with x1 < x2. Assign the R & D personnel number at the x1-th position in the coding of the current solution to the x2-th position and move the R & D personnel numbers from the (x1 + 1)-th position to the x2-th position one position to the left. For the trial production stage coding, randomly and without replacement, draw two integers from the interval [n + 1, n + m], and assign them to y1 and y2 with y1 < y2. Assign the production line number at the y1-th position in the coding of the current solution to the y2-th position and move the R & D personnel numbers from the (y1 + 1)-th position to the y2-th position one position to the left.

[0120] Neighborhood Structure 7: Define variables x1, x2, y1, y2. For the R & D stage coding, randomly and without replacement, draw two integers from the interval [1, n], and assign them to x1 and x2 with x1 < x2. Assign the R & D personnel number at the x2-th position in the coding of the current solution to the x1-th position and move the R & D personnel numbers from the x1-th position to the (x2 - 1)-th position one position to the right. For the trial production stage coding, randomly and without replacement, draw two integers from the interval [n + 1, n + m], and assign them to y1 and y2 with y1 < y2. Assign the production line number at the y2-th position in the coding of the current solution to the y1-th position and move the R & D personnel numbers from the y1-th position to the (y2 - 1)-th position one position to the right.

[0121] Neighborhood Structure 8: Define variables x1, x2, x3, y. For the coding in the R & D stage, randomly and without replacement draw three integers within the interval [1, n], and assign them to x1, x2, and x3, and x1 < x2 < x3. The R & D processes corresponding to the x1-th position, the x2-th position, and the x3-th position belong to the critical path set. Assign the R & D personnel number at the x1-th position in the current solution's coding to the x2-th position, the R & D personnel number at the x2-th position to the x3-th position, and the R & D personnel number at the x3-th position to the x1-th position; For the coding in the trial production stage, randomly draw an integer within [n + 1, n + m], assign it to y, and randomly draw an integer within the interval [1, b] for the production line number corresponding to the y-th position in the current solution's coding and assign it to the y-th position in the current solution's coding.

[0122] In the embodiments of the present invention, the above eight neighborhood structures are designed according to the actual problem background, including the change of the assignment scheme of the R & D processes on the critical path, the change of the assignment scheme of the non-critical path R & D processes, and the change of the assignment scheme of all R & D processes, which improves the ability of the algorithm to globally search for the optimal solution.

[0123] In step S6, compare the fitness value of the new solution x 1 with the fitness value of the local optimal solution x 2 . If the fitness value of s 2 is less than the fitness value of x 1 , let x 1 = x 2 , and continue to search for the local optimal solution based on the current neighborhood structure; Otherwise, let s = s + 1 and transfer to S7.

[0124] The calculation formula of the fitness value is expressed as follows:

[0125]

[0126] Among them, Z min represents the weighted combination of quality robustness and solution robustness, and uses minimizing the project duration deviation and minimizing the expected process deviation to measure the robustness;

[0127] C max represents the total time span of the R & D and trial production of multiple high-end equipment in the actual scheduling;

[0128] represents the total time span of the R & D and trial production of multiple high-end equipment in the predicted scheduling;

[0129] C ij represents the completion time of the R & D process j in high-end equipment i in the R & D stage in the actual scheduling;

[0130] represents the completion time of R&D process j in high-end equipment i during the R&D phase in the forecast scheduling;

[0131] β1 and β2 are adjustment coefficients of the robustness weight, satisfying β1+β2=1.

[0132] The total time span of the R&D and trial production of the above-mentioned high-end equipment in actual scheduling is C max The calculation formula is as follows:

[0133]

[0134]

[0135]

[0136] Among them, ES il represents the earliest start time of high-end equipment i on production line l during the trial production phase, so min(ES il ) indicates the earliest start time of production line 1;

[0137] represents the actual completion time of high-end equipment i in the R&D stage;

[0138] t i represents the time taken to produce high-end equipment i, where high-end equipment i is the high-end equipment assigned to be produced at l;

[0139] w il represents the waiting time of high-end equipment i on production line l;

[0140] It represents the completion time of high-end equipment u arranged before high-end equipment i on production line l.

[0141] In step S7, determine whether s≤NS is established. If so, return to S5; otherwise, set k=k+1 and go to S8;

[0142] In step S8, it is determined that k≤k max Is it true? If so, record the optimal solution px for the kth time k And the global optimal solution gx up to the kth iteration k , return to S4; otherwise, go to S9;

[0143] In step S9, the algorithm terminates and outputs the current global optimal solution x best , for x best Decode and output set PS p and AS l , P.S. pIt represents the process set formed by the R&D processes assigned by the pth R&D personnel and including the sequence of R&D processes, AS l It represents the high-end equipment assigned to the lth production line and the high-end equipment set including the production sequence.

[0144] Targeting x best The decoding process is as follows:

[0145] Based on the global optimal solution x best The first part of the coding sequence traverses the R&D personnel numbers until p>a is terminated, and finds the process set PS formed by the R&D processes assigned by the pth R&D personnel and containing the R&D process sequence p .

[0146] Based on the global optimal solution x best The second part of the coding sequence traverses the production line number until l>b ends, and finds the high-end equipment set AS assigned to the l-th production line and including the production sequence l .

[0147] Finally, through the above PS p and AS l Assign R&D personnel and production lines separately to achieve the linear weighted sum Z of the robustness of the scheduling plan quality and the robustness of the solution min Minimum, that is, the maximum completion time is as short as possible and the R&D process deviation is as small as possible to ensure the robustness of the scheduling plan.

[0148] In summary, compared with the existing technology, the present invention has the following beneficial effects:

[0149] 1. The embodiment of the present invention provides the optimal solution x obtained by the above method. best The provided solution assigns R&D personnel and production lines to achieve a linear weighted sum Z of the robustness of the scheduling solution quality and the robustness of the solution min Minimum, that is, the maximum completion time is as short as possible and the R&D process deviation is as small as possible to ensure the robustness of the scheduling plan.

[0150] 2. In the embodiment of the present invention, when generating the initial solution x 0 When coding the R&D phase, a greedy strategy is adopted. According to the basic R&D working hours of each R&D process of high-end equipment and the R&D process network, the critical path set of the R&D phase of each high-end equipment product is calculated based on the greedy strategy to meet the capacity coefficient α. p ≥1 R&D personnel are assigned to the R&D processes in the critical path set to obtain the greedy initial solution x 0 The coding sequence in the R&D phase reduces the overall number of iterations and increases the speed at which the algorithm converges to the optimal solution.

[0151] 3. The embodiment of the present invention solves the initial solution x 0 The particle movement based on the particle swarm algorithm performs a shaking operation, which makes the current initial solution approach the current optimal solution recorded in the previous iteration and generates another point in the feasible domain. This avoids falling into the local optimum too much in the current feasible domain and avoids too many invalid iterations, thereby improving the efficiency of the algorithm's global search for the optimal solution.

[0152] 4. The embodiment of the present invention designs eight neighborhood structures based on the actual problem background, including changes in the assignment scheme of R&D processes on the critical path, changes in the assignment scheme of R&D processes on non-critical paths, and changes in the assignment scheme of all R&D processes, thereby improving the algorithm's ability to globally search for the optimal solution.

[0153] It should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply the existence of any such actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article, or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or device. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or device comprising the element.

[0154] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A robust scheduling method for high-end equipment R&D and trial production based on buffer time setting, characterized in that: The method includes the following steps: S1. Set input parameters for the variable neighborhood search algorithm. The input parameters combine the R & D processes in the R & D stage, the data of R & D personnel, and the production line data in the trial production stage during the R & D and trial production processes of high-end equipment; S2. Set operating parameters for the variable neighborhood search algorithm, including: The maximum number of iterations k of the algorithm max ; Neighborhood structure number NS; Iteration count initialization k=0; Neighborhood structure count initialization s=1; S3. Encode the R&D stage based on the greedy strategy based on the R&D process and R&D personnel data of the high-end equipment R&D stage, randomly generate the trial production stage code based on the production line data of the high-end equipment trial production stage, and combine the two parts of the code to generate the greedy initial solution x 0 ; S4, Particle movement based on particle swarm algorithm for greedy initial solution x 0 Perform Shaking operation to obtain new solution x 1 ; S5. New solution x based on the constructed sth neighborhood structure 1 Perform local search to obtain the current local optimal solution x 2 ; S6, Comparison of new solutions x 1 The fitness value and local optimal solution x 2 The size of the fitness value, if x 2 The fitness value is less than x 1 The fitness value of x 1 =x 2 , continue to search for the local optimal solution based on the current neighborhood structure; if not, set s = s + 1 and go to S7; S7. Judge whether s ≤ NS holds. If it holds, return to S5; otherwise, let k = k + 1 and transfer to S8; S8. Determine k≤k max Is it true? If so, record the optimal solution px for the kth time k And the global optimal solution gx up to the kth iteration k , return to S4; otherwise, go to S9; S9, the algorithm terminates and outputs the current global optimal solution x best , and x best Decode and output set PS p and AS l , P.S. p It represents the process set formed by the R&D processes assigned by the pth R&D personnel and including the sequence of R&D processes, AS l It represents the high-end equipment assigned to the lth production line and the high-end equipment set including the production sequence; Among them, the fitness value calculation formula in S6 is expressed as follows: Among them, Z min It represents a weighted combination of quality robustness and solution robustness, and uses minimizing project duration deviation and minimizing expected process deviation to measure the robustness. C max Indicates the total time span of R&D and trial production of multiple high-end equipment in actual scheduling; Indicates the total time span of R&D and trial production of multiple high-end equipment in forecast scheduling; C ij represents the completion time of R&D process j in high-end equipment i during the R&D phase in actual scheduling; represents the completion time of R&D process j in high-end equipment i during the R&D phase in the forecast scheduling; β1 and β2 are adjustment coefficients of the robustness weight, satisfying β1 + β2 = 1; Among them, ES il represents the earliest start time of high-end equipment i on production line l during the trial production phase, so min(ES il ) indicates the earliest start time of production line 1; represents the actual completion time of high-end equipment i in the R&D stage; t i represents the time taken to produce high-end equipment i, where high-end equipment i is the high-end equipment assigned to be produced at l; w il represents the waiting time of high-end equipment i on production line l; It represents the completion time of high-end equipment u that is assigned to be produced before high-end equipment i on production line l.

2. A robust scheduling method for high-end equipment R&D and trial production based on buffer time setting according to claim 1, characterized in that: The specific content of S3 includes: S31. Based on the basic R&D working hours of each R&D process of high-end equipment and the R&D process network, the critical path set of the R&D stage of each high-end equipment product is calculated based on the greedy strategy to meet the capacity coefficient α. p ≥1 R&D personnel are assigned to the R&D processes in the critical path set to obtain the greedy initial solution x 0 coding sequences during the development phase; S32. Set the trial production phase to produce only one piece of each high-end equipment. Based on the total number of high-end equipment types and the number of production lines available during the trial production phase, match each high-end equipment with a production line based on a random generation strategy to obtain the greedy initial solution x. 0 Coding sequence in the pilot stage.

3. A robust scheduling method for high-end equipment R&D and trial production based on buffer time setting according to claim 1, characterized in that: The specific content of S4 includes: Determine whether k=0 is true, if so, set x 1 =x 0 ; Otherwise, get the optimal solution px of the kth iteration recorded in the last iteration process k And the global optimal solution gx up to the kth iteration k , for the initial solution x 0 The new solution x is obtained by moving the particles and rounding them up to get the value of Shaking. 1 , the particle movement method is as follows: x 1 =x 0 +v k in k =ωv k-1 +c1random(0,1)(px k -x 0 )+c2random(0,1)(gx k -x 0 ) v k represents the velocity of the particle at the kth iteration; w represents the inertia weight; C1 represents the cognitive coefficient, which is used to adjust the direction of px k Step length of movement; c2 represents the social coefficient, which is used to adjust the gx k The step size of the movement.

4. The robust scheduling method for high-end equipment R&D and trial production based on buffer time setting according to claim 1 is characterized in that: The eight neighborhood structures in S5 include: Neighborhood structure 1: Define variables x1, x2, y. For the coding in the R & D stage, randomly and without replacement draw two integers within the interval [1, n], and assign them to x1 and x2 with x1 < x2. The R & D processes corresponding to the x1-th and x2-th positions belong to the critical path set. Mutate the R & D personnel numbers at the x1-th and x2-th positions in the coding of the current solution. Randomly draw two R & D personnel with replacement from the set of R & D personnel with the ability coefficient α p ≥ 1 and assign them to the x1-th and x2-th positions in the coding; for the coding in the trial production stage, randomly draw an integer within the interval [n + 1, n + m], assign it to y, and randomly draw an integer within the interval [1, b] for the production line number corresponding to the y-th position in the coding of the current solution and assign it to the y-th position in the coding of the current solution; Neighborhood structure 2: Define variables x1, x2, y. For the R & D stage coding, randomly and without replacement extract two integers within the interval [1, n], and assign them to x1 and x2 with x1 < x2, and reverse the R & D personnel numbers between the x1-th and x2-th positions in the current solution's coding; for the trial production stage coding, randomly extract an integer within the interval [n + 1, n + m], assign it to the variable y, and randomly extract an integer within the interval [1, b] for the production line number corresponding to the y-th position in the current solution's coding and assign it to the y-th position; Neighborhood structure 3: Define variables x1, x2, y. For the R & D stage coding, randomly and without replacement extract two integers within the interval [1, n], and assign them to x1 and x2 with x1 < x2, and respectively reverse the R & D personnel numbers on both sides of the x1-th and x2-th positions in the current solution's coding; for the trial production stage coding, randomly extract an integer within the interval [n + 1, n + m], assign it to the variable y, and randomly extract an integer within the interval [1, b] for the production line number corresponding to the y-th position in the current solution's coding and assign it to the y-th position; Neighborhood structure 4: Define variables x1, x2, y1, y2. For the R & D stage coding, randomly and without replacement extract two integers within the interval [1, n], and assign them to x1 and x2 with x1 < x2. The R & D processes corresponding to the x1-th and x2-th positions do not belong to the critical path set, and exchange the R & D personnel numbers at the x1-th and x2-th positions in the current solution's coding; for the trial production stage coding, randomly and without replacement extract two integers within the interval [n + 1, n + m], and assign them to y1 and y2 with y1 < y2, and exchange the production line numbers corresponding to the y1-th and y2-th positions in the current solution's coding; Neighborhood Structure 5: Define variables x1, x2, y1, y2. For the coding in the R & D stage, randomly and without replacement, draw two integers from the interval [1, n], and assign them to x1 and x2 with x1 < x2. The R & D processes corresponding to the x1-th and x2-th positions belong to the critical path set. Swap the R & D personnel numbers at the x1-th and x2-th positions in the coding of the current solution. For the coding in the trial production stage, randomly and without replacement, draw two integers from the interval [n + 1, n + m], and assign them to y1 and y2 with y1 < y2. Swap the production line numbers at the y1-th and y2-th positions in the coding of the current solution. Neighborhood Structure 6: Define variables x1, x2, y1, y2. For the coding in the R & D stage, randomly and without replacement, draw two integers from the interval [1, n], and assign them to x1 and x2 with x1 < x2. Assign the R & D personnel number at the x1-th position in the coding of the current solution to the x2-th position and move the R & D personnel numbers from the (x1 + 1)-th position to the x2-th position one position to the left. For the coding in the trial production stage, randomly and without replacement, draw two integers from the interval [n + 1, n + m], and assign them to y1 and y2 with y1 < y2. Assign the production line number at the y1-th position in the coding of the current solution to the y2-th position and move the production line numbers from the (y1 + 1)-th position to the y2-th position one position to the left. Neighborhood Structure 7: Define variables x1, x2, y1, y2. For the coding in the R & D stage, randomly and without replacement, draw two integers from the interval [1, n], and assign them to x1 and x2 with x1 < x2. Assign the R & D personnel number at the x2-th position in the coding of the current solution to the x1-th position and move the R & D personnel numbers from the x1-th position to the (x2 - 1)-th position one position to the right. For the coding in the trial production stage, randomly and without replacement, draw two integers from the interval [n + 1, n + m], and assign them to y1 and y2 with y1 < y2. Assign the production line number at the y2-th position in the coding of the current solution to the y1-th position and move the production line numbers from the y1-th position to the (y2 - 1)-th position one position to the right. Neighborhood Structure 8: Define variables x1, x2, x3, y. For the coding in the R & D stage, randomly and without replacement, draw three integers from the interval [1, n], and assign them to x1, x2 and x3 with x1 < x2 < x3. The R & D processes corresponding to the x1-th, x2-th and x3-th positions belong to the critical path set. Assign the R & D personnel number at the x1-th position in the coding of the current solution to the x2-th position, the R & D personnel number at the x2-th position to the x3-th position, and the R & D personnel number at the x3-th position to the x1-th position. For the coding in the trial production stage, randomly draw an integer from [n + 1, n + m], assign it to y, and randomly draw an integer from the interval [1, b] and assign it to the production line number at the y-th position in the coding of the current solution.

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