A mobile multi-robot flexible job-shop scheduling method
By combining a three-layer encoded genetic algorithm with constraint programming, the scheduling of flexible workshops is optimized, solving the complex scheduling problems of multi-robot collaborative processing and time window constraints, and achieving efficient scheduling optimization and accurate resource allocation.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HUAZHONG UNIV OF SCI & TECH
- Filing Date
- 2026-03-17
- Publication Date
- 2026-06-19
AI Technical Summary
Existing flexible job shop scheduling methods struggle to achieve effective scheduling optimization when dealing with multi-robot collaborative processing, robot movement behavior, and time window constraints. This results in low solution efficiency, long computation time, and difficulty in balancing global search capability and scheduling accuracy.
A hybrid optimization method combining a three-layer encoded genetic algorithm and constraint programming is adopted to optimize the scheduling process of the flexible workshop by rationally coordinating the execution sequence of processes, robot selection and collaborative processing mode, and combining robot movement time and time window constraints.
It achieves effective scheduling optimization of flexible workshops under the conditions of robot mobility characteristics and time window constraints, improves the applicability and accuracy of scheduling models, reduces waiting or conflict situations in scheduling schemes, and improves computational efficiency.
Smart Images
Figure CN122243055A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of intelligent manufacturing and scheduling optimization technology, specifically relating to a scheduling method for a mobile multi-robot flexible workshop, and more specifically, to a hybrid intelligent scheduling method for optimizing production scheduling in a flexible workshop under the conditions of robot mobility, multi-robot collaborative processing mode and time window constraints. Background Technology
[0002] With the development of intelligent manufacturing technology, multi-robot systems are widely used in fields such as aerospace manufacturing, equipment manufacturing, and the processing of large structural components. Flexible workshops are typically characterized by numerous processes, complex processing paths, and strong resource selectivity. In actual production, different processes can often be completed by multiple robots, thus forming a flexible production environment with selectable processing modes.
[0003] In mobile, multi-robot flexible workshops, robots not only perform processing tasks but also need to move between different workpieces. The robot's movement and processing are coupled in time and space. Especially in scenarios requiring collaborative processing with multiple robots, a single process may require multiple robots to participate simultaneously. The scheduling process must not only satisfy the sequential constraints between processes but also consider multiple constraints such as robot collaboration, resource competition, and movement time, significantly increasing the complexity of the scheduling problem. Furthermore, in actual production environments, different processes often have time-series requirements. For example, adjacent processes must be connected within a limited time, or a certain time interval must be maintained before the next process can begin, creating time window constraints with varying degrees of leniency. These time window constraints further increase the constraint dimension of the scheduling problem, requiring the scheduling process to consider not only process sequence and resource allocation but also the execution intervals between processes in the time dimension.
[0004] Existing flexible job shop scheduling methods primarily focus on scenarios with fixed equipment or immovable resources, typically ignoring robot movement within the shop or only using simplified methods to handle movement time. This makes it difficult to accurately reflect resource occupancy in actual production processes. Furthermore, some studies, when dealing with time window constraints, only consider simple process sequence relationships, failing to simultaneously characterize tight and loose constraints between different processes, leading to discrepancies between scheduling results and actual production needs. Some studies employ heuristic algorithms or mathematical programming methods to solve scheduling problems. However, when facing complex scheduling problems involving selectable processing modes, multi-robot collaborative processing constraints, robot movement time, and time window constraints, these methods often suffer from low solution efficiency, long computation times, or difficulty in balancing global search capabilities with scheduling accuracy.
[0005] Therefore, in flexible workshop environments with selectable processing modes, multi-robot collaborative processing requirements, robot mobility, and time window constraints, how to jointly optimize the sequence of process execution, allocation of processing resources, collaborative processing modes, and time connection relationships of processes while ensuring scheduling feasibility remains a technical challenge that urgently needs to be addressed in existing technologies. Summary of the Invention
[0006] To address the problems of high scheduling complexity, tight coupling between robot movement behavior and processing, difficulty in unified modeling of multi-robot collaborative processing and process selection modes, and high difficulty in scheduling optimization under time window constraints in the scheduling process of mobile multi-robot flexible workshops, the present invention aims to propose a scheduling method for mobile multi-robot flexible workshops. By reasonably coordinating the process execution sequence, robot selection, collaborative processing mode, and process time connection relationship, the method effectively optimizes the scheduling process of flexible workshops while considering the mobility characteristics of robots and time window constraints.
[0007] To achieve the above objectives, according to one aspect of the present invention, a method for scheduling a mobile multi-robot flexible workshop is provided, comprising the following steps: S1. Workshop scheduling information acquisition stage: Based on the basic scheduling information of the mobile multi-robot flexible operation workshop, the initial position and spatial layout information of the workpiece are automatically allocated through dynamic grid layout. S2. Genetic Algorithm Individual Encoding Construction Stage: Based on the basic scheduling information obtained in step S1, a three-layer encoded genetic algorithm is constructed to perform a global search for cooperative patterns in the scheduling problem of mobile multi-robot flexible workshops; S3. Genetic Evolution and Dynamic Parameter Control Stage: The genetic algorithm in step S2 is used to perform evolutionary search on the constructed individuals, and the process execution order, robot selection and collaborative processing mode are jointly optimized through crossover and mutation operations; S4. Construction of the CP model for movement time and time window constraints: Based on the process execution sequence, robot selection and collaborative processing mode determined by step S3, a scheduling model with movement time and time window constraints is constructed. The robot's initial position and workpiece spatial layout information obtained in step S1 are used to calculate the movement time required for the robot to perform adjacent processes between different workpieces. The movement time constraints and the time window constraints between processes are introduced into the scheduling modeling process to reflect the coupling characteristics between robot processing behavior, movement behavior and process time connection. S5.CP Model Optimization Maximum Completion Time Stage: Based on the movement time and time window constraint scheduling model constructed in step S4, constraint programming is used to uniformly optimize and iterate the start and end times of each process. Under the premise of satisfying process sequence constraints, collaborative processing constraints, movement time constraints, and time window constraints, the scheduling scheme of the mobile multi-robot flexible workshop is obtained with minimizing the maximum completion time as the optimization objective.
[0008] Preferably, the basic scheduling information in step S1 includes the process structure information of multiple workpieces, the optional robot resource information corresponding to each process, the collaborative processing type information of the process, and the initial position of the robot and the spatial layout information of the workpiece. At the same time, the time window constraint information between processes is obtained to describe the connection requirements of adjacent processes in the time dimension.
[0009] Preferably, the initial position coordinates of the workpiece in step S1 are ( The robot's movement time between workpieces is calculated using Manhattan distance based on the workpiece spatial layout. The expression for this time is:
[0010] in, For robots to remove workpieces Move the position to the workpiece Time required, ( ) is the workpiece Position coordinates, ( ) is the workpiece The location coordinates.
[0011] Preferably, the three-layer coding in step S2 is as follows: the first layer coding is used to represent the execution order of the process to depict the arrangement relationship of different processes in the time dimension; the second layer coding is used to represent the robot selection result corresponding to each process to describe the processing resource allocation scheme under flexible resource conditions; and the third layer coding is used to represent the collaborative processing mode decision of each process, describing the single robot processing mode and the multi-robot collaborative processing mode through collaborative process decision variables.
[0012] As a preferred option, step S3 specifically involves: during the genetic evolution process, dynamically adjusting the population size participating in the genetic operation in each generation according to the current generation number, and simultaneously dynamically setting the upper limit of the solution time for the constraint programming model, thereby achieving resource coordination and allocation between the genetic search process and precise scheduling computation while ensuring search quality.
[0013] As a preferred option, the expression for the function regulating the number of individuals participating in crossover mutation is:
[0014] in, Indicates the initial population size. This represents the minimum number of crossover individuals that we want to retain in the final stage, and its value is set to 2. The parameter is used to adjust the steepness of the function; The function inflection point has a value of 0, ensuring that the number of individuals participating in crossover mutation in the population decreases round by round from 100 to 2; The expression for the time upper limit control function in the constrained programming model is:
[0015] in, To find the minimum time required, For the longest solution time, The inflection point of the function is used to ensure that the solution time increases progressively from 0.2 seconds to 20 seconds.
[0016] Preferably, step S4 specifically involves: decoding the individual workpieces. The decoding process is arranged sequentially according to the encoding order. The start time of each process depends on the completion time of the previous process and the current available robot time. If the robot is performing a task for the first time, it moves from the origin to the workpiece position. If the robot is performing tasks continuously, it moves from the previous workpiece position (…). , Move to the current workpiece position. , Based on the Manhattan distance, the travel time is calculated, and the initial maximum completion time is finally obtained. .
[0017] Preferably, each iteration of optimization in step S5 includes the following steps: S51 Identify the current best individual: Find the individual with the smallest objective function value in the current population, denoted as... ; S52 Genetic Operation: Identify the positions of all possible cooperative steps, randomly select a subset for crossover, and use probability... Perform MX crossover with mutation probability Perform single-point mutation; S53 Optimization of the scheduling model with travel time and time window constraints: Call the CP model solver to optimize the maximum completion time and update the global optimal solution; S54: After multiple iterations, output the final result of the scheduling.
[0018] Preferably, the objective function expression for the CP model in step S53 is:
[0019] in, For process Processing time period The maximum completion time.
[0020] Preferably, the optimization process in step S53 includes the following steps: S531: Calculate the upper limit of the solution time for each round; S532: Create an interval variable for each process, the expression of which is:
[0021] in, For process Use configuration pattern Processing, For process In configuration The processing time below, To move the robot from the origin to the workpiece Location and time; S533: Each task can only be processed by one robot in one cooperative mode. Its expression is:
[0022] in, For workpiece index, For a collection of workpieces, For process sets, For process index, Configure an index for the robot. For process The available configuration set, It is a processing mode. Indicate process In a specific configuration The set of available patterns below; S534: Establish a priority relationship between each process step, expressed as follows:
[0023] S535: This sets each robot task assignment to be conflict-free, and automatically inserts movement time between tasks. Its expression is:
[0024] in, For configuration The execution order of all tasks. A matrix storing the time it takes for the robot to move between various workpieces. A set of optional robot configurations; S536: Set a time window constraint for different processes of the same workpiece to meet a specified priority processing sequence. The expression is as follows:
[0025]
[0026] in, For process After completion, proceed to the next process. The minimum waiting time before starting To proceed to the next process after completion Maximum allowed waiting time before starting; S537: When selecting cooperative mode, the same interval variable is added to the task sequences of two robots simultaneously to ensure synchronized start and synchronized end. The expression is:
[0027]
[0028] in, For process Use configuration pattern Processing, For process Use configuration pattern Processing; After solving, the objective function value is calculated, and the global optimal solution is updated.
[0029] In summary, the technical solutions conceived by this invention have the following beneficial effects compared with the prior art: The method of this invention effectively optimizes the scheduling process of flexible workshops by reasonably coordinating the execution sequence of processes, robot selection, collaborative processing mode, and process time connection, while taking into account the mobility characteristics of robots and time window constraints.
[0030] Specifically, (1) In the process of scheduling optimization, the present invention considers the mobility characteristics of robots, the collaborative processing mode of multiple robots, the process selection constraints and the time window constraints at the same time. It can comprehensively depict the actual production characteristics of mobile multi-robot flexible workshops and help improve the applicability of the scheduling model to real manufacturing scenarios.
[0031] (2) This invention uses a three-layer encoded genetic algorithm to jointly model and optimize the process execution sequence, robot selection and collaborative processing mode, avoiding the limitations of scheduling optimization only for a single decision dimension, and is conducive to maintaining good global search capability in complex scheduling space.
[0032] (3) In the process of genetic evolution, the present invention dynamically adjusts the population size involved in genetic operations and the upper limit of the constraint planning solution time, so as to realize the resource coordination and configuration between the genetic search process and the precise scheduling calculation, which helps to control the overall computing overhead while ensuring the scheduling quality.
[0033] (4) In the scheduling modeling stage, the present invention introduces robot movement time constraints and combines them with time window constraints between processes to coordinate the robot processing behavior, movement behavior and process time connection relationship in a unified manner. This helps to reduce the waiting or conflict situations that may occur in the scheduling scheme and improve the executability of the scheduling results in the actual production environment.
[0034] (5) The present invention adopts a hybrid optimization method that combines genetic algorithm and constraint programming. Based on the genetic algorithm to determine the collaborative processing mode and resource allocation scheme, constraint programming is used to accurately optimize the process time, with the goal of minimizing the maximum completion time, which helps to obtain a scheduling scheme that meets multiple constraints. Attached Figure Description
[0035] Figure 1 This is a schematic diagram of the skin distribution using 10 workpieces as an example.
[0036] Figure 2 This is a schematic diagram of the three-layer coding chromosome structure according to an embodiment of the present invention.
[0037] Figure 3 This is a schematic diagram of the crossover and mutation process in an embodiment of the present invention.
[0038] Figure 4 This is a flowchart of the GA-CP algorithm.
[0039] Figure 5 This is a Gantt chart diagram illustrating a real-world GA-CP solution. Detailed Implementation
[0040] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.
[0041] Please see Figures 1-5This invention provides a mobile multi-robot flexible workshop scheduling method. Considering robot mobility, multi-robot collaborative processing constraints, selectable processing modes, and time window constraints, it optimizes the scheduling process of the flexible workshop through a hybrid optimization approach combining genetic algorithms and constraint programming. The technical solution of this invention will be described in detail below with reference to specific embodiments, focusing on scheduling data modeling, scheduling code construction, genetic evolution process, and constraint programming scheduling results. Specifically, it includes the following steps: S1. Workshop scheduling information acquisition stage: Based on the basic scheduling information of the mobile multi-robot flexible operation workshop, the initial position and spatial layout information of the workpiece are automatically allocated through dynamic grid layout. The basic scheduling information includes the process structure information of multiple workpieces, the available robot resource information corresponding to each process, the collaborative processing type information of the processes, and the initial position of the robot and the spatial layout information of the workpieces. Simultaneously, it acquires the time window constraint information between processes to describe the connection requirements of adjacent processes in the time dimension. The initial position coordinates of the workpiece in step S1 are (…). The robot's movement time between workpieces is calculated using Manhattan distance based on the workpiece spatial layout. The expression for this time is:
[0042] in, For robots to remove workpieces Move the position to the workpiece Time required, ( ) is the workpiece Position coordinates, ( ) is the workpiece The location coordinates.
[0043] In this embodiment, a flexible workshop scheduling scenario is considered, comprising multiple workpieces and multiple mobile robots. The workshop includes workpieces... , , Each workpiece consists of several processes, different processes have selectable robot resources, and there are time window constraints between some processes, as shown in Table 1.
[0044] Table 1
[0045] Table 1 lists the process number for each workpiece, the time constraint type between processes, and the processing time for each process when it can be executed by different robots. The time constraint types include no time window constraint, loose time window constraint, and tight time window constraint, which describe the time connection requirements of adjacent processes. Different numbers of robots performing the same process will have different processing times, thus forming a process selectable processing mode.
[0046] The number of robots is 5, of which , As a collaborative robot, it can collaboratively perform some processes. (Workpiece) It includes 4 processes. can be Execution time: 6 minutes; no time window constraint. can be Execution, processing time is 6 minutes, loose time window constraint (with interval 10 minutes) can be Execution time: 3 minutes; no time window constraint. can be , or The processing times for the three robots were 9 minutes, 7 minutes, and 4 minutes respectively, with no time window constraints. (Workpiece) It includes 4 processes. can be Execution time: 4 minutes; no time window constraint. can be Execution, processing time is 8 minutes, tight time window constraint (with...) interval 10 minutes) can be or The execution and processing time is 3 minutes. can be or The execution time for the two robots is 4 minutes and 5 minutes respectively, with no time window constraint. (Workpiece) It includes 4 processes. can be Execution time: 4 minutes; no time window constraint. can be Execution, processing time is 10 minutes, loose time window constraint (with interval 10 minutes) can be or Execution times are 6 minutes and 9 minutes respectively, with tight time window constraints (and...). interval 10 minutes) can be , or The processing times for the three robots were 6 minutes, 4 minutes, and 4 minutes respectively, with no time window constraints.
[0047] S2. Genetic Algorithm Individual Encoding Construction Stage: Based on the basic scheduling information obtained in step S1, a three-layer encoded genetic algorithm is constructed to perform a global search for cooperative patterns in the scheduling problem of mobile multi-robot flexible workshops; The three-layer coding is as follows: the first layer of coding is used to represent the execution order of the process to depict the arrangement relationship of different processes in the time dimension; the second layer of coding is used to represent the robot selection result corresponding to each process to describe the processing resource allocation scheme under flexible resource conditions; and the third layer of coding is used to represent the collaborative processing mode decision of each process, describing the single robot processing mode and the multi-robot collaborative processing mode through collaborative process decision variables.
[0048] In this embodiment, for the aerospace skin processing scenario, a dynamic grid layout scheme is automatically generated based on the number of workpieces. The system automatically calculates the optimal row and column distribution matrix according to the total number of workpieces to be processed. Figure 2 The layout of 10 workpieces is displayed in the image.
[0049] In the genetic algorithm, the initial population size is set to 100, the number of iterations is 20, and both the crossover probability and mutation probability are set to 0.7. The steepness parameter of the control function is... It is 0.8.
[0050] Population initialization: Generate 100 random chromosomes. The OS layer (process sequence) randomly generates the process arrangement. The RS layer (robot selection) randomly selects robots. In the CS layer (cooperative mode selection), the first 20% of individuals adopt the single-machine processing mode, and the remaining 80% of individuals are randomly assigned processing modes.
[0051] Combination Figure 3 The OS layer (process sequence) is (1,2,3,2,1,3,1,2,3,1,2,3), and the tasks are arranged according to... Arranged in order, each task is numbered... The second occurrence indicates the first time that the workpiece appears. Each process step is represented by a robot. The CS layer (collaboration mode selection) is (0,1,0,0,0,0,0,0,0,0,0,0), where 0 represents single-machine processing and 1 represents collaborative processing by two robots. The RS layer (robot selection) is (0,0,0,2,0,1,1,1,0,1,2,2), corresponding to the robot allocation for each process step.
[0052] S3. Genetic Evolution and Dynamic Parameter Control Stage: The genetic algorithm in step S2 is used to perform evolutionary search on the constructed individuals, and the process execution order, robot selection and collaborative processing mode are jointly optimized through crossover and mutation operations; Step S3 specifically involves: during the genetic evolution process, dynamically adjusting the population size participating in genetic operations in each generation based on the current generation number, and simultaneously dynamically setting the upper limit of the solution time for the constraint programming model, thereby achieving resource coordination and allocation between the genetic search process and precise scheduling computation while ensuring search quality.
[0053] The expression for the function regulating the number of individuals participating in crossover variation is:
[0054] in, Indicates the initial population size. This represents the minimum number of crossover individuals that we want to retain in the final stage, and its value is set to 2. The parameter is used to adjust the steepness of the function; The function inflection point has a value of 0, ensuring that the number of individuals participating in crossover mutation in the population decreases round by round from 100 to 2; The expression for the time upper limit control function in the constrained programming model is:
[0055] in, To find the minimum time required, For the longest solution time, The inflection point of the function is used to ensure that the solution time increases progressively from 0.2 seconds to 20 seconds.
[0056] S4. Construction of the CP model for movement time and time window constraints: Based on the process execution sequence, robot selection and collaborative processing mode determined by step S3, a scheduling model with movement time and time window constraints is constructed. The robot's initial position and workpiece spatial layout information obtained in step S1 are used to calculate the movement time required for the robot to perform adjacent processes between different workpieces. The movement time constraints and the time window constraints between processes are introduced into the scheduling modeling process to reflect the coupling characteristics between robot processing behavior, movement behavior and process time connection. In this embodiment, 100 individuals are decoded. The decoding process is arranged sequentially according to the encoding order. The start time of each step depends on the completion time of the previous step and the current available robot time. Considering the movement time, if the robot is performing a task for the first time, it moves from the origin to the workpiece position. If the robot is performing tasks continuously, it moves from the previous workpiece position (…). , Move to the current workpiece position. , Based on the Manhattan distance, the travel time is calculated, and the initial maximum completion time is finally obtained. .
[0057] S5.CP Model Optimization Maximum Completion Time Stage: Based on the movement time and time window constraint scheduling model constructed in step S4, constraint programming is used to uniformly optimize and iterate the start and end times of each process. Under the premise of satisfying process sequence constraints, collaborative processing constraints, movement time constraints, and time window constraints, the scheduling scheme of the mobile multi-robot flexible workshop is obtained with minimizing the maximum completion time as the optimization objective.
[0058] In this embodiment, 20 rounds of iterative optimization are performed, and each round of iterative optimization includes the following steps: S51 Identify the current best individual: Find the individual with the smallest objective function value in the current population, denoted as... This individual will participate in subsequent crossover mutation operations; S52 genetic manipulation: combination Figure 3 Crossover mutation operations only apply to collaborative processes, and apply to each selected individual. , with the current best individual Perform crossover operations with crossover probability Performing MPX crossover involves identifying the locations of all possible collaborative processes, randomly selecting a subset for crossover, and then performing crossover with probability. Perform MX crossover with mutation probability Perform single-point mutation; S53 Optimization of the scheduling model with travel time and time window constraints: Call the CP model solver to optimize the maximum completion time and update the global optimal solution; The objective function expression for the CP model in step S53 is:
[0059] in, For process Processing time period The maximum completion time.
[0060] The optimization process includes the following steps: S531: Calculate the upper limit of the solution time for each round; S532: Create an interval variable for each process, the expression of which is:
[0061] in, For process Use configuration pattern Processing, For process In configuration The processing time below, To move the robot from the origin to the workpiece Location and time; S533: Each task can only be processed by one robot in one cooperative mode. Its expression is:
[0062] in, For workpiece index, For a collection of workpieces, For process set For process index, Configure an index for the robot. For process The available configuration set, It is a processing mode. Indicate process In a specific configuration The set of available patterns below; S534: Establish a priority relationship between each process step, expressed as follows:
[0063] S535: This sets each robot task assignment to be conflict-free, and automatically inserts movement time between tasks. Its expression is:
[0064] in, For configuration The execution order of all tasks. A matrix storing the time it takes for the robot to move between various workpieces. A set of optional robot configurations; S536: Set a time window constraint for different processes of the same workpiece to meet a specified priority processing sequence. The expression is as follows:
[0065]
[0066] in, For process After completion, proceed to the next process. The minimum waiting time before starting To proceed to the next process after completion Maximum allowed waiting time before starting; S537: When selecting cooperative mode, the same interval variable is added to the task sequences of two robots simultaneously to ensure synchronized start and synchronized end. The expression is:
[0067]
[0068] in, For process Use configuration pattern Processing, For process Use configuration pattern Processing; After solving, the objective function value is calculated, and the global optimal solution is updated.
[0069] S54: After multiple iterations, output the final result of the scheduling.
[0070] In this embodiment, after 20 iterations, the final result of the output scheduling is given, including the maximum completion time, the number of collaborative processes, the number of processes per machine, and the objective function value.
[0071] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for scheduling a mobile, multi-robot flexible workshop, characterized in that, Includes the following steps: S1. Workshop scheduling information acquisition stage: Based on the basic scheduling information of the mobile multi-robot flexible operation workshop, the initial position and spatial layout information of the workpiece are automatically allocated through dynamic grid layout. S2. Genetic Algorithm Individual Encoding Construction Stage: Based on the basic scheduling information obtained in step S1, a three-layer encoded genetic algorithm is constructed to perform a global search for cooperative patterns in the scheduling problem of mobile multi-robot flexible workshops; S3. Genetic Evolution and Dynamic Parameter Control Stage: The genetic algorithm in step S2 is used to perform evolutionary search on the constructed individuals, and the process execution order, robot selection and collaborative processing mode are jointly optimized through crossover and mutation operations; S4. Construction of the CP model for movement time and time window constraints: Based on the process execution sequence, robot selection and collaborative processing mode determined by step S3, a scheduling model with movement time and time window constraints is constructed. The robot's initial position and workpiece spatial layout information obtained in step S1 are used to calculate the movement time required for the robot to perform adjacent processes between different workpieces. The movement time constraints and the time window constraints between processes are introduced into the scheduling modeling process to reflect the coupling characteristics between robot processing behavior, movement behavior and process time connection. S5.CP Model Optimization Maximum Completion Time Stage: Based on the movement time and time window constraint scheduling model constructed in step S4, constraint programming is used to uniformly optimize and iterate the start and end times of each process. Under the premise of satisfying process sequence constraints, collaborative processing constraints, movement time constraints, and time window constraints, the scheduling scheme of the mobile multi-robot flexible workshop is obtained with minimizing the maximum completion time as the optimization objective.
2. The mobile multi-robot flexible workshop scheduling method as described in claim 1, characterized in that, In step S1, the basic scheduling information includes the process structure information of multiple workpieces, the optional robot resource information corresponding to each process, the collaborative processing type information of the process, and the initial position of the robot and the spatial layout information of the workpiece. At the same time, the time window constraint information between processes is obtained to describe the connection requirements of adjacent processes in the time dimension.
3. The method for scheduling a mobile multi-robot flexible workshop as described in claim 2, characterized in that, The initial position coordinates of the workpiece in step S1 are ( The robot's movement time between workpieces is calculated using Manhattan distance based on the workpiece spatial layout. The expression for this time is: in, For robots to remove workpieces Move the position to the workpiece Time required, ( ) is the workpiece Position coordinates, ( ) is the workpiece The location coordinates.
4. The method for scheduling a mobile multi-robot flexible workshop as described in claim 1, characterized in that, In step S2, the three layers of coding are as follows: the first layer of coding is used to represent the execution order of the process to depict the arrangement relationship of different processes in the time dimension; the second layer of coding is used to represent the robot selection result corresponding to each process to describe the processing resource allocation scheme under flexible resource conditions; and the third layer of coding is used to represent the collaborative processing mode decision of each process, describing the single robot processing mode and the multi-robot collaborative processing mode through collaborative process decision variables.
5. The mobile multi-robot flexible workshop scheduling method as described in claim 1, characterized in that, Step S3 specifically involves: during the genetic evolution process, dynamically adjusting the population size participating in genetic operations in each generation based on the current generation number, and simultaneously and dynamically setting the upper limit of the solution time for the constraint programming model.
6. The mobile multi-robot flexible workshop scheduling method as described in claim 5, characterized in that, The expression for the function regulating the number of individuals participating in crossover variation is: in, Indicates the initial population size. This represents the minimum number of crossover individuals that we want to retain in the final stage, and its value is set to 2. The parameter is used to adjust the steepness of the function; The function inflection point has a value of 0, ensuring that the number of individuals participating in crossover mutation in the population decreases round by round from 100 to 2; The expression for the time upper limit control function in the constrained programming model is: in, To find the minimum time required, For the longest solution time, The inflection point of the function is used to ensure that the solution time increases progressively from 0.2 seconds to 20 seconds.
7. The mobile multi-robot flexible workshop scheduling method as described in claim 1, characterized in that, Step S4 specifically involves decoding the individual workpieces. The decoding process arranges the operations sequentially according to the encoding order. The start time of each operation depends on the completion time of the previous operation and the current available robot time. If the robot is performing a task for the first time, it moves from the origin to the workpiece position. If the robot is performing tasks continuously, it moves from the previous workpiece position (…). , Move to the current workpiece position. , Based on the Manhattan distance, the travel time is calculated, and the initial maximum completion time is finally obtained. .
8. The mobile multi-robot flexible workshop scheduling method as described in claim 1, characterized in that, Each iteration of optimization in step S5 includes the following steps: S51 Identify the current best individual: Find the individual with the smallest objective function value in the current population, denoted as... ; S52 Genetic Operation: Identify the positions of all possible cooperative steps, randomly select a subset for crossover, and use probability... Perform MX crossover with mutation probability Perform single-point mutation; S53 Optimization of the scheduling model with travel time and time window constraints: Call the CP model solver to optimize the maximum completion time and update the global optimal solution; S54: After multiple iterations, output the final result of the scheduling.
9. A mobile multi-robot flexible workshop scheduling method as described in claim 8, characterized in that, The objective function expression for the CP model in step S53 is: in, For process Processing time period The maximum completion time.
10. The mobile multi-robot flexible workshop scheduling method as described in claim 1, characterized in that, The optimization process in step S53 includes the following steps: S531: Calculate the upper limit of the solution time for each round; S532: Create an interval variable for each process, the expression of which is: in, For process Use configuration pattern Processing, For process In configuration The processing time below, To move the robot from the origin to the workpiece Location and time; S533: Each task can only be processed by one robot in one cooperative mode. Its expression is: in, For workpiece index, For a collection of workpieces, For process sets, For process index, Configure an index for the robot. For process The available configuration set, It is a processing mode. Indicate process In a specific configuration The set of available patterns below; S534: Establish a priority relationship between each process step, expressed as follows: S535: This sets each robot task assignment to be conflict-free, and automatically inserts movement time between tasks. Its expression is: in, For configuration The execution order of all tasks. A matrix storing the time it takes for the robot to move between various workpieces. A set of optional robot configurations; S536: Set a time window constraint for different processes of the same workpiece to meet a specified priority processing sequence. The expression is as follows: in, For process After completion, proceed to the next process. The minimum waiting time before starting To proceed to the next process after completion Maximum allowed waiting time before starting; S537: When selecting cooperative mode, the same interval variable is added to the task sequences of two robots simultaneously to ensure synchronized start and synchronized end. The expression is: in, For process Use configuration pattern Processing, For process Use configuration pattern Processing; After solving, the objective function value is calculated, and the global optimal solution is updated.