Multi-valve assembly production line robot scheduling method based on improved MOPSO algorithm

Abstract

The invention relates to a multi-valve assembly line robot scheduling method based on an improved MOPSO algorithm, and the method comprises the steps: firstly constructing a process dependency digraph, defining constraint conditions and decision variables, then determining a multi-objective optimization function, and carrying out the solving through an improved multi-objective particle swarm optimization algorithm, the improved multi-objective particle swarm optimization algorithm comprises the steps of generating an initial particle swarm by adopting an oxidation strategy, dynamically adjusting an inertia weight, a learning factor and a mutation probability, performing adaptive mutation on the updated particle swarm and the like. Compared with the prior art, the method can solve the defects in the prior art, remarkably improves the accuracy, robustness and practicability of industrial robot task scheduling, and achieves efficient and reliable multi-robot cooperative scheduling.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent manufacturing and industrial automation, and more particularly to a robot scheduling method for a multi-valve assembly production line based on an improved MOPSO algorithm. Background Art

[0002] In the modern valve manufacturing industry, mixed assembly lines for multiple valve varieties have become an important production model for improving production efficiency and responding to market demand. However, existing multi-robot task scheduling technology faces many technical bottlenecks when handling complex valve assembly processes, including:

[0003] (1) Traditional scheduling algorithms have difficulty effectively handling the waiting constraints for line changes between different valve types. In actual production, when switching from type A valve to type B valve, and from type B valve to type C valve, preset tooling adjustment time and production line cleaning time are required. This timing constraint is often simplified or ignored in existing scheduling models, resulting in significant deviations between theoretical scheduling plans and actual production execution;

[0004] (2) Existing multi-objective optimization algorithms generally suffer from poor convergence performance and low solution quality when faced with large-scale valve assembly tasks. In particular, when simultaneously optimizing the three objectives of production cycle, load balancing, and system robustness, traditional particle swarm optimization (PSO) algorithms are prone to falling into local optimality and lack effective constraint processing mechanisms to ensure the engineering feasibility of the generated solutions.

[0005] (3) The existing scheduling system does not accurately model the robot's expertise. When dynamically allocating tasks, it fails to fully consider the efficiency differences and learning curve effects of the robot in specific valve processes, resulting in unreasonable resource allocation and affecting overall production efficiency.

[0006] (4) Lack of an effective mechanism for handling complex dependencies. There are complex dependencies between valve assembly processes. For example, some processes must be started after a specific process is completed. However, existing scheduling algorithms often use simplified dependency models that cannot accurately reflect actual assembly constraints and easily produce unworkable scheduling solutions.

[0007] Therefore, there is an urgent need for an intelligent scheduling technology that can comprehensively consider line change waiting time, multi-objective optimization, robot expertise and complex dependency constraints to meet the technical needs of the modern valve manufacturing industry for efficient, flexible and reliable production scheduling. Summary of the Invention

[0008] The present invention aims to provide a robot scheduling method for a multi-valve assembly production line based on an improved MOPSO algorithm to address the deficiencies in the prior art and achieve efficient and reliable multi-robot collaborative scheduling.

[0009] In order to achieve the above object, the present invention adopts the following technical solutions:

[0010] A robot scheduling method for a multi-valve assembly production line based on an improved MOPSO algorithm comprises the following steps:

[0011] S1. Build a directed graph of process dependencies and define constraints and decision variables.

[0012] S2. Determine the multi-objective optimization function: minimize the production cycle, minimize the robot load imbalance and maximize the system robustness;

[0013] S3. Using multi-objective particle swarm optimization algorithm to solve the problem; the steps include:

[0014] A diversified strategy is used to generate the initial particle swarm.

[0015] Dynamically adjust the inertia weight, learning factor and mutation probability, perform adaptive particle swarm evolutionary search and update the particle swarm,

[0016] Adaptively mutate the updated particle swarm and generate candidate solutions through local search enhancement.

[0017] When the preset number of iterations is reached, a compromise solution is selected based on the multi-attribute decision-making method, and the scheduling feasibility is verified.

[0018] Furthermore, in S1, the constraints include: resource allocation constraints, process priority constraints, robot specialization constraints, industrial environment constraints and / or line change constraints.

[0019] Furthermore, in S3, the diversified strategies include: random allocation strategy, load balancing strategy and expertise-oriented strategy.

[0020] Furthermore, in S3, the inertia weight, learning factor, and mutation probability are dynamically adjusted, including:

[0021] Inertia weight decreases linearly:

[0022]

[0023] Among them, ω max =0.9,ω min =0.4, T max is the maximum number of iterations;

[0024] Dynamic adjustment method of learning factor:

[0025]

[0026] Adaptive attenuation of mutation probability:

[0027] p mut=p mut,init ·e -λ·t

[0028] c 1,init ,c 1,final are the initial and final values ​​of the cognitive learning factor, c 2,init ,c 2,final are the initial and final values ​​of the social learning factor, p mut,init is the initial value of the mutation probability, and λ is the attenuation coefficient.

[0029] Furthermore, in S3, after executing the adaptive particle swarm evolutionary search, a fast non-dominated sorting is used to identify the Pareto optimal solution set, and solutions are screened based on the crowding distance to maintain diversity.

[0030] Furthermore, after the particle swarm is updated, intelligent constraint repair is performed, including dependency checking and load balancing redistribution.

[0031] Furthermore, in S3, adaptive mutation includes:

[0032] Load balancing variation: swapping tasks between high-load and low-load robots;

[0033] Expertise-guided variation: Strengthen the matching between robot skills and tasks;

[0034] Random mutation: Randomly adjust task assignments to maintain population diversity.

[0035] Furthermore, the local search includes generating candidate solutions through neighborhood search using exchange operations and redistribution operations; wherein the execution intensity of the local search is adaptively controlled based on the convergence speed of the multi-objective particle swarm optimization algorithm.

[0036] Furthermore, a compromise solution is selected based on a multi-attribute decision-making method, including:

[0037] The optimization objective is weighted and normalized, and the comprehensive distance from the ideal point is determined according to the following formula, and a compromise solution is selected based on the comprehensive distance;

[0038]

[0039] Among them, w r is the standardized target weight, and are ideal solution and anti-ideal solution respectively, f r (a) is the rth function value of particle a.

[0040] Furthermore, verifying the feasibility of scheduling includes:

[0041] Check process dependencies and timing conflicts;

[0042] Generate task execution Gantt chart;

[0043] And calculate the production cycle, equipment utilization and robustness indicators under disturbance environment

[0044] Through the above technical solutions, it can be seen that the present invention discloses a multi-valve assembly production line robot scheduling method based on the improved MOPSO algorithm. Compared with the existing technology, it can significantly improve the accuracy, robustness and practicality of industrial robot task scheduling; specifically, it includes:

[0045] 1. By establishing a three-dimensional optimization system for production cycle, load balancing, and system robustness, this paper achieves a significant breakthrough from traditional two-dimensional optimization to three-dimensional collaborative optimization. Combined with an improved MOPSO algorithm, this invention can minimize load imbalances between robots while ensuring the shortest production cycle, and significantly improve the performance stability of the scheduling scheme in the face of uncertainties such as equipment failures and network delays.

[0046] 2. The introduction of a line change waiting time perception mechanism ensures high consistency between theoretical scheduling and actual execution, avoiding the disconnect between the two in traditional methods and significantly reducing the frequency and cost of production plan changes.

[0047] 3. To address the poor convergence performance of the traditional MOPSO algorithm when handling large-scale tasks, a comprehensive optimization mechanism consisting of adaptive parameter adjustment, improved mutation strategy, and local search enhancement is proposed. By dynamically adjusting the inertia weight and learning factor, combined with adaptive mutation based on task priority and an external archive maintenance strategy based on crowding distance, the algorithm's global search capability and solution quality are significantly improved, enabling the algorithm to find high-quality Pareto optimal solutions within a reasonable time.

[0048] 4. By introducing expertise factors and experience accumulation mechanisms, the system can dynamically adjust the robot's adaptability score for different processes based on its historical performance, thereby achieving intelligent task allocation based on capability matching and maximizing the expertise of each robot.

[0049] 5. By establishing a precise dependency matrix and constraint propagation algorithm, the generated scheduling solution is ensured to strictly meet all process constraints. At the same time, an efficient constraint repair mechanism is integrated to detect and correct constraint violations in real time during the optimization process, ensuring the feasibility of the solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0051] Figure 1 This is a flow chart of the robot scheduling method for a multi-valve assembly production line based on the improved MOPSO algorithm;

[0052] Figure 2 This is an example flow chart of the robot scheduling method for a multi-valve assembly production line based on the improved MOPSO algorithm;

[0053] Figure 3 This is the exploded view of the ball valve 410H19113.100;

[0054] Figure 4 is the multi-objective convergence graph;

[0055] Figure 5 These are population diversity transformation diagram, algorithm convergence analysis diagram, and Pareto frontier evolution diagram. DETAILED DESCRIPTION

[0056] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0057] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0058] This embodiment of the present invention discloses a robot scheduling method for multi-valve assembly lines based on an improved MOPSO algorithm, addressing the problem of multi-robot collaborative task scheduling in industrial environments. This method comprehensively considers three key objectives: minimizing production cycle time, optimizing load balancing, and improving system robustness. It utilizes an intelligent particle evolution mechanism to efficiently search for Pareto optimal solutions.

[0059] In the embodiment of the present invention, the robot scheduling method of the multi-valve assembly production line is as follows: Figure 1 , including the following steps:

[0060] S1. Build a directed graph of process dependencies and define constraints and decision variables.

[0061] S2. Determine the multi-objective optimization function: minimize the production cycle, minimize the robot load imbalance and maximize the system robustness;

[0062] S3. Using multi-objective particle swarm optimization algorithm to solve the problem; the steps include:

[0063] A diversified strategy is used to generate the initial particle swarm.

[0064] Dynamically adjust the inertia weight, learning factor and mutation probability, perform adaptive particle swarm evolutionary search and update the particle swarm,

[0065] Adaptively mutate the updated particle swarm and generate candidate solutions through local search enhancement.

[0066] When the preset number of iterations is reached, a compromise solution is selected based on the multi-attribute decision-making method, and the scheduling feasibility is verified.

[0067] In an exemplary embodiment, the valve assembly operation scheduling problem is described as follows:

[0068] Receive user orders through MES The order contains m types of valve assembly requirements of different specifications. Valve category set V = {V1, V2, ..., V m}, where each type of valve V i The order volume is The specific operation of valve assembly is performed by K heterogeneous robots, and the robot set is R = {R1, R2, ..., R k Each type of valve must complete w j Daozi assembly process As a typical NP-hard problem, considering industrial constraints such as robot resource allocation, dependencies between assembly processes, robot specialization capabilities, equipment failure rate, network delay, etc., an improved PSO algorithm is adopted to minimize the total assembly cycle, robot load balancing, and system robustness as optimization goals to achieve intelligent scheduling of multi-robot assembly tasks in a networked dynamic environment.

[0069] Further, refer to Figure 2 , the scheduling steps are:

[0070] S1. Construct a mathematical model for multi-robot task allocation: Establish a directed graph of process dependencies, where nodes represent assembly processes and directed edges represent the constraints between previous and subsequent processes. At the same time, design a hierarchical dependency constraint structure based on the assembly characteristics of different valve types.

[0071] Then define the constraints and decision variables;

[0072] In this embodiment, the decision variable is the task-robot assignment matrix;

[0073] The constraints include the following five aspects:

[0074] ① Resource allocation constraints:

[0075] To optimize the efficiency of parts transfer, the valve assembly is divided into multiple sub-assembly processes as the minimum assembly unit. Each process is assigned to a unique robot:

[0076]

[0077] in, Is the decision variable, representing the process P i,j Is it assigned to robot R? k , M represents the number of robots, k is the robot serial number index, i represents the valve category index, j represents the process serial number index, P i，j represents the jth process in the i-th type of valve; Represents the j-th process of any i-type valve.

[0078] At the same time, the decision variable cannot exceed 1, that is, a process can only be performed by one robot R at a time. k implement:

[0079]

[0080] where Φ(t)={(i,k)|T i,k ≤t≤F i,k} represents the set of processes being executed at time t, T i,k Process P i,j The startup time, F i,k Process P i,j completion time.

[0081] ②Process priority constraints

[0082] During the assembly process, the execution of certain assembly steps must be based on the completion of the previous assembly steps. Figure 3 In the exploded view of the 410H19113.100 ball valve assembly, the valve seat must be assembled after the wave spring. This is a common rigid dependency between processes, known as process rigidity priority. Weak dependencies also exist between processes. For example, nut assembly can be performed simultaneously with assembly of the main and auxiliary valve bodies. This type of dependency is known as general process priority.

[0083] Define process precedence relationships Indicates process P i,l Must be in process P i,hCompleted before. The process priority constraint is expressed as:

[0084]

[0085] Rigid priorities satisfy the following relationship:

[0086]

[0087] Generally, priority is achieved by affecting the sorting weight:

[0088] w i,h =d i,h ·ρ flexible (P i,h )

[0089] where d i,h is the influence coefficient of the process on the total completion time. Under the premise of meeting the rigid priority, by dynamically adjusting d i,h value to reduce the total assembly time.

[0090] ③Robot specialization constraints

[0091] Given the complexity of valve assembly, different processes require different robot precision and stability, so heterogeneous robots are used for assembly. Although heterogeneous robots can complete all processes, they each have their own strengths, which are primarily reflected in their efficiency in completing these processes, specifically in the assembly time.

[0092] Introducing robot specialization and efficiency constraints

[0093]

[0094] t i,j Process P i,j In R k Theoretical assembly time on P i,j ∈Spec(R k ) indicates that the jth process of the i-th type valve belongs to robot R k Specialized process, Indicates that the j-th process of the i-th type valve does not belong to robot R k Specialized process, g k (t) is the specialization efficiency improvement coefficient (time-varying), defined as:

[0095]

[0096] Among them, N k (t) is the robot R k The total number of specialized processes executed up to time t, φ is the learning rate parameter, l k≥0 is the non-specialization efficiency reduction coefficient.

[0097] ④Industrial environment constraints

[0098] In actual industrial scenarios, due to the large variability of different working conditions, robots are easily affected by various random interference factors in different situations, including hardware failures, network delays, and unstable communications. These factors may have an impact on the established task allocation plan. To verify the robustness of the system, its mathematical model is defined as follows:

[0099] (1) Network delay constraints:

[0100]

[0101] in Represents sub-process P i',j' to P i,j The network delay of i', j' represents the j'th process of the i'th type valve, but it cannot overlap with i, j, that is, it is not the same process of the same type of valve. Normal distribution:

[0102]

[0103] (2) Dynamic fault constraints:

[0104]

[0105] e k For Robot R k The efficiency factor, f k is the fault status indicator variable, The failure recovery time follows an exponential distribution in For Robot R k The average failure recovery rate.

[0106] Among them, robots have a certain probability of failure and need to be repaired and reassigned tasks.

[0107] Robot R k The failure probability P fail (R k ,t) is related to its cumulative load:

[0108]

[0109] where k k For Robot R k The failure rate parameter, L k (t) is the time t robot R k The robot's failure and recovery process can be modeled as a Markov chain, where:

[0110]

[0111] c k =0.05 is the robot R k The failure probability, v k =0.1 is the attenuation coefficient of the load on the fault effect, L k (t) is the time t robot R k The cumulative load, L k (t) indicates rounding down.

[0112] ⑤Line change constraints

[0113] In a multi-robot dynamic assembly task, after completing the assembly of a group of valves of the same type, the production line needs to switch to another group of valves of a different type. The line switching operation will introduce additional waiting time, which is recorded as the line switching waiting time τ i→l , represents the time required to switch from valve type i to valve type l.

[0114] The line change constraint requires that a line change waiting time must be arranged between tasks of different valve types to ensure the correct switching of the production line. The specific expression is as follows: in: Indicates the start time of the first task of valve type l; represents the completion time of the last task of valve type i; τ i→l is the line change waiting time for switching from valve type i to valve type l.

[0115] The calculation formula for line change waiting time is: Where: τ i→i+1 represents the line switching waiting time from the i-th type valve to the i+1-th type valve; τ total It is the total line switching waiting time in the entire scheduling cycle.

[0116] S2. Determine the multi-objective optimization function: minimize the production cycle, minimize the robot load imbalance and maximize the system robustness;

[0117] In this embodiment, under the premise of satisfying process constraints and resource constraints, the optimal task allocation strategy and scheduling scheme are sought to minimize the following multiple objectives: minimizing the total assembly time, robot load balancing, and strong anti-interference performance of the system.

[0118] In one embodiment,

[0119] 1) The production cycle objective function takes into account the robot efficiency difference, learning effect and fault recovery time; the expression is:

[0120]

[0121] in: Indicates valve V i The last step w j The completion time, is the number of orders, u i For valve V i The production cycle time is defined as:

[0122]

[0123] This goal reflects the shortest time required for the entire order to be completed.

[0124] For Robot R k The actual assembly time for the jth subassembly of the i-th type valve is affected by multiple factors, including robot specialization, failure dynamics, and network fluctuations:

[0125]

[0126] Where: Robot specialization and efficiency constraint time variable t i,k is the theoretical assembly time, For robot specialization and efficiency constraints, dynamic fault constraint time variables Network Fluctuation Constraint Time Variable The expression is as follows:

[0127]

[0128] Among them, P delay =0.001, other symbols are the same as above. Process P i,k Completion time F i,k It can be expressed as:

[0129]

[0130] 2) The load balancing objective uses the coefficient of variation to quantify the uniformity of workload distribution among robots; the expression is:

[0131]

[0132] in: is the load standard deviation;

[0133] For Robot R k The total workload within the planning period T;

[0134] is the average workload of all robots.

[0135] 3) The robustness objective is based on the conditional value at risk theory and evaluates the performance stability of the system under disturbance conditions. The expression is:

[0136]

[0137] Where: G(y,ξ) represents the performance degradation of scheduling scheme y under the disturbance scenario ξ, which is defined as:

[0138]

[0139] Where: C max (y,0) represents the completion time under no disturbance, Ξ represents a set of finite disturbance scenarios, including robot failure and network delay, CVaR α It is the conditional risk value with a confidence level of α, which is used to measure the risk in extreme cases. w1 and w2 are the robustness indicator weights, satisfying w1+w2=1.

[0140] S3. Use multi-objective particle swarm optimization algorithm for solution; Based on the above mathematical model, this application uses a modified multi-objective particle swarm optimization algorithm (MOPSO) for solution. Its core is to dynamically adjust the task allocation strategy by simulating the flight behavior of particles in the search space to approach the Pareto optimal frontier.

[0141] In one embodiment, the solving step includes:

[0142] S31, using a diversified strategy to generate an initial particle swarm. Particle swarm initialization is the starting point of the algorithm, and its quality directly affects the search efficiency. In this embodiment, the diversified strategies include: random allocation strategy, load balancing strategy and expertise-oriented strategy.

[0143] Random assignment strategy: Each task is randomly assigned to any robot to ensure a wide coverage of the search space:

[0144]

[0145] Among them, s i (t) represents the allocation status of particle i on task j, and k is the robot serial number.

[0146] Load balancing strategy: Dynamically assign tasks based on the current load of the robots, giving priority to assigning tasks to robots with lighter loads:

[0147]

[0148] in, represents the cumulative load of robot k in the first j-1 tasks.

[0149] Expertise-oriented strategy: Utilize the robot skill matching relationship to give priority to assigning tasks to robots that are good at the task:

[0150]

[0151] The initial particle swarm generated by the above strategy not only ensures the diversity of the search space but also ensures the quality of the initial solution.

[0152] S32, dynamically adjust the inertia weight, learning factor and mutation probability, perform adaptive particle swarm evolution search and update the particle swarm,

[0153] In one embodiment, the inertia weight, learning factor, and mutation probability are dynamically adjusted to balance global exploration and local exploitation. Specifically, the adjustment includes:

[0154] Inertia weight decreases linearly

[0155]

[0156] Among them, ω max =0.9,ω min =0.4, T max is the maximum number of iterations.

[0157] Dynamic adjustment of cognitive and social learning factors

[0158]

[0159] Adaptive attenuation of mutation probability

[0160] p mut =p mut,init ·e -λ·t

[0161] c 1,init ,c 1,final are the initial and final values ​​of the cognitive learning factor, c 2,init ,c 2,final are the initial and final values ​​of the social learning factor. mut,init is the initial value of the mutation probability, and λ is the attenuation coefficient. Further, the fitness evaluation is performed, including:

[0162] Task scheduling considering dependencies, calculating actual execution time, and computing multi-objective functions.

[0163] Then the individual historical optimal is updated according to the evaluation results.

[0164] In a preferred embodiment, the Pareto optimal solution set is stored in an external archive, and an external archive management mechanism is introduced, that is, a fast non-dominated sorting algorithm is used to identify non-dominated solutions. When the archive capacity exceeds the limit, solutions are filtered based on the crowding distance metric to maintain the uniformity and diversity of the solution set. In this embodiment,

[0165] The non-dominated solutions a and b are defined as:

[0166]

[0167] The degree of congestion is:

[0168]

[0169] According to an embodiment of the present invention, the evolution of the particle swarm is achieved by updating the speed and position, and its core formula is as follows:

[0170] (1) Speed ​​update

[0171] Particle velocity is affected by inertia weight, cognitive learning factor, and social learning factor:

[0172] v a (t+1)=ω·v a (t)+c1·r1·(p a (t)-s a (t))+c2·r2·(g(t)-s a (t))

[0173] ω: Inertia weight, which controls the particle's dependence on historical velocity;

[0174] c1, c2: cognitive and social learning factors, controlling the effects of individual experience and group experience respectively;

[0175] r1, r2: random numbers, introducing randomness to enhance exploration capabilities;

[0176] p a (t): individual optimal position of particle a;

[0177] g(t): global optimal position.

[0178] (2) Location Update

[0179] The particle positions are updated based on the velocity and discretized to ensure the feasibility of the solution:

[0180] s a (t+1)=round(s a (t)+v a (t+1))

[0181] At the same time, the position is checked for bounds constraints:

[0182]

[0183] Furthermore, to improve search efficiency, this application adopts an improved position-velocity update formula and introduces a global leader selection mechanism based on crowding distance to constrain the updated particle positions and ensure the feasibility of the solution:

[0184]

[0185] Where D is the process dependency matrix, t represents the number of algorithm iterations, and round(·) is a rounding operation that converts the updated position into an integer to ensure that the task is assigned to a specific robot.

[0186] To further optimize the above technical solution, this application adopts intelligent constraint repair, that is, designing a multi-level constraint repair operator to handle process dependency violation problems, including:

[0187] Dependency graph analysis;

[0188] By building a task dependency graph Identify constraint violation nodes.

[0189] Load balancing redistribution;

[0190] Reassign conflicting tasks:

[0191]

[0192] S33. Adaptively mutate the updated particle swarm and generate candidate solutions through local search enhancement. In one embodiment, adaptive selection of three mutation strategies is implemented:

[0193] 1. Load balancing variation

[0194] Alleviate workload imbalances by swapping tasks between high-load and low-load robots:

[0195]

[0196] Where rand(1,·): ensures that the position is at least 1, that is, the task must be assigned to a robot, k represents the robot number, represents the position of particle a on dimension i after mutation, HighLoadSet represents the high-load task set,

[0197] 2. Expertise-guided variation

[0198] Enhanced robot skill matching optimization:

[0199]

[0200] 3. Random mutation

[0201] Maintaining population diversity:

[0202]

[0203] The selection probability of the mutation strategy is dynamically adjusted according to the characteristics of the current solution:

[0204]

[0205] where p strategy Represents the selection probability of different mutation strategies.

[0206] In one embodiment, local search enhancement performs a neighborhood search on high-quality solutions in an external archive, generates candidate solutions using swap and redistribution operations, and records performance metrics:

[0207]

[0208] in represents the position of particle a in dimension x after the neighborhood operation, swap represents the exchange operation, reallocate(·) represents the redistribution operation, and p swap represents the probability of a swap operation.

[0209] The execution probability and intensity of local search are adaptively controlled according to the convergence state of the algorithm:

[0210]

[0211] where p local represents the execution probability of local search.

[0212] S34. When the preset number of iterations is reached, a compromise solution is selected based on a multi-attribute decision-making method, and the scheduling feasibility is verified, and the final result is output.

[0213] After obtaining the candidate solution, this application first determines whether the current number of iterations is less than the preset number of iterations. If so, return to S32 and repeat the above steps; if not, select a compromise solution based on the multi-attribute decision-making method and verify the scheduling feasibility.

[0214] In one embodiment, the TOPSIS multi-attribute decision-making method is used to select the optimal compromise solution from the Pareto front, including:

[0215] The optimization objective is weighted and normalized, and the comprehensive distance from the ideal point is determined according to the following formula, and a compromise solution is selected based on the comprehensive distance;

[0216]

[0217] Among them, w r is the target weight, and are ideal solutions and anti-ideal solutions respectively.

[0218] In one embodiment, verifying scheduling feasibility includes:

[0219] Check process dependencies and timing conflicts;

[0220] Generate task execution Gantt chart;

[0221] And calculate the production cycle, equipment utilization and robustness indicators under disturbance environment, among which:

[0222] Production cycle

[0223] Makespan=max k (F k (T))

[0224] Equipment utilization

[0225]

[0226] Scheduling robustness, by simulating disturbance scenarios and calculating the degree of performance degradation:

[0227]

[0228] Where: Makespan: production cycle, which means the maximum time required to complete all tasks; max k Take the maximum value operation for all robots k. This means that the production cycle is determined by the last robot to complete the task; (F k (T)): Completion time of robot k at time T. It represents the end time after robot k performs all assigned tasks. Accumulate the execution time of all tasks. T total : Total time, which can be the entire scheduling period or production cycle. This value is used to normalize the utilization rate to make it a proportional value. max (ξ): Maximum completion time under disturbance scenario ξ. Disturbance scenarios may include uncertainties such as equipment failure and task delay. C max (0): Maximum completion time under no disturbance (nominal) conditions. This is the ideal production cycle, without any random events.

[0229] The advantages of this application over the prior art include: the multi-valve assembly line robot scheduling system based on the improved MOPSO algorithm of the present invention can significantly improve the accuracy, robustness and practicality of industrial robot task scheduling, as shown in the following:

[0230] (1) Three-dimensional multi-objective collaborative optimization effect

[0231] This invention innovatively establishes a three-dimensional optimization system for production cycle, load balancing, and system robustness, achieving a significant breakthrough from traditional two-dimensional optimization to three-dimensional collaborative optimization. Using an improved MOPSO algorithm, the system minimizes load imbalances between robots while ensuring the shortest production cycle. It also significantly improves the scheduling solution's performance stability in the face of uncertainties such as equipment failures and network delays.

[0232] (2) Advantages of accurate modeling of line change waiting time

[0233] This invention, for the first time, introduces a line change wait time perception mechanism into a robotic scheduling system. By establishing a phased production scheduling model and a line change wait time matrix, it achieves a high degree of consistency between theoretical scheduling and actual execution. The system automatically calculates the earliest start time for each stage—type A valve, then type B valve, then type C valve—and reserves the necessary line change preparation time in the scheduling plan. This effectively avoids the disconnect between theoretical scheduling and actual production, a problem inherent in traditional methods, and significantly reduces the frequency and cost of production plan changes.

[0234] (3) Robot expertise intelligent matching effect

[0235] By establishing a robot efficiency model based on learning curve theory and a dynamic expertise scoring mechanism, the system accurately identifies and fully leverages each robot's strengths. This increases robot efficiency in specialized areas by 20-30%, significantly improving task execution quality. The system dynamically adjusts the robot's adaptability score for different processes based on its historical performance, enabling intelligent task allocation based on capability matching and effectively leveraging the synergy of multi-robot systems.

[0236] (4) Efficient processing of complex constraints

[0237] The three-tiered constraint processing architecture constructed by this invention can simultaneously handle complex constraints such as internal process dependencies, inter-valve timing constraints, and resource conflict avoidance. Through a constraint propagation algorithm and intelligent repair mechanism, the system can detect and correct constraint violations in real time during the optimization process. Compared to traditional methods that require multiple rounds of manual adjustments, this system can automatically generate feasible scheduling solutions that meet all process constraints, significantly reducing the cost of manual intervention.

[0238] (5) Adaptive algorithm optimization performance

[0239] To address the poor convergence performance of the traditional MOPSO algorithm when handling large-scale tasks, this paper proposes adaptive parameter adjustment, an improved mutation strategy, and a local search enhancement mechanism, significantly improving algorithm performance. Dynamic adjustment of the inertia weight and learning factor increases algorithm convergence speed; an adaptive mutation strategy based on task priority improves solution quality; and an external archive maintenance strategy based on crowding distance ensures a uniform distribution of the Pareto front. When handling a typical scheduling problem involving 20 tasks and three robots, the algorithm is able to find a high-quality optimal solution within a reasonable time.

[0240] (6) Risk quantification and robustness assurance

[0241] An innovative robustness assessment method based on CVaR theory is introduced, using Monte Carlo simulation technology to evaluate the performance stability of scheduling solutions under uncertain environments. The system can quantify and analyze the impact of risk factors such as equipment failures, network delays, and efficiency fluctuations on production plans, providing decision makers with risk-controlled scheduling solutions. Compared with traditional deterministic scheduling methods, this significantly improves the production system's anti-interference capabilities and operational stability.

[0242] (7) Intelligent decision-making and dynamic adaptability

[0243] The system integrates diverse initialization strategies, adaptive parameter adjustment, and intelligent constraint repair mechanisms, enabling it to automatically adjust optimization strategies based on diverse production scenarios and task characteristics. The system intelligently selects the optimal task-robot combination in response to factors such as shifting task priorities, differences in robot expertise, and complex process dependencies. As the system's runtime increases, the accuracy of the robot expertise model and efficiency predictions based on historical data continues to improve, leading to continuous optimization of scheduling results and demonstrating its robust adaptive learning capabilities.

[0244] In order to verify the above effects of this application, a verification was conducted in a ball valve assembly workshop, which is configured as follows:

[0245] 1. Robot configuration:

[0246] Number of industrial robots: 3 six-axis articulated robots

[0247] Working radius: 1611mm

[0248] Load capacity: 16kg

[0249] Repeat positioning accuracy: ±0.03mm

[0250] The robot efficiency coefficients are set as: Robot1 (1.2), Robot2 (1.0), Robot3 (0.8).

[0251] 2. Production task configuration

[0252] Valve type: 3 orders each for Type A, Type B, and Type C

[0253] Number of processes: 6 for Type A, 7 for Type B, and 7 for Type C, for a total of 60 assembly tasks.

[0254] 3. Process constraint parameters

[0255] Theoretical assembly time for type A: [23, 34, 23, 44, 12, 32] seconds

[0256] Theoretical assembly time for type B: [13, 24, 23, 34, 42, 32, 16] seconds

[0257] C-type theoretical assembly time: [24, 35, 25, 46, 14, 22, 22] seconds

[0258] Line change waiting time: A→B 30 seconds, B→C 40 seconds

[0259] 4. Algorithm parameter settings

[0260] Particle swarm algorithm: 50 particles, 300 iterations, 100 file capacity

[0261] Inertia weight 0.9→0.4, cognitive factor 2.0→0.5, social factor 2.0→2.5

[0262] Mutation probability 0.1 (adaptive adjustment)

[0263] 5. Industrial environment parameters:

[0264] Learning efficiency γ0 = 0.8, learning coefficient θ = 0.05, penalty coefficient λ = 0.2

[0265] Network delay: average 0.5 seconds ± 0.1 seconds, failure rate 0.05, recovery rate 1.0 times / hour

[0266] 6. Multi-objective optimization

[0267] f1: Minimize production cycle; f2: Minimize load imbalance; f3: Maximize robust robot expertise distribution

[0268] Robot 1: Type A process 1, Type B process 2, Type C process 3

[0269] Robot 2: Type A process 3, Type B process 4, Type C process 5

[0270] Robot 3: Type A process 4, Type B process 6, Type C process 7

[0271] Task dependencies (code 1 and 2 are weakly dependent and can be performed simultaneously or sequentially)

[0272] Type A: Process 1, 2 → 3 → 4 → 5, 6

[0273] Type B: Process 1, 2 → 3 → 4 → 5, 6 → 7

[0274] Type C: Process 1, 2 → 3 → 4 → 5, 6 → 7

[0275] 7. Line change mechanism

[0276] Staged scheduling: Type A production (tasks 1-18) → line change 30 seconds → Type B production (tasks 19-39) → line change 40 seconds → Type C production (tasks 40-60)

[0277] 8. Constraint Repair Strategy

[0278] Dependency conflict: Redistribute by load sorting, with a maximum of 100 iterations

[0279] Mutation operators: load balancing (40%), expertise-oriented (35%), and random perturbation (25%) performance evaluation and experimental results.

[0280] Test environment:

[0281] Hardware platform: Intel i7-12700K, 32GB DDR4, RTX 3080

[0282] Software environment: MATLAB R2023a

[0283] Number of simulation runs: 20 independent experiments

[0284] After testing, the multi-objective convergence diagram is as follows Figure 4 As shown, the population diversity transformation diagram, algorithm convergence analysis diagram, and Pareto frontier evolution diagram are as follows Figure 5 .

[0285] in, Figure 4 In the convergence curve for Objective 1, the horizontal axis represents the number of iterations, indicating the progress of the algorithm's iterations, and the vertical axis represents the production cycle (in seconds), reflecting the time required to complete all tasks. This graph shows how the production cycle objective function value changes with the number of iterations. The curve fluctuates significantly in the initial stages, indicating that the algorithm rapidly explores the solution space. As the number of iterations increases, the curve gradually stabilizes, indicating that the algorithm is converging on this objective and the production cycle gradually approaches the optimal value (approximately 820 seconds). This demonstrates that the algorithm effectively optimizes task scheduling and shortens overall production time.

[0286] Figure 4In the convergence curve for objective 2, the horizontal axis represents the number of iterations, and the vertical axis represents the degree of load imbalance, which measures the degree of balance among the task loads of each robot. The curve starts at a high value and gradually decreases as the number of iterations increases, approaching zero. This indicates that the algorithm effectively improved the balance of task distribution during the optimization process, reduced load differences between robots, and ultimately achieved a more balanced task distribution.

[0287] Figure 4 Objective 3 is the robustness convergence curve. The horizontal axis represents the number of iterations, and the vertical axis represents the robustness index, reflecting the scheduling solution's ability to adapt to environmental changes (such as delays and failures). The curve shows an overall upward trend, indicating that the scheduling solution's robustness is continuously improving. Although there are slight fluctuations during the process, it eventually stabilizes, indicating that the optimized scheduling solution can better cope with uncertainties and ensure the stability of the production process.

[0288] further, Figure 5 The population diversity curve shows that while initially low, it gradually increases and stabilizes with increasing iterations. This indicates that the algorithm effectively balances exploration and exploitation during the optimization process, avoiding local optima and maintaining population diversity, which facilitates the discovery of higher-quality solutions. The algorithm convergence analysis curve shows an overall downward trend, indicating that the algorithm is gradually converging toward the Pareto optimal frontier. The decrease in the index value indicates that the obtained non-dominated solutions are closer to the true Pareto frontier, reflecting improved algorithm optimization performance. Ultimately, the algorithm stabilizes in the later stages of the iteration, indicating convergence. The Pareto front evolution curve shows that the size of the Pareto front rapidly increases in the initial stages and then gradually stabilizes. This indicates that the algorithm continuously discovers high-quality non-dominated solutions during the optimization process, providing more high-quality scheduling options for decision-making. Ultimately, the size of the front stabilizes at a high level, indicating that the algorithm has effectively explored the Pareto frontier.

[0289] The present invention effectively solves the scheduling conflict problem in multi-robot collaborative operation by introducing line change waiting time constraints and an improved multi-objective particle swarm optimization algorithm, significantly improving production efficiency while ensuring product quality, and has good industrial application value and promotion prospects.

[0290] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0291] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A robot scheduling method for a multi-valve assembly production line based on an improved MOPSO algorithm, characterized in that: include: S1. Build a directed graph of process dependencies and define constraints and decision variables. S2. Determine the multi-objective optimization function: minimize the production cycle, minimize the load imbalance and maximize the system robustness; S3. Using an improved multi-objective particle swarm optimization algorithm to solve the problem; the steps include: A diversified strategy is used to generate the initial particle swarm. Dynamically adjust the inertia weight, learning factor and mutation probability, and update the particle swarm after adaptive particle swarm evolution search. Adaptively mutate the updated particle swarm and generate candidate solutions through local search enhancement. When the preset number of iterations is reached, a compromise solution is selected based on the multi-attribute decision-making method, and the scheduling feasibility is verified.

2. The production line robot scheduling method according to claim 1, characterized in that: In S1, the constraints include: resource allocation constraints, process priority constraints, robot specialization constraints, industrial environment constraints and / or line change constraints.

3. The production line robot scheduling method according to claim 1, characterized in that: In S3, the diversification strategies include: random allocation strategy, load balancing strategy and expertise-oriented strategy.

4. The production line robot scheduling method according to claim 1, characterized in that: In S3, the inertia weight, learning factor, and mutation probability are dynamically adjusted, including: Inertia weight decreases linearly: Among them, ω max Indicates the maximum inertia weight, ω min Indicates the minimum inertia weight, T max is the maximum number of iterations; t represents the current number of iterations; Dynamic adjustment method of learning factor: Adaptive attenuation of mutation probability: p mut =p mut,init ·e -λ·t c 1,init ,c 1,final are the initial and final values ​​of the cognitive learning factor, c 2,init ,c 2,final are the initial and final values ​​of the social learning factor, p mut,init is the initial value of the mutation probability, and λ is the attenuation coefficient.

5. The production line robot scheduling method according to claim 1, characterized in that: In S3, after performing adaptive particle swarm evolutionary search, fast non-dominated sorting is used to identify the Pareto optimal solution set, and solutions are screened based on crowding distance to maintain diversity.

6. The production line robot scheduling method according to claim 1, characterized in that: After the particle swarm is updated, intelligent constraint repair is performed, including dependency checking and load balancing redistribution.

7. The production line robot scheduling method according to claim 1, characterized in that: In S3, adaptive mutation includes: Load balancing variation: swapping tasks between high-load and low-load robots; Expertise-guided variation: Strengthen the matching between robot skills and tasks; Random mutation: Randomly adjust task assignments to maintain population diversity.

8. The production line robot scheduling method according to claim 1, characterized in that: The local search includes generating candidate solutions through neighborhood search, exchange operation and redistribution operation; among them, the execution intensity of the local search is adaptively controlled based on the convergence speed of the multi-objective particle swarm optimization algorithm.

9. The production line robot scheduling method according to claim 1, characterized in that: Select a compromise solution based on a multi-attribute decision-making approach, including: The optimization objective is weighted and normalized, and the comprehensive distance from the ideal point is determined according to the following formula, and a compromise solution is selected based on the comprehensive distance; Among them, w r is the standardized target weight, and are ideal solution and anti-ideal solution respectively, f r (a) is the rth function value of particle a.

10. The production line robot scheduling method according to claim 1, characterized in that: Verifying scheduling feasibility includes: Check process dependencies and timing conflicts; Generate task execution Gantt chart; And calculate the production cycle, equipment utilization and robustness indicators under disturbance environment.

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