PCB dust-free workshop AGV residence point configuration optimization method and system based on complex semi-open queuing network

Abstract

The application relates to the technical field of PCB production, in particular to a PCB dust-free workshop AGV residence point configuration optimization method and system based on a complex semi-open queuing network, which solves problems by constructing a semi-open queuing network and introducing approximate mean analysis, accurately depicts the random competition and congestion transmission relationship between an external order queue and an internal AGV closed loop under limited AGV resources, can accurately quantify the average order waiting time under different residence point layouts and AGV quantity combinations, and overcomes the defects that traditional methods cannot handle system randomness. An integer nonlinear programming model with the minimum weighted sum of AGV configuration cost and order delay cost as the target is constructed, joint and collaborative optimization of residence point space position and AGV configuration quantity is realized, the total operation cost is greatly reduced, a systematic quantitative decision tool is provided for scientific configuration of the AGV system of the dust-free workshop, and the method has engineering practical value.

Description

Technical Field

[0001] This application relates to the field of PCB manufacturing technology, specifically to a method and system for optimizing the configuration of AGV residence points in PCB cleanrooms based on complex semi-open queuing networks. Background Technology

[0002] With the increasing variety of PCB products and the growing complexity of processes, cleanroom AGV material handling systems face the prominent problem of difficulty in coordinating and optimizing the layout of dwell points and the number of AGVs.

[0003] Traditional methods typically separate the planning of AGV locations from the configuration of AGV numbers, lacking comprehensive consideration of factors such as the random arrival of AGV transport tasks, shared charging resources among multiple AGV locations, and AGV power constraints. This leads to drawbacks in actual operation, such as excessively long waiting times for transport tasks, severe delays in order delivery, or over-configuration of AGVs.

[0004] In addition, existing queuing network models are mostly designed for purely open or purely closed-loop systems, lacking a systematic modeling method that integrates queuing network performance evaluation with the optimization of the spatial layout of dwell points. There is an urgent need for a quantitative decision-making method that can jointly optimize the dwell point location and the number of AGV configurations, while taking into account the system's randomness and power constraints. Summary of the Invention

[0005] In view of this, the purpose of this application is to provide a method and system for optimizing the configuration of AGV residence points in PCB cleanrooms based on complex semi-open queuing networks, so as to solve the problems in the background art.

[0006] To achieve the above objectives, this application adopts the following technical solution:

[0007] The method for optimizing the dwell point configuration of AGVs in a PCB cleanroom based on a complex half-open queuing network, as described in this application, includes the following steps:

[0008] The system acquires location information of multiple dwelling points and processing areas in the cleanroom, AGV handling process information, AGV kinematic data, AGV available power, and AGV power consumption rate. The AGV handling process information includes multiple handling stages, and the location information of the dwelling points are candidate locations.

[0009] Based on the location information of the multiple dwelling points and processing areas, and the AGV handling process information, a semi-open queuing network based on a single dwelling point is constructed. Based on the semi-open queuing network and AGV kinematic data, the expected service time and the coefficient of variation of the square of the expected service time of multiple handling links are calculated. Based on the semi-open queuing network, the expected service time of the multiple handling links, the available power of the AGV, and the power consumption rate of the AGV, the AGV charging probability of each dwelling point is calculated.

[0010] The half-open queuing network is solved based on the expected service time of the multiple handling links, the coefficient of variation of the square of the expected service time, and the AGV charging probability to obtain the estimated order throughput time and the average waiting time of the external order queue.

[0011] Based on the estimated order throughput time, the average waiting time of the external order queue, the pre-configured production plan, and process parameters, an integer nonlinear programming model is constructed, and the integer nonlinear programming model is solved to obtain the location of the dwell point and the number of AGVs configured at the dwell point. The integer nonlinear programming model includes an objective function aimed at minimizing the overall cost and various physical constraints.

[0012] In one embodiment of this application, the rules of the half-open queuing network include:

[0013] Corresponding to a single residence point outpost The quantity is AGV;

[0014] outpost Responsible for carrying out transport tasks The delivery rate of the transport task Arrival at the rest stop Matching with idle AGVs at the synchronization station;

[0015] Each transport task The execution is divided into three steps: the AGV goes to the previous process area; the AGV loads the PCB processed in the previous process and sends it to the next process area; the AGV unloads the PCB and returns to its designated residence point.

[0016] If the AGV's battery level drops below the limit after returning to its dwell point, it will proceed to the charging point in the workshop to recharge, and then return to its dwell point after charging is complete.

[0017] If all AGVs at the station are busy, the transport task will wait in the task queue at the synchronization station for the AGV to return to the station after completing the task.

[0018] The workshop handling tasks arrive randomly at a preset rate, following a Poisson distribution.

[0019] Each AGV at its designated location will perform tasks on a first-come, first-served basis, and can only perform one task at a time.

[0020] AGVs can travel along fixed bidirectional paths in the workshop.

[0021] In one embodiment of this application, the expected service time and the coefficient of variation of the square of the expected service time for multiple transport stages are calculated based on the half-open queuing network and AGV kinematic data, including:

[0022] The Manhattan distance for each handling process is determined based on the location information of the multiple rest points and processing areas.

[0023] The expected service time for each transport process is calculated based on the AGV speed and the Manhattan distance of each transport process; and the coefficient of variation of the square of the expected service time for each transport process is calculated.

[0024] In one embodiment of this application, the AGV charging probability at each dwell point is calculated based on the semi-open queuing network, the expected service time of the multiple handling links, the available power of the AGV, and the power consumption rate of the AGV, including:

[0025] Obtain the allocation probability of a transport task being assigned to a dwelling point, wherein the allocation probability is a pre-allocated average probability or a weighted probability;

[0026] The expected service times of multiple target handling stages are summed to obtain the total expected time; the product of the total expected time and the allocation probability is calculated to obtain the expected time for the dwell point to complete one handling task. ;

[0027] Based on the AGV power consumption rate and the expected duration Calculate the power consumption of the station to complete one transport task. , ,in, For the index of the residence point, For AGV index;

[0028] Based on the available power of the AGV and the power consumption Calculate the number of tasks that the AGV can perform. , and the number of tasks that the AGV can perform. Total order arrival rate at the station and outposts Number of AGVs configured Calculate the dwell point The probability that an AGV needs to be recharged after completing a transport task is: , .

[0029] In one embodiment of this application, the semi-open queuing network is solved based on the expected service time of the multiple handling links, the coefficient of variation of the square of the expected service time, and the AGV charging probability to obtain the estimated order throughput time and the average waiting time of the external order queue, including:

[0030] Identify multiple independent arrival flows from multiple dwelling points to a charging point, and aggregate the multiple independent arrival flows into a single equivalent total arrival flow, wherein the total arrival flow flows into the charging service node;

[0031] Calculate the coefficient of variation of the squared arrival time interval of the total arrival flow. and the coefficient of variation of the square of the total arrival flow service time of the service node. Wherein, the coefficient of squared variation and the squared coefficient of variation The mathematical expression is:

[0032]

[0033]

[0034] In the formula, These are the weighting coefficients. The weighted coefficient of variation, The average service time for the total arrival flow. Reaching the flow weight, To reach the stream index, For the first The average coefficient of variation of the arriving streams For the first Service time for each arrival stream;

[0035] Based on the squared coefficient of variation and the squared coefficient of variation Calculate the average waiting time of the AGV and the total dwell time of the AGV at the charging point The average waiting time of the AGV and the total dwell time of the AGV at the charging point The mathematical expression is:

[0036]

[0037]

[0038] In the formula, The arrival rate of the total arrival flow. The total service time of the arrival stream. The number of service nodes;

[0039] Based on the expected service time of the multiple handling stages, the coefficient of variation of the square of the expected service time, the charging probability of the AGV, and the average waiting time of the AGV. and the total dwell time of the AGV at the charging point Calculate the average waiting time of the external order queue ;

[0040] Based on the average waiting time of the external order queue Calculate the estimated order throughput time .

[0041] In one embodiment of this application, the estimated order throughput time The mathematical expression is:

[0042]

[0043] In the formula, For path The probability, For path No. Processing time of the process, For path No. The average waiting time of the transport task in the depot queue after the process is completed. For path No. The actual time spent on the handling tasks after the process is completed.

[0044] In one embodiment of this application, the average waiting time Based on the expected service time of the multiple handling stages, the coefficient of variation of the square of the expected service time, the charging probability of the AGV, and the average waiting time of the AGV. and the total dwell time of the AGV at the charging point The approximate mean was obtained through analysis.

[0045] In one embodiment of this application, the mathematical expression of the objective function of the integer nonlinear programming model is:

[0046]

[0047] In the formula, Total operating costs For the station number, For the outpost The number of AGVs, The cost per unit time for AGV usage. For indicator functions, For expected order throughput time, The standard production delivery date stipulated by the company. For workshop material arrival rate;

[0048] The mathematical expressions for the multiple physical constraints of the integer nonlinear programming model are as follows:

[0049]

[0050]

[0051]

[0052]

[0053]

[0054] In the formula, It is a set of positive integers. This is the set of available coordinate points in the workshop. and For two different outposts, To assemble at the base, For the outpost The closed-loop network of the queuing network after removing the concurrency includes The throughput of the AGV, For the outpost The system stability margin, For the outpost Order delivery rate.

[0055] In one embodiment of this application, the integer nonlinear programming model is solved to obtain the location of the dwelling point and the number of AGVs configured at the dwelling point, including:

[0056] Chromosome coding is constructed based on the location of the dwell point and the number of AGVs configured at the dwell point;

[0057] An improved genetic algorithm is executed based on the chromosome encoding to obtain the location of the dwelling point and the number of AGVs configured at the dwelling point, thus constructing the optimal solution for the chromosome encoding. In the improved genetic algorithm, two individuals are randomly selected each time, and the one with better fitness is selected to enter the next generation. This process is repeated until the population size remains unchanged. The crossover operator uses simulated binary crossover, and the mutation operator uses local perturbation mutation. After the crossover and mutation operations, boundary constraint verification and repair operations are performed, and the best individual from the previous generation directly replaces the worst individual in the new generation.

[0058] After each generation of evolution is completed, a hill-climbing neighborhood search is performed on the current best individual. If the newly generated individual is better than the original best individual, the current best solution is replaced, and the worst individual in the population is replaced by this individual.

[0059] This application also provides a PCB cleanroom AGV dwell point configuration optimization system based on complex semi-open queuing networks, including:

[0060] The acquisition module is used to acquire the location information of multiple dwelling points and processing areas in the cleanroom, AGV handling process information, AGV kinematic data, AGV available power and AGV power consumption rate. The AGV handling process information includes multiple handling links, and the location information of the dwelling points is candidate locations.

[0061] The relevant parameter calculation module is used to calculate the expected service time and the coefficient of variation of the square of the expected service time of multiple handling links based on the location information of the multiple dwelling points and the processing area, the AGV handling process information, and the AGV kinematic data; and to calculate the AGV charging probability of each dwelling point based on the expected service time of the multiple handling links, the available power of the AGV, and the AGV power consumption rate.

[0062] The half-open network solving module is used to construct a half-open queuing network based on a single dwell point, and solve the half-open queuing network based on the expected service time of the multiple handling links, the coefficient of variation of the square of the expected service time, and the charging probability of the AGV to obtain the estimated order throughput time and the average waiting time of the external order queue.

[0063] The dwell point configuration module is used to construct an integer nonlinear programming model based on the estimated order throughput time, the average waiting time of the external order queue, the pre-configured production plan, and process parameters, and solve the integer nonlinear programming model to obtain the location of the dwell point and the number of AGVs configured at the dwell point. The integer nonlinear programming model includes an objective function with the goal of minimizing the overall cost and various physical constraints.

[0064] The beneficial effects of this application are as follows: The AGV dwell point configuration optimization method and system for PCB cleanrooms based on complex semi-open queuing networks accurately characterizes the random competition and congestion transmission relationship between the external order queue and the internal AGV closed loop under limited AGV resources by constructing a semi-open queuing network and introducing approximate mean analysis for solution. It can accurately quantify the average waiting time of orders under different dwell point layouts and AGV quantity combinations, overcoming the shortcomings of traditional methods in handling system randomness. The arrival flow of multi-dwelling charging vehicles at centralized charging points is equivalently aggregated, and a GI / G / m queuing model is introduced to calculate the average queuing waiting time and total dwell time of AGVs at charging nodes. This allows the queuing network solution process to effectively account for the impact of AGV endurance constraints on handling efficiency, avoiding overly optimistic configuration schemes due to neglecting charging congestion. An integer nonlinear programming model is constructed with the objective of minimizing the weighted sum of AGV configuration cost and order delay cost. An improved genetic algorithm with embedded hybrid chromosome encoding, constraint repair operators, and hill-climbing local search is used for solution, achieving joint and collaborative optimization of dwell point spatial location and AGV configuration quantity. This method significantly reduces total operating costs while providing a systematic quantitative decision-making tool for the scientific configuration of AGV systems in cleanrooms, and has practical engineering value. Attached Figure Description

[0065] The present application will be further described below with reference to the accompanying drawings and embodiments:

[0066] Figure 1 This is a schematic diagram of a cleanroom in one embodiment of this application;

[0067] Figure 2 This is a flowchart illustrating an embodiment of the PCB cleanroom AGV dwell point configuration optimization method based on a complex half-open queuing network.

[0068] Figure 3 This is a schematic diagram of a single-dwelling-point AGV transportation task queuing network model in one embodiment of this application;

[0069] Figure 4 This is a schematic diagram illustrating the equivalent arrival-dependent service node transformation of the charging service node in this application;

[0070] Figure 5 This is a schematic diagram of chromosome encoding in one embodiment of this application;

[0071] Figure 6 This is a structural diagram of a PCB cleanroom AGV dwell point configuration optimization system based on a complex semi-open queuing network, as shown in one embodiment of this application. Detailed Implementation

[0072] Figure 1This is a schematic diagram of a cleanroom in one embodiment of this application, as shown below. Figure 1 As shown, the AGV material handling process is introduced using an AGV material transport system in a PCB cleanroom of a certain enterprise as an example. Figure 1 The diagram shows a cleanroom, which includes a PCB processing area, AGV (Automated Guided Vehicle) docking points, and charging points. AGVs handle PCB transport tasks between the various processing areas (Task 1, Task 2, Task 3, Task 4). Each transport task is executed in three phases (a, b, c). Idle AGVs remain at their assigned docking points. When a process is completed, the receiving machine in that area places the finished PCB at a designated location and sends a request signal to the transport system, assigning an AGV to perform the transport task (a). The AGV transports the PCB to the next processing area (b), then returns to its assigned docking point (c) and becomes idle again. In the system, each type of transport task is handled by only one docking point (e.g., transport task 1 is handled only by docking point I), while each docking point can simultaneously serve multiple types of transport tasks (e.g., docking point II handles material transport for both tasks 2 and 3). When a task arrives, if an idle AGV is available at the docking point, it is served immediately; otherwise, the task enters a queue to wait for service.

[0073] Considering the range constraints of AGVs, a centralized charging point is set up in the cleanroom, equipped with multiple charging piles to meet the charging needs of all AGVs at their respective stops. The centralized charging point is equipped with... There are 4 parallel charging piles, each with the same service capacity. When the AGV arrives, it randomly selects an available pile for charging. After completing a transport task and returning to its resting point, the AGV determines whether it needs to be charged based on its remaining battery power. When the battery power is lower than a preset threshold, the AGV goes to a charging point to charge (4.d). After charging, it returns to its original resting point to continue waiting (4.e).

[0074] The order throughput time of PCB production in the workshop depends on the processing time of each process and the circulation time of AGVs transporting PCBs between different process areas. This transport time is affected by factors such as the location of the depot and the number of AGVs. Insufficient AGVs lead to excessively long task waiting times, increasing order delay costs, while increasing the number of AGVs increases configuration costs. To minimize total operating costs, this paper proposes a two-stage depot configuration optimization framework. The first stage models the AGV workflow at the depot as a half-open queuing network, obtaining the average waiting time of transport tasks in the depot queue and the order throughput time. The second stage constructs an integer nonlinear programming model with the objective function of minimizing AGV configuration costs and order delay costs. The calculated order throughput time is substituted into the model as a known expression, and an improved genetic algorithm is designed to solve the problem, yielding the optimal depot location and AGV configuration.

[0075] The overall idea of ​​this invention is to regard the PCB cleanroom AGV material handling system as a semi-open queuing network coupled with an external order queue and an internal AGV closed loop. Through the performance evaluation of the queuing network and the iterative linkage of intelligent optimization algorithms, the joint optimization of the dwell point location and the number of AGVs can be achieved.

[0076] Specifically, firstly, the workshop layout, AGV kinematics, and endurance parameters are extracted to calculate the expected service time and its fluctuation characteristics for each handling stage, and the AGV charging probability is quantified based on the power consumption model. Secondly, a single-station semi-open queuing network is constructed. By equating the centralized charging node shared by multiple stations to the arrival-dependent service node, the Approximate Mean Value Analysis (AMVA) algorithm is used to iteratively solve the closed-loop network throughput and the average waiting time of external orders, thereby estimating the overall order throughput time. Finally, with the goal of minimizing the weighted sum of AGV configuration cost and order delay cost, and constrained by system stability and layout feasibility, an integer nonlinear programming model is established. An improved genetic algorithm with embedded hybrid coding, constraint repair, and hill-climbing local search is designed to solve the model, outputting the optimal station coordinates and AGV quantity configuration scheme.

[0077] This solution achieves coordinated optimization of spatial layout and equipment configuration through a three-layer progressive framework of physical modeling, queuing analysis, and intelligent optimization. It provides systematic quantitative decision support for the low-cost and high-efficiency configuration of AGV transportation systems in cleanrooms. The specific implementation method is described below.

[0078] Figure 2 This is a flowchart illustrating a method for optimizing the dwell point configuration of AGVs in a PCB cleanroom based on a complex half-open queuing network, as shown in one embodiment of this application. Figure 2 As shown, the AGV dwell point configuration optimization method for PCB cleanrooms based on complex half-open queuing networks in this application includes the following steps:

[0079] S210, acquire the location information of multiple dwelling points and processing areas in the cleanroom, AGV handling process information, AGV kinematic data, AGV available power and AGV power consumption rate, wherein the AGV handling process information includes multiple handling links, and the location information of the dwelling points is candidate locations;

[0080] The location information of the multiple dwelling points and processing areas in the cleanroom, as well as the AGV handling process information, are as described above.

[0081] Let the battery voltage of the AGV be... (V), battery capacity is (A·h), assuming the AGV needs to be charged when the battery level is below 5%, a fully charged battery can provide... The amount of electricity, of which The unit is joule (J).

[0082] S220: Based on the location information of the multiple dwelling points and the processing area, and the AGV handling process information, a semi-open queuing network based on a single dwelling point is constructed. Based on the semi-open queuing network and AGV kinematic data, the expected service time and the coefficient of variation of the square of the expected service time of multiple handling links are calculated. Based on the semi-open queuing network, the expected service time of the multiple handling links, the available power of the AGV, and the power consumption rate of the AGV, the AGV charging probability of each dwelling point is calculated.

[0083] Figure 3 This is a schematic diagram of a single-dwelling-point AGV transportation task queuing network model in one embodiment of this application, established based on the above-described AGV transportation system operation flow. Figure 2 The single dwell point shown The job queuing network model is equipped with a number of The AGV is responsible for performing transport tasks. The delivery rate is used to determine the transportation task. Arrival at the rest stop At the synchronization station, it is matched with an idle AGV. Each handling task... The execution is divided into three steps: the AGV moves to the previous process area ( ); The AGV loads the PCBs processed in the previous process and delivers them to the next process area. ); The AGV unloads the PCB and returns to its designated dwell point. If the AGV's battery level is below the limit after returning to its resting point (…), ), and they headed to the charging point in the workshop ( ), to charge ( After charging is complete, return to the rest stop. If all AGVs at the station are busy, the transport task waits in the task queue at the synchronization station for the AGV to return to the station after completing its task.

[0084] The model satisfies the following assumptions:

[0085] (1) The workshop handling tasks arrive randomly at a certain rate, following a Poisson distribution;

[0086] (2) Each AGV at each station shall perform tasks according to the first-come, first-served (FCFS) principle, and may only perform one task at a time;

[0087] (3) AGVs can travel along fixed bidirectional paths in the workshop, so path conflicts and blockages can be ignored.

[0088] The process of calculating the charging probability of the AGV at the dwell point, the expected service time of multiple handling links, and the coefficient of variation of the square of the expected service time based on the above semi-open queuing network is as follows:

[0089] (1) Charging probability

[0090] (1-1) Obtain the allocation probability of a transport task being assigned to a dwelling point, wherein the allocation probability is a pre-allocated average probability or a weighted probability;

[0091] (1-2) Sum the expected service times of multiple target handling links to obtain the total expected time; calculate the product of the total expected time and the allocation probability to obtain the expected time for the dwell point to complete one handling task. ;

[0092] outpost The time it takes for an AGV to complete one transport task is ,but ,in, For transport tasks Assigned to the station The probability of allocation, For transport tasks Service time for AGVs to travel to the upstream process area. For transport tasks Service time for AGVs to deliver goods to the downstream processing area. For transport tasks The AGV returns from the downstream process area to its dwell point. Duration;

[0093] (1-3) Based on the power consumption rate of the AGV and the expected duration Calculate the power consumption of the station to complete one transport task. , ,in, For the index of the residence point, For AGV index;

[0094] When the AGV is running, its power consumption per second is Then the station The average power consumption of an AGV to complete one transport task is ;

[0095] (1-4) Based on the available power of the AGV and the power consumption Calculate the number of tasks that the AGV can perform. , and the number of tasks that the AGV can perform. Total order arrival rate at the station and outposts Number of AGVs configured Calculate the dwell point The probability that an AGV needs to be recharged after completing a transport task is: , .

[0096] A fully charged battery can perform an average of [number] transport tasks. Because the task orders at each rest stop are evenly distributed to the AGVs at that rest stop, The AGV executes an average of [number] times per second. For this transport task, the maximum operating time of a fully charged AGV is: .

[0097] Assuming the waiting time between each two transport tasks is equal, then the dwell point... The probability that an AGV needs to be charged after completing a transport task is:

[0098]

[0099] (2) Expected service time and coefficient of variation of expected service time for multiple handling links

[0100] (2-1) Determine the Manhattan distance for each handling process based on the location information of the multiple dwelling points and processing areas;

[0101] (2-2) Calculate the expected service time of each transport process based on the speed of the AGV and the Manhattan distance of each transport process; and calculate the squared coefficient of variation of the expected service time of each transport process.

[0102] The above describes the calculation method for each material handling process. Specifically, the material handling task process of an AGV can be divided into three parts: dwell points. Received transport task Upon request, the assigned AGV proceeds to the preceding process area for the task. Once there, the AGV loads the completed PCBs and transports them to the following process area. Upon arrival at the following process area, the AGV unloads the loaded PCBs and returns to its designated stop. Because the AGV's route is fixed, the stop point... The AGV went to carry out the transport task. Expected service time for the front-end process area for:

[0103]

[0104] in For the outpost With transport task Manhattan distance between upstream processing areas, coefficient of variation of squared service time for:

[0105]

[0106] In the formula, Indicates the second moment;

[0107] outpost The expected service time for AGVs to transport PCBs from the front-end area to the back-end area and its squared coefficient of variation for:

[0108]

[0109]

[0110] in For the task The Manhattan distance between the upstream and downstream processing areas, The time required for the AGV to load or unload PCBs. The expected service time after the AGV arrives at the downstream process area, unloads the PCBs, and returns to its designated resting point. and its squared coefficient of variation for:

[0111]

[0112]

[0113] For the task Post-processing areas and residence points The Manhattan distance between them.

[0114] Furthermore, the expected service time during the charging process and the corresponding coefficient of variation are calculated as follows:

[0115] When charging is required, the AGV travels from its rest point to the charging point. The expected service time is:

[0116]

[0117] In the formula, The Manhattan distance for the AGV from its rest point to its charging point;

[0118] For the outpost The Manhattan distance between the charging point and the charging station. The coefficient of variation of the square is:

[0119]

[0120] The charging process of the AGV at the charging point follows a uniform distribution. Therefore, the expected service time during the charging process for:

[0121]

[0122] In the formula, Indicates the range of battery capacity.

[0123] Coefficient of squared variation for:

[0124]

[0125] in .

[0126] After charging is complete, the AGV returns to its designated rest point, with an expected service time of [time missing]. for:

[0127]

[0128] In the formula, The Manhattan distance for the AGV to return to its original station.

[0129] Coefficient of squared variation for:

[0130]

[0131] S230, the half-open queuing network is solved based on the expected service time of the multiple handling links, the coefficient of variation of the square of the expected service time, and the AGV charging probability to obtain the estimated order throughput time and the average waiting time of the external order queue.

[0132] Because the charging points in the cleanroom are responsible for charging AGVs from various stations, their queuing network nodes... It is a service node that aggregates multiple arrival flows, with internal arrival flows serving as dwell points. AGVs that need charging The external arrival flow consists of AGVs that need charging at other docking points. ). Figure 4 This is a schematic diagram illustrating the equivalent arrival-dependent service node transformation for the charging service node in this application, as shown below. Figure 4 As shown, in order to solve this multi-arrival flow process, the service node for AGV charging is replaced with an arrival-dependent server (ADS). The dwell time of the AGV at the charging point is equal to the sum of the average service time in the service node and the multi-arrival flow waiting time.

[0133] For service nodes The total arrival flow is a single superimposed flow formed by the aggregation of individual arrival flows. The average arrival interval and its coefficient of variation of this total arrival flow are: and ,in Each individual arriving flow is at the service node. Being served for the same amount of time ( The service, the total flow to the node Service hours are ,in Furthermore, the busy rate of each individual arriving flow served by the service node is... Therefore The busy rate of the total service arrival flow Coefficient of variation of the squared arrival interval of the total arrival flow and the coefficient of variation of the square of the total arrival flow service time of the service node. The calculation formula is shown below.

[0134]

[0135]

[0136] In the formula, These are the weighting coefficients. The weighted coefficient of variation, The average service time for the total arrival flow. Reaching the flow weight, To reach the stream index, For the first The average coefficient of variation of the arriving streams For the first The service time of each arrival stream; among which , and , It is the reciprocal of the sum of squares of the proportions of each arriving flow, used to measure the differences between the sub-flows.

[0137] After multiple arrivals are aggregated Transformed into ADS, the total arrival flow's waiting queue can be viewed as a GI / G / m queue, and the average waiting time of the AGV is:

[0138]

[0139] Therefore, the total dwell time of the AGV at the charging point is the sum of the average waiting time and the average charging time:

[0140]

[0141] The arrival rate of the total arrival flow. The total service time of the arrival stream. The number of service nodes;

[0142] Then, the average order waiting time is calculated using approximate mean value analysis. The parameters used in the approximate mean value analysis (AMVA) method are as follows:

[0143] This refers to the sequence number of the service node in the closed-loop queuing network. ;

[0144] This represents the number of AGVs in the queuing network. ;

[0145] For service nodes The number of parallel servers;

[0146] For service nodes The first-order moment of service time;

[0147] For service nodes Service time in two phases;

[0148] For service nodes The access frequency is determined based on the fixed process flow path of the AGV handling task;

[0149] For service nodes Average time to leave during the first mission;

[0150] For the system has AGV service node There are The probability of the platform;

[0151] For when the system has The probability that all servers are busy when there are AGVs running;

[0152] For when the system has When using AGVs, the service node The length of the queue at that location;

[0153] This represents the number of orders waiting in the external order queue.

[0154] This represents the average waiting time for orders in the external order queue.

[0155] The iterative solution steps are as follows.

[0156] a. Initialization , , .

[0157] b. Preprocessing. For ,

[0158]

[0159] c. Iterative solution. For ,

[0160] c.1. For ,

[0161]

[0162] c.2.

[0163]

[0164] c.3. Regarding as well as ,

[0165]

[0166] c.4. For ,like ,but ,otherwise

[0167]

[0168] c.5. For ,

[0169]

[0170] c.6. For ,like ,but ,otherwise

[0171]

[0172] Based on this method, the closed-loop queuing network is equivalent to a load-dependent server (LDS) node, and the configuration of the LDS can be solved. The external task waiting time and other performance indicators of the AGV system are used to calculate the order throughput time.

[0173]

[0174]

[0175] in , For the order arrival rate of the queuing network, For the outpost The queuing network, excluding the concurrency unit, transforms into a closed-loop network containing... Throughput of AGVs:

[0176]

[0177]

[0178] Then based on Order throughput time estimation is performed. Order throughput time refers to the complete time cycle from when a PCB enters the cleanroom, through all processing steps, until it leaves the cleanroom. Affected by the differences in the PCB processing paths within the cleanroom, order throughput time can be represented as the weighted sum of the completion time of each path and its corresponding path probability. The completion time of a single path mainly consists of two parts: the processing time in the process area and the transportation time of the AGV transportation system. The AGV transportation time is further broken down into the average waiting time of the handling task in the waiting point queue and the actual AGV handling time. For each PCB AGV handling operation, the average waiting time of the corresponding handling task in the waiting point queue must be calculated. Therefore, order throughput time can be expressed as:

[0179]

[0180] in For path The probability, For path No. Processing time of the process For path No. The average waiting time of the transport task in the depot queue after the process is completed. For path No. The actual time taken for the handling task after the process is completed (the sum of the service times of the three handling processes).

[0181] S240, based on the estimated order throughput time, the average waiting time of the external order queue, the pre-configured production plan and process parameters, an integer nonlinear programming model is constructed, and the integer nonlinear programming model is solved to obtain the location of the dwell point and the number of AGVs configured at the dwell point. The integer nonlinear programming model includes an objective function with the goal of minimizing the overall cost and various physical constraints.

[0182] The mathematical expression for the objective function of the integer nonlinear programming model is:

[0183]

[0184] In the formula, Total operating costs For the station number, For the outpost The number of AGVs, The cost per unit time for AGV usage. For indicator functions, For expected order throughput time, The standard production delivery date stipulated by the company. For workshop material arrival rate;

[0185] The mathematical expressions for the multiple physical constraints of the integer nonlinear programming model are as follows:

[0186]

[0187]

[0188]

[0189]

[0190]

[0191] In the formula, It is a set of positive integers. This is the set of available coordinate points in the workshop. and For two different outposts, To assemble at the base, For the outpost The closed-loop network of the queuing network after removing the concurrency includes The throughput of the AGV, For the outpost The system stability margin, For the outpost Order delivery rate.

[0192] Objective function Part 1 The second part is the sum of the configuration costs per unit time for AGVs at all resident locations. The costs incurred due to delays in workshop delivery, including The arrival rate of PCB materials in the workshop. For 0-1 variables, when hour Otherwise, it is 0.

[0193] Ensure that the number of AGVs at each station is a positive integer.

[0194] Ensure the dwell point is located at available coordinates in the workshop. The set of workshop coordinate points after removing the points occupied by the process area and the charging points.

[0195] To ensure that the various outposts do not overlap.

[0196] and It is a system stability constraint. For the outpost The queuing network, excluding the concurrency unit, transforms into a closed-loop network containing... The throughput of an AGV. In a stable system, the system's maximum throughput is greater than zero, and the material arrival rate cannot exceed the system's maximum throughput, i.e. ,therefore .

[0197] This application proposes an improved genetic algorithm to solve the above mathematical model. Figure 5 This is a schematic diagram of chromosome encoding in one embodiment of this application. Figure 5 This refers to the chromosome encoding method used in the genetic algorithm. To effectively meet various constraints, after individual initialization, crossover, and mutation operations, the coordinates of each individual are verified by a repair operator: if a point falls into the prohibited point set or overlaps with a selected point, the point is randomly regenerated until the constraints are met; for the AGV quantity encoding, boundary pruning is used to ensure that its value is within the feasible region.

[0198] The selection operator employs a binary tournament mechanism: each time, two individuals are randomly selected, and the one with the better fitness is chosen to enter the next generation. This process is repeated until the population size remains constant. The crossover operator uses simulated binary crossover, and the mutation operator uses local perturbation mutation. After both crossover and mutation operations, boundary constraint verification and repair operations are performed to maintain population diversity. To avoid losing excellent solutions, the algorithm introduces an elite retention strategy, directly replacing the worst individual in the new generation with the best individual from the previous generation, ensuring the algorithm's convergence performance.

[0199] After each generation of evolution, a hill-climbing neighborhood search is performed on the current best individual. If a newly generated individual is better than the original best individual, it replaces the current best solution and replaces the worst individual in the population. This strategy can effectively improve the convergence speed and search accuracy of the algorithm without increasing the population size.

[0200] This application presents an optimization method for AGV dwell point configuration in a PCB cleanroom based on a complex semi-open queuing network. By constructing a semi-open queuing network and introducing approximate mean analysis for solution, it accurately characterizes the random competition and congestion transmission relationship between the external order queue and the internal AGV closed loop under limited AGV resources. It can precisely quantify the average waiting time of orders under different dwell point layouts and AGV quantity combinations, overcoming the shortcomings of traditional methods in handling system randomness. The method equivalently aggregates the arrival flow of multi-dwelling charging vehicles at centralized charging points and introduces a GI / G / m queuing model to calculate the average queuing waiting time and total dwell time of AGVs at charging nodes. This allows the queuing network solution process to effectively account for the impact of AGV endurance constraints on handling efficiency, avoiding overly optimistic configuration schemes due to neglecting charging congestion. An integer nonlinear programming model is constructed with the objective of minimizing the weighted sum of AGV configuration cost and order delay cost. An improved genetic algorithm with embedded hybrid chromosome encoding, constraint repair operators, and hill-climbing local search is used for solution, achieving joint and collaborative optimization of dwell point spatial location and AGV configuration quantity. This method significantly reduces total operating costs while providing a systematic quantitative decision-making tool for the scientific configuration of AGV systems in cleanrooms, and has practical engineering value.

[0201] like Figure 6 As shown, this application also provides a PCB cleanroom AGV dwell point configuration optimization system based on a complex half-open queuing network, including:

[0202] The acquisition module is used to acquire the location information of multiple dwelling points and processing areas in the cleanroom, AGV handling process information, AGV kinematic data, AGV available power and AGV power consumption rate. The AGV handling process information includes multiple handling links, and the location information of the dwelling points is candidate locations.

[0203] The relevant parameter calculation module is used to calculate the expected service time and the coefficient of variation of the square of the expected service time of multiple handling links based on the location information of the multiple dwelling points and the processing area, the AGV handling process information, and the AGV kinematic data; and to calculate the AGV charging probability of each dwelling point based on the expected service time of the multiple handling links, the available power of the AGV, and the AGV power consumption rate.

[0204] The half-open network solving module is used to construct a half-open queuing network based on a single dwell point, and solve the half-open queuing network based on the expected service time of the multiple handling links, the coefficient of variation of the square of the expected service time, and the charging probability of the AGV to obtain the estimated order throughput time and the average waiting time of the external order queue.

[0205] The dwell point configuration module is used to construct an integer nonlinear programming model based on the estimated order throughput time, the average waiting time of the external order queue, the pre-configured production plan, and process parameters, and solve the integer nonlinear programming model to obtain the location of the dwell point and the number of AGVs configured at the dwell point. The integer nonlinear programming model includes an objective function with the goal of minimizing the overall cost and various physical constraints.

[0206] This application presents a PCB cleanroom AGV dwell point configuration optimization system based on a complex semi-open queuing network. By constructing a semi-open queuing network and introducing approximate mean analysis for solution, it accurately portrays the random competition and congestion transmission relationship between the external order queue and the internal AGV closed loop under limited AGV resources. It can accurately quantify the average waiting time of orders under different dwell point layouts and AGV quantity combinations, overcoming the shortcomings of traditional methods in handling system randomness. The system equivalently aggregates the arrival flow of multi-dwelling charging vehicles at centralized charging points and introduces a GI / G / m queuing model to calculate the average queuing waiting time and total dwell time of AGVs at charging nodes. This allows the queuing network solution process to effectively account for the impact of AGV endurance constraints on handling efficiency, avoiding overly optimistic configuration schemes due to neglecting charging congestion. An integer nonlinear programming model is constructed with the objective of minimizing the weighted sum of AGV configuration cost and order delay cost. An improved genetic algorithm with embedded hybrid chromosome encoding, constraint repair operators, and hill-climbing local search is used for solution, achieving joint and collaborative optimization of dwell point spatial location and AGV configuration quantity. This method significantly reduces total operating costs while providing a systematic quantitative decision-making tool for the scientific configuration of AGV systems in cleanrooms, and has practical engineering value.

Claims

1. A method for optimizing the dwell point configuration of AGVs in a PCB cleanroom based on a complex semi-open queuing network, characterized in that, include: The system acquires location information of multiple dwelling points and processing areas in the cleanroom, AGV handling process information, AGV kinematic data, AGV available power, and AGV power consumption rate. The AGV handling process information includes multiple handling stages, and the location information of the dwelling points are candidate locations. Based on the location information of the multiple dwelling points and processing areas, and the AGV handling process information, a semi-open queuing network based on a single dwelling point is constructed. Based on the semi-open queuing network and AGV kinematic data, the expected service time and the coefficient of variation of the square of the expected service time of multiple handling links are calculated. Based on the semi-open queuing network, the expected service time of the multiple handling links, the available power of the AGV, and the power consumption rate of the AGV, the AGV charging probability of each dwelling point is calculated. The half-open queuing network is solved based on the expected service time of the multiple handling links, the coefficient of variation of the square of the expected service time, and the AGV charging probability to obtain the estimated order throughput time and the average waiting time of the external order queue. Based on the estimated order throughput time, the average waiting time of the external order queue, the pre-configured production plan, and process parameters, an integer nonlinear programming model is constructed, and the integer nonlinear programming model is solved to obtain the location of the dwell point and the number of AGVs configured at the dwell point. The integer nonlinear programming model includes an objective function aimed at minimizing the overall cost and various physical constraints.

2. The method for optimizing the AGV dwell point configuration in a PCB cleanroom based on a complex semi-open queuing network according to claim 1, characterized in that, The rules of the half-open queuing network include: Corresponding to a single station outpost The quantity is AGV; outpost Responsible for carrying out transport tasks The delivery rate of the transport task Arrival at the rest stop Matching with idle AGVs at the synchronization station; Each transport task The execution is divided into three steps: the AGV goes to the previous process area; the AGV loads the PCB processed in the previous process and sends it to the next process area; the AGV unloads the PCB and returns to its designated residence point. If the AGV's battery level drops below the limit after returning to its dwell point, it will proceed to the charging point in the workshop to recharge, and then return to its dwell point after charging is complete. If all AGVs at the station are busy, the transport task will wait in the task queue at the synchronization station for the AGV to return to the station after completing the task. The workshop handling tasks arrive randomly at a preset rate, following a Poisson distribution. Each AGV at its designated location will perform tasks on a first-come, first-served basis, and can only perform one task at a time. AGVs can travel along fixed bidirectional paths in the workshop.

3. The method for optimizing the configuration of AGV dwell points in a PCB cleanroom based on a complex semi-open queuing network according to claim 2, characterized in that, Based on the semi-open queuing network and AGV kinematic data, the expected service time and the coefficient of variation of the square of the expected service time for multiple handling stages are calculated, including: The Manhattan distance for each handling process is determined based on the location information of the multiple rest points and processing areas. The expected service time for each transport process is calculated based on the AGV speed and the Manhattan distance of each transport process; and the coefficient of variation of the square of the expected service time for each transport process is calculated.

4. The method for optimizing the AGV dwell point configuration in a PCB cleanroom based on a complex semi-open queuing network according to claim 2, characterized in that, Based on the semi-open queuing network, the expected service time of the multiple handling stages, the available power of the AGV, and the power consumption rate of the AGV, the AGV charging probability at each dwell point is calculated, including: Obtain the allocation probability of a transport task being assigned to a dwelling point, wherein the allocation probability is a pre-allocated average probability or a weighted probability; The expected service times of multiple target handling stages are summed to obtain the total expected time; the product of the total expected time and the allocation probability is calculated to obtain the expected time for the dwell point to complete one handling task. ; Based on the AGV power consumption rate and the expected duration Calculate the power consumption of the station to complete one transport task. , ,in, For the index of the residence point, For AGV index; Based on the available power of the AGV and the power consumption Calculate the number of tasks that the AGV can perform. , and the number of tasks that the AGV can perform. Total order arrival rate at the station and outposts Number of AGVs configured Calculate the dwell point The probability that an AGV needs to be recharged after completing a transport task is: , .

5. The method for optimizing the AGV dwell point configuration in a PCB cleanroom based on a complex semi-open queuing network according to claim 1, characterized in that, The semi-open queuing network is solved based on the expected service time of the multiple handling stages, the coefficient of variation of the square of the expected service time, and the AGV charging probability to obtain the estimated order throughput time and the average waiting time of the external order queue, including: Identify multiple independent arrival flows from multiple dwelling points to a charging point, and aggregate the multiple independent arrival flows into a single equivalent total arrival flow, wherein the total arrival flow flows into the charging service node; Calculate the coefficient of variation of the squared arrival time interval of the total arrival flow. and the coefficient of variation of the square of the total arrival flow service time of the service node. Wherein, the coefficient of squared variation and the squared coefficient of variation The mathematical expression is: In the formula, These are the weighting coefficients. The weighted coefficient of variation, The average service time for the total arrival flow. Reaching the flow weight, To reach the stream index, For the first The average coefficient of variation of the arriving streams For the first Service time for each arrival stream; Based on the squared coefficient of variation and the squared coefficient of variation Calculate the average waiting time of the AGV and the total dwell time of the AGV at the charging point The average waiting time of the AGV and the total dwell time of the AGV at the charging point The mathematical expression is: In the formula, The arrival rate of the total arrival flow. The total service time for the arrival stream. The number of service nodes; Based on the expected service time of the multiple handling stages, the coefficient of variation of the square of the expected service time, the charging probability of the AGV, and the average waiting time of the AGV. and the total dwell time of the AGV at the charging point Calculate the average waiting time of the external order queue ; Based on the average waiting time of the external order queue Calculate the estimated order throughput time .

6. The method for optimizing the AGV dwell point configuration in a PCB cleanroom based on a complex semi-open queuing network according to claim 5, characterized in that, The estimated order throughput time The mathematical expression is: In the formula, For path The probability, For path No. Processing time of the process, For path No. The average waiting time of the transport task in the depot queue after the process is completed. For path No. The actual time spent on the handling tasks after the process is completed.

7. The method for optimizing the AGV dwell point configuration in a PCB cleanroom based on a complex semi-open queuing network according to claim 6, characterized in that, The average waiting time Based on the expected service time of the multiple handling stages, the coefficient of variation of the square of the expected service time, the charging probability of the AGV, and the average waiting time of the AGV. and the total dwell time of the AGV at the charging point The approximate mean was obtained through analysis.

8. The method for optimizing the AGV dwell point configuration in a PCB cleanroom based on a complex semi-open queuing network according to claim 1, characterized in that, The mathematical expression for the objective function of the integer nonlinear programming model is: In the formula, Total operating costs For the station number, For the outpost The number of AGVs, The cost per unit time for AGV usage. For indicator functions, For expected order throughput time, The standard production delivery date stipulated by the company. For workshop material arrival rate; The mathematical expressions for the multiple physical constraints of the integer nonlinear programming model are as follows: In the formula, It is a set of positive integers. This is the set of available coordinate points in the workshop. and For two different outposts, To assemble at the base, For the outpost The closed-loop network of the queuing network after removing the concurrency includes The throughput of the AGV, For the outpost The system stability margin, For the outpost Order delivery rate.

9. The method for optimizing the configuration of AGV dwell points in a PCB cleanroom based on a complex semi-open queuing network according to claim 8, characterized in that, Solving the integer nonlinear programming model yields the locations of the dwell points and the number of AGVs configured at each dwell point, including: Chromosome coding is constructed based on the location of the dwell point and the number of AGVs configured at the dwell point; An improved genetic algorithm is executed based on the chromosome encoding to obtain the location of the dwelling point and the number of AGVs configured at the dwelling point, thus constructing the optimal solution for the chromosome encoding. In the improved genetic algorithm, two individuals are randomly selected each time, and the one with better fitness is selected to enter the next generation. This process is repeated until the population size remains unchanged. The crossover operator uses simulated binary crossover, and the mutation operator uses local perturbation mutation. After the crossover and mutation operations, boundary constraint verification and repair operations are performed, and the best individual from the previous generation directly replaces the worst individual in the new generation. After each generation of evolution is completed, a hill-climbing neighborhood search is performed on the current best individual. If the newly generated individual is better than the original best individual, the current best solution is replaced, and the worst individual in the population is replaced by this individual.

10. A PCB cleanroom AGV dwell point configuration optimization system based on complex semi-open queuing networks, characterized in that, include: The acquisition module is used to acquire the location information of multiple dwelling points and processing areas in the cleanroom, AGV handling process information, AGV kinematic data, AGV available power and AGV power consumption rate. The AGV handling process information includes multiple handling links, and the location information of the dwelling points is candidate locations. The relevant parameter calculation module is used to calculate the expected service time and the coefficient of variation of the square of the expected service time of multiple handling links based on the location information of the multiple dwelling points and the processing area, the AGV handling process information, and the AGV kinematic data; and to calculate the AGV charging probability of each dwelling point based on the expected service time of the multiple handling links, the available power of the AGV, and the AGV power consumption rate. The half-open network solving module is used to construct a half-open queuing network based on a single dwell point, and solve the half-open queuing network based on the expected service time of the multiple handling links, the coefficient of variation of the square of the expected service time, and the charging probability of the AGV to obtain the estimated order throughput time and the average waiting time of the external order queue. The dwell point configuration module is used to construct an integer nonlinear programming model based on the estimated order throughput time, the average waiting time of the external order queue, the pre-configured production plan, and process parameters, and solve the integer nonlinear programming model to obtain the location of the dwell point and the number of AGVs configured at the dwell point. The integer nonlinear programming model includes an objective function with the goal of minimizing the overall cost and various physical constraints.

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