AGV configuration optimization method and system based on queuing network

Abstract

The invention provides an AGV configuration optimization method and system based on a queuing network, and relates to the technical field of resource configuration optimization. The method comprises the following steps: firstly, constructing a queuing network, decomposing each intelligent manufacturing unit in an intelligent manufacturing workshop into a plurality of types of nodes, decomposing the motion process of each AGV node into transfer processes of different state spaces, obtaining an AGV node state transfer rate, constructing and solving an AGV node state transfer balance equation set, and obtaining performance indexes of the intelligent manufacturing workshop; and based on the performance indexes, constructing an AGV number configuration optimization model, and solving the AGV number configuration optimization model by using a particle swarm algorithm to obtain an optimization result. The AGV configuration optimization problem can be expanded to a multi-layer workshop or large-scale flexible operation scene through establishment of the queuing network, the expansibility and adaptability of the method are improved, a state space decomposition method is introduced, and the modeling complexity and the calculation complexity are reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of resource configuration optimization, and more specifically, to an AGV configuration optimization method and system based on a queuing network. Background Art

[0002] Resource allocation optimization is a problem that studies how to formulate corresponding optimization goals under limited resource conditions and apply mathematical methods or simulation methods to find the optimal or approximately optimal resource allocation and utilization method. It is widely used in actual production and manufacturing. For example, in the intelligent manufacturing workshop responsible for electrode column processing, Figure 1 As shown, the process involves five main processes: straightening and cutting, cold heading, thread rolling, electroplating, and packaging. The straightening and cutting and packaging areas utilize only one piece of processing equipment, while the cold heading, thread rolling, and electroplating processes utilize multiple pieces of processing equipment simultaneously. Each piece of processing equipment is equipped with a buffer zone before and after each piece of equipment. Raw material arrives in coils, is straightened in the straightening and cutting area, and then cut into bars. The bars, in boxes, are then stored in the buffer zone behind the cutting station, where an AGV is called for transfer. The AGV's transfer task is to load the workpieces from the buffer zone after straightening and cutting, transport them to the cold heading area, and then unload them into the free buffer zone before cold heading. The AGV can only unload and depart when a free buffer zone is available. The number of AGVs and the configuration of their buffer zones significantly impact workshop production efficiency. Each AGV has only one loading point during transport, but some processing areas offer multiple unloading points depending on unloading requirements. If the AGV's speed and capacity are too low, workpieces cannot be transferred in a timely manner, forcing the production cycle to be extended. If the AGV's capacity is too large, the probability of waiting for unloading increases, reducing AGV utilization and also increasing processing time. Therefore, optimizing the configuration of unmanned automated transport equipment such as AGVs can significantly reduce production costs and improve production efficiency.

[0003] In a smart manufacturing digital workshop responsible for electrode column processing, the integration of an automated material transportation system (AGV) with a flexible manufacturing system (FMS) presents challenges in evaluating system performance, as mass customization requires flexible production methods. Traditional research often considers the material transportation system and the FMS as independent systems, with limited consideration of their coupling. For example, research on queuing models for material transportation systems focuses on closed queuing networks with limited buffers, ignoring batch transport. For manufacturing systems, investment cost optimization models with dual production performance constraints are used to model and solve the problem. However, this research also fails to consider the automated material handling system. Current approaches to optimizing AGV resource allocation involve modeling the material transportation system and the FMS using multi-objective optimization models and combining them with intelligent optimization algorithms. For example, simulation models are used to model system performance, followed by genetic algorithms for solution. The feasibility of AGV configurations is dynamically evaluated during the optimization process, balancing computational efficiency and solution accuracy. However, this approach restricts AGVs to fixed routes and a single service area, making it unsuitable for large-scale production scenarios. Current research also includes methods that build performance indicator calculation models for batch production systems based on random process theory and embed heuristic algorithms to obtain optimal workshop AGV resource configuration. However, this method has high modeling complexity and is difficult to expand and apply to multi-layer or large-scale flexible operation workshops, resulting in poor scalability. Summary of the Invention

[0004] In order to solve the problem that the current AGV configuration optimization method for intelligent manufacturing digital workshops used for electrode column processing has high modeling complexity and poor scalability, which makes it unsuitable for large-scale production, the present invention proposes an AGV configuration optimization method and system based on a queuing network. A queuing network is established to extend the AGV configuration optimization problem to multi-layer workshops or large-scale flexible operation scenarios, and at the same time, a state space decomposition method is introduced to reduce modeling complexity.

[0005] In order to achieve the above technical effects, the technical solutions of the present invention are as follows:

[0006] A method for optimizing AGV configuration based on a queuing network, the method comprising the following steps:

[0007] Each intelligent manufacturing unit in the intelligent manufacturing workshop is divided into several types of nodes. The intelligent manufacturing workshop includes several intelligent manufacturing units. In each intelligent manufacturing unit, the workpiece is transported based on AGV. Each AGV is independently used as an AGV node, and all nodes constitute a queuing network;

[0008] Decompose the motion process of each independent node into the transfer process of different state spaces to obtain the AGV node state transfer rate;

[0009] Based on the AGV node state transfer rate, the AGV node state transfer balance equation is constructed to form the AGV node state transfer balance equation group;

[0010] Solve the state equilibrium equations to obtain the performance indicators of the intelligent manufacturing workshop;

[0011] An AGV quantity configuration optimization model is constructed, and the performance indicators of the intelligent manufacturing workshop are embedded in the particle swarm algorithm. The AGV quantity configuration optimization model is solved based on the particle swarm algorithm to obtain the configuration optimization results.

[0012] In this technical solution, a queuing network is first constructed, each intelligent manufacturing unit within the intelligent manufacturing workshop is decomposed into several types of nodes, the movement process of each AGV node is decomposed into the transition process of different state spaces, the AGV node state transition rate is obtained, and the AGV node state transition equilibrium equations are constructed and solved to obtain the performance indicators of the intelligent manufacturing workshop. Based on the performance indicators, an AGV quantity configuration optimization model is constructed, and the particle swarm algorithm is used to solve the AGV quantity configuration optimization model to obtain the optimization results. The establishment of a queuing network can extend the AGV configuration optimization problem to multi-layer workshops or large-scale flexible operation scenarios, improving the scalability and adaptability of this method. The introduction of the state space decomposition method reduces the modeling complexity and computational complexity.

[0013] Preferably, each intelligent manufacturing unit of the intelligent manufacturing workshop includes a processing device and two buffer areas located before and after the processing device. The workpiece waits for processing in the buffer area located before the processing device and waits for AGV transfer in the buffer area located after the processing device.

[0014] Each intelligent manufacturing unit in the intelligent manufacturing workshop is divided into several types of nodes, including: input nodes, fork nodes and aggregation nodes;

[0015] Each AGV is independently used as an AGV node, and the AGV node includes a single-target AGV node and a multi-target AGV node;

[0016] The AGV node has several states in the intelligent manufacturing workshop, including waiting for workpiece loading, transferring workpieces, waiting for workpiece unloading and empty vehicle return; among them, if the number of AGV workpiece unloading points is one and only one, the AGV node is a single-target AGV node; if the number of AGV workpiece unloading points is greater than one, the AGV node is a multi-target AGV node.

[0017] Preferably, the process of decomposing the movement process of each independent node into the transfer process of different state spaces to obtain the node state transfer rate is as follows:

[0018] For single-target AGV node Aij , the expression for defining the state space of a single-target AGV node is:

[0019] A ij {(W ij ,S ij ); 0≤W ij ≤C ij +1,S ij =w,o,l,b;i=3M,1≤j≤R i}

[0020] Among them, W ij S represents the number of workpieces carried by the jth trolley at level i, ij represents the state of the jth AGV node in the i-th level. w, o, l, and b represent the four AGV states of waiting for loading at the loading point, transporting cargo to the unloading point, waiting for unloading at the unloading point, and returning empty to the loading point. C ij represents the cargo capacity of the jth AGV node in the i-th level, M represents the number of production processes, and R i The number of processing equipment at each level of units;

[0021] Calculate the state transition rate of the single-target AGV node, which represents the transition probability from the current node state to the next node state and the AGV transportation rate V ij The product of , including:

[0022] The single-target AGV node returns to state A with an empty vehicle ij (0, b) transfer to waiting for workpiece loading state A ij (0,w), the expression of transfer rate is:

[0023] The single-target AGV node returns to state A with an empty vehicle ij (0,b) transfer to the transfer workpiece state A ij {(W ij ,o),1≤W ij ≤C ij}, the expression of transfer rate is:

[0024] Where k represents the number of workpieces transported by AGV, 1≤k≤C;

[0025] Single-target AGV node is transporting goods to the unloading point state A ij {(W ij ,o),1≤W ij ≤C ij}Transfer to the waiting workpiece unloading state A ij {(W ij ,l),0 <W ij ≤Cij}, the expression of transfer rate is: V ij PB i+1,1 (k);

[0026] Among them, PB i+1,1 (k) is the transfer probability of a single-target AGV node waiting for workpiece unloading;

[0027] Single-target AGV node in transfer state A ij {(W ij ,o),1≤W ij ≤C ij} Unload all workpieces and transfer to empty car return state A ij (0,b), the transfer rate is

[0028] Preferably, the state transition equation indicates that the entry probability and exit probability of a certain state of a single-target AGV node are equal, the entry probability is the product of the transition rate from the entry state to the current state and the steady-state probability of the entry state, and the exit probability is the product of the transition rate from the current state to the exit state and the steady-state probability of the exit state.

[0029] Preferably, the process of solving the state equilibrium equations is:

[0030] The state transition probability and state steady-state probability of all single-target AGV nodes are set to 0, and the expression is:

[0031]

[0032] in, represents the steady-state probability of all node states, represents the probability that the jth node at level 3i+1 is idle, represents the probability of the jth node at level 3i+1 being blocked, is the probability that the j-th node at level 3i+2 is blocked before the node;

[0033] Traverse all single-target AGV nodes, define the state space of all single-target AGV nodes, and calculate the transition rate between the states of single-target AGV nodes;

[0034] Based on the state balance equation and the conversion rate between single-target AGV nodes, the state transfer matrix is ​​constructed to calculate the steady-state probability of the single-target AGV node state;

[0035] Based on the transition rate between single-target AGV node states and the steady-state probability between single-target AGV node states, the probability of single-target AGV node being blocked during state transition is calculated;

[0036] Determine whether the steady-state probability of a single-target AGV node state exceeds a preset threshold. If so, return to calculate the transition rate between node states; if not, output the steady-state probabilities of all single-target AGV node states to calculate the performance indicators of the intelligent manufacturing workshop.

[0037] Preferably, the performance indicators of the intelligent manufacturing workshop include average output rate and average production cycle, and the calculation process is respectively:

[0038] For a single-target AGV node in an intelligent manufacturing workshop, the effective processing rate of the final processing link is 3M+1 is the average output rate θ, which is expressed as:

[0039]

[0040] Calculate the product of the steady-state probability of all states of a single AGV node and the number of workpieces in the corresponding state to obtain the average number of workpieces of a single AGV node;

[0041] Calculate the sum of the average number of workpieces of all AGV nodes to get the average work-in-progress WIP;

[0042] Calculate the average production cycle T, the expression is:

[0043]

[0044] Preferably, the objective function of the constructed AGV quantity configuration optimization model is expressed as:

[0045]

[0046] The constraint expression is:

[0047] E{Γ(X:ξ)}≤Γ max

[0048] E{θ(X:ξ)}≥θ min

[0049] X∈N +

[0050] Among them, X represents the total investment cost of AGV configuration in the workshop, which is a non-negative integer vector, Q represents the average output rate of the workshop, and x i represents the model combination of the i-th level AGV, Γ represents the mathematical expectation of the random function, ξ represents the total investment cost of the AGV configuration in the workshop, θ represents the average production cycle of the system, E{Γ(X:ξ)} represents the average production cycle, and E{θ(X:ξ)} represents the average output rate.

[0051] Preferably, the process of solving the AGV quantity configuration optimization model based on the particle swarm algorithm is as follows:

[0052] S1. Initialize the position and velocity of each particle in the particle swarm;

[0053] S2. Calculate the fitness of each particle in the swarm and update the optimal position of each particle based on the fitness.

[0054] S3. Based on the optimal position of the individual particle, update the global optimal position and number of iterations of the particle swarm;

[0055] S4. Determine whether the number of iterations is less than the maximum number of iterations. If so, update the particle speed based on the current optimal position of the individual particle and the global optimal position of the current particle swarm. Update the particle position based on the updated particle speed and return to S2. If the number of iterations is not less than the maximum number of iterations, configure the AGV according to the optimized number of AGVs and configure the intelligent manufacturing workshop with AGVs.

[0056] Preferably, the particle swarm algorithm-based solution to the AGV quantity configuration optimization model further includes embedding the performance indicators of the intelligent manufacturing workshop into the particle swarm algorithm using particles corresponding to the performance indicators of the intelligent manufacturing workshop during the solution process, wherein the process is as follows:

[0057] S21. Importing the individual position of each particle into the queuing network, wherein the individual position of each particle is a mapping configured for the number of each AGV;

[0058] S22. Use the Gauss-Seidel iterative method to solve the steady-state probability of all nodes in all states. Based on the solution, calculate the performance indicators of the queuing network corresponding to each particle;

[0059] S23. The performance index of the queuing network corresponding to each particle is used as the fitness corresponding to the position of each individual particle, and the performance index of the intelligent manufacturing workshop is embedded in the particle swarm algorithm.

[0060] This application also proposes an AGV configuration optimization system based on a queuing network, the system comprising:

[0061] A queuing network construction unit is used to decompose each intelligent manufacturing unit in an intelligent manufacturing workshop into several types of nodes. The intelligent manufacturing workshop includes several intelligent manufacturing units. Workpieces are transported between each intelligent manufacturing unit based on the AGV system. Each AGV acts as an AGV node, and all nodes constitute a queuing network.

[0062] AGV node motion decomposition unit, used to describe the operation process of each node as the transition process between different states and analyze the state transition rate of each node;

[0063] An AGV node state transfer balance equation group construction unit is used to construct a state transfer balance equation for each node based on the state transfer rate of each node to form a state transfer balance equation group for each node;

[0064] AGV node state transfer balance equation solving unit, used to solve the state balance equations and obtain the performance indicators of the intelligent manufacturing workshop;

[0065] The AGV quantity configuration optimization unit is used to build an AGV quantity configuration optimization model, embed the performance indicators of the intelligent manufacturing workshop into the particle swarm algorithm, solve the AGV quantity configuration optimization model based on the particle swarm algorithm, and obtain the configuration optimization result.

[0066] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0067] This paper proposes a queuing network-based AGV configuration optimization method and system. First, a queuing network is constructed, each intelligent manufacturing unit within the intelligent manufacturing workshop is decomposed into several types of nodes, and the motion process of each AGV node is decomposed into transition processes in different state spaces. The AGV node state transition rate is obtained, and a set of AGV node state transition equilibrium equations is constructed and solved to obtain the performance indicators of the intelligent manufacturing workshop. Based on the performance indicators, an AGV quantity configuration optimization model is constructed, and the AGV quantity configuration optimization model is solved using a particle swarm algorithm to obtain the optimization results. The establishment of a queuing network can extend the AGV configuration optimization problem to multi-layer workshops or large-scale flexible operation scenarios, improving the scalability and adaptability of the present method. The introduction of a state space decomposition method reduces the modeling and computational complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 A schematic diagram showing an intelligent manufacturing workshop responsible for electrode column processing proposed in the background technology of the present invention;

[0069] Figure 2 A schematic diagram showing a flow chart of an AGV configuration optimization method based on a queuing network proposed in Example 1 of the present invention;

[0070] Figure 3 A schematic diagram showing the structure of a queuing network model based on an intelligent manufacturing workshop proposed in Example 2 of the present invention;

[0071] Figure 4 A state space diagram showing a single-target AGV node proposed in Example 2 of the present invention;

[0072] Figure 5 A state space diagram showing a multi-target AGV node proposed in Example 2 of the present invention;

[0073] Figure 6A schematic diagram showing a process of solving the AGV quantity configuration optimization model based on the particle swarm algorithm proposed in Example 2 of the present invention;

[0074] Figure 7 A schematic diagram showing a process of embedding the performance indicators of an intelligent manufacturing workshop into a particle swarm algorithm by using particles corresponding to the performance indicators of the intelligent manufacturing workshop proposed in Example 2 of the present invention;

[0075] Figure 8 A schematic diagram showing the structure of an AGV configuration optimization system based on a queuing network proposed in Example 3 of the present invention;

[0076] Figure 9 The state space diagram of the AGV front node proposed in Example 4 of the present invention is shown;

[0077] Figure 10 The state space diagram of the AGV rear node proposed in Example 4 of the present invention is shown as follows:

[0078] Figure 11 The figure shows the state space diagram of the input node proposed in the fourth embodiment of the present invention. DETAILED DESCRIPTION

[0079] The accompanying drawings are for illustrative purposes only and are not to be construed as limiting this patent;

[0080] In order to better illustrate this embodiment, some parts of the drawings may be omitted, enlarged, or reduced, and do not represent the actual size;

[0081] It is understandable to those skilled in the art that descriptions of certain well-known contents may be omitted in the drawings.

[0082] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0083] The positional relationships described in the drawings are for illustrative purposes only and should not be construed as limiting this patent;

[0084] Example 1

[0085] This embodiment proposes an AGV configuration optimization method based on a queuing network. The flowchart of this method is shown in FIG. Figure 2 , including the following steps:

[0086] S1. Each intelligent manufacturing unit in the intelligent manufacturing workshop is divided into several types of nodes. The intelligent manufacturing workshop includes several intelligent manufacturing units. Within each intelligent manufacturing unit, workpieces are transported based on AGVs. Each AGV acts as an AGV node, and all nodes form a queuing network.

[0087] S2. Decompose the motion process of each independent node into the transition process of different state spaces and obtain the AGV node state transition rate;

[0088] S3. Based on the AGV node state transfer rate, construct the AGV node state transfer balance equation to form the AGV node state transfer balance equation group;

[0089] S4. Solve the state balance equations to obtain the performance indicators of the intelligent manufacturing workshop;

[0090] S5. Construct an AGV quantity configuration optimization model, embed the performance indicators of the intelligent manufacturing workshop into the particle swarm algorithm, solve the AGV quantity configuration optimization model based on the particle swarm algorithm, and obtain the configuration optimization results.

[0091] In this embodiment, a queuing network is first constructed. Each intelligent manufacturing unit within the intelligent manufacturing workshop is decomposed into several types of nodes. The motion process of each AGV node is decomposed into transition processes in different state spaces. The AGV node state transition rate is obtained, and a set of AGV node state transition equilibrium equations is constructed and solved to obtain the performance indicators of the intelligent manufacturing workshop. Based on the performance indicators, an AGV quantity configuration optimization model is constructed and solved using a particle swarm algorithm to obtain the optimization results. The establishment of a queuing network can extend the AGV configuration optimization problem to multi-layer workshops or large-scale flexible operation scenarios, improving the scalability and adaptability of this method. The introduction of the state space decomposition method reduces the modeling and computational complexity.

[0092] Example 2

[0093] In this embodiment, each intelligent manufacturing unit of the intelligent manufacturing workshop includes a processing device and two buffer areas located before and after the processing device. The workpiece waits for processing in the buffer area located before the processing device and waits for AGV transfer in the buffer area located after the processing device.

[0094] Each intelligent manufacturing unit in the intelligent manufacturing workshop is divided into three types of nodes, including input nodes, bifurcation nodes and aggregation nodes;

[0095] Each AGV is independently used as an AGV node, and the AGV node includes a single-target AGV node and a multi-target AGV node;

[0096] The AGV node has several states in the intelligent manufacturing workshop, including waiting for workpiece loading, transferring workpieces, waiting for workpiece unloading and empty vehicle return; among them, if the number of AGV workpiece unloading points is one and only one, the AGV node is a single-target AGV node; if the number of AGV workpiece unloading points is greater than one, the AGV node is a multi-target AGV node.

[0097] Specifically, the structural diagram of the queuing network model constructed based on the intelligent manufacturing workshop is as follows: Figure 3 As shown in the figure, the WB class node includes the buffer area and processing equipment before the processing equipment, the B class node includes the buffer area after the processing equipment, and the A class node includes the virtual processing equipment. The processing time of the virtual equipment is set to 0;

[0098] The intelligent manufacturing unit in the workshop consists of M levels, each level contains three types of nodes, and the total number of nodes is Among them, the input node is the first process node; the aggregation node is generally the node composed of the buffer area before the processing equipment and the processing equipment; the fork node is generally the node composed of the buffer area after the processing equipment and the virtual equipment; for example, the node WB in the figure 11 is the input node, node WB 41 、WB 71 、......、WB 3M-2,,1 、WB 3M+1,1 is the aggregation node, node A 61 、A 62 、A 3M,1 is a bifurcation node; the arrows in the figure are the motion trajectories of the AGV nodes represented abstractly, among which the node WB 3M+1,1 The node with the target is a single-target AGV node, and the others are multi-target AGV nodes.

[0099] The node types of the queuing network are shown in Table 1:

[0100] Table 1

[0101]

[0102] In this embodiment, the movement process of each independent node is decomposed into the transfer process in different state spaces to obtain the node state transfer rate. The process is:

[0103] For single-target AGV node A ij , the expression for defining the state space of a single-target AGV node is:

[0104] A ij {(W ij ,S ij ); 0≤W ij ≤C ij +1,S ij =w,o,l,b;i=3M,1≤j≤R i}

[0105] Among them, W ij S represents the number of workpieces carried by the jth trolley at level i, ijrepresents the state of the jth AGV node in the i-th level. w, o, l, and b represent the four AGV states of waiting for loading at the loading point, transporting cargo to the unloading point, waiting for unloading at the unloading point, and returning empty to the loading point. C ij represents the cargo capacity of the jth AGV node in the i-th level, M represents the number of production processes, and R i The number of processing equipment at each level of units;

[0106] Calculate the state transition rate of the single-target AGV node, which represents the transition probability from the current node state to the next node state and the AGV transportation rate V ij The product of , including:

[0107] The single-target AGV node returns to state A with an empty vehicle ij (0, b) transfer to waiting for workpiece loading state A ij (0,w), the expression of transfer rate is:

[0108] The single-target AGV node returns to state A with an empty vehicle ij (0, b) transfer to the transfer workpiece state A ij {(W ij ,o),1≤W ij ≤C ij}, the expression of transfer rate is:

[0109] Where k represents the number of workpieces transported by AGV, 1≤k≤C;

[0110] Single-target AGV node is transporting goods to the unloading point state A ij {(W ij ,o),1≤W ij ≤C ij}Transfer to the waiting workpiece unloading state A ij {(W ij ,l),0 <W ij ≤C ij}, the expression of transfer rate is: V ij PB i+1,1 (k);

[0111] Among them, PB i+1,1 (k) is the transfer probability of a single-target AGV node waiting for workpiece unloading;

[0112] Single-target AGV node in transfer state A ij {(W ij ,o),1≤W ij ≤C ij} Unload all workpieces and transfer to empty car return state A ij(0,b), the transfer rate is

[0113] Specifically, the state space diagram of a single-target AGV node is as follows: Figure 4 As shown in the figure, there are four states in which the AGV node can be observed: loading point waiting for loading A ij (0,w), transporting goods to unloading point A ij (W ij ,o), waiting for unloading at the unloading point A ij (W ij ,l) and return to A with an empty vehicle ij (0, b); the four states are circled in the figure with ovals. The AGV switches randomly between the four modes following a Markov process, and the state transitions are always confined to the preset operating trajectory, which is abstractly represented by the arrows in the figure.

[0114] When the AGV arrives at the loading node, if there is no workpiece, it will go from state A to state ij (0,b) transfers to A ij (0,w), the transition probability is If there are k workpieces (with probability P i-1,j (k),0≤k≤N 3M+1 ), then the state of transporting goods to the unloading point is transferred, and the transfer probability is The expression is:

[0115]

[0116] The transport rate of AGV is V ij , the expression is:

[0117]

[0118] in, is the distance between the loading point and the rth unloading point of the jth AGV node at level i, v i is the average rate of the i-th level AGV node;

[0119] AGV from state A ij (0,l) transfers to state A ij The transfer rate of (0,w) is From state A ij (0,l) transfers to state A ij {(W ij ,o),1≤W ij ≤C ij The transfer rate of The behavior of AGV loading workpieces at a node can be decomposed into the following stages: Waiting stage: AGV stays at the loading node, and the arrival rate of workpieces is Loading transfer phase: When the workpiece arrives, the AGV arrives at an effective rate Transfer state; transport phase: AGV is V ij The transport speed goes to unloading node A ij {(W ij ,o),0 <W ij ≤C ij Unloading decision stage: After arriving at the unloading node, the decision rule for the next state of the AGV is: compare the number of workpieces carried W ij and the number of vacancies at the unloading node k i+1,ξ , when k i+1,ξ ≥W ij When the AGV is loaded with all workpieces, it can directly enter the empty vehicle return state A ij (0,b), when k i+1,ξ <W ij When AGV changes from state A ij {(W ij ,o),0 <W ij ≤C ij}, transfer to state A ij {(W ij ,l),0 <W ij ≤C ij AGV returns to state A empty ij The probability of (0,b) is AGV waiting for unloading state A ij (W ij -k i+1,ξ ,l) is PB i+1,ξ (k); where A ij (W ij ,l) indicates that the buffer area of ​​the AGV unloading node is full, but there are still W items left on the AGV. ij workpieces are not unloaded; and the machine tool at the unloading point is moving at a rate μ ij Continuously process the workpiece. Once a workpiece enters the machine tool from the buffer area, the AGV unloads a workpiece. ij When it decreases to 0, it turns to empty and returns to state A. ij (0,b).

[0120] In addition, the AGV unloading node is the only destination for each vehicle, which is prone to queue unloading. It is necessary to calculate the average unloading rate. When considering the congestion during queue unloading, the calculation expression is:

[0121]

[0122] in, It represents the effective unloading rate of AGV, and the expression is:

[0123]

[0124] Among them, a is the blocking node, p is the blocked node, is the frequency of AGV traveling between nodes p and a;

[0125] K r For AGV at unloading point WB i+1,k The probability of unloading at position r is expressed as:

[0126]

[0127] in, Block c for node k k nodes, Block c for node k k There are nodes, p ranks τth in the queue; when τ = 1, the expression is:

[0128]

[0129] When τ=2, the expression is:

[0130]

[0131] Specifically, it is known that the driving speed of AGV is V ij Therefore, the time the car spends in each state can be calculated in segments: the time for cargo transportation and empty return state is calculated as Because the AGV task transportation process is a birth and death update process, the steady-state probability in each state It can be calculated that the expression for the average waiting time of AGV in task execution is:

[0132]

[0133] In addition, for multi-target nodes, after loading the workpiece, there are multiple unloading points that can be reached. When the AGV arrives at the target node, if there is no available space at the node, it must wait until a vacant space appears and unloading is completed before leaving. In addition, the cart may queue at the unloading node due to congestion, that is, there is a coupling relationship between AGV nodes at the same level, which increases the complexity of system analysis and solution. The state space diagram of the multi-target AGV node is shown in the figure below. Figure 5 As shown;

[0134] The state space expression of the multi-target AGV node is defined as:

[0135] A ij (W ij ,S ij ,K)

[0136] Among them, the variable Wij Number of loaded workpieces; S ij Describes the AGV operation status, K means the AGV goes to the Kth buffer area in the optional unloading point;

[0137] The figure is similar to the single-target AGV state: waiting for loading A at the loading point ij (0,w,r), transport the cargo to unloading point A ij (1,o,1),A ij (2,o,1),A ij (C ij ,o,1) Waiting for unloading at the unloading point A ij (N i1 ,l,1) and empty car returns to A ij (0,b,r); AGV is in the empty state and returns to A ij In the (0,b,r) state, if there is no workpiece to be transported, Transfer rate to the loading point to wait for loading A ij (0,w,r), when the state changes from waiting to be carried to the state of carrying workpieces, the transfer rate is Among them, ξ is the probability of AGV going to the ξth processing center;

[0138] If there are workpieces that need to be transported, The transfer rate is transferred to the second unloading point A ij (1,o,2),A ij (2,o,2),......,A ij (C ij ,o,2);

[0139] When the trolley carries the workpiece to the unloading area, if there is enough space for unloading, the VM ij The transfer rate is transferred to the empty car return node, and the expression is:

[0140]

[0141] When the trolley carries the workpiece to the unloading area, if there is not enough space to unload, the VE ij Transfer rate to the unloading point to wait for unloading A ij (N i1 ,l,1) status, is the effective processing rate of the workpiece on the jth device in the i-th level.

[0142] In this embodiment, the state transition equation represents that the probability of transitioning into a state of a single-target AGV node is equal to the probability of transitioning out of it. The transition probability is the product of the transition rate from the transition state to the current state and the steady-state probability of the transition state. The transition probability is the product of the transition rate from the current state to the transition state and the steady-state probability of the transition state.

[0143] When the AGV returns to state A with an empty vehicle ij When (0,b) arrives at the loading node, there are two possible state transitions: there is a workpiece waiting, and it transitions to state A. ij {(W ij ,o),1≤W ij ≤C ij}, the transfer rate is If there is no workpiece waiting, enter state A ij (0,w), the transfer rate is The state transition balance equation requires the balance between the transition out state and the transition into state, so the transition from other states to the empty vehicle return state must also be considered: 1) When there is space to unload, the AGV moves from state A to the empty vehicle return state. ij {(W ij ,o),1≤W ij ≤C ij}Transfer to state A ij (0,b), the transfer rate is 2) When there is no space to unload, the AGV first turns to A ij {(W ij ,l),0 <W ij ≤C ij}, until the uninstallation is complete, it will be transferred to A ij (0,b) state, the transfer rate is

[0144] Specifically, the state A of the single-target AGV node ij (0,b) transition process, and from state and The process of transitioning to this state forms the state transition equilibrium equation as follows:

[0145]

[0146] in, For node A ij The steady-state probability in the corresponding state;

[0147] The expressions of other state transfer balance equations of single-target AGV nodes are:

[0148]

[0149] in, is the effective rate at which workpieces arrive at the jth device at the i-th level

[0150]

[0151] Where 2≤W ij ≤C ij

[0152]

[0153] In this embodiment, the process of solving the state equilibrium equations is as follows:

[0154] The state transition probability and state steady-state probability of all single-target AGV nodes are set to 0, and the expression is:

[0155]

[0156] in, represents the steady-state probability of all node states, represents the probability that the jth node at level 3i+1 is idle, represents the probability of the jth node at level 3i+1 being blocked, is the probability that the j-th node at level 3i+2 is blocked before the node;

[0157] Traverse all single-target AGV nodes, define the state space of all single-target AGV nodes, and calculate the transition rate between the states of single-target AGV nodes;

[0158] Based on the state balance equation and the conversion rate between single-target AGV nodes, the state transfer matrix is ​​constructed to calculate the steady-state probability of the single-target AGV node state;

[0159] Based on the transition rate between single-target AGV node states and the steady-state probability between single-target AGV node states, the probability of single-target AGV node being blocked during state transition is calculated;

[0160] Determine whether the steady-state probability of a single-target AGV node state exceeds a preset threshold. If so, return to calculate the transition rate between node states; if not, output the steady-state probabilities of all single-target AGV node states to calculate the performance indicators of the intelligent manufacturing workshop.

[0161] In this embodiment, the performance indicators of the intelligent manufacturing workshop include average output rate and average production cycle, and the calculation process is as follows:

[0162] For a single-target AGV node in an intelligent manufacturing workshop, the effective processing rate of the final processing link is 3M+1 is the average output rate θ, which is expressed as:

[0163]

[0164] Calculate the product of the steady-state probability of all states of a single AGV node and the number of workpieces in the corresponding state to obtain the average number of workpieces of a single AGV node;

[0165] Calculate the sum of the average number of workpieces of all AGV nodes to get the average work-in-progress WIP;

[0166] Calculate the average production cycle T, the expression is:

[0167]

[0168] In this embodiment, the objective function of the constructed AGV quantity configuration optimization model is expressed as:

[0169]

[0170] The constraint expression is:

[0171] E{Γ(X:ξ)}≤Γ max

[0172] E{θ(X:ξ)}≥θ min

[0173] X∈N +

[0174] Among them, X represents the total investment cost of AGV configuration in the workshop, which is a non-negative integer vector, Q represents the average output rate of the workshop, and x i represents the model combination of the i-th level AGV, v represents the mathematical expectation of the random function, ξ represents the total investment cost of the AGV configuration in the workshop, θ represents the average production cycle of the system, E{Γ(X:ξ)} represents the average production cycle, and E{θ(X:ξ)} represents the average output rate.

[0175] In this embodiment, the particle swarm algorithm is used to solve the AGV quantity configuration optimization model. The flow chart is as follows: Figure 6 As shown, the process is:

[0176] S1. Initialize the position and velocity of each particle in the particle swarm;

[0177] S2. Calculate the fitness of each particle in the swarm and update the optimal position of each particle based on the fitness.

[0178] S3. Based on the optimal position of the individual particle, update the global optimal position and number of iterations of the particle swarm;

[0179] S4. Determine whether the number of iterations is less than the maximum number of iterations. If so, update the particle speed based on the current optimal position of the individual particle and the global optimal position of the current particle swarm. Update the particle position based on the updated particle speed and return to S2. If the number of iterations is not less than the maximum number of iterations, configure AGV for the intelligent manufacturing workshop according to the optimized AGV resource configuration.

[0180] Specifically, the expression for the position of the mth particle in the particle swarm is:

[0181]

[0182] Where i = 1, 2, ..., D, D is the total number of levels, and r is a random number in (0, 1);

[0183] The expression for the velocity of the mth particle in the particle swarm is:

[0184] V mi =r(V max -V min )+V min

[0185] Where i=1,2,...,D, D is the total number of stages, V max 、V min Indicates the upper and lower limits of particle velocity;

[0186] By running the queuing network model, the workshop performance index and fitness value of each particle are quickly calculated. If the constraints are met, the optimal fitness value of a single particle is directly calculated. Otherwise, the fitness value of the particle is penalized and degraded before the optimal fitness value of the single particle is calculated. The expression of the optimal fitness value of a single particle is:

[0187] P best (i)=(P i1 ,P i2 ,…,P iD )

[0188] Where i = 1, 2, ..., N, N is the population size;

[0189] The expression of the optimal fitness value of the particle swarm is:

[0190] G best (i)=(G i1 ,G i2 ,…,G iD )

[0191] The expression for updating the global optimal speed of the particle swarm is:

[0192]

[0193] Among them, w is the parameter that controls the convergence of the algorithm, w∈R + , c1, c2 are acceleration constants, r1, r2 are random numbers, where r1, r2∈(0,1), k is the number of iterations;

[0194] In this embodiment, the particle swarm algorithm is used to solve the AGV quantity configuration optimization model, and the particle swarm algorithm is also used to embed the performance indicators of the intelligent manufacturing workshop into the particle swarm algorithm during the solution process. The flow chart is as follows: Figure 7 As shown, the process is:

[0195] S21. Importing the individual position of each particle into the queuing network, wherein the individual position of each particle is a mapping configured for the number of each AGV;

[0196] S22. Use the Gauss-Seidel iterative method to solve the steady-state probability of all nodes in all states. Based on the solution, calculate the performance indicators of the queuing network corresponding to each particle;

[0197] S23. The performance index of the queuing network corresponding to each particle is used as the fitness corresponding to the position of each individual particle, and the performance index of the intelligent manufacturing workshop is embedded in the particle swarm algorithm.

[0198] Example 3

[0199] This embodiment proposes an AGV configuration optimization system based on a queuing network. The structural diagram of the method is shown in FIG. Figure 8 Shown, including:

[0200] A queuing network construction unit is used to decompose each intelligent manufacturing unit in an intelligent manufacturing workshop into several types of nodes. The intelligent manufacturing workshop includes several intelligent manufacturing units. Workpieces are transported between each intelligent manufacturing unit based on the AGV system. Each AGV acts as an AGV node, and all nodes constitute a queuing network.

[0201] AGV node motion decomposition unit, used to describe the operation process of each node as the transition process between different states and analyze the state transition rate of each node;

[0202] An AGV node state transfer balance equation group construction unit is used to construct a state transfer balance equation for each node based on the state transfer rate of each node to form a state transfer balance equation group for each node;

[0203] AGV node state transfer balance equation solving unit, used to solve the state balance equations and obtain the performance indicators of the intelligent manufacturing workshop;

[0204] The AGV quantity configuration optimization unit is used to build an AGV quantity configuration optimization model, embed the performance indicators of the intelligent manufacturing workshop into the particle swarm algorithm, solve the AGV quantity configuration optimization model based on the particle swarm algorithm, and obtain the configuration optimization result.

[0205] Example 4

[0206] In this embodiment, the AGV front node is analyzed. The AGV front node is the buffer area behind the processing equipment, that is, the loading point. The AGV obtains the workpiece from the AGV front node and enters the workpiece carrying state. This node has the core characteristics of "single arrival and batch departure". The state space diagram of the AGV front node is as follows: Figure 9 As shown in the figure; when the AGV arrives, if there is no workpiece at the node, it enters the waiting state (0, w); if there is a workpiece, it enters the loading state (1, o), (2, o), ..., (C i+1,j ,o), the state balance equations between nodes are expressed as:

[0207]

[0208] In this embodiment, the AGV post-node is analyzed. The AGV post-node contains a processing device and its front buffer area. The characteristic is that multiple AGVs can be unloaded at this node. According to whether there are subsequent nodes, this type of node can be divided into two categories for specific analysis in order to calculate the node outflow rate. There are a total of (N ij +2)*2+C i+1,j The state space diagram of the node after AGV is as follows Figure 10 As shown in the figure: is the effective outflow rate of the next node. When the unloading node is the last node, otherwise The calculation expression is:

[0209]

[0210] in addition, It represents the average speed of the AGV returning to the loading node, and the expression is:

[0211]

[0212] AGV transport rate V ij The calculation expression is:

[0213]

[0214] The number of workpieces delivered each time is distributed as follows: The expression is:

[0215]

[0216] In this embodiment, the input node is analyzed, and the state space diagram of the input node is as follows: Figure 11 As shown, The transfer probability of the input node transferring to the AGV node to carry the workpiece is expressed as:

[0217]

[0218] in, It represents the time required for the AGV to complete the loading and unloading process without waiting for loading, i represents the i-th buffer area in the same level node, Indicates the time required for the trolley to return empty.

[0219] Obviously, the above embodiments of the present invention are merely examples for the purpose of clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Those skilled in the art will appreciate that other variations or modifications can be made based on the above description. It is not necessary and impossible to enumerate all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the claims of the present invention.

Claims

1. An AGV configuration optimization method based on a queuing network, characterized in that: The following steps are involved: Each intelligent manufacturing unit in the intelligent manufacturing workshop is decomposed into several types of nodes. The intelligent manufacturing workshop includes several intelligent manufacturing units. Between each intelligent manufacturing unit, the workpiece is transferred based on the AGV system. Each AGV acts as an AGV node, and all nodes form a queuing network. Describe the operation process of each node as the transition process between different states, and analyze the state transition rate of each node; Based on the state transfer rate of each node, the state transfer balance equation of each node is constructed to form a state transfer balance equation group of each node; Solve the state equilibrium equations to obtain the performance indicators of the intelligent manufacturing workshop; An AGV quantity configuration optimization model is constructed, and the performance indicators of the intelligent manufacturing workshop are embedded in the particle swarm algorithm. The AGV quantity configuration optimization model is solved based on the particle swarm algorithm to obtain the configuration optimization results.

2. The AGV configuration optimization method based on a queuing network according to claim 1, characterized in that: Each intelligent manufacturing unit in the intelligent manufacturing workshop includes a processing device and two buffer areas located before and after the processing device. The workpiece waits for processing in the buffer area before the processing device and waits for AGV transfer in the buffer area after the processing device. Decompose each intelligent manufacturing unit in the intelligent manufacturing workshop into several types of nodes, including: input nodes, bifurcation nodes and aggregation nodes; The AGV node includes a single-target AGV node and a multi-target AGV node; the AGV node has several states in the intelligent manufacturing workshop, including waiting for workpiece loading, transferring workpieces, waiting for workpiece unloading and empty vehicle return; among them, if the number of AGV workpiece unloading points is one and only one, the AGV node is a single-target AGV node; if the number of AGV workpiece unloading points is greater than one, the AGV node is a multi-target AGV node.

3. The AGV configuration optimization method based on a queuing network according to claim 2, characterized in that: The operation process of each node is described as the transition process between different states. The state transition rate of each node is analyzed. The process is: For single-target AGV node A ij , the expression for defining the state space of a single-target AGV node is: A ij {(W ij ,S ij );0≤W ij ≤C ij +1,S ij =w,o,l,b;i=3M,1≤j≤R i } Among them, W ij S represents the number of workpieces carried by the jth trolley at level i, ij represents the state of the jth AGV node in the i-th level. w, o, l, and b represent the four AGV states of waiting for loading at the loading point, transporting cargo to the unloading point, waiting for unloading at the unloading point, and returning empty to the loading point. C ij represents the cargo capacity of the jth AGV node in the i-th level, M represents the number of production processes, and R i The number of processing equipment at each level of units; Calculate the state transition rate of the single-target AGV node, which represents the transition probability from the current node state to the next node state and the AGV transportation rate V ij The product of , including: The single-target AGV node returns to state A with an empty vehicle ij (0, b) transfer to waiting for workpiece loading state A ij (0,w), the expression of transfer rate is: The single-target AGV node returns to state A with an empty vehicle ij (0, b) transfer to the transfer workpiece state A ij {(W ij ,o),1≤W ij ≤C ij }, the expression of transfer rate is: Where k represents the number of workpieces transported by AGV, 1≤k≤C; Single-target AGV node is transporting goods to the unloading point state A ij {(W ij ,o),1≤W ij ≤C ij }Transfer to the waiting workpiece unloading state A ij {(W ij ,l),0 <W ij ≤C ij }, the expression of transfer rate is: V ij PB i+1,1 (k); Among them, PB i+1,1 (k) is the transfer probability of a single-target AGV node waiting for workpiece unloading; Single-target AGV node in transfer state A ij {(W ij ,o),1≤W ij ≤C ij } Unload all workpieces and transfer to empty car return state A ij (0,b), the transfer rate is 4. The AGV configuration optimization method based on a queuing network according to claim 3 is characterized in that: The state transition equation indicates that the entry probability and exit probability of a certain state of a single-target AGV node are equal, the entry probability is the product of the transition rate from the entry state to the current state and the steady-state probability of the entry state, and the exit probability is the product of the transition rate from the current state to the exit state and the steady-state probability of the exit state.

5. The AGV configuration optimization method based on a queuing network according to claim 2, characterized in that: The process of solving the state equilibrium equations is as follows: The state transition probability and state steady-state probability of all single-target AGV nodes are set to 0, and the expression is: in, represents the steady-state probability of all node states, represents the probability that the jth node at level 3i+1 is idle, represents the probability of the jth node at level 3i+1 being blocked, is the probability that the j-th node at level 3i+2 is blocked before the node; Traverse all single-target AGV nodes, define the state space of all single-target AGV nodes, and calculate the transition rate between the states of single-target AGV nodes; Based on the state balance equation and the conversion rate between single-target AGV nodes, the state transfer matrix is ​​constructed to calculate the steady-state probability of the single-target AGV node state; Based on the transition rate between single-target AGV node states and the steady-state probability between single-target AGV node states, the probability of single-target AGV node being blocked during state transition is calculated; Determine whether the steady-state probability of a single-target AGV node state exceeds a preset threshold. If so, return to calculate the transition rate between node states; if not, output the steady-state probabilities of all single-target AGV node states to calculate the performance indicators of the intelligent manufacturing workshop.

6. The AGV configuration optimization method based on a queuing network according to claim 5, characterized in that: The performance indicators of the intelligent manufacturing workshop include average output rate and average production cycle, and the calculation process is as follows: For a single-target AGV node in an intelligent manufacturing workshop, the effective processing rate of the final processing link is 3M+1 is the average output rate θ, which is expressed as: Calculate the product of the steady-state probability of all states of a single AGV node and the number of workpieces in the corresponding state to obtain the average number of workpieces of a single AGV node; Calculate the sum of the average number of workpieces of all AGV nodes to get the average work-in-progress WIP; Calculate the average production cycle T, the expression is:

7. The AGV configuration optimization method based on a queuing network according to claim 6, characterized in that: The objective function of the constructed AGV quantity configuration optimization model is expressed as: The constraint expression is: E{Γ(X:ξ)}≤Γ max E{θ(X:ξ)}≥θ min X∈N + Among them, X represents the total investment cost of AGV configuration in the workshop, which is a non-negative integer vector, Q represents the average output rate of the workshop, and x i represents the model combination of the i-th level AGV, Γ represents the mathematical expectation of the random function, ξ represents the total investment cost of the AGV configuration in the workshop, θ represents the average production cycle of the system, E{Γ(X:ξ)} represents the average production cycle, and E{θ(X:ξ)} represents the average output rate.

8. The AGV configuration optimization method based on a queuing network according to claim 7, characterized in that: The process of solving the AGV quantity configuration optimization model based on the particle swarm algorithm is as follows: S1. Initialize the position and velocity of each particle in the particle swarm; S2. Calculate the fitness of each particle in the swarm and update the optimal position of each particle based on the fitness. S3. Based on the optimal position of the individual particle, update the global optimal position and number of iterations of the particle swarm; S4. Determine whether the number of iterations is less than the maximum number of iterations. If so, update the particle speed based on the current optimal position of the individual particle and the global optimal position of the current particle swarm. Update the particle position based on the updated particle speed and return to S2. If the number of iterations is not less than the maximum number of iterations, configure the AGV according to the optimized number of AGVs and configure the intelligent manufacturing workshop with AGVs.

9. The AGV configuration optimization method based on a queuing network according to claim 8, characterized in that: The particle swarm algorithm-based solution to the AGV quantity configuration optimization model also includes, during the solution process, using particles corresponding to the performance indicators of the intelligent manufacturing workshop to embed the performance indicators of the intelligent manufacturing workshop into the particle swarm algorithm, and the process is as follows: S21. Importing the individual position of each particle into the queuing network, wherein the individual position of each particle is a mapping configured for the number of each AGV; S22. Use the Gauss-Seidel iterative method to solve the steady-state probability of all nodes in all states. Based on the solution, calculate the performance indicators of the queuing network corresponding to each particle; S23. The performance index of the queuing network corresponding to each particle is used as the fitness corresponding to the position of each individual particle, and the performance index of the intelligent manufacturing workshop is embedded in the particle swarm algorithm.

10. An AGV configuration optimization system based on a queuing network, characterized in that: The system is used to implement the method according to any one of claims 1 to 9, comprising: A queuing network construction unit is used to decompose each intelligent manufacturing unit in an intelligent manufacturing workshop into several types of nodes. The intelligent manufacturing workshop includes several intelligent manufacturing units. Workpieces are transported between each intelligent manufacturing unit based on the AGV system. Each AGV acts as an AGV node, and all nodes constitute a queuing network. AGV node motion decomposition unit, used to describe the operation process of each node as the transition process between different states and analyze the state transition rate of each node; An AGV node state transfer balance equation group construction unit is used to construct a state transfer balance equation for each node based on the state transfer rate of each node to form a state transfer balance equation group for each node; AGV node state transfer balance equation solving unit, used to solve the state balance equations and obtain the performance indicators of the intelligent manufacturing workshop; The AGV quantity configuration optimization unit is used to build an AGV quantity configuration optimization model, embed the performance indicators of the intelligent manufacturing workshop into the particle swarm algorithm, solve the AGV quantity configuration optimization model based on the particle swarm algorithm, and obtain the configuration optimization result.

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