Multi-AGV scheduling and path planning joint optimization method applied to intelligent storage

Abstract

The invention provides a multi-AGV scheduling and path planning joint optimization method applied to intelligent warehousing, and the method comprises the steps: building a multi-AGV scheduling and path planning joint optimization model, and enabling the optimization target of the multi-AGV scheduling and path planning joint optimization model to be the minimum maximum operation completion time; and solving the proposed joint optimization model based on a biased random key genetic algorithm (BRKGA) to obtain a population optimal solution and corresponding maximum operation completion time of all AGVs. According to the method, a conflict-free path planning algorithm is adopted as a decoding scheme of population individuals in the biased random key genetic algorithm, so that a path planning scheme corresponding to a scheduling scheme represented by the individuals is obtained, and meanwhile, a local search strategy and a restart mechanism are added in the biased random key genetic algorithm; while the solving accuracy and convergence speed of the algorithm are improved, premature convergence of the population is prevented, so that a better result is obtained.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of intelligent warehousing, and in particular to a method for joint optimization of multi-AGV scheduling and path planning applied to intelligent warehousing. BACKGROUND

[0002] In the traditional warehousing logistics industry, the goods are mainly transported by manual work or driving forklifts. In the face of an increasing number of transport operations, the traditional warehousing logistics industry can only complete the task by increasing the number of workers or extending the working hours. Therefore, more and more enterprises have adopted automated guided vehicles (AGVs) with high reliability and strong adaptability to transport work tasks, so as to reduce labor costs and improve the work efficiency of the warehouse.

[0003] In a multi-AGV intelligent warehousing system, multiple AGVs can cooperate to complete more complex transport operations. How to schedule and plan the paths of multiple AGVs has become a key optimization problem for efficient operation of intelligent warehousing. The multi-AGV scheduling needs to allocate the transport operations to be processed to different AGVs and determine the optimal operation execution sequence for each device. The multi-AGV path planning is to plan a conflict-free transport path for each AGV according to the shortest transport path and the shortest transport time. The scheduling decision provides spatial position constraints for path planning, and the path planning result provides a task completion time index for scheduling optimization. These two problems are mutually restrictive and influence each other. Only studying the scheduling problem or the path planning problem cannot achieve overall optimization. Therefore, a method for joint optimization of multi-AGV scheduling and path planning in intelligent warehousing is needed. SUMMARY

[0004] In view of the above problems, the present application provides a method for joint optimization of multi-AGV scheduling and path planning applied to intelligent warehousing, which solves the problem of considering multi-AGV scheduling and path planning at the same time.

[0005] In order to solve the above technical problems, the present application provides the following technical solutions:

[0006] In the first aspect, the present application discloses a method for joint optimization of multi-AGV scheduling and path planning applied to intelligent warehousing, comprising:

[0007] Step S100. A joint optimization model of multi-AGV scheduling and path planning is constructed, and the goal of the joint optimization model of multi-AGV scheduling and path planning is to minimize the maximum operation completion time of all AGVs. The decision variable in the joint optimization model of multi-AGV scheduling and path planning is At the moment from the grid to the grid variable , at the time of loading the carrying operation variable , at the time of unloading the carrying operation variable ; at the time of returning to the parking area ; the time of returning to the parking area , the maximum operation completion time of all AGVs ;

[0008] Step S200. Based on the biased random key genetic algorithm, the multi-AGV scheduling and path planning joint optimization model is solved to obtain the population optimal solution and the maximum operation completion time of all AGVs.

[0009] Further, in S100, the objective function of the multi-AGV scheduling and path planning joint optimization model is to minimize the maximum operation completion time of all AGVs, and the objective function is as follows:

[0010]

[0011] The constraint conditions in the multi-AGV scheduling and path planning joint optimization model include:

[0012] Condition 1. Each AGV needs to start from the parking area grid:

[0013]

[0014] wherein, and represent the grid, represent the grid that can be reached in one step, represent the grid where the parking area is located, represent the AGV set;

[0015] Condition 2. AGVs need to travel in the specified travel direction when traveling:

[0016]

[0017] wherein, represent the set of all grids, represent the set of times;

[0018] Condition 3. If AGV arrives at grid at time , then at time the AGV needs to either drive out of the grid or wait at the grid:

[0019]

[0020] Condition 4. At most one AGV is allowed to enter or park at a grid other than the outbound station at any time :

[0021]

[0022] where denotes the set of outbound station grids, denotes the number of AGVs;

[0023] Condition 5. Each handling task can be loaded only once:

[0024]

[0025] where denotes the grid of the storage location where the handling task is located, denotes the set of handling tasks;

[0026] Condition 6. Each handling task can be unloaded only once:

[0027]

[0028] where denotes the outbound station grid assigned to the handling task ;

[0029] Condition 7. The same handling task can be loaded and unloaded only by the same AGV:

[0030]

[0031] Condition 8. The same AGV can perform at most one handling task at the same time:

[0032]

[0033] where denotes the number of handling tasks;

[0034] Condition 9. A handling task must be loaded before it can be unloaded:

[0035]

[0036] Condition 10. An AGV must drive into a storage location before it can load a handling task from the storage location:

[0037]

[0038] Condition 11. AGV must enter the outbound station before unloading the handling operation at the outbound station

[0039]

[0040] Condition 12. AGV needs to return to the parking area after completing all handling operations:

[0041]

[0042]

[0043] Condition 13. AGV must enter the parking area grid before returning to the grid at

[0044]

[0045] Condition 14. AGV completion time:

[0046]

[0047] Condition 15. Maximum operation completion time of all AGVs:

[0048] .

[0049] Further, in S200, the multi-AGV scheduling and path planning joint optimization model is solved based on the biased random key genetic algorithm to obtain the population optimal solution and the maximum operation completion time of all AGVs, specifically including:

[0050] Step S201. Set the parameters of the algorithm, including the turning penalty coefficient , population size , elite population size , number of mutated individuals , biased genetic probability , maximum local search number , generation threshold for executing restart mechanism , maximum iteration number and maximum running time ;

[0051] Step S202. An individual is generated using a heuristic algorithm based on the principle of job equalization and nearest distance, and the remaining individuals are randomly generated to form an initial population ; set the iteration number , and the restart counter ;​

[0052] Step S203. Generating a new population by evolution operator;

[0053] Step S204. Calculating the fitness of all individuals in the population;

[0054] Step S205. Performing local search on the optimal individual in the newly generated population, if the fitness of the individual obtained by local search is greater than the fitness of the original individual, then replacing the original individual with the new individual and updating the population;

[0055] Step S206. Judging whether the optimal solution is improved, if not, then ; otherwise ;

[0056] Step S207. Judging whether the number of generations without improvement reaches the threshold of starting the restart mechanism, i.e. judging whether the condition is met, if yes, then executing step S208, otherwise executing step S209;

[0057] Step S208. Executing the restart mechanism;

[0058] Step S209. Judging whether the number of iterations reaches the maximum number of iterations or the maximum running time has been exceeded, if yes, then the algorithm terminates and the optimal solution of the population and the corresponding maximum job completion time are obtained; otherwise, , executing step S203.

[0059] Further, in step S202, a heuristic algorithm based on job equalization and nearest distance principle is used to generate an individual, and the specific method includes: the heuristic algorithm based on job equalization and nearest distance principle randomly selects a job each time, and assigns an AGV to the job according to the principle of least number of jobs assigned to the AGV and nearest distance, if the number of jobs of the AGV and the distance of the job to be assigned are the same, then randomly assigning an AGV and updating the current position of the AGV, repeating the above process until all jobs are assigned.

[0060] Further, step S203 specifically includes:

[0061] Step S2031. According to the fitness of all individuals in the population, the population is divided into two sub-populations, i.e. elite population and non-elite population, the size of the elite population is , and the size of the non-elite population is , wherein is the population size;

[0062] Step S2032. Performing the copying process: copying the elite population Individuals are directly replicated into the new population;

[0063] Step S2033. Perform the mutation process: Randomly generate One mutated individual was directly added to the new population, among which... ;

[0064] Step S2034. Perform the crossover process: Generate a new population by crossing two parents. There are two individuals; one parent comes from a random individual in the elite population, and the other parent comes from a random individual in the non-elite population; the probability of the elite parent's gene being passed on to the next generation is greater than the probability of the non-elite parent's gene being passed on; during the crossover process, a uniform crossover method is used, and each gene from the elite parent has a higher probability of being passed on to the next generation. The probability of a gene being passed on to the next generation is high, while the probability of a gene being passed on to the next generation from a non-elite parent is low. .

[0065] Further, step S204 includes:

[0066] Step S2041. Input the location of each AGV in the parking area, the handling operation assigned to each AGV, the location of the storage location for each handling operation, and the location of the outbound station. Without considering AGV conflicts, use the improved A* algorithm to plan a complete handling path for each AGV, and set the time... ;

[0067] Step S2042. Calculate the number of grid cells occupied by each AGV within the time window and the maximum job completion time. ;

[0068] Step S2043. Determine the first... Does the presence of multiple AGVs in the same grid cell exist within a given time unit, i.e., does a conflict occur between AGVs? If so, then all grid cells where conflicts occur within the current time unit are recorded as a set. If not, proceed to step S2044; otherwise, proceed to step S2045.

[0069] Step S2044. In Randomly select a conflict grid To handle AGV collisions, all AGVs that collide at the current collision grid within the current time period are denoted as a set. And define according to the set priority rules The priority of each AGV is determined, with the highest priority AGV being in the [number]th [position]. Prioritize passing through conflict grids within a time unit. The other AGVs wait in their original positions for one time unit and update their paths; after the update is complete, proceed to step S2042.

[0070] Step S2045. Calculate the maximum job completion time. ,like , Execute step S2042; otherwise, the algorithm terminates and obtains the maximum job completion time. .

[0071] Further, in step S2044, the priority rule is defined according to the settings. The priority of each AGV is determined, and the priority rules specifically include: First rule: Judgment Did each AGV remain in the conflict grid at the previous moment? First, assign high priority to the AGV that is stuck in the conflict grid; Second rule: If the first rule is not true, calculate... The length of the complete transport path for each AGV is used to assign high priority to the AGV with the longest path; the third rule: if neither the first nor the second rule is true, calculate... The first rule assigns priority to AGVs with fewer conflict nodes in their complete transport path. The second rule assigns priority to AGVs with more transport operations if the first, second, and third rules are not met. The third rule assigns priority to AGVs with more transport operations if the first, second, third, and fourth rules are not met. Priority of each AGV in the system.

[0072] Further, in step S205, a local search is performed on the optimal individual in the newly generated population. The local search method specifically includes an insertion-neighborhood-based local search method and a swap-neighborhood-based local search method. Specifically, the insertion-neighborhood-based local search method includes: designating the AGVs with the longest and shortest task completion times as... and The corresponding handling operation sequences are denoted as follows: and ,from Randomly select a transport job and insert it into In any position to be searched, and then according to the greedy criterion, if If the value decreases, replace the original individual with a new one and update the settings. and Then, the search strategy is applied to the new individual; otherwise, the search strategy is applied to the original individual. The job is then inserted into other search locations until all search locations have been searched or the maximum number of local searches has been reached. The local search ends and the population is updated. the optimal individual in the current population; the local search method based on the exchange neighborhood specifically includes: after the local search method based on the insertion neighborhood is performed, if the number of the carrying operation is not less than 2, the local search based on the exchange neighborhood is performed on the individual; the random exchange the completion order of any two operations in the current population, the new individual generated is compared with the original individual, if the fitness of the new individual is higher, the original individual is replaced by the new individual, otherwise, the original individual is reserved.

[0073] Further, in S208, a restart mechanism is executed, and the specific method includes: only the optimal individual in the current population is reserved, an individual is obtained through a heuristic algorithm based on operation equalization and the nearest distance principle, and the remaining individuals are randomly generated to form a new population.

[0074] The above technical solutions provided by the present application have at least the following beneficial effects:

[0075] The present application solves the joint optimization problem of multi-AGV scheduling and path planning by constructing a joint optimization model of multi-AGV scheduling and path planning and a biased random key genetic algorithm, increases the local search strategy based on the insertion neighborhood and the exchange neighborhood and the restart mechanism in the biased random key genetic algorithm, accelerates the convergence speed of the algorithm, and avoids the algorithm from falling into local optimization due to premature convergence of the population; the biased random key genetic algorithm uses a conflict-free path planning algorithm as a decoding scheme of the population individual, plans a conflict-free carrying path for the AGV according to the scheduling scheme, and thus realizes the joint optimization of multi-AGV scheduling and path planning in intelligent warehousing.

[0076] The technical solutions of the present application will be further described in detail below through the drawings and examples. BRIEF DESCRIPTION OF DRAWINGS

[0077] The drawings are used to provide a further understanding of the present application, and constitute a part of the specification, together with the embodiments of the present application, to explain the present application, and do not constitute a limitation on the present application. In the drawings:

[0078] Figure 1 It is a flow chart of a method for joint optimization of multi-AGV scheduling and path planning in intelligent warehousing in the embodiment 1 of the present application;

[0079] Figure 2 It is a functional schematic diagram of an intelligent warehousing environment in the embodiment 1 of the present application;

[0080] Figure 3 It is a schematic diagram of an evolutionary operator in the embodiment 1 of the present application;

[0081] Figure 4 It is a schematic diagram of a uniform crossover method in the embodiment 1 of the present application;

[0082] Figure 5 Grid map used in different cases in Example 2 of the present application

[0083] Figure 6 Graph of small-scale experimental results in Example 2 of the present application

[0084] Figure 7 Graph of large-scale experimental results in Example 2 of the present application

[0085] Figure 8 Convergence curve graph of five algorithms in Example 2 of the present application

[0086] Figure 9 Average calculation time graph of five algorithms in Example 2 of the present application DETAILED DESCRIPTION

[0087] Exemplary embodiments of the present disclosure will be described in detail below with reference to the accompanying drawings. Although exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided so that the present disclosure can be more thoroughly understood and the scope of the present disclosure can be accurately conveyed to those skilled in the art.

[0088] Example 1

[0089] To solve the problems in the prior art, an embodiment of the present application provides a method for joint optimization of multi-AGV scheduling and path planning applied in intelligent warehousing, as shown in Figure 1 , which comprises the following steps:

[0090] Step S100. A joint optimization model of multi-AGV scheduling and path planning is constructed, and the goal of the joint optimization model of multi-AGV scheduling and path planning is to minimize the maximum job completion time of all AGVs; the decision variable in the joint optimization model of multi-AGV scheduling and path planning is the variable from grid to grid at time , the variable loading the carrying job at time , the variable unloading the carrying job at time ; the variable returning to the parking area at time ; the time of returning to the parking area, and the maximum job completion time of all AGVs ;

[0091] Specifically, this paper introduces the joint optimization problem of multi-AGV scheduling and path planning applied in intelligent warehousing. For example... Figure 2 As shown, the layout of the intelligent warehouse mainly includes an outbound area, a storage area, and an AGV parking area. The storage area has multiple rows of storage locations, with aisles between them for AGVs to travel through. The left side of the warehouse is the AGV parking area, where AGVs must park when there are no handling operations. The right side of the storage area is the outbound area, which has multiple outbound stations that can handle outbound tasks simultaneously. When a handling operation is assigned to an AGV, the AGV first travels from the parking area to the target storage location, then moves the target goods from the storage area to the assigned outbound station, and then executes the next task. After all handling operations are completed, the AGV must return to the parking area to await system scheduling. Therefore, the joint optimization problem of multi-AGV scheduling and path planning in this embodiment can be described as: In an intelligent warehouse, there exists... One moving operation and Each AGV can only perform one transport operation at a time, and each transport operation can only be completed by one AGV. The position of the AGV in the parking area... Arbitrary handling operations Location of the cargo space and handling operations The assigned outbound station location All of these are known. AGV scheduling needs to determine the handling operations that each AGV needs to complete and the order in which these operations are completed; while AGV path planning needs to determine the route that each AGV takes to complete each handling operation, as well as its travel path when idle and the time it takes for the AGV to pass through each node.

[0092] In constructing the multi-AGV scheduling and path planning joint optimization model, the model must meet the following assumptions: (1) all AGVs travel at a constant speed, and the travel time of an AGV between two adjacent grids is 1 time unit; (2) all AGVs can only travel in the four horizontal and vertical directions, and cannot travel along the diagonal or in any direction; (3) there is a partition between the storage locations, and AGVs cannot pass through the bottom of the storage location; (4) the loading and unloading times of AGVs are not considered, i.e., the loading and unloading times are very short and can be ignored; (5) all handling operations are known in advance, and all AGVs are available for scheduling at time zero; (6) the AGVs have sufficient power during the handling process and will not fail, i.e., the effects of AGV failure and insufficient power during the journey are not considered; (7) the process of packing and shipping the goods after unloading is not considered; (8) the paths traveled by AGVs entering and exiting the picking station are different, and the head-on conflict when AGVs enter and exit the picking station is not considered. Before constructing the multi-AGV scheduling and path planning joint optimization model, the set symbols, parameter symbols, and decision variables used in the model are first defined in Table 1. Table 1 is the set symbol, Table 2 is the parameter symbol, and Table 3 is the decision variable.

[0093] Table 1

[0094]

[0095] Table 2

[0096]

[0097] Table 3

[0098]

[0099] In this embodiment, through the symbols and variables in Tables 1-3, the objective function of the multi-AGV scheduling and path planning joint optimization model is obtained as follows:

[0100]

[0101] The specific constraint conditions in the multi-AGV scheduling and path planning joint optimization model are as follows:

[0102]

[0103] where constraint indicates that each AGV needs to start from the parking area grid. Constraint indicates that the AGV needs to travel in the specified travel direction when traveling. Constraint indicates that if the AGV arrives at grid at time , then at At any given moment, the AGV needs to either move away from the grid or wait in place within the grid. (Constraint) This means that at any given time, at most one AGV can enter or park in a grid other than the exit station. This constraint is a conflict-free path planning constraint for AGVs. This indicates that each transport operation can only be loaded once. (Constraint) This means that each handling operation can only unload once. (Constraint) This indicates that only one AGV can load and unload the same transport operation. (Constraint) This indicates that the same AGV can perform at most one transport operation at a time. (Constraint) This indicates that loading must be completed before unloading can occur. (Constraint) This indicates that the AGV must first enter this storage location before it can perform loading and handling operations on the rack. (Constraint) This indicates that the AGV must first enter the outbound station location before it can unload and transport materials at the outbound station. (Constraint) and This indicates that the AGV needs to return to the parking area after completing all transport operations. (Constraint) Indicates that the AGV is in When returning to a parking area grid, the vehicle must first enter that grid. (Constraint) Indicates the completion time of the AGV. Constraint This represents the maximum job completion time for all AGVs in the system. (Constraint) - This constrains the range of values ​​for decision variables.

[0104] Step S200. Solve the joint optimization model of multi-AGV scheduling and path planning based on the biased random key genetic algorithm to obtain the population optimal solution and the maximum job completion time of all AGVs.

[0105] Specifically, step S200 includes:

[0106] Step S201. Set the algorithm parameters, including the steering penalty coefficient. Population size Elite population size Number of variant individuals The probability of biased inheritance Maximum number of local searches Algebraic threshold for executing the restart mechanism Maximum number of iterations and maximum running time ;

[0107] Step S202. Using a heuristic algorithm based on the principles of equal job distribution and nearest proximity, generate one individual and randomly generate the remaining individuals to form the initial population. Set the number of iterations. Restart the counter In step S202, an individual is generated using a heuristic algorithm based on the principles of equal job distribution and nearest distance. The specific method includes: the heuristic algorithm based on the principles of equal job distribution and nearest distance randomly selects a job each time, and assigns an AGV to the job according to the principle of minimizing the number of jobs already assigned to the AGV and proximity. If the number of jobs and the distance to the job to be assigned of the AGV are the same, then the AGV is randomly assigned and the current position of the AGV (the outbound station position assigned to the job) is updated. The above process is repeated until all jobs have been assigned.

[0108] The encoding scheme of a biased random key genetic algorithm is in a continuous interval Random real numbers are generated, and the gene length of an individual is equal to the number of transport jobs. For ease of understanding, we assume that... Taiwan AGV and A moving operation, for The sequence of transport operations, where each individual can represent a scheduling scheme, and each individual can be used... An individual's genes can be represented as... Any gene of an individual Need to meet Any gene of an individual Then it can be decoded into a handling operation according to the following formula. Assigned to the The AGV has been completed;

[0109]

[0110] in This indicates rounding down to the nearest integer. (If it's a handling operation...) and handling operations The corresponding gene and All are decoded into the same AGV. At this point, the order of the handling operations is as follows: and The size is determined, if Then the handling operation Prior to handling operations Execute, otherwise transport operation. Prior to handling operations Execute. But if Then it needs to be based on and The order in which genes appear in an individual determines the priority of transport tasks. For example: if the number of transport tasks is 5 ( The number of AGVs is 2. Assume that the randomly generated individuals are... ,but The handling sequence is as follows , The handling sequence is as follows ;

[0111] Assuming the job Assigned to ,Operation exist In the transport sequence , The number of assignments is The encoding method of the individuals generated by the heuristic algorithm based on the principle of equal task distribution and nearest distance, and the local search strategy, is as follows:

[0112]

[0113] To make it easier to understand, let's take the example above again: and Given that the transport operation sequences are {1,5,3} and {4,2}, then according to the encoding method in the above formula, the individual components of this scheduling scheme are... .

[0114] Step S203. Generate a new population using evolutionary operators;

[0115] Among them, such as Figure 3 As shown, step S203 specifically includes:

[0116] Step S2031. Based on the fitness of all individuals in the population, divide the population into two subpopulations: an elite population and a non-elite population. The size of the elite population is... The size of the non-elite population is ,in Population size;

[0117] Step S2032. Perform the replication process: transfer the elite population Individuals are directly replicated into the new population;

[0118] Step S2033. Perform the mutation process: randomly generate One mutated individual was directly added to the new population, among which... ;

[0119] Step S2034. Perform the crossover process: Generate a new population by crossing two parents. There are two individuals; one parent comes from a random individual in the elite population, and the other parent comes from a random individual in the non-elite population; the probability of the elite parent's genes being passed on to the next generation is greater than the probability of the non-elite parent's genes being passed on; during the crossover process, a uniform crossover method is used, such as... Figure 4 As shown, each gene in the elite parents has The probability of a gene being passed on to the next generation is high, while the probability of a gene being passed on to the next generation from a non-elite parent is low. To make it easier to understand, assume there are 5 tasks, 2 AGVs, and the probability of elite inheritance. Elite individuals Non-elite individuals According to uniform crossover, the possible offspring are: .

[0120] Step S204. Calculate the fitness of all individuals in the population;

[0121] Specifically, step S204 includes:

[0122] Step S2041. Input the location of each AGV in the parking area, the handling operation assigned to each AGV, the location of the storage location for each handling operation, and the location of the outbound station. Without considering AGV conflicts, use the improved A* algorithm to plan a complete handling path for each AGV, and set the time... ;

[0123] Step S2042. Calculate the number of grid cells occupied by each AGV within the time window and the maximum job completion time. ;

[0124] Step S2043. Determine the first... Does the presence of multiple AGVs in the same grid cell exist within a given time unit, i.e., does a conflict occur between AGVs? If so, then all grid cells where conflicts occur within the current time unit are recorded as a set. If not, proceed to step S2044; otherwise, proceed to step S2045.

[0125] Step S2044. In Randomly select a conflict grid To handle AGV collisions, all AGVs that collide at the current collision grid within the current time period are denoted as a set. And define according to the set priority rules The priority of each AGV is determined, with the highest priority AGV being in the [number]th [position]. Prioritize passing through conflict grids within a time unit. The other AGVs wait in their original positions for one time unit, and their paths are updated; after the update is complete, step S2042 is executed; in step S2044, the priority rules are defined according to the settings. The priority of each AGV is determined, and the priority rules specifically include: First rule: Judgment Did each AGV remain in the conflict grid at the previous moment? First, assign high priority to the AGV that is stuck in the conflict grid; Second rule: If the first rule is not true, calculate... The length of the complete transport path for each AGV is used to assign high priority to the AGV with the longest path; the third rule: if neither the first nor the second rule is true, calculate... The first rule assigns priority to AGVs with fewer conflict nodes in their complete transport path. The second rule assigns priority to AGVs with more transport operations if the first, second, and third rules are not met. The third rule assigns priority to AGVs with more transport operations if the first, second, third, and fourth rules are not met. Priority of each AGV in the system.

[0126] Step S2045. Calculate the maximum job completion time. ,like , Execute step S2042; otherwise, the algorithm terminates and obtains the maximum job completion time. .

[0127] Step S205. Perform a local search on the optimal individual in the newly generated population. If the fitness of the individual obtained through the local search is greater than that of the original individual, replace the original individual with the new individual and update the population. The local search method in step S205 includes two methods: a local search based on insertion neighborhood and a local search based on exchange neighborhood. Specifically, the local search method based on insertion neighborhood includes: denoting the AGV with the longest and shortest task completion times as... and The corresponding handling operation sequences are denoted as follows: and ,from Randomly select a transport job and insert it into In any position to be searched, and then according to the greedy criterion, if If the value decreases, replace the original individual with a new one and update the settings. and Then, the search strategy is applied to the new individual; otherwise, the search strategy is applied to the original individual. The job is then inserted into other search locations until all search locations have been searched or the maximum number of local searches has been reached. The local search ends and the population is updated. The optimal individual in the neighborhood; the local search method based on the exchange neighborhood specifically includes: after executing the local search method based on the insertion neighborhood, if If the number of transport operations is not less than 2, then a local search based on the exchange neighborhood is performed on that individual; random exchange... The order in which any two tasks are completed is used to compare the resulting new individual with the original individual. If the new individual has higher fitness, it replaces the original individual; otherwise, the original individual is retained.

[0128] Step S206. Determine if the optimal solution has been improved. If not, then ;otherwise ;

[0129] Step S207. Determine whether the unimproved algebra has reached the algebra threshold for starting the restart mechanism, i.e., determine whether the condition is met. If the condition is met, proceed to step S208; otherwise, proceed to step S209.

[0130] Step S208. Execute the restart mechanism, the specific method of which includes: only retaining the best individual in the current population, obtaining an individual through a heuristic algorithm based on the principle of equal job distribution and nearest distance, and randomly generating the remaining individuals to form a new population;

[0131] Step S209. Determine the number of iterations. Has the maximum number of iterations been reached? If the maximum running time has been exceeded, and the condition is met, the algorithm terminates and obtains the population-optimal solution and the corresponding maximum job completion time; otherwise, Execute step S203.

[0132] This paper discloses a method for joint optimization of multi-AGV scheduling and path planning in intelligent warehousing. It solves the joint optimization problem of multi-AGV scheduling and path planning by constructing a joint optimization model and a biased random key genetic algorithm. The biased random key genetic algorithm incorporates a local search strategy based on insertion and exchange neighborhoods, and a restart mechanism. This accelerates the algorithm's convergence speed while preventing it from getting trapped in local optima due to premature population convergence. The biased random key genetic algorithm uses a conflict-free path planning algorithm as the decoding scheme for the population individuals, planning conflict-free transport paths for AGVs according to the scheduling scheme, thereby achieving joint optimization of multi-AGV scheduling and path planning in intelligent warehousing.

[0133] Example 2

[0134] To verify the effectiveness of the partially randomized key genetic algorithm disclosed in Example 1, this example sets up various scales of computational tests to verify the effectiveness and stability of the partially randomized key genetic algorithm under different scales of computational tests. The raster maps used in the computational tests are as follows: Figure 5 As shown in Table 4, the scale settings consist of 15 small-scale experiments and 32 large-scale experiments. The experiments can be divided into multiple groups based on different numbers of handling operations and AGVs. In each group, 5 cases are randomly generated. The stopping position of the AGV, the location of the handling operation, and the assigned outbound station location are all randomly generated in each case. The final result of the algorithm in each group is the average value of all cases in that group.

[0135] Table 4

[0136]

[0137] In small-scale experiments, the model was solved using the Gurobi solver and tested against the BRKGA proposed in this invention to verify the accuracy of BRKGA in small-scale problems. Since Gurobi could not solve the problem in large-scale experiments, five comparative algorithms were set up to verify the effectiveness of BRKGA: (1) a heuristic algorithm based on job distribution and proximity principle; (2) BRKGA-A: the algorithm does not use a local search strategy, and is otherwise consistent with BRKGA; (3) BRKGA-B: the algorithm does not use a restart mechanism, and is otherwise consistent with BRKGA; (4) GA: a genetic algorithm, with the maximum number of iterations consistent with BRKGA; (5) IDE: an improved differential evolution algorithm, with the maximum number of iterations consistent with BRKGA.

[0138] In small-scale experiments, the model parameters are set as follows: In all experiments, the BRKGA algorithm parameters were set as follows: .

[0139] The experimental results of Gurobi and BRKGA in 15 small-scale experiments are as follows: Figure 6 As shown, LB is the optimal lower bound, Makespan is the optimal solution value, Gap is the difference between the algorithm and the optimal lower bound, and Time is the algorithm's running time. According to... Figure 6The results show that under a 3600-second runtime constraint, Gurobi can find and prove the optimal solution in 7 sets of examples, while the proposed BRKGA can also find the optimal solution in the corresponding examples. In the remaining 8 sets of examples, as the number of jobs or AGVs increases, Gurobi can no longer prove the optimal solution or only finds a feasible solution, and the solution time also increases exponentially. In 3 sets of examples, BRKGA and Gurobi have the same solution results, while in the remaining 5 sets of examples, BRKGA's solution results are better than Gurobi's. The average solution time of BRKGA remains within 60 seconds, and the average gap between the solution result and the optimal lower bound is only 9.75%, indicating that BRKGA has accuracy and good solution efficiency.

[0140] Since Gurobi cannot be solved in medium- to large-scale experiments, and the effectiveness of the algorithm cannot be proven using the lower bound, the Percentage Relative Difference (PRD) is used to verify the effectiveness of the algorithm. The calculation method is shown in the following formula.

[0141]

[0142] in, This represents the shortest maximum job completion time obtained by algorithm A in this example. This represents the shortest maximum job completion time obtained by all algorithms in this example.

[0143] Figure 7 The table shows the mean and standard deviation of the PRD obtained by the six algorithms in a large-scale experiment. The bolded values ​​are the best values ​​for each group. Based on the experimental results in the table, we can obtain:

[0144] (1) In all the examples, the mean PRD of BRKGA was lower than that of the other 5 algorithms, indicating that the solution quality of BRKGA is better than that of the other 5 algorithms. Except for the four sets of examples where the minimum standard deviation was obtained by GA and BRKGA-B, the minimum standard deviation was obtained by BRKGA in the other examples. Moreover, the mean standard deviation of BRKGA was only 0.963, indicating that the solution performance of BRKGA is more stable than that of other algorithms.

[0145] (2) The mean PRD values ​​of BRKGA-A and BRKGA-B are 8.1 times and 5.1 times that of BRKGA, respectively, and the mean standard deviation of both algorithms is higher than that of BRKGA. This indicates that the local search strategy and restart mechanism added to BRKGA can help the algorithm escape local optima to a certain extent, thereby improving the solution quality and stability. Since the mean PRD value and mean standard deviation of BRKGA-B are lower than those of BRKGA-A, it also shows that the local search strategy has a greater effect on improving the solution quality and stability of the algorithm than the restart mechanism.

[0146] (3) From the overall results, the solution performance of the six algorithms from high to low is BRKGA, BRKGA-B, BRKGA-A, IDE, GA and heuristic algorithm, indicating that the BRKGA series of algorithms can achieve better solution performance in this problem than IDE and GA.

[0147] To observe the convergence speed of the five algorithms other than the heuristic algorithm, a 6×90 example was used as an example, and convergence curves of the five algorithms were plotted under this example, as shown below. Figure 8 As shown in the diagram, the convergence curves reveal that BRKGA-B converges the fastest, but its solution is not optimal, while BRKGA-A converges the slowest but provides a better solution. BRKGA's solution is significantly lower than the other algorithms, yet it converges quickly, indicating that BRKGA possesses both good convergence speed and accuracy.

[0148] Figure 9 The figure shows the solution times of five algorithms in a large-scale experiment. Heuristic algorithms, whose average solution time is less than 1 second, are not shown. The results show that BRKGA-A has the shortest average computation time, indicating that while the local search strategy improves the algorithm's solution performance, it increases the runtime cost, but this is still within an acceptable range. BRKGA-B and BRKGA have similar runtimes, indicating that the restart mechanism does not significantly increase the algorithm's runtime cost. BRKGA's average runtime is significantly lower than GA and IDE, indicating that BRKGA is also superior to GA and IDE in terms of solution efficiency. Although BRKGA's runtime is higher than BRKGA-A and BRKGA-B, its average PRD is significantly lower than other algorithms, thus BRKGA achieves a good balance between solution quality and runtime.

[0149] In summary, this implementation first constructs a joint optimization model for multi-AGV scheduling and path planning with the objective of minimizing the maximum task completion time of all AGVs. Secondly, a biased random key genetic algorithm is proposed for solving the model. This algorithm uses a conflict-free path planning algorithm as the decoding scheme for each individual AGV in the population, and plans conflict-free transport paths for the AGVs based on the scheduling scheme, thereby achieving joint optimization of multi-AGV scheduling and path planning. Furthermore, this invention adds a local search strategy based on insertion and exchange neighborhoods, along with a restart mechanism, to the algorithm. This accelerates the convergence speed while preventing the algorithm from getting trapped in local optima due to premature population convergence. As a result, BRKGA exhibits significant advantages in accuracy, stability, and solution efficiency, improving the algorithm's overall performance.

Claims

1. A method applied to joint optimization of multi-AGV scheduling and path planning in intelligent warehousing, characterized in that, Comprising: Step S100. A multi-AGV scheduling and path planning joint optimization model is constructed, a target of the multi-AGV scheduling and path planning joint optimization model being minimum maximum job completion time of all AGVs; decision variables in the multi-AGV scheduling and path planning joint optimization model being At time, the variable from the grid to the grid , At time, the variable loading the handling job , represents the grid position of the storage location of the handling job ; At time, the variable unloading the handling job , represents the grid position of the outbound station to which the handling job is assigned; At time, the variable returning to the parking area , represents the grid position of the parking area ; Time of returning to the parking area ; maximum job completion time of all AGVs Step S200. Solving the multi-AGV scheduling and path planning joint optimization model based on the biased random key genetic algorithm to obtain the population optimal solution and the maximum job completion time of all AGVs.

2. The method of optimizing according to claim 1, wherein, In S100, the objective function of the multi-AGV scheduling and path planning joint optimization model is to minimize the maximum job completion time of all AGVs, and the objective function is as follows: The constraint conditions in the multi-AGV scheduling and path planning joint optimization model include: Condition 1. Each AGV needs to start from the parking area grid: wherein, and denotes a grid, denotes a grid a set of grids reachable in one step, denotes the grid in which the parking area is located, denotes a set of AGVs; Condition 2. AGV needs to travel in the specified direction when traveling: wherein, denotes all sets of grids, denotes a set of times; Condition 3. If the AGV is at time... Reaching the grid So in At any given moment, the AGV needs to either move away from the grid or wait in place within the grid. Condition 4. At most one AGV enters or parks in a grid other than the outbound station at any time : wherein, representing the set of storage station grids, represents the number of AGVs; Condition 5. Each handling job can be loaded only once: wherein, represents a handling operation located in a storage grid, represents a set of handling operations; Condition 6. Each handling job can be unloaded only once: wherein, indicates a carrying operation allocated outbound station grid; Condition 7. The same AGV can load and unload the same handling job: Condition 8. The same AGV can execute at most one handling job at the same time: wherein represents the number of handling operations; Condition 9. Handling job must be unloaded after loading: Condition 10. AGV must enter the location before loading the handling job at the location: Condition 11. AGV must enter the location before unloading the handling job at the location Condition 12. AGV needs to return to the parking area after completing all handling jobs: Condition 13. AGV is in When returning to the parking area grid at the moment, it must first drive into the grid Condition 14. AGV completion time: Condition 15, the maximum job completion time of all AGVs: 。 3. The method of optimizing according to claim 1, wherein, In S200, the multi-AGV scheduling and path planning joint optimization model is solved based on the biased random key genetic algorithm to obtain the population optimal solution and the maximum job completion time of all AGVs, which specifically includes: Step S201. Set parameters of the algorithm, including steering penalty coefficient , population size , elite population size , number of mutated individuals , biased genetic probability , maximum local search number , threshold of generation number for executing restart mechanism , maximum iteration number and maximum running time ; Step S202. Generate an initial population by using a heuristic algorithm based on the principle of job equalization and distance proximity ; set the iteration number , restart the counter ; Step S203. Generate a new population through evolution operators; Step S204. Calculate the fitness of all individuals in the population; Step S205. Perform local search on the optimal individual in the newly generated population, and if the fitness of the individual obtained through local search is greater than the fitness of the original individual, replace the original individual with the new individual and update the population; Step S206. Determine whether the optimal solution is improved, if not, then ; otherwise ; Step S207. Determine whether the unimproved algebra has reached the algebra threshold for starting the restart mechanism, i.e., determine whether the condition is met. If the condition is met, proceed to step S208; otherwise, proceed to step S209. Step S208. Execute the restart mechanism; Step S209. Determine the iteration number whether the maximum iteration number is reached or the maximum running time has been exceeded, if the conditions are met, the algorithm terminates and the population optimal solution and the corresponding maximum job completion time are obtained; otherwise, Step S203 is performed.

4. The method for joint optimization of multi-AGV scheduling and path planning applied in intelligent warehousing according to claim 1, characterized in that, In step S202, a heuristic algorithm based on job equal division and nearest distance principle is used to generate an individual, and the specific method includes: the heuristic algorithm based on job equal division and nearest distance principle randomly selects a job each time, and assigns AGV to the job according to the principle of least number of jobs assigned to AGV and nearest distance, if the job number and distance of AGV are the same, randomly assign AGV and update the current position of AGV, repeat the above process until all jobs are assigned.

5. The method of optimizing according to claim 3, wherein, Step S203 specifically includes: Step S2031. According to the fitness of all individuals in the population, the population is divided into two sub-populations, an elite population and a non-elite population, the size of the elite population is , and the size of the non-elite population is , wherein is the population size. Step S2032. Perform the replication process: replicate the individuals of the elite population directly into the new population; Step S2032. Perform the replication process: replicate the individuals of the elite population directly into the new population; Step S2033. Perform the mutation process: randomly generate One mutated individual was directly added to the new population, among which... ; Step S2034. Perform the crossover process: Generate a new population by crossing two parents. There are two individuals; one parent comes from a random individual in the elite population, and the other parent comes from a random individual in the non-elite population; the probability of the elite parent's gene being passed on to the next generation is greater than the probability of the non-elite parent's gene being passed on; during the crossover process, a uniform crossover method is used, and each gene from the elite parent has a higher probability of being passed on to the next generation. The probability of a gene being passed on to the next generation is high, while the probability of a gene being passed on to the next generation from a non-elite parent is low. .

6. The method of optimizing according to claim 3, wherein, Step S204 specifically includes: Step S2041. Input the position of each AGV in the parking area, the handling task assigned to each AGV, the location of each handling task, and the location of the outbound station. Plan a complete handling path for each AGV using the improved A* algorithm without considering AGV conflicts, and let the time ; Step S2042. Calculate the grid occupied by each AGV in the time window and the maximum job completion time ; Step S2043. Determine whether there are multiple AGVs in the same grid in the same time unit, i.e. whether a conflict occurs between AGVs; if so, record all the grids in conflict in the current time as a set , execute step S2044, otherwise, execute step S2045. Step S2044. Determine whether the number of AGVs in the set is greater than a preset threshold value; if so, execute step S2046, otherwise, execute step S2047. Step S2044. In Randomly select a conflict grid To handle AGV collisions, all AGVs that collide at the current collision grid within the current time period are denoted as a set. And define according to the set priority rules The priority of each AGV is determined, with the highest priority AGV being in the [number]th [position]. Prioritize passing through conflict grids within a time unit. The other AGVs wait in their original positions for one time unit and update their paths; after the update is complete, proceed to step S2042. Step S2045. Calculate the maximum job completion time , if , , perform step S2042, otherwise, the algorithm ends and the maximum job completion time is obtained .

7. The method of optimizing according to claim 6, wherein, In step S2044, the priority of each AGV is defined according to the set priority rule, which specifically includes: a first rule of judging whether each AGV stays in the conflict grid at the last time , giving the AGV staying in the conflict grid a high priority; a second rule of calculating the length of the complete carrying path of each AGV if the first rule is not established, and giving the AGV with the longest path length a high priority; a third rule of calculating the number of conflict nodes in the complete carrying path of each AGV if the first rule and the second rule are not established, and giving the AGV with the fewest conflict nodes a high priority; a fourth rule of giving the AGV with more carrying tasks a high priority if the first rule, the second rule and the third rule are not established; and a fifth rule of randomly determining the priority of each AGV if the first rule, the second rule, the third rule and the fourth rule are not established. ​​​​​ 8. The method of optimizing according to claim 3, wherein, In step S205, a local search is performed on the optimal individual in the newly generated population, and the local search method specifically includes an insertion neighborhood-based local search method and an exchange neighborhood-based local search method; wherein the insertion neighborhood-based local search method specifically includes: taking the AGVs with the longest and shortest job completion times in all AGVs as and respectively, taking the corresponding transport job sequences as and respectively, randomly selecting one transport job from and inserting it into any to-be-searched position of , and then according to the greedy criterion, if is reduced, replacing the original individual with the new individual and updating and , and then continuing to perform the search strategy on the new individual, or else continuing to perform the search strategy on the original individual, inserting the job into other to-be-searched positions, until all to-be-searched positions have been searched or the maximum local search number is reached , the local search ends and the optimal individual in the population is updated; the exchange neighborhood-based local search method specifically includes: after the insertion neighborhood-based local search method is performed, if the number of transport jobs in is not less than 2, performing the exchange neighborhood-based local search on the individual; randomly exchanging the completion order of any two jobs in , comparing the new individual with the original individual, and if the fitness of the new individual is higher, replacing the original individual with the new individual, or else retaining the original individual.

9. The method of optimizing according to claim 3, wherein, In step S208, the restart mechanism is executed, and the specific method includes: only the optimal individual is retained in the current population, an individual is obtained through the heuristic algorithm based on job equal division and nearest distance principle, and the remaining individuals are randomly generated to form a new population.

10. An electronic device, comprising: Comprising: One or more processors; Memory for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the optimization method as claimed in any one of claims 1 to 9.

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