Linear reciprocating multi-RGV collaborative operation warehouse-in and warehouse-out scheduling method

Abstract

The invention discloses a linear reciprocating multi-RGV collaborative operation warehouse-in and warehouse-out scheduling method, and relates to the technical field of RGV scheduling control. Historical warehouse-in and warehouse-out task data of the RGV in the system are collected and sorted, the linear track is rasterized, and the serial number of the linear track, warehouse-in and warehouse-out platforms and related data of the RGV are extracted; arranging buffer area positions which can be selected on a linear track in the system, determining the sequence number of the current buffer area position, and carrying out task allocation on the RGV; taking the maximum time consumed by minimizing the RGV to complete the task as a target function, and establishing an RGV warehouse-in and warehouse-out scheduling mathematical model; and solving the buffer area position and the optimal time of task execution of the RGV through a genetic algorithm. The buffer area is arranged on the linear track to avoid RGV collision, the total time for the RGV to complete the task is minimized by optimizing the position of the buffer area, an intelligent algorithm is adopted to solve an RGV warehouse-in and warehouse-out operation scheduling scheme, and the operation efficiency and the adaptability and flexibility of the system are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of RGV scheduling control, and specifically to an inbound and outbound scheduling method for linear reciprocating multi-RGV collaborative operation. Background Art

[0002] The linear reciprocating RGV inbound and outbound scheduling system is divided into a single RGV mode and a multi-RGV collaborative operation mode according to different operation modes. With the continuous improvement of the requirements for efficiency and safety in the logistics industry, the traditional single RGV mode can no longer meet the growing logistics task demands, while the multi-RGV collaborative operation mode increases the risk of vehicle collisions. However, the existing system lacks the ability to quickly respond and adjust routes in case of emergencies or task changes, reducing the adaptability of the system. Therefore, there is an urgent need to design an inbound and outbound scheduling method for linear reciprocating multi-RGV collaborative operation to adapt to the changing task demands and complex working environments. Summary of the Invention

[0003] To solve the deficiencies in the background art, the present invention provides an inbound and outbound scheduling method for linear reciprocating multi-RGV collaborative operation, which avoids RGV collisions by setting a buffer zone on the linear track, minimizes the total time for RGVs to complete tasks by optimizing the buffer zone position, and uses an intelligent algorithm to solve the RGV inbound and outbound operation scheduling scheme, improving the operation efficiency, as well as the adaptability and flexibility of the system.

[0004] To achieve the above object, the present invention adopts the following technical solutions: An inbound and outbound scheduling method for linear reciprocating multi-RGV collaborative operation, comprising the following steps:

[0005] Step 1: Collect and organize the historical inbound and outbound task data of RGVs in the system, including the set N = {1, 2,..., n} of RGVs, the task content M = {1, 2,..., m}, record each task = [task number, starting coordinate, ending coordinate, task type], the task type being an outbound task or an inbound task, rasterize the linear track, and extract the set L = {0, 1, 2,..., l} of linear track serial numbers, the set S chu of outbound platforms, the set S ru of inbound platforms, and the average speed v of the RGVs;

[0006] Step 2: Organize the buffer positions that can be selected on the straight track, determine the current buffer position serial number XP. The buffer divides the straight track into two regions, A and B. Define the RGV in region A as RGV1 and the RGV in region B as RGV2. For the same-region tasks where both the task start and end points are in region A or B, assign the tasks to RGV1 or RGV2 in that region to complete independently. For the cross-region tasks where the task start and end points are in regions A and B respectively, assign the tasks to RGV1 and RGV2 to complete collaboratively, and mark the task type according to the positions of the task start and end points to determine whether the assigned task is an outbound task or an inbound task;

[0007] Step 3: Taking the minimization of the maximum time consumed by the RGV to complete the tasks as the objective function, divide the total time to complete the tasks into the adjustment time required for the RGV to move from the current position to the task start point, the transportation and loading / unloading time required to execute the tasks, and the waiting time required beside the buffer when executing cross-region tasks, and establish the RGV inbound and outbound scheduling mathematical model;

[0008] Step 4: Solve the buffer positions and optimal time for the RGV to execute tasks through the genetic algorithm.

[0009] Further, when selecting the buffer position in Step 2, calculate the serial number x of the middle position of the straight track according to the total length of the straight track, and the buffer position serial number

[0010] Further, the RGV inbound and outbound scheduling mathematical model in Step 3 is as follows:

[0011] Objective function:

[0012] min(max{T j ,j = 1, 2})

[0013] T j = T tj + T fj + T wj

[0014]

[0015]

[0016] In the formula, T j represents the total time for the j-th RGV to complete the assigned tasks, T tj represents the adjustment time required for the j-th RGV to move from the current position to the task start point, T fj represents the transportation and loading / unloading time required for the j-th RGV to execute the tasks, T wj represents the waiting time required for the j-th RGV beside the buffer when executing cross-region tasks, R1i and R2 i are both binary variables, representing whether the i-th task executed by RGV1 and RGV2 is a same-region task or a cross-region task respectively. If R1 i and R2 i take the value of 0, it means a same-region task. If R1 i and R2 i take the value of 1, it means a cross-region task. X ij is a binary variable. If the j-th RGV executes the i-th task, it takes the value of 1; otherwise, it takes the value of 0. Y iu is a binary variable. If the i-th task is executed immediately after the u-th task, it takes the value of 1; otherwise, it takes the value of 0. XE uj represents the serial number of the end position where the j-th RGV executes the u-th task. XS ij represents the serial number of the start position where the j-th RGV executes the i-th task. XE ij represents the serial number of the end position where the j-th RGV executes the i-th task. d represents the length of a unit grid on the straight track, and T z represents the time for loading and unloading goods;

[0017] Constraint conditions:

[0018]

[0019]

[0020] In the formula, TS uj represents the start time of the u-th task, and TE ij represents the end time of the i-th task.

[0021] Furthermore, the specific steps of step four include:

[0022] 4.1 Encoding method

[0023] Determine the RGV, task start point, and task end point, and generate a chromosome using the real number encoding method. The length of the chromosome is equal to the total number of tasks m, and it consists of a digital sequence randomly generated from 1 to m without repetition. Each number corresponds to a task number, and the digital sequence represents the task execution order;

[0024] 4.2 Population initialization

[0025] Create an initial population by randomly generating multiple chromosomes through encoding;

[0026] 4.3 Calculation of task completion time

[0027] Determine whether the current task is a same-region task. If the current task is a same-region task, first calculate the adjustment time of RGV1 or RGV2 for executing the task from the current position to the task start point, and then calculate the transportation and loading / unloading time of RGV1 or RGV2 for executing the task from the task start point to the task end point. The total time for completing the task is obtained by summation. If the current task is a cross-region task, first calculate the adjustment time of RGV1 or RGV2 in the region where the task start point is located from the current position to the task start point, and calculate the transportation and loading / unloading time of this RGV1 or RGV2 from the task start point to the buffer. Then calculate the adjustment time of RGV2 or RGV1 in the region where the task end point is located from the current position to the buffer, and calculate the transportation and loading / unloading time of this RGV2 or RGV1 from the buffer to the task end point. In addition, according to the arrival times of RGV1 and RGV2 at the buffer, calculate the waiting time required beside the buffer. The total time for completing the task is obtained by summation. Finally, determine whether all tasks are completed. If so, proceed to step 4.4. If not, repeat step 4.3;

[0028] 4.4. Fitness function solution

[0029] For each chromosome in the population, calculate the maximum value Z of the times for RGV1 and RGV2 to complete all their respective tasks through the fitness function, and set the initial task maximum time threshold Z for iteration max , when Z is greater than Z during the iteration max then update Z max to Z, and calculate the fitness of each chromosome, which is expressed as:

[0030]

[0031] 4.5. Binary tournament selection

[0032] Each time, randomly select two pairs of chromosomes from the population for comparison, and select the chromosome with higher fitness to enter the next-generation population;

[0033] 4.6. Crossover

[0034] Randomly select two crossover points in the parental chromosomes respectively, and copy the two crossover points and the digital sequence between them to the corresponding offspring. For the regions outside the two crossover points, fill them in according to the order of the other parent. If the number has already appeared in the sequence between the crossover points, skip this number and continue to fill the next number. If the number has not appeared, directly fill this number;

[0035] 4.7. Mutation

[0036] Determine whether each chromosome mutates according to the set mutation probability. If a chromosome mutates, randomly select two numbers from the chromosome and swap their positions to change the original task order. If a chromosome does not mutate, keep the original order. Each mutated chromosome is added to the new population until the number of chromosomes reaches the maximum population size.

[0037] 4.8. Set the maximum number of iterations

[0038] Generate a new population through iteration and determine whether the set maximum number of iterations is reached. If not, use the current population to continue executing step 4.3. If so, stop and output the scheduling result and total time of the RGV under this buffer.

[0039] Compared with the prior art, the beneficial effects of the present invention are as follows: On the basis of considering the task order, the method of the present invention sets a buffer area on the linear track, enabling each RGV to operate independently within its respective area to avoid collisions, and minimizing the total time for the RGV to complete tasks by optimizing the buffer position, improving the inbound and outbound operation efficiency. By determining the buffer area for both obstacle avoidance and scheduling, and using an intelligent algorithm to solve the RGV inbound and outbound operation scheduling scheme, it is easier to adapt to different operating conditions and environmental changes, thereby improving the adaptability and flexibility of the system. Compared with the traditional linear reciprocating RGV system, it can improve the conveying capacity of the system without increasing the system complexity and meet larger-scale inbound and outbound requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 is a flowchart of the method of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0041] The following will clearly and completely describe the technical solutions in the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0042] As Figure 1 shown, an inbound and outbound scheduling method for collaborative operation of multiple linear reciprocating RGVs includes the following steps:

[0043] Step 1: Collect and organize the historical inbound and outbound task data of the RGVs in the system, rasterize the linear track, and extract the linear track serial numbers, inbound and outbound platforms, and RGV-related data. Specifically:

[0044] 1.1. Collect the historical order data within the system and organize the task content of the RGV. Let \(N = \{1, 2, \ldots, n\}\) represent the set of all RGVs, where \(n\) is the total number of RGV vehicles, and let \(M = \{1, 2, \ldots, m\}\) represent the task content, where \(m\) is the total number of tasks. Denote each task as \([task\ number, starting\ coordinate, ending\ coordinate, task\ type]\), and the task type is either an outbound task or an inbound task. Generate an Excel data table for the task content \(M\).

[0045] 1.2. Perform rasterization processing on the straight track, and extract the set of straight track serial numbers \(L=\{0, 1, 2, \ldots, l\}\), the set of outbound platforms \(S\) chu , the set of inbound platforms \(S\) ru and the average speed \(v\) of the RGV.

[0046] Step 2: Organize the buffer positions that can be selected on the straight track in the system, determine the current buffer position serial number \(XP\), and allocate tasks to the RGVs. Specifically:

[0047] 2.1. The buffer divides the straight track into two regions, \(A\) and \(B\). Define the RGVs in region \(A\) as \(RGV1\), and the RGVs in region \(B\) as \(RGV2\). Then the operating region of \(RGV1\) on the straight track is \([0, XP)\), and the operating region of \(RGV2\) on the straight track is \((XP, l]\), so that \(RGV1\) and \(RGV2\) operate in their respective fixed regions \(A\) and \(B\) to avoid collisions.

[0048] 2.2. Calculate the serial number of the middle position of the straight track based on the total length of the straight track, and set it as \(x\). To prevent uneven tasks, the buffer position serial number

[0049] 2.3. Allocate tasks to the RGVs in the corresponding region according to the region where the task starts. For tasks within the same region, that is, tasks whose starting and ending points are both in region \(A\) or \(B\), allocate the tasks to \(RGV1\) or \(RGV2\) within that region to complete independently; for cross-region tasks, that is, tasks whose starting and ending points are in regions \(A\) and \(B\) respectively, allocate the tasks to \(RGV1\) and \(RGV2\) to complete collaboratively. If the task starting point is in region \(A\) or \(B\), and the task ending point is in region \(B\) or \(A\), first, \(RGV1\) or \(RGV2\) loads the goods at the task starting point and transports them to the buffer, and then \(RGV2\) or \(RGV1\) transports the goods from the buffer to the task ending point and unloads them. In addition, make a type mark for the task according to the positions of the task starting and ending points to determine whether the assigned task is an outbound task or an inbound task.

[0050] Step 3: Take minimizing the maximum time consumed by the RGV to complete the tasks as the objective function, and establish a mathematical model for RGV inbound and outbound scheduling. Specifically:

[0051] 3.1. Design the objective function. Divide the total time to complete the task into the adjustment time required for the RGV to move from the current position to the starting point of the task, the transportation and loading / unloading time required to execute the task, and the waiting time required beside the buffer when performing cross-region tasks, thereby improving the transparency and accuracy of the measurement of each time component. The objective function is expressed as follows:

[0052] min(max{T j , j = 1, 2})

[0053] T j = T tj + T fj + T wj

[0054] In the formula, T j represents the total time for the j-th RGV to complete the assigned task, T tj represents the adjustment time required for the j-th RGV to move from the current position to the starting point of the task, T fj represents the transportation and loading / unloading time required for the j-th RGV to execute the task, T wj represents the waiting time required for the j-th RGV beside the buffer when performing cross-region tasks;

[0055] 3.2. Calculate the adjustment time between RGV1 and RGV2 when moving from the completion of the u-th task to the starting point of the i-th task respectively. The calculation formula is as follows:

[0056]

[0057] In the formula, R1 i and R2 i are both binary variables, representing whether the i-th task executed by RGV1 and RGV2 is a same-region task or a cross-region task respectively. If the values of R1 i and R2 i are 0, it means it is a same-region task. If the values of R1 i and R2 i are 1, it means it is a cross-region task. X ij is a binary variable, which takes the value of 1 if the j-th RGV executes the i-th task, and 0 otherwise. Y iu is a binary variable, which takes the value of 1 if the i-th task is executed immediately after the u-th task, and 0 otherwise. XE uj represents the serial number of the end position of the j-th RGV executing the u-th task, XS ij represents the serial number of the starting position of the j-th RGV executing the i-th task, and d represents the length of a unit grid on the straight track;

[0058] 3.3. Calculate the transportation and loading / unloading times of RGV1 and RGV2 respectively from the task starting point to the task ending point when executing the \(i\)th task. The calculation formula is as follows:

[0059]

[0060] In the formula, \(X_{E}\) ij represents the serial number of the ending position of the \(j\)th RGV when executing the \(i\)th task, and \(T\) z represents the time for loading and unloading goods;

[0061] 3.4. Set the constraint conditions, including:

[0062] To ensure that there are tasks in the same area that need to be executed by RGV1 and RGV2, the condition to be satisfied is:

[0063]

[0064] To ensure that there are cross - area tasks that need to be executed by RGV1 and RGV2, the condition to be satisfied is:

[0065]

[0066] To ensure that all tasks are completed, the condition to be satisfied is:

[0067]

[0068] To ensure that the same RGV does not start another task before completing one task, the condition to be satisfied is:

[0069]

[0070] In the formula, \(T_{S}\) uj represents the start time of the \(u\)th task, and \(T_{E}\) ij represents the end time of the \(i\)th task.

[0071] Step 4: Solve the buffer positions and optimal times for the RGV to execute tasks through the genetic algorithm. Specifically:

[0072] 4.1. Encoding method

[0073] Determine the RGV, task starting point, and task ending point, and use the real - number encoding method to generate chromosomes. The length of the chromosome is equal to the total number of tasks \(m\), and it consists of a digital sequence of randomly generated and non - repeating numbers from 1 to \(m\). Each number corresponds to a task number, and the digital sequence represents the task execution order;

[0074] 4.2. Population initialization

[0075] Create an initial population by randomly generating multiple chromosomes through encoding;

[0076] 4.3 Calculation of Task Completion Time

[0077] Determine whether the current task is a same-region task. If the current task is a same-region task, first calculate the adjustment time of RGV1 or RGV2 for executing the task from the current position to the task start point, and then calculate the transportation and loading / unloading time of RGV1 or RGV2 for executing the task from the task start point to the task end point. The total time for completing the task is obtained by summation. If the current task is a cross-region task, first calculate the adjustment time of RGV1 or RGV2 within the region where the task start point is located from the current position to the task start point, and calculate the transportation and loading / unloading time of this RGV1 or RGV2 from the task start point to the buffer. Then calculate the adjustment time of RGV2 or RGV1 within the region where the task end point is located from the current position to the buffer, and calculate the transportation and loading / unloading time of this RGV2 or RGV1 from the buffer to the task end point. In addition, according to the arrival times of RGV1 and RGV2 at the buffer, calculate the waiting time required beside the buffer. The total time for completing the task is obtained by summation. Finally, determine whether all tasks are completed. If so, proceed to step 4.4; if not, repeat step 4.3;

[0078] 4.4 Solution of Fitness Function

[0079] For each chromosome in the population, calculate the maximum value Z among the times for RGV1 and RGV2 to complete all their respective tasks through the fitness function, and set the initial task maximum time threshold Z for iteration max When Z is greater than Z during the iteration process max update Z max to Z, and calculate the fitness of each chromosome, which is expressed as:

[0080]

[0081] 4.5 Binary Tournament Selection

[0082] Achieve the goal of survival of the fittest by directly comparing chromosomes, so as to guide the population to evolve in a better direction. Each time, randomly select two paired chromosomes from the population for comparison, and select the chromosome with higher fitness to enter the next-generation population. Enhance the diversity of the population through random sampling to prevent the algorithm from prematurely falling into local optimality during the search process, thereby maintaining the exploration ability for the global optimal solution;

[0083] 4.6 Crossover

[0084] Randomly select two crossover points in the parental chromosome respectively, and copy the two crossover points and the digital sequence between them to the corresponding offspring. For the regions outside the two crossover points, fill them in according to the order of the other parent. If the number has already appeared in the sequence between the crossover points, skip this number and continue to fill the next number. If the number has not appeared, directly fill this number;

[0085] 4.7. Mutation

[0086] Judge whether each chromosome undergoes mutation according to the set mutation probability. If a chromosome undergoes mutation, randomly select two numbers from the chromosome and exchange their positions to change the original task order; if a chromosome does not undergo mutation, keep the original order; each mutated chromosome is added to the new population until the number of chromosomes reaches the maximum population number;

[0087] 4.8. Set the maximum number of iterations

[0088] Generate a new population through iteration, and judge whether the set maximum number of iterations is reached. If not, use the current population to continue to execute step 4.3. If so, stop and output the scheduling result and total time of the RGV under this buffer.

[0089] Implement the above genetic algorithm using programming software (such as MATLAB, Python), input data such as RGV, the coordinates of the inbound and outbound platforms of the linear track, and task orders, and solve the optimal time and buffer position for the RGV to complete the tasks.

[0090] For those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and can be implemented in other specific forms without departing from the spirit or basic characteristics of the present invention. Therefore, in any aspect, the embodiments should be regarded as exemplary and non-restrictive. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, all changes falling within the meaning and scope of the equivalent conditions of the claims are intended to be included in the present invention. Any reference signs in the claims should not be regarded as limiting the claims involved.

[0091] In addition, it should be understood that although this specification is described according to the embodiments, not every embodiment only contains an independent technical solution. This narrative way of the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for dispatching warehouse in and out of a linear reciprocating multi-RGV collaborative operation, characterized by: The following steps are involved: Step 1: Collect and organize the historical in-and-out task data of RGVs in the system, including the set of RGVs N = {1,2,...,n}, the task content M = {1,2,...,m}, record each task = [task number, starting point coordinates, end point coordinates, task type], the task type is out-of-stock task or in-stock task, and rasterize the linear track to extract the linear track sequence number set L = {0,1,2,...,l}, the out-of-stock platform set S chu , storage platform collection S ru and RGV average velocity v; Step 2: Sort out the selectable buffer positions on the linear track, determine the current buffer position serial number XP, and divide the linear track into two areas, A and B, define the RGV in area A as RGV1, and the RGV in area B as RGV2. For tasks in the same area whose starting and ending points are both in area A or area B, assign the tasks to RGV1 or RGV2 in the area to complete independently. For cross-area tasks whose starting and ending points are in area A and area B respectively, assign the tasks to RGV1 and RGV2 to complete collaboratively, and mark the tasks according to the positions of the starting and ending points to determine whether the assigned tasks belong to outbound tasks or inbound tasks. Step 3: Taking minimizing the maximum time consumed by RGV to complete the task as the objective function, the total time to complete the task is divided into the adjustment time required for RGV from the current position to the starting point of the task, the transportation and loading and unloading time required to perform the task, and the waiting time required by the buffer zone when performing cross-regional tasks, and the mathematical model of RGV in-and-out scheduling is established; Step 4: Use genetic algorithm to solve the buffer location and optimal time for RGV to execute tasks.

2. The method for dispatching warehousing and warehousing of linear reciprocating multiple RGVs in collaborative operation according to claim 1, characterized in that: When selecting the buffer position in step 2, the serial number x of the middle position of the straight track is calculated according to the total length of the straight track, and the serial number of the buffer position is 3. The method for dispatching warehousing in and out of a linear reciprocating multi-RGV collaborative operation according to claim 1, characterized in that: The mathematical model of RGV in-and-out scheduling in step 3 is as follows: Objective function: min(max{T j ,j=1,2}) T j =T tj +T fj +T wj Where, T j It represents the total time for the jth RGV to complete the assigned task, T tj represents the adjustment time required for the jth RGV to move from its current position to the starting point of the task, T fj represents the transportation and loading and unloading time required for the jth RGV to perform its mission, T wj R1 represents the waiting time required by the jth RGV to perform a cross-region task next to the buffer. i and R2 i are binary variables, indicating whether the i-th task executed by RGV1 and RGV2 is a same-region task or a cross-region task. i and R2 i A value of 0 indicates a task in the same region. i and R2 i A value of 1 indicates a cross-region task. ij is a binary variable. If the jth RGV executes the ith task, the value is 1, otherwise it is 0. iu is a binary variable. If the i-th task is executed immediately after the u-th task, the value is 1, otherwise the value is 0. uj Indicates the end position sequence number of the jth RGV executing the uth task, XS ij Indicates the starting position number of the jth RGV executing the i-th task, XE ij represents the end position number of the jth RGV performing the i-th task, d represents the length of the unit grid on the straight track, T z Indicates the time of loading and unloading of cargo; Constraints: Where, TS uj Indicates the starting time of the uth task, TE ij Indicates the end time of the i-th task.

4. A method for dispatching in and out of a warehouse for coordinated operation of multiple linear reciprocating RGVs according to claim 3, characterized in that: said step 4 specifically comprises: 4.1 Encoding method Determine the RGV, the task start point and the task end point, and use real number coding to generate chromosomes. The length of the chromosome is equal to the total number of tasks m. The chromosome consists of a digital sequence of randomly generated and non-repeating numbers from 1 to m. Each number corresponds to a task number, and the digital sequence represents the order of task execution. 4.2 Population Initialization Create an initial population by randomly generating multiple chromosomes through coding; 4.

3. Task completion time calculation Determine whether the current task is a task in the same area. If the current task is a task in the same area, first calculate the adjustment time between the current position of RGV1 or RGV2 executing the task and the starting point of the task, then calculate the transportation and loading and unloading time between the starting point of the task and the end point of the task, and obtain the total time to complete the task by summing them up. If the current task is a cross-area task, first calculate the adjustment time between the current position of RGV1 or RGV2 in the area where the task starting point is located and the starting point of the task, and calculate the transportation and loading and unloading time of RGV1 or RGV2 from the starting point of the task to the buffer zone, then calculate the adjustment time between the current position of RGV2 or RGV1 in the area where the task end point is located and the buffer zone, and calculate the transportation and loading and unloading time of RGV2 or RGV1 from the buffer zone to the task end point. In addition, according to the time when RGV1 and RGV2 arrive at the buffer zone, calculate the waiting time required next to the buffer zone, and obtain the total time to complete the task by summing them up. Finally, determine whether the task is completed. If so, proceed to step 4.4, if not, repeat step 4.

3. 4.

4. Fitness function solution For each chromosome in the population, the maximum value Z of the time it takes for RGV1 and RGV2 to complete their respective tasks is calculated through the fitness function, and the maximum task time threshold Z at the beginning of the iteration is set. max , when Z is greater than Z during the iteration max When Z max Update to Z, and calculate the fitness of each chromosome as: 4.

5. Binary Tournament Selection Each time, two pairs of chromosomes are randomly selected from the population for comparison, and the chromosome with higher fitness is selected to enter the next generation population; 4.6 Crossover Randomly select two crossover points in the parent chromosome, and copy the two crossover points and the number sequence between them to the corresponding offspring. For the area outside the two crossover points, fill it in according to the order of the other parent. If the number has appeared in the sequence between the crossover points, skip it and continue to fill in the next number. If the number has not appeared, fill it directly. 4.7 Mutation Determine whether each chromosome mutates according to the set mutation probability. If the chromosome mutates, two numbers are randomly selected from the chromosome and exchanged to change the original task order. If the chromosome does not mutate, the original order is maintained. Each mutated chromosome is added to the new population until the number of chromosomes reaches the maximum population number. 4.

8. Set the maximum number of iterations Generate a new population through iteration and determine whether the maximum number of iterations is reached. If not, continue to execute step 4.3 using the current population. If yes, stop and output the scheduling results and total time of RGV in the buffer.

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