Resource constraint workshop scheduling method and system based on multi-target graph neural network

Abstract

The invention provides a resource constraint workshop scheduling method and system based on a multi-target graph neural network, and belongs to the technical field of workshop scheduling. Constructing a resource-constrained workshop scheduling model according to the obtained workpiece set and workshop scheduling resources; performing nodal representation on the workshop scheduling model by using a disjunction graph, and expressing the state, action and reward value of the workshop scheduling model after nodal representation by using a Markov decision-making method; based on a multi-target graph neural network, determining the optimal action of the next step from the action space shown by the disjunction graph according to the current state; and executing workshop scheduling according to the determined optimal action. According to the method, high efficiency and high precision of optimal action selection can be kept on the basis of comprehensively considering all constraint conditions, and then reasonable resource constraint workshop scheduling is achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of workshop scheduling, and in particular relates to a resource-constrained workshop scheduling method and system based on a multi-objective graph neural network. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] In discrete manufacturing, workshop scheduling is a crucial link. Workshop scheduling can effectively plan the execution order of jobs and coordinate the production tasks of each workshop to ensure that relevant performance indicators are optimized while meeting all practical operating constraints. It involves the reasonable allocation and sorting of production tasks under the constraints of limited resources to maximize production efficiency. However, in actual operations, workshop scheduling faces many challenges. Workshop scheduling problems usually involve the constraints of multiple resources. The scheduling system needs to formulate a reasonable production plan based on these constraints and the needs of production tasks. This plan needs to ensure that production tasks can be completed within the specified time while maximizing resource utilization. However, existing workshop scheduling methods generally have some technical problems, such as:

[0004] Traditional scheduling methods mainly rely on manual experience and coordination, lacking an effective response mechanism to achieve effective technical adjustments to production plans, and the workshop information in the production process is complex and changeable, making it difficult to achieve fast and effective workshop scheduling. On this basis, technical personnel in related fields began to combine heuristic methods for production scheduling, but heuristic methods are usually based on some empirical rules or intuitive judgments, and they can often only find a feasible local optimal solution, rather than a global optimal solution. This means that in a complex workshop scheduling environment, heuristic methods may not be able to fully consider all possible job combinations and sequences, thereby limiting their optimization effect; at the same time, the performance of heuristic methods depends largely on the selected dispatching rules or priority rules. Different rules may lead to completely different scheduling results. However, there is no universally applicable rule that can adapt to all workshop environments, and improperly selected rules will seriously affect the scheduling effect. Therefore, the existing workshop scheduling methods have the problems of low efficiency and insufficient precision. Summary of the invention

[0005] In order to overcome the shortcomings of the above-mentioned prior art, the present invention provides a resource-constrained workshop scheduling method and system based on a multi-objective graph neural network, which can maintain high efficiency and high precision of optimal action selection on the basis of comprehensive consideration of all constraints, thereby realizing reasonable resource-constrained workshop scheduling.

[0006] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions:

[0007] A first aspect of the present invention provides a resource-constrained workshop scheduling method based on a multi-objective graph neural network.

[0008] The resource-constrained shop scheduling method based on multi-objective graph neural network includes:

[0009] Obtain a collection of workpieces to be processed and workshop scheduling resources;

[0010] Building a resource-constrained workshop scheduling model according to the workpiece set and the workshop scheduling resources;

[0011] The workshop scheduling model is represented by nodes using a disjunctive graph, and the state, action and reward value of the workshop scheduling model after the node representation is expressed by using a Markov decision method;

[0012] Based on a multi-objective graph neural network, the optimal action for the next step is determined from the action space shown in the disjunctive graph according to the current state; and workshop scheduling is performed according to the determined optimal action.

[0013] Furthermore, the workshop scheduling model includes an objective function, multi-level constraints for full resource scheduling, and a solution function for solving the objective function; wherein the objective function is set with three weighted fitness targets of completion time, total energy consumption and total waiting time, and each weighted fitness target corresponds to a weighted value.

[0014] Furthermore, a disjunctive graph is used to represent the shop scheduling model in a node-based manner. Specifically, the disjunctive graph is represented by G = (O, C∪D); wherein O represents the set of all operations including the start node and the end node, the priority constraints of the same workpiece operation are represented in the set C, and D represents the disjunctive arc connecting the operations on the same machine tool.

[0015] Furthermore, the Markov decision method is used to express the state, action and reward value of the workshop scheduling model after node representation. Specifically, the state includes node state and speed state; wherein the node state is composed of five tuples: processing time, earliest start time, latest start time, processing speed and required resources.

[0016] Furthermore, the action is represented by a multi-action mechanism, which includes an action space of process pairs and an action space of speed distribution; the reward value is represented by a weighted sum of three objectives in the objective function as the reward value.

[0017] Furthermore, the multi-objective graph neural network consists of a graph isomorphism network and a graph attention network; wherein, a global embedding mechanism based on the graph isomorphism network is used to capture global information to achieve node embedding; a local embedding mechanism based on the graph attention network is used to capture neighborhood and local information from conjunction and disjunction adjacent nodes to achieve graph embedding; subsequently, speed features are embedded through a fully connected network to achieve speed distribution embedding.

[0018] Furthermore, after all embeddings are generated for nodes, graphs, and speed assignments, the process pair action scores and speed action scores are calculated; all process pair action scores and speed action scores are score-flattened and input into the softmax function to obtain the probability of selecting a suitable action; and the optimal action is determined based on the obtained probability.

[0019] A second aspect of the present invention provides a resource-constrained workshop scheduling system based on a multi-objective graph neural network.

[0020] Resource-constrained shop scheduling system based on multi-objective graph neural network, including:

[0021] The data acquisition module is configured to: acquire a set of workpieces to be processed and workshop scheduling resources;

[0022] The workshop scheduling model building module is configured to: build a resource-constrained workshop scheduling model according to the workpiece set and the workshop scheduling resources;

[0023] The disjunctive graph representation module is configured to: use a disjunctive graph to represent the shop scheduling model in a node-based manner, and use a Markov decision method to express the state, action and reward value of the shop scheduling model after the node-based representation;

[0024] The workshop scheduling module is configured to: determine the optimal action for the next step from the action space shown in the disjunctive graph according to the current state based on the multi-objective graph neural network; and execute workshop scheduling according to the determined optimal action.

[0025] The third aspect of the present invention provides a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the steps in the resource-constrained workshop scheduling method based on a multi-objective graph neural network as described in the first aspect of the present invention.

[0026] The fourth aspect of the present invention provides an electronic device, including a memory, a processor, and a program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps in the resource-constrained workshop scheduling method based on a multi-objective graph neural network as described in the first aspect of the present invention are implemented.

[0027] One or more of the above technical solutions have the following beneficial effects:

[0028] The present invention constructs a resource-constrained workshop scheduling model based on the acquired workpiece set and workshop scheduling resources; wherein the workshop scheduling model includes an objective function, multi-level constraints for full resource scheduling, and a solution value function for solving the objective function. After comprehensively considering all constraints, a multi-objective graph neural network integrating a graph isomorphism network and a graph attention network is used for global embedding and local embedding respectively, which well avoids the problem that the existing model is prone to fall into local optimality, and can be applied to scheduling and allocation tasks with more constraints and objectives. Therefore, the present invention can maintain high efficiency and high precision of optimal action selection on the basis of comprehensively considering all constraints, thereby realizing reasonable resource-constrained workshop scheduling.

[0029] Advantages of additional aspects of the present invention will be given in part in the following description, and in part will become obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0031] Figure 1 This is a flow chart of a resource-constrained workshop scheduling method based on a multi-objective graph neural network in Example 1 of the present invention.

[0032] Figure 2 It is a schematic diagram of an undirected disjunctive graph in Embodiment 1 of the present invention.

[0033] Figure 3 It is a schematic diagram of a directed disjunctive graph in Embodiment 1 of the present invention.

[0034] Figure 4 This is a schematic diagram of expressing node status in Embodiment 1 of the present invention.

[0035] Figure 5 It is a schematic diagram of expressing the speed state in the first embodiment of the present invention.

[0036] Figure 6 Schematic diagram of disjunctive and conjunction type nodes in Embodiment 1 of the present invention.

[0037] Figure 7 This is a diagram of the algorithm framework based on a multi-objective graph neural network in Example 1 of the present invention.

[0038] Figure 8 Schematic diagram of the training curve of the Taillard data set in Example 1 of the present invention.

[0039] Fig. 9 Schematic diagram of variance analysis of CPLEX and MOGNN in Example 1 of the present invention.

[0040] Fig.10 Schematic diagram of variance analysis of HV values ​​of multiple algorithms compared with the multi-objective optimization algorithm in Example 1 of the present invention.

[0041] Fig.11 Schematic diagram of variance analysis of IGD values ​​of multiple algorithms compared with the multi-objective optimization algorithm in Example 1 of the present invention.

[0042] Fig.12 Schematic diagram of variance analysis of HV values ​​of multiple algorithms in comparison with other reinforcement learning algorithms in Example 1 of the present invention.

[0043] Fig.13 Schematic diagram of variance analysis of IGD values ​​of multiple algorithms in comparison with other reinforcement learning algorithms in Example 1 of the present invention. DETAILED DESCRIPTION

[0044] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0045] It should be noted that the terms used herein are for describing specific embodiments only and are not intended to be limiting of exemplary embodiments according to the present invention.

[0046] In the absence of conflict, the embodiments of the present invention and the features of the embodiments may be combined with each other.

[0047] Embodiment 1

[0048] This embodiment discloses a resource-constrained workshop scheduling method based on a multi-objective graph neural network.

[0049] like Figure 1 As shown, the resource-constrained workshop scheduling method based on multi-objective graph neural network includes:

[0050] Step S1, obtaining a set of workpieces to be processed and workshop scheduling resources;

[0051] Step S2: constructing a resource-constrained workshop scheduling model according to the workpiece set and workshop scheduling resources;

[0052] Step S3, the workshop scheduling model is represented by nodes using a disjunctive graph, and the state, action and reward value of the workshop scheduling model after the node representation is expressed by using the Markov decision method;

[0053] Step S4: Based on the multi-objective graph neural network, determine the optimal action for the next step from the action space shown in the disjunctive graph according to the current state; and execute workshop scheduling according to the determined optimal action.

[0054] Based on the above process, the present invention can maintain high efficiency and high precision of optimal action selection on the basis of comprehensive consideration of all constraints, thereby realizing reasonable resource-constrained workshop scheduling. To facilitate the understanding of the technical solution of the present invention, the specific implementation steps in the technical solution of the present invention are further explained and illustrated below.

[0055] Step S1: Obtain a set of workpieces to be processed and workshop scheduling resources.

[0056] This embodiment is oriented to the workshop scheduling problem with resource constraints, in which multi-level constraints including effective resources, transportation, group switching time and variable speed are embedded. In the workshop scheduling problem considered, n workpieces will be processed on m machine tools in a predefined route, where each workpiece has a different route from other workpieces. To be processed on a specified machine tool, each process should wait for the required resources to be available. Assume that there are h reusable resources, each of which has a certain number of isomorphic resources. Overlap with machine tools, resources and processes is not allowed. That is, the subsequent process should wait for the predecessor of the same workpiece and the predecessor on the same machine tool to complete. At the same time, resources are not available until the corresponding process is completed. All jobs are divided into a certain number of groups. The preparation time is considered for jobs in different groups, which is also a typical reality in many industries. For example, in a prefabricated component system, a machine tool that processes different workpieces with different molds should increase the setup time to select and clean the mold, while workpieces using the same mold have no additional setup time. In addition, all jobs belonging to the same group should be transported by the same vehicle, so transportation constraints are also considered.

[0057] In order to prepare for the construction of the workshop scheduling model and facilitate the interpretation of the subsequent model, this embodiment first explains the parameters, subscripts and decision variables used in the subsequent process. Specifically, it is stipulated that the workpiece subscript is j, p, the process subscript is i, q, the machine tool subscript is k, the resource subscript is u, each machine tool processing position subscript is r, each resource processing position subscript is v, the group subscript is f, the speed subscript is s, the total number of workpieces is n, the total number of machine tools is m, the total number of resources is h, and the total number of processes is , the total number of speeds is ζ, the total number of groups is τ, and the i-th process of workpiece j is O j，i If process O j，i Assigned to machine tool k for processing, the corresponding position setting = 1; otherwise = 0, recorded as M j，i，k If workpiece j is assigned to be processed in factory f, the corresponding position is set to 1; otherwise, it is set to 0, which is recorded as F j，f . Process O j，i The processing time is pt j，i , process O j，i The start time is S j，i , process Oj，i The completion time is E j，i The start time and completion time of machine tool k at position r are SM k，r and EM k，r ; The start time and completion time of resource u at position v are RS v，u and RE v，u The maximum completion time is C max , the resource requirement of workpiece j is RR j , the total energy consumption is TEC, the unit processing energy consumption is UE, the total waiting time of AGV is TWT; the maximum number is L.

[0058] Furthermore, this embodiment also specifies four decision variables, namely, X j，i，r，k :0 / 1 variable, Y j，i，v，u :0 / 1 variable, Z j，i，s : 0 / 1 variables and U j，f，r : 0 / 1 variable. Among them, X j，i，r，k :0 / 1 variable means: If process O j，i Processing at position r of machine tool k, then X j，i，r，k =1; otherwise, X j，i，r，k = 0. j，i，v，u :0 / 1 variable means if process O j，i Processing at position v of resource u, then Y j，i，v，u =1; otherwise, Y j，i，v，u = 0. Z j，i，s :0 / 1 variable means if process O j，i The processing speed is set to s, then Z j，i，s =1; otherwise, Z j，i，s = 0. j，f，r : 0 / 1 variable means that if workpiece j is processed at processing position r in factory f, then U j，f，r =1; otherwise U h，f，r =0.

[0059] Step S2: construct a resource-constrained workshop scheduling model based on the workpiece set and workshop scheduling resources.

[0060] The workshop scheduling model includes an objective function, multi-level constraints for all resource scheduling, and a solution function for solving the objective function. Specifically, the constructed workshop scheduling model is expressed as:

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[0090] Among them, formula (1) is the objective function for calculating weighted fitness, and three weighted fitness targets are set: completion time, total energy consumption TEC, and total waiting time TWT, and each weighted fitness target corresponds to a weighted value; formula (2)-formula (27) are multi-level constraints for full resource scheduling; formula (28) and formula (29) are solution functions for solving the objective function, which are used to calculate the two targets TEC and TWT respectively.

[0091] Furthermore, equations (2) and (3) are non-negative constraints, which are used to ensure that the start time and finish time of each process are not negative; equation (4) is used to ensure that each process should select a unique processing position on the specified machine tool, and equation (5) is used to ensure that each processing position on each machine tool should be uniquely selected by one process. Equation (6) is used to ensure that the machine tool assigned to each workpiece is predetermined; the relationship between the finish time, start time, processing time and processing speed is given in equation (7). Equations (8) and (9) are used to ensure that the processing process does not allow overlap; among them, equation (8) ensures that each processing position at each resource can only be processed by one process, and each process should select a processing position for each required resource (see equation (11)). Equations (12) and (13) ensure that the start time and finish time of each resource processing position should be positive. Equations (14)-(17) are used to ensure that the start and finish times of the set process should be equal to the corresponding processing position at each required resource. Equation (18) ensures that the processing positions of each resource should not overlap with each other. Formula (19) ensures that the process should be assigned to the processing position of each resource from left to right, that is, there should not be any empty position on each resource. Formula (20) ensures that each process should select a processing speed. Formulas (21)-(24) are used to ensure that the start and completion time of the processing position on each machine tool is equal to the corresponding processing process. Formula (25) ensures that if each process should select a processing position on the assigned group, formula (26) ensures that each processing position on each group should be selected by a process. Formula (27) ensures that the processing positions on each group should be selected from left to right without any skipping.

[0092] Step S3: The workshop scheduling model is represented by nodes using a disjunctive graph, and the Markov decision method is used to express the state, action and reward value of the workshop scheduling model after the node representation.

[0093] Step S3-1: The workshop scheduling model is represented by nodes using a disjunctive graph.

[0094] The disjunctive graph is used to represent the shop scheduling model in a node-based manner. Specifically, the disjunctive graph is represented as G = (O, C∪D); where Indicates that the starting node O is included S and end node O TFor the workshop scheduling problem, the priority constraints of the same workpiece operation are represented in set C, and D represents the disjunctive arcs connecting the operations on the same machine tool. Disjunctive graphs are divided into undirected disjunctive graphs and directed disjunctive graphs.

[0095] like Figure 2 In the undirected disjunctive graph shown, C contains all solid lines and D contains all dashed lines. The number next to each arc represents the weight value between the two nodes, that is, the processing time of the previous operation. 1，1 and O 1，2 Connected by the arc marked 10, this means that O 1，1 The processing time is 10. In the workshop scheduling problem of this embodiment, the machine tool allocation for each operation (process) is predetermined. For example, {0 1，1 , O 2，2 , O 3，2}, {O 2，1 , O 1，2 , O 3，3} and {O 3，1 , O 1，3 , O 2，3}.

[0096] In the disjunctive graph, each node has two types of adjacent nodes, namely, conjunctive and disjunctive adjacent operations; the first of which are operations on the same workpiece, and the second are operations assigned on the same machine tool. 1，1 The adjacent nodes of are:

[0097] N(O 1，1 )={O 1，2 , O 1，3}∪{O 2，2 , O 3，2}(30)

[0098] The main task of the scheduling problem is to determine the direction of each separation arc to minimize some objective. For example, Figure 3 A graph with directed disjunctive arcs is shown; the sequence of workpieces processed on three machine tools is: 1，1 , O 2，2 , O 3，2},{O 2，1 , O 1，2 , O 3，3} and {O 3，1 , O 1，3 , O 2，3}.

[0099] Step S3-2: Use the Markov decision method to express the states, actions and reward values ​​of the post-node workshop scheduling model.

[0100] The Markov decision method is used to express the key components of reinforcement learning such as the state, action and reward value of the workshop scheduling model after node representation; among them, the state includes node state and speed state.

[0101] Step S3-2-1, Node status

[0102] The node state consists of five tuples, namely x j，i =<pt j，i , μ j，i , v j，i , δ j，i , γ j，i >∈R 5 ; Among them, pt j，i Indicates O j，i Processing time, μ j，i Indicates O j，i The earliest start time, v j，i Yes j，i The latest start time, δ j，i Yes j，i Processing speed, γ j，i Yes j，i the resources required.

[0103] like Figure 4 An example of node status representation is shown in FIG. 1 , in which the processing time, the earliest start time and the latest start time of the workpiece are 25, 123 and 130 respectively. j，i On the critical path, that is, the process is a critical process and μ j，i =v j，i . This means Figure 4 The speed level of this process is set to 3, requiring the first and third resources.

[0104] Step S3-2-2: Speed ​​status

[0105] set up represents the total number of processes with a processing speed equal to s, Indicates the maximum number of allocated processes for all speed levels, Indicates the minimum number of allocated processes for all speed levels. Specifically, Figure 5 Three characteristics of velocity are shown, namely:

[0106] (a) in, Indicates the scale for each speed level;

[0107] (b) in,

[0108] (c) in,

[0109] Step S3-2-3, Action

[0110] The representation of actions adopts a multi-action mechanism. Specifically, the multi-action mechanism includes an action space of process pairs and an action space of speed allocation. The detailed information of the action space is as follows: (1) Process pair action. For the JSP considered with group switching time and limited resource constraints, it is difficult to estimate the true critical path. Therefore, the present invention randomly selects a pair of processes on the connecting arc in the graph and exchanges them. (2) Speed ​​allocation action. Randomly select an operation and assign a random speed to it.

[0111] Step S3-2-4: Conversion mechanism

[0112] At step t+1, a new state S is generated based on the current state using the selected “process pair action” and “speed distribution action” t+1 . Process to Action Space and speed distribution action The space is feasible and is not empty at any step.

[0113] Step S3-2-4, reward value

[0114] The reward value is represented by the weighted sum of the three objectives in the objective function. Specifically:

[0115]

[0116] in, is the optimal target value, if the target value fit(s t+1 ) is better than Then use fit(s t+1 )replace

[0117] Step S4: Based on the multi-objective graph neural network, determine the optimal action for the next step from the action space shown in the disjunctive graph according to the current state; and execute workshop scheduling according to the determined optimal action.

[0118] Strategy of the present invention θ (a t |s t ) is used to calculate the current state s t Select an appropriate action a from the action space tThe multi-objective graph neural network consists of a graph isomorphism network and a graph attention network. In order to effectively capture node information, the global embedding mechanism based on the graph isomorphism network (GIN) is used to capture global information to achieve node embedding; the local embedding mechanism based on the graph attention network (GAT) is used to capture neighborhood and local information from conjunction and disjunction of adjacent nodes to achieve graph embedding; then, the speed features are embedded through a fully connected network to achieve speed distribution embedding.

[0119] Step S4-1: Global embedding mechanism

[0120] As an extended graph neural network (GNN), GIN has a powerful ability to map different graph structures into different embedding spaces, so it can distinguish non-isomorphic structures.

[0121] In the initialization phase, each node V∈O is Then, at k iterations, the embedding of each node is updated as follows:

[0122]

[0123] Where K represents the total number of iterations, is the global embedding of node P at iteration k-1, and U∈N(V) is the set of neighboring nodes of V including conjunction and disjunction neighboring operations. MLP k () is the multi-layer perceptron (MLP) at iteration k. Based on the embedding of each node, the global embedding of the entire graph at iteration k is calculated as follows:

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[0125] Finally, the final embedding after each node iteration and the global embedding of the entire graph are as follows:

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[0128] Step S4-2: Local embedding mechanism

[0129] like Figure 6 As shown in (a) and (b) in Figure 2, the GAT method is used to further capture information from the conjunction and disjunction adjacent nodes. Although these two subgraphs have the same set of nodes, the arcs in them are different from each other.

[0130] For each node V∈O, The update calculation of word embedding in step k is as follows:

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[0135] in, and are two graph attention layers, which are used to capture the information of conjunction and disjunction of adjacent nodes in iteration k respectively; N C (V) and N D (V) are the two neighbor node sets of the conjunction and disjunction arcs respectively, is the embedding set of neighboring processes in the same workpiece and the same machine, l G is a local embedding of the entire graph.

[0136] Finally, the global and local embeddings for each node and the entire graph are calculated as follows:

[0137]

[0138] Step S4-3: Speed ​​embedding mechanism

[0139] The three features of speed are embedded through a simple fully connected network, where the input length is equal to three, the two hidden layers have 128 nodes, and ReLu is selected as the active function. Specifically, formula (41) gives the calculation method of speed embedding, that is:

[0140]

[0141] Step S4-4: Action score

[0142] After all embeddings are generated for nodes, graphs, and speed assignments, two types of action scores should be calculated, namely, process-pair action scores and speed action scores. (1) For process-pair action scores A score , first embed the graph Connect to each node embedding Next, the superimposed embedding is fed into To obtain the latent vector Then, multiply by its transpose Get the score A for each pair of processes score (2) For the speed action score S score , embed the velocity into r ζ and Multiply them together to obtain a matrix for each pair of operation and speed level.

[0143] Finally, the action scores and speed action scores of all processes are flattened and input into the softmax function to obtain the probability of selecting a suitable action; the optimal action is determined based on the obtained probability. Specifically:

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[0147] It should be further noted that the reward value calculated in equation (31) is the weighted value of all objectives. However, in order to adapt to solving multi-objective optimization problems, a set of Pareto solutions should be generated. To solve this problem, a well-known weighted sum method is embedded in the multi-objective processing mechanism, which can convert multiple objective values ​​into a single value. Therefore, the reward value can be obtained with certainty.

[0148] To solve the multi-objective problem, N network models are trained and tested to generate a set of Pareto solutions. To this end, a set of uniformly distributed weight values ​​λ = {λ i |i=1,2,...,N}, where M is the total number of targets. Based on the weighted vector, the fitness in the i-th network model can be calculated as follows:

[0149]

[0150] In order to achieve collaborative optimization among N network models and improve training performance, this embodiment introduces a neighborhood knowledge transfer mechanism, which can be described in Algorithm 2. The main reasons for using the neighborhood knowledge transfer heuristic are: (1) The network models in the neighborhood have similar weight values, so the network parameters have similar characteristics. Therefore, parameter sharing is reasonable; (2) The training process can be effectively performed by using the knowledge sharing method. Therefore, the convergence ability of network training can be enhanced. Algorithm 2 is specifically shown in Table 1:

[0151] Table 2 Neighborhood knowledge transfer strategy algorithm

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[0154] Further, Figure 7 The multi-objective graph neural network model framework proposed in this embodiment is shown, and the main steps are as follows:

[0155] First, the features of each instance are calculated and fed into the network as input data. These features include five values ​​related to the operation pair and three features about speed. Next, all these features are fed into three types of networks, namely GIN for capturing global embedding, GAT for capturing embedding related to local or neighboring features, and FCN for capturing features related to speed. The global embedding and local neighboring embedding are then fed into the MPL network to fuse the two embeddings to generate tensors, which are dispatched to calculate the action selection probability and speed of the operation pair. Then, after selecting the operation pair and speed assignment, the reward value of the current state is calculated, and the corresponding network parameters are updated using the loss function value. Finally, the next state is used to update the current state for the next iteration.

[0156] In order to verify the superiority of the shop scheduling method provided by the present invention, this embodiment also provides a detailed experimental comparison and analysis to verify the efficiency and effectiveness of the proposed algorithm.

[0157] About the experimental environment configuration: The algorithm proposed in this invention is implemented in Python, using Pytorch as the development framework. All compared algorithms are performed in an Ubuntu 20.04LTS 64-bit system with a 16vCPU Intel(R)Xeon(R)Platinum 8350C CPU@2.60GHz and an NVIDIA GeForce RTX 3090(24GB).

[0158] Three algorithms were selected for detailed comparison: (1) CPLEX was selected to implement the mathematical model discussed in the problem formulation part, and the results were collected and compared with the algorithm of the present invention to verify the effectiveness of the proposed algorithm; (2) Two types of DRL and GNN were selected to verify the efficiency of the proposed network model; (3) Three heuristic methods and meta-heuristic methods were selected to further compare the performance of the algorithm of the present invention with existing algorithms.

[0159] Furthermore, during the comparison process, two commonly used metrics are used to calculate the differences between different types of compared algorithms: (1) Hypervolume (HV) is used to calculate the volume in the target space covered by the compared algorithms; and (2) Inverted generational distance (IGD) is used to calculate the average distance from the obtained solution set to the reference point.

[0160] Regarding experimental examples: This embodiment uses two types of instances; the first type contains ten small instances, ranging from 3-jobs-2-machines to 4-jobs-4-machines, and uses small instances to test the effectiveness of the CPLEX model; the second type contains instances extended from widely used datasets, which include two sets, namely, training datasets and test datasets. The training dataset is extended from five widely used sets of instances in the Taillard dataset, ranging from (10 10), (15 10), (15 15), (20 10) and (2015); the test dataset is extended based on the following well-known public datasets, namely Taillard (Taillard, 1993), ABZ (Adams et al., 1988), FT (Fisher, 1963), LA (Lawrence, 1984), SWV (Storer et al., 1992), ORB (Applegate & Cook, 1991) and YN (Yamada & Nakano, 1992). Unlike the classic dataset, this embodiment extends these examples by adding family setup time, processing speed data and limited resources. All of these examples can be downloaded directly from the relevant website.

[0161] In order to test the training convergence ability of the MOGNN (multi-objective graph neural network) algorithm proposed in the present invention, this embodiment selects 10 10 Taillard data sets. Figure 8 The training curves of the selected datasets are shown. From the training curves, it can be seen that the proposed network has better training convergence ability for the considered problem, that is, it is not easy to fall into the local optimum.

[0162] Experiment 1: Comparison with CPLEX model

[0163] To test the effectiveness of the MILP model, this example compares the MOGNN and MILP models in detail, where the latter is coded with CPLEX and the stopping criterion for each instance is set to 5400 seconds. For a fair comparison, for each instance, the same weights are set in the MILP model as in MOGNN. Therefore, for each case, 21 results are obtained by MOGNN and CPLEX, which are then collected to obtain the Pareto set to calculate the HV results.

[0164] Table 2 Comparison of MOGNN and MILP models

[0165]

[0166]

[0167] The comparison results of ten small-scale instances are shown in Table 2, where the two numbers in the first column represent the job number and the machine number. From Table 2, we can conclude that: (1) among the given 10 small-scale instances, the MOGNN algorithm proposed in the present invention obtains 9 better results; (2) the average performance in the last row further shows that the proposed MOGNN has better robustness than CPLEX.

[0168] In order to show whether there are significant differences between MOGNN and CPLEX, analysis of variance (ANOVA) was performed on this basis. Fig. 9 As shown, compared with CPLEX, the MOGNN proposed in the present invention shows competitive performance. Therefore, the effectiveness comparison between the MOGNN model and the MILP model and the efficiency comparison between the network model are verified.

[0169] Experiment 2: Comparison with CPLEX model

[0170] In order to verify the efficiency of the proposed MOGNN algorithm in solving multi-objective optimization problems, this embodiment selects multiple multi-objective evolutionary algorithms such as ARMOEA, CCMO, CMOEA_MS and NSGA-III for comparison. The main reason for selecting these MOEAs (multi-objective evolutionary algorithms) is that all of these algorithms can effectively solve different types of multi-objective optimization problems, which have been encoded in the public platform PlatEMO. Therefore, it is easy to make a fair comparison with these multi-objective algorithms.

[0171] Table 3 shows the detailed comparison results of the HV values, and it can be observed that: (1) Considering the eight sets of TAI datasets, the proposed MOGNN algorithm obtains five better results. The second best algorithm for solving the tai dataset is CCMO, which obtains two better results. Therefore, considering the eight sets of TAI datasets, MOGNN is significantly better than the other comparison algorithms; (2) For other instances, including ABC, YN, SWV, LA, and FT, the proposed MOGNN algorithm also obtains better results; (3) From the last row in Table 3, it can be seen that the average HV value obtained by MOGNN is 0.7898, which is significantly better than the other four comparison algorithms.

[0172] Table 3 Comparison of HV results with multi-objective optimization algorithm

[0173]

[0174] Table 4 shows the detailed comparison results of IGD values, from which it can be concluded that: (1) considering the eight groups of TAI datasets, MOGNN obtains four better results; (2) except for the TAI instance, the proposed MOGNN can obtain better results than the other groups of instances, which shows the efficiency of the proposed network in solving optimization problems with different structures; (3) the last row shows that the average IGD value obtained by the proposed algorithm is about 2.5 times lower than that of the other compared algorithms.

[0175] Table 4 Comparison of IGD results with multi-objective optimization algorithm

[0176]

[0177]

[0178] Fig.10 ANOVA comparison of HV values ​​between MOGNN, ARMOEA, CCMO, CMOEA_MS, and NSGA-III is shown, while Fig.11 The variance calculation comparison of IGD values ​​is shown. From these two figures, it can be seen that the performance of the proposed MOGNN algorithm is competitive considering the convergence and diversity capabilities.

[0179] Experiment 3: Comparison with other reinforcement learning algorithms

[0180] In order to verify the efficiency of the MOGNN algorithm proposed in the present invention compared with other deep learning algorithms, this embodiment selects two recently published methods, namely the DRL algorithm and the GNN algorithm. The main reasons for selecting these two algorithms are: (1) DRL is a recently published classic JSP algorithm, and its framework is similar to the proposed MOGNN; (2) GNN is an efficient algorithm for solving flexible JSP problems and can easily solve the considered JSP problem.

[0181] Table 5 shows the comparison of HV values ​​between MOGNN, DRL and GNN. It can be seen from Table 5 that: (1) considering different types of instances, the proposed MOGNN obtains better HV results, significantly better than the second-best algorithm, i.e., DRL; (2) the average performance shown in the last row shows that MOGNN is significantly competitive among the three compared algorithms. At the same time, Fig.12 The ANOVA comparison of HV values ​​between DRL, GNN, and MOGNN is shown, further verifying the efficiency of the proposed network model.

[0182] Table 5 Comparison of HV results with other reinforcement learning algorithms

[0183]

[0184] Table 6 gives a comparison of the IGD values ​​considering MOGNN, DRL and GNN. The results in Table 6 also verify that the proposed algorithm has better performance in terms of convergence and robustness; at the same time, Fig.13 The efficiency of considering the IGD indicator is further shown.

[0185] Table 6 Comparison of IGD results with other reinforcement learning algorithms

[0186]

[0187] Based on the comparison of three different types of experiments, it is further verified that the present invention can maintain high efficiency and high precision of optimal action selection on the basis of comprehensive consideration of all constraints, thereby achieving reasonable resource-constrained workshop scheduling.

[0188] Embodiment 2

[0189] This embodiment discloses a resource-constrained workshop scheduling system based on a multi-objective graph neural network.

[0190] Resource-constrained shop scheduling system based on multi-objective graph neural network, including:

[0191] The data acquisition module is configured to: acquire a set of workpieces to be processed and workshop scheduling resources;

[0192] The workshop scheduling model building module is configured to: build a resource-constrained workshop scheduling model according to the workpiece set and the workshop scheduling resources;

[0193] The disjunctive graph representation module is configured to: use a disjunctive graph to represent the shop scheduling model in a node-based manner, and use a Markov decision method to express the state, action and reward value of the shop scheduling model after the node-based representation;

[0194] The workshop scheduling module is configured to: determine the optimal action for the next step from the action space shown in the disjunctive graph according to the current state based on the multi-objective graph neural network; and execute workshop scheduling according to the determined optimal action.

[0195] Embodiment 3

[0196] The purpose of this embodiment is to provide a computer-readable storage medium.

[0197] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the resource-constrained workshop scheduling method based on a multi-objective graph neural network as described in the first embodiment of the present disclosure.

[0198] Embodiment 4

[0199] The purpose of this embodiment is to provide an electronic device.

[0200] An electronic device includes a memory, a processor, and a program stored in the memory and executable on the processor. When the processor executes the program, the steps in the resource-constrained workshop scheduling method based on a multi-objective graph neural network as described in the first embodiment of the present disclosure are implemented.

[0201] The steps involved in the apparatuses of the above embodiments 2, 3 and 4 correspond to the method embodiment 1, and the specific implementation methods can refer to the relevant description part of embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood to include any medium that can store, encode or carry an instruction set for execution by a processor and enable the processor to execute any method in the present invention.

[0202] Those skilled in the art should understand that the modules or steps of the present invention described above can be implemented by a general-purpose computer device, or alternatively, they can be implemented by a program code executable by a computing device, so that they can be stored in a storage device and executed by the computing device, or they can be made into individual integrated circuit modules, or multiple modules or steps therein can be made into a single integrated circuit module for implementation. The present invention is not limited to any specific combination of hardware and software.

[0203] Although the above describes the specific implementation mode of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without creative work are still within the scope of protection of the present invention.

Claims

1. Resource-constrained shop scheduling method based on multi-objective graph neural network, characterized in that: include: Obtain a collection of workpieces to be processed and workshop scheduling resources; Building a resource-constrained workshop scheduling model according to the workpiece set and the workshop scheduling resources; The workshop scheduling model is represented by nodes using a disjunctive graph, and the state, action and reward value of the workshop scheduling model after the node representation is expressed by using a Markov decision method; Based on a multi-objective graph neural network, the optimal action for the next step is determined from the action space shown in the disjunctive graph according to the current state; and workshop scheduling is performed according to the determined optimal action.

2. The resource-constrained workshop scheduling method based on a multi-objective graph neural network according to claim 1, characterized in that: The workshop scheduling model includes an objective function, multi-level constraints for full resource scheduling, and a solution function for solving the objective function; wherein the objective function is provided with three weighted fitness targets of completion time, total energy consumption, and total waiting time, and each weighted fitness target corresponds to a weighted value.

3. The resource-constrained workshop scheduling method based on a multi-objective graph neural network according to claim 1, characterized in that: The disjunctive graph is used to represent the shop scheduling model in a node-based manner. Specifically, the disjunctive graph is represented by G=(O,C∪D); wherein O represents the set of all operations including the start node and the end node, the priority constraints of the operations on the same workpiece are represented in the set C, and D represents the disjunctive arcs connecting the operations on the same machine tool.

4. The resource-constrained workshop scheduling method based on multi-objective graph neural network according to claim 1, characterized in that: The Markov decision method is used to express the state, action and reward value of the shop scheduling model after node representation. Specifically, the state includes node state and speed state; wherein the node state is composed of five tuples: processing time, earliest start time, latest start time, processing speed and required resources.

5. The resource-constrained workshop scheduling method based on multi-objective graph neural network according to claim 4 is characterized in that: The action is represented by a multi-action mechanism, which includes an action space for process pairs and an action space for speed distribution; the reward value is represented by a weighted sum of three objectives in an objective function as the reward value.

6. The resource-constrained shop scheduling method based on a multi-objective graph neural network according to claim 1, characterized in that: The multi-objective graph neural network consists of a graph isomorphism network and a graph attention network; wherein, a global embedding mechanism based on the graph isomorphism network is used to capture global information to achieve node embedding; a local embedding mechanism based on the graph attention network is used to capture neighborhood and local information from conjunction and disjunction adjacent nodes to achieve graph embedding; subsequently, speed features are embedded through a fully connected network to achieve speed distribution embedding.

7. The resource-constrained workshop scheduling method based on a multi-objective graph neural network according to claim 6, characterized in that: After all embeddings are generated for nodes, graphs, and speed assignments, the process pair action scores and speed action scores are calculated; all process pair action scores and speed action scores are flattened and input into the softmax function to obtain the probability of selecting a suitable action; the optimal action is determined based on the obtained probability.

8. Resource-constrained workshop scheduling system based on multi-objective graph neural network, characterized by: include: The data acquisition module is configured to: acquire a set of workpieces to be processed and workshop scheduling resources; The workshop scheduling model building module is configured to: build a resource-constrained workshop scheduling model according to the workpiece set and the workshop scheduling resources; The disjunctive graph representation module is configured to: use a disjunctive graph to represent the shop scheduling model in a node-based manner, and use a Markov decision method to express the state, action and reward value of the shop scheduling model after the node-based representation; The workshop scheduling module is configured to: determine the optimal action for the next step from the action space shown in the disjunctive graph according to the current state based on the multi-objective graph neural network; and execute workshop scheduling according to the determined optimal action.

9. A computer-readable storage medium having a program stored thereon, characterized in that: When the program is executed by a processor, the steps in the resource-constrained workshop scheduling method based on a multi-objective graph neural network as described in any one of claims 1 to 7 are implemented.

10. An electronic device comprising a memory, a processor, and a program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps in the resource-constrained workshop scheduling method based on a multi-objective graph neural network as described in any one of claims 1 to 7 are implemented.

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