Directed acyclic graph modeling-based inter-vehicle path planning method for single-load automatic guided vehicle

Abstract

Aiming at the construction of an automatic warehouse logistics system of a digital workshop production line, the invention provides a single-load automatic guided vehicle workshop path planning method based on directed acyclic graph modeling, and the method comprises the functions of task selection, task execution sequence planning and the like. The method comprises a fusion algorithm framework based on a binary discrete particle swarm optimization algorithm and a genetic algorithm component, and can solve and fully consider the diversity of task selection strategies in a short time according to information such as known task arrival time and transportation starting point, so that normal production is ensured; and the task execution sequence with the shortest total driving distance is the optimal (or close to the optimal) task execution sequence.

Description

Technical Field

[0001] The present invention relates to the field of automated guided vehicle scheduling, and in particular to a single-carrier automated guided vehicle workshop path planning method based on directed acyclic graph modeling. Background Art

[0002] Automated Guided Vehicles (AGVs) are a typical type of unmanned material handling equipment. With the digital transformation and upgrade of workshops and the introduction of automated warehousing and logistics systems, AGVs have become widely used in manufacturing plants. Ideally, manufacturing companies aim to achieve higher efficiency while maintaining service levels. Common AGV task execution schemes follow a first-come, first-served principle. However, with the growth of batch production, this first-come, first-served approach leads to a large number of meaningless repetitive paths and disordered path planning. This not only reduces the efficiency of smart manufacturing workshops but also increases mechanical wear and tear on AGVs. Repetitive path planning increases AGV energy consumption and mechanical wear, leading to premature AGV shutdowns and, in severe cases, even production interruptions. Therefore, to further improve production efficiency while ensuring stable production processes, it is necessary to implement reasonable AGV path planning.

[0003] AGV path planning technology involves representing the application environment and path search techniques based on this representation. Representing the application environment is the first step in the implementation process. Common environmental representation methods include topological graphs, grid maps, and visibility graphs. Searching for the optimal path based on the representation of the AGV application environment is a key technology in the implementation of AGV path planning. Existing path planning algorithms can be divided into two categories: traditional methods and artificial intelligence-based methods. Traditional path planning algorithms include exact solutions based on mathematical models (such as mixed integer programming or linear programming), graph search algorithms (such as Dijkstra's algorithm, A* algorithm, D* algorithm, and artificial potential field methods), and sampling-based path planning methods (such as probabilistic roadmap methods and rapidly exploring random trees). Traditional methods are not well suited for real-time path planning. This is because as the complexity of the environment and the scale of the path search problem increase, the computational cost of the algorithm increases dramatically, and they are unable to respond promptly to environmental uncertainties. Artificial intelligence-based path planning algorithms include swarm intelligence optimization algorithms (such as genetic algorithms, particle swarm optimization algorithms, ant colony algorithms, and artificial bee colony algorithms) and reinforcement learning methods. The path planning method based on artificial intelligence is not only suitable for static path planning under specific environmental conditions, but also has a strong ability to deal with uncertainties in the environment. Summary of the Invention

[0004] In view of this, the present invention considers the actual problem background and proposes a single-load automatic guided vehicle workshop path planning method based on directed acyclic graph modeling, and correspondingly proposes a fusion algorithm framework based on the binary particle swarm optimization algorithm (BPSO) (hereinafter referred to as the "BPSO fusion framework"), as well as a dynamic traveling salesman problem model based on directed acyclic graph modeling (DAGDTSP). DAGDTSP is based on the idea of ​​the TSP problem and abstracts tasks into directed graph nodes. For solving the DAGDTSP model, the present invention proposes a customized improved genetic algorithm (IGA) to solve the task execution sequence that makes the total transportation distance the shortest. The BPSO fusion algorithm framework considers the impact of task selection strategies on solving the optimal scheduling plan. By solving the DAGDTSP evaluation particle, it finally outputs the scheduling plan for the globally optimal particle, thereby achieving the following effect: compared with the baseline scheduling plan that obeys the first-come, first-served principle, the AGV can normally complete all tasks under the optimized scheduling plan solved by the algorithm proposed by the institute, and effectively reduce the total transportation distance.

[0005] The present invention adopts the following technical solution: a single-carrier automatic guided vehicle workshop path planning method based on directed acyclic graph modeling, comprising the following steps:

[0006] Constructing a task selection strategy model based on the shop floor layout and a dynamic distance traveling salesman problem model based on directed acyclic graph modeling;

[0007] Obtaining the number of task selection strategies based on the task selection strategy model;

[0008] The solution strategy is determined according to the number of task selection strategies, and the dynamic distance traveling salesman problem model based on directed acyclic graph modeling under different task selection strategies is solved:

[0009] When the number of task selection strategies is less than the threshold, an exhaustive strategy is used to traverse and solve the optimal scheduling scheme under each task selection strategy, and the one with the shortest total AGV driving distance is selected; otherwise, a strategy based on the BPSO algorithm is used to obtain the optimal scheduling scheme of the global optimal particle.

[0010] The workshop layout includes:

[0011] The points in the warehouse area are divided into five categories: working points, preparation points, high-speed points, obstacle points, and charging points. According to the needs of business logic, the warehouse area includes unloading area, finished product storage area and empty pallet area.

[0012] When the AGV transports the pallet carrying the workpiece in the unloading area to the finished product storage area, the AGV completes an outbound task; when the AGV transports the empty pallet in the empty pallet area to the unloading area, the AGV completes an inbound task.

[0013] The task selection strategy model is as follows:

[0014] For the task selection strategy model space Ω * , the number of task selection strategies is |Ω * |:

[0015]

[0016] Among them, r is the number of working points in the unloading area; C is the maximum capacity of the pallet; R i is the number of tasks that have reached the i-th work point.

[0017] The dynamic distance traveling salesman problem model based on directed acyclic graph modeling is as follows:

[0018]

[0019]

[0020] Among them, X v is the shortest effective path for total transport distance, D(·) represents the distance function between nodes; p c Indicates the charging point, Ω v represents the valid path space, Represents Ω v The i-th path in , the path is used to characterize the task execution order, express The first mission transportation starting point, express The starting point of the j-th task transportation, express The transport destination of the jth task, express The transport destination of the j+1th task; P H is the set of high-speed points in the warehouse, and p is P H At a certain point in the graph, M is the number of outbound tasks being executed; a node represents an executed task, and an edge represents the execution order between two tasks;

[0021] The edges in the path need to satisfy the following constraints, including:

[0022] The first constraint is the execution order constraint between the outbound task and the inbound task;

[0023] The second constraint is the execution order constraint between outbound tasks;

[0024] The third constraint is the order of the completion time of the outbound task and the arrival time of the inbound task;

[0025] Each node is visited once, and the path that meets the first and second constraints is defined as a possible path; the possible path that meets the third constraint is defined as a valid path; and the possible path that does not meet the third constraint is defined as an invalid path.

[0026] The genetic algorithm is used to solve the dynamic distance traveling salesman problem model based on directed acyclic graph modeling under a fixed task selection strategy, including the following steps:

[0027] 1.1) Chromosome representation: direct representation is used to encode the possible paths into chromosomes;

[0028] 1.2) Population initialization: Multiple random topological sortings obtained by the Kahn algorithm are used as alternative scheduling schemes;

[0029] 1.3) Fitness:

[0030] When the chromosome corresponds to the effective path space Ω v The fitness of the path in is the total transportation distance;

[0031] When a chromosome corresponds to an invalid path, the fitness is a fixed penalty value, which is greater than the total transport distance of all corresponding valid paths in the current population;

[0032] 1.4) Through selection, crossover and mutation operations, the optimal scheduling solution under the fixed task selection strategy is obtained.

[0033] The strategy based on the BPSO algorithm is used to obtain the optimal scheduling solution for the global optimal particles, including the following steps:

[0034] 2.1) Particle Representation: The task selection strategy is expressed by the position vector of the particle. The position vector space of the particle is the task selection strategy model space Ω * ;

[0035] 2.2) Particle swarm initialization:

[0036] The process of randomly generating a particle's position vector is as follows: Generate the task selection strategy model space Ω * The subspace of Ω, that is, the vector space Ω i ,1≤i≤r, r is the number of working points in the blanking area;

[0037] Then, randomly select a vector from each subspace;

[0038] Finally, the selected vectors are sequentially concatenated;

[0039] 2.3) Fitness: For each particle, a genetic algorithm is used to find the optimal scheduling solution under a fixed task selection strategy by mapping the particle's position vector to the task selection strategy.

[0040] The fitness of a particle is:

[0041] When the optimal scheduling scheme of the particle corresponds to the effective path space Ω v The fitness of the path in is the total transportation distance;

[0042] When the particle's optimized scheduling plan corresponds to an invalid path, the fitness is a fixed penalty value that is greater than the total transport distance of all corresponding valid paths in the current population;

[0043] 2.4) Update the particle's velocity and position through each iteration:

[0044] In the kth iteration of the BPSO algorithm, the N-dimensional position vector of the i-th particle in the population is recorded as The velocity vector is The iterative update calculation formula of the particle in the dth dimension is as follows:

[0045]

[0046]

[0047] Among them, w represents the inertia coefficient, C1 and C2 are called learning factors, represents the historical optimal position of the individual particle, Represents the position of the global optimal particle, rand() is a random number in the interval [0,1];

[0048] If the updated calculated Not in Ω * In the process, correction calculation is performed so that The details are as follows:

[0049] The corresponding position vector

[0050] if Updated to until

[0051] 2.5) After reaching the number of iterations, the optimization scheduling plan corresponding to the position vector of the global optimal particle is output.

[0052] The present invention has the following beneficial effects and advantages:

[0053] 1. Stability and efficiency. It can consider different task selection strategies and different task execution orders to solve AGV scheduling solutions, effectively reducing the total AGV transportation distance while ensuring the normal completion of various transportation tasks.

[0054] 2. Flexibility and scalability: in the face of different strategy scales, it can dynamically choose to execute exhaustive and particle swarm optimization solution strategies, taking into account both solution speed and quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is the overall flow chart of the present invention;

[0056] Figure 2 It is an abstract topology of the AGV working environment;

[0057] Figure 3 Schematic diagram of the test questions for 10 outbound tasks;

[0058] Figure 4 Schematic diagram of the genetic algorithm crossover operator operation based on the test problem of 10 outbound tasks;

[0059] Figure 5 Schematic diagram of the genetic algorithm mutation operator operation based on the test problem of 10 outbound tasks;

[0060] Figure 6 This is the initial infographic for the 160 outbound tasks;

[0061] Figure 7 A detailed execution information diagram of the tasks selected for execution under the optimized scheduling plan;

[0062] Figure 8 Schematic diagram of the benchmark scheduling scheme for the test problem of 160 outbound tasks;

[0063] Figure 9 Schematic diagram of the optimized scheduling solution for the test problem of 160 outbound tasks;

[0064] Figure 10 A schematic diagram of the detailed timing relationship of some tasks under the optimized scheduling scheme; DETAILED DESCRIPTION

[0065] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0066] The present invention combines the actual problem background to carry out mathematical modeling and algorithm design. The detailed description of the problem background is as follows:

[0067] The specific problem addressed by this invention stems from a manufacturing company that has built an automated production line integrated with an automated warehousing and logistics system. This automated warehousing and logistics system, located at the final stage of the production line, is responsible for transporting and managing the storage of finished couplings from the processing line to the warehouse. KUKA robots transfer workpieces from the machine to the warehouse unloading area, while automated guided vehicles (AGVs) transport pallets containing workpieces from the unloading area to the workpiece storage area. The goal of this invention is to provide a transportation task scheduling solution for this automated logistics and warehousing system that manages the transportation and storage of finished products while reducing transportation distances and thereby improving the system's efficiency. AGVs complete workpiece transport tasks within the warehouse area of ​​this automated logistics and warehousing system. The warehouse area is divided into five categories: work points, preparation points, high-speed points, obstacle points, and charging points. Based on business logic requirements, the warehouse area is divided into unloading areas, finished product storage areas, and empty pallet areas. Each work point in the unloading area can accommodate a maximum of one pallet, while each work point in the empty pallet area and finished product storage area can accommodate a maximum of three pallets. In this invention, the completion of a workpiece's processing is defined as the arrival of a shipping task. When the AGV transports the pallet carrying the workpieces from the unloading area to the finished product storage area, the AGV completes an outbound task. Correspondingly, when the AGV transports the empty pallet from the empty pallet area to the unloading area, the AGV completes an inbound task. Pallets and workpieces can only be placed at work points. For the same work point, after completing an outbound task, the AGV needs to ensure that the subsequent workpieces arriving at that point are placed on the pallet through timely inbound operations. After completing all tasks, the AGV will return to the nearest high-speed point. The AGV uses laser SLAM navigation technology, and there is a unique shortest path between any two topological points. Therefore, the problem studied by the present invention is to determine the optimal (or near-optimal) task execution order in the face of multiple outbound tasks with known arrival times, with the goal of minimizing the total travel distance of the AGV. Under this order, the AGV starts from the initial position, and through timely outbound and inbound operations, it transports all workpieces to the finished product storage area and finally stays at the high-speed point. In addition to the above description, the present invention also makes the following assumptions:

[0068] The AGV, production line, and KUKA robot operate continuously without any faults, regardless of the AGV's low battery level.

[0069] AGV travels at a constant speed during transportation;

[0070] At the initial moment, each workstation in the unloading area has an empty pallet, each workstation in the empty pallet area has three empty pallets stacked, and there are no pallets in the finished product storage area;

[0071] At the initial moment, the AGV is at the charging point;

[0072] Regarding the time it takes for an AGV to complete a task, only the travel time between the starting point and the end point is considered, not the time for loading and unloading operations.

[0073] The single-carrier automated guided vehicle workshop path planning method based on directed acyclic graph modeling follows the idea of ​​selecting tasks and executing them to establish a mathematical model and design an algorithm. The algorithm proposed in this invention is based on the following mathematical model:

[0074] 1) Task selection strategy model. Since a pallet can hold multiple workpieces, for each unloading point, there are multiple outbound task selection strategies to ensure the minimum number of outbound tasks. Each outbound task will generate an inbound task.

[0075] 2) Based on the Directed Acyclic Graph (DAGDTSP), the dynamic distance traveling salesman problem (DAGDTSP) model treats each selected task as a node. The goal is to find a path that visits every node once and minimizes the total distance traveled by the AGV, while also satisfying the execution order constraints between some tasks.

[0076] Mathematical Model 1) - Task selection strategy model is described in detail as follows:

[0077] Let the task set X={x1,...,x i ,...,x N ,x N+1 ,...,x N+i ,...,x 2N x1,...,x N The outbound tasks are to arrive at the unloading area in sequence. Outbound task x i The corresponding warehousing task is x N+i .remember Represents the set of tasks to be executed by executing the task selection strategy, where M represents the number of outbound tasks to be executed. The corresponding warehousing task is The scheduling plan is expressed as X e The maximum capacity of the tray is C, X and X e The inclusion relationship between them changes with the value of C, as shown in the following formula:

[0078]

[0079] The pallet can hold multiple workpieces. Therefore, not every workpiece needs to be shipped out by AGV after it is completed. The number of work points in the unloading area is r, and the task sequence of arriving at the i-th work point is R i is the number of tasks that have arrived at the i-th work point. N represents the total number of outbound tasks. Among them, the quantitative relationship is as follows:

[0080]

[0081]

[0082] for When the AGV transports the pallet out of the work point after the task arrives, it is called Tasks are selected. Based on the principle that each work point in the blanking area has the least number of tasks to perform, a common selection strategy is: If j%C=0 or j=R i ,but The task is determined to be executed. In the present invention, this task selection strategy is referred to as the benchmark task strategy. Under the benchmark task selection strategy, the plan in which tasks are executed in the order of arrival is called the benchmark scheduling plan. In the present invention, the benchmark scheduling plan is the reference object for evaluating the optimal (or near-optimal) scheduling plan.

[0083] Under a given set of tasks, in addition to the benchmark task selection strategy, there are other strategies that can minimize the number of outbound tasks performed by AGV at each work point in the unloading area. In the BPSO fusion framework, the task selection strategy is first formulated according to the principle of minimizing the number of outbound tasks, and then the exhaustive and particle swarm optimization strategies are adopted according to the size of the selection strategy space to solve the optimal (or near-optimal) scheduling solution. Therefore, it is necessary to analyze the spatial complexity of the task selection strategy. At the i-th work point in the unloading area, the AGV completes at least The total number of outbound tasks selected by AGV is at least For task sequences remember in, Indicates outbound tasks It is executed by AGV, that is, it is selected as the task node in the DAGDTSP model. With X e The affiliation between them depends on B i The corresponding element value in is expressed as follows:

[0084]

[0085] In the present invention, the formulation of the task selection strategy is based on the principle of minimum number of outbound tasks, that is, to ensure that the number of outbound tasks of AGV at each work point in the unloading area is minimum. i The following two constraints should be met:

[0086]

[0087]

[0088] Note B i The permutation and combination space of the elements in is Ω i , correspondingly, when the first constraint is met, the combination space is When the second constraint is met, the combination space When both conditions are met at the same time, the combined space can be recorded in and In the space of , the number of elements in the permutation and combination can be quantified as follows:

[0089]

[0090]

[0091] Also let the set B=(b1,...,b i ,...,b N ), b i ∈{0,1}, corresponding to X c Whether the outbound task in is executed. Then there is a quantitative relationship between B and the set of outbound tasks selected for execution at each work point in the unloading area:

[0092]

[0093] Remember vector space The Cartesian product is Ω * , the number of selection strategies for the executed tasks is |Ω * |, specifically defined as follows:

[0094]

[0095] Mathematical Model 2) - The dynamic distance traveling salesman problem model (DAGDTSP) based on directed acyclic graph is described in detail as follows:

[0096] For the set of tasks to be executed In the present invention, Represented as a four-tuple That is, the transportation starting point, transportation end point, arrival time and completion time of the task. For the unloading area, finished product storage area and empty pallet area of ​​the warehouse, their work point sets are respectively recorded as P I 、P G 、P R For any work point p in the warehouse i, the number of pallets is |p i |. Any two points p i 、p j There is a unique shortest path, the distance is recorded as D(p i ,p j ). Therefore, for the outbound task Issued together with the arrival of the task; outbound task The transport destination According to the nearest neighbor principle, the finished product storage area P G Internal distance transportation starting point The nearest point is expressed as follows:

[0097]

[0098] Issued together with the arrival of the task; The AGV transports the pallet carrying the workpiece to Similarly, for the warehousing task Transportation starting point Select according to the principle of shortest total distance, that is, the path (outbound task The end -Warehousing tasks Starting point -Warehousing tasks The end ) is the shortest, which can be expressed as follows:

[0099]

[0100] The end point of the incoming task is the same as the starting point of the corresponding outgoing task, that is, The AGV starts to move the pallet with the workpiece from Transport to moment; The AGV transports the empty pallet to moment.

[0101] In the present invention, the set of tasks to be executed is Create a directed acyclic graph G =<V,e> ,V=X e , where V represents the set of nodes in G and E represents the set of directed edges in G. represents a known directed edge, Indicates a task Before The following three constraints are defined for the edges in the path:

[0102] The first constraint is about the execution order between outbound tasks and inbound tasks, which can be expressed as: if and but

[0103] The second constraint is about the execution order of outbound tasks, which can be expressed as: if and but

[0104] The third constraint is about the order between the completion time of the outbound task and the arrival time of the inbound task, which can be expressed as: Should be Complete before arrival, i.e.

[0105] Each node is visited once, and the path that satisfies the first and second constraints is defined as a possible path. The possible path that satisfies the third constraint is defined as a valid path. The possible path that does not satisfy the third constraint is defined as an invalid path. The transfer distance between two task nodes in G is the shortest path distance between the end point of the predecessor task and the starting point of the successor task. The goal of solving the DAGDTSP model is to find a valid path with the minimum total distance. The solution space of the possible path and the valid path is defined as Ω respectively. p and Ω v ,Ω v ∈Ω p . Define Ω v The i-th task execution sequence in Also remember the charging point p c , record the high-speed point set P in the warehouse H By solving the DAGDTSP model, we can obtain the shortest effective path X v Expressed as:

[0106]

[0107]

[0108] According to the above mathematical model, the present invention designs a corresponding solution algorithm:

[0109] 1) For the DAGDTSP model, a customized genetic algorithm (IGA) is proposed to solve the scheduling solution that minimizes the total AGV transportation distance under a certain task selection strategy;

[0110] 2) When solving the optimal scheduling solution, considering the impact of task selection strategy on solving the optimal scheduling solution, a fusion framework based on the binary particle swarm optimization (BPSO) algorithm is proposed;

[0111] The customized genetic algorithm design includes chromosome representation, population initialization, fitness function, and genetic operators, which are described as follows:

[0112] 1.1) Chromosome Representation: Direct representation is a typical path encoding technique in existing research, typically representing a path as a sequence of node identification numbers. In the DAGDTSP model, the encoding length is fixed, and there are no invalid paths such as loops. Therefore, the present invention chooses direct representation for chromosome encoding when designing the genetic algorithm.

[0113] 1.2) Population Initialization: A chromosome represents a topological order in a directed acyclic graph. The Kahn algorithm is a typical topological sorting method that works by sequentially selecting nodes with in-degree 0 and inserting them into the visited node sequence. When using the Khan algorithm to initialize the population, in order to generate a random topological sort, faced with multiple nodes with in-degree 0, this paper introduces a random selection operation to achieve randomness in the initialization of the population.

[0114] 1.3) Fitness Function: A chromosome represents the topological order in a directed acyclic graph, i.e., the possible paths defined in the DAGDTSP model. It is important to note that a possible path may be an invalid path. Therefore, the fitness of a chromosome is calculated in two ways: when the chromosome is a valid path, the fitness is the total transport distance; when the chromosome is an invalid path, a fixed penalty value is assigned, which is much larger than the distance of all valid paths in the current population.

[0115] 1.4) Genetic operators, including selection operators, crossover operators, and mutation operators:

[0116] 1.4.1) Selection Operator: Based on the principle of survival of the fittest, the selection operation makes individuals with higher fitness values ​​more likely to be selected for the next generation. Since chromosomes can represent both valid and invalid paths, and valid paths often make up a small fraction of a population, an elitist strategy is used as the selection strategy. The elite group consists of all valid paths in the current population. This elitist strategy prevents chromosomes representing valid paths from being eliminated after the selection operator.

[0117] 1.4.2) Crossover Operator: After selection, individuals are crossed to produce a variety of promising offspring. The crossover operation is the key method for generating new individuals and is also an important feature that distinguishes genetic algorithms from other evolutionary algorithms. Let two parent chromosomes P1, P2∈Ω p, the crossover operation is completed in the following four steps:

[0118] Step 1: Randomly select two tasks Let Y=Y1∪Y2, Y1 and Y2 are respectively and subsequences between;

[0119] Step 2: For If the encoding order If it does not hold true for P1 and P2, then according to the nearest principle, replace y to Before or Then, we can get P′1, P′2;

[0120] Step 3: Exchange between P′1 and P′2 The subsequence of the elements in is obtained, P″1, P″2;

[0121] Step 4: For P″1, P″2, if the relative positions of any two genes (i.e., tasks) on the chromosome do not satisfy the first constraint or the second constraint, adjust the positions of the corresponding genes so that they are adjacent and satisfy both constraints. By adjusting the gene positions of P″1, P″2, the resulting chromosome is denoted as C1, C2∈Ω p .

[0122] 1.4.3) Mutation operator: Mutation is responsible for adding new features to individuals, thereby maintaining the variability of the population to prevent premature termination in the genetic algorithm. For the parent chromosome P1∈Ω p The mutation operation is mainly completed in two steps: outbound task mutation and inbound task mutation:

[0123] Step 1: Randomly select several outbound tasks on P1 and change their positions. Based on the nearest neighbor principle, three tasks on P1 are selected and recorded as Coding order On P1, random adjustment exist and The encoding position between , we get P′1. Then, as described in Step 4 of the crossover operation, adjust the encoding order of P′1 to obtain P″1∈Ω p , otherwise P″1=P′1;

[0124] Step 2: Randomly select several warehousing tasks in P″1 and change their positions. Based on the nearest neighbor principle, Coding order Established on P″1. Random adjustment exist and The encoding position between them is C1∈Ω p .

[0125] The BPSO-based fusion algorithm framework design includes particle representation, population initialization, fitness function, and particle velocity and position update mechanisms. The algorithm framework also adopts an adaptive solution strategy to accommodate different task selection strategies and scales. The algorithm framework design is described in detail below:

[0126] 2.1) Particle representation: In the particle swarm algorithm, individuals are called particles. The solution to the problem is represented by particles at different positions. Each particle has two properties: position and velocity. In this study, the velocity and position of the particle are both represented as an N-dimensional vector. N is the number of all outbound tasks. In the particle's position vector, the value of each dimension indicates whether the corresponding task is executed. If it is executed, it is 1, otherwise it is 0. In the particle's velocity vector, the value limit of each dimension is expressed in the form of probability, which is limited between [0,1]. The particle's position vector space is the Cartesian product Ω in the task selection strategy model. * ;

[0127] 2.2) Particle swarm initialization: Particle swarm initialization adopts random method. The process of randomly generating a particle position vector is as follows: First, generate vector space Ω i , all vectors with 1≤i≤r, and then randomly select a vector from each space, and finally sequentially splice the selected vectors. For the velocity vector of each particle, each dimension is randomly assigned a value in the interval [0,1];

[0128] 2.3) Fitness Function: For each particle, the set of selected tasks is obtained by mapping the particle's position vector to the task selection strategy. The customized genetic algorithm proposed in this paper aims to minimize the total distance traveled by the AGV and solves the task execution order under a specific task selection strategy, i.e., the optimal (or near-optimal) scheduling solution. The fitness of a particle is defined as the total distance traveled by the AGV in the optimal (or near-optimal) scheduling solution under the corresponding task selection strategy.

[0129] 2.4) Speed ​​and position update: During the iterative search for the optimal solution, the position of the particle in the solution space usually changes continuously. Each particle determines the speed and position of the next iteration based on its own historical best position and the position of the global best particle in the population. In this paper, the particle update adopts the update mechanism of the BPSO algorithm. The BPSO algorithm maps the dimensions of the solution from a continuous range to discrete values ​​in the interval [0, 1] based on the property of PSO that was originally adapted to the continuous solution space. Regarding the particle update mechanism, during the k-th iteration of the BPSO algorithm, the N-dimensional position vector of the i-th particle in the population is recorded as The velocity vector is The iterative update calculation formula of the particle in the dth dimension is as follows:

[0130]

[0131]

[0132] Among them, w represents the inertia coefficient, which decreases linearly with the number of iterations; C1 and C2 are called learning factors, which are used to adjust the step size of the particle flying towards the optimal value of the individual position and the optimal value of the group position, respectively. represents the optimal value of the individual particle position, Represents the optimal value of the group position, and rand() is a random number in the interval [0,1].

[0133] It should be noted that if the calculated Not in Ω * In the process, a correction calculation is required to make Known Corresponding record During the correction calculation process, if Updated to until The correction calculation process can be expressed as follows:

[0134]

[0135] 2.5) Adaptive Solution Strategy: The BPSO fusion framework proposes different solution strategies based on the scale of the task selection strategy. If the task selection strategy scale is less than a threshold, the exhaustive strategy is executed; otherwise, the BPSO-based strategy is executed. The exhaustive strategy iterates through the optimal scheduling solutions for each task selection strategy and selects the one with the shortest total AGV travel distance. The BPSO-based strategy treats each selection strategy as a particle, iteratively updates the particle position and velocity, and outputs the optimized scheduling solution for the globally optimal particle.

[0136] This embodiment provides a method for workshop path planning for a single-carrier automated guided vehicle based on directed acyclic graph modeling, including:

[0137] 1) Task selection strategy model, based on the principle that each work point in the unloading area has the least number of tasks to be executed, maps all task selection strategies for a given production task into a finite binary vector space. Taking the production plan of 10 workpieces as an example, the topology of the AGV working environment is as follows: Figure 2As shown in the figure, the transport starting points of the 10 workpieces are 152, 157, and 158. Let the maximum capacity of the pallet be C = 2. Figure 3 As shown in Figure 2, if the AGV adopts the benchmark task selection strategy to determine the tasks to be executed, the tasks to be executed are 2, 4, 6, 8, 9, 10, 12, 14, 16, 18, 19, and 20.

[0138] 2) Based on the Directed Acyclic Graph model, the Dynamic Distance Traveling Salesman Problem (DAGDTSP) model treats all tasks under a given task selection strategy as nodes to be visited. The node distance is the distance between the end point and the starting point of two consecutively executed tasks. The node distance changes with the working environment (the number of pallets at each point). The constraints on the order of task execution (local order constraints on task execution, order constraints on outbound task execution, and task completion-arrival time constraints) are modeled as directed edges that must be satisfied by the DAGDTSP sorting. Figure 3 As shown in Figure 3, under the benchmark task selection strategy, the AGV selects task nodes 2, 4, 6, 8, 9, 10, 12, 14, 16, 18, 19, and 20 for execution. The known directed edges are (2,12), (12,8), (4,14), (14,8), (8,18), (6,16), (16,9), (9,19), (10,20), (2,9), (2,10), (4,9), (4,10), and (6,10).

[0139] 3) A customized improved genetic algorithm (IGA) for solving the DGADTSP problem encodes the order in which the AGVs execute tasks based on the concept of task nodes in the DAGDTSP model. A fitness function and genetic operators are also designed specifically for this problem to penalize invalid paths. The genetic algorithm terminates when a fixed number of iterations is reached.

[0140] 3.1) Crossover operator implementation example, such as Figure 4 In the test problem of 10 outbound tasks, the parent chromosome P1 = (2, 12, 4, 14, 8, 18, 6, 16, 10, 20, 9, 19), P2 = (2, 12, 4, 14, 6, 16, 9, 19, 8, 18, 10, 20), and the crossover process is as follows:

[0141] Step 1: Randomly select two tasks Let Y=Y1∪Y2, Y1 and Y2 are respectively and The subsequence between , then Y1 = {12, 4, 14}, Y2 = {12, 4, 14, 6, 16, 9, 19}, Y = {12, 4, 14, 6, 16, 9, 19, 8};

[0142] Step 2: When y=6,16,9,19, the encoding order It does not hold on P1. According to the nearest principle, replace 6, 16, 9, and 19 in P1. Previously, we got P′1=(2,12,4,14,8,18,6,16,10,20,9,19). Coding order It holds true on P2, so P′2=P2;

[0143] Step 3: Swap the subsequence (2, 12, 4, 14, 6, 16, 9, 19, 8) of P′1 with P2 ′ The subsequence (2,12,4,14,8,19,16,9,6) is transferred to the other side, and P″1 = (2,12,4,14,6,16,9,19,8,18,10,20), P″2 = (2,12,4,14,8,19,16,9,6);

[0144] Step 4: Since P″1∈Ω p , then C1=P″1. Due to Adjust P″2 to get C2=(2,12,4,14,8,6,16,9,19,18,10,20),C2∈Ω p .

[0145] 3.2) Mutation operator implementation example, such as Figure 5 In the test problem of 10 outbound tasks, the parent chromosome P1 = (2, 12, 4, 14, 6, 16, 8, 18, 9, 19, 10, 20), P2 = (2, 12, 4, 14, 6, 8, 16, 18, 9, 19, 10, 20), the mutation process is as follows:

[0146] Step 1: Randomly select outbound task 8 on P1 and change its position. Based on the nearest neighbor principle, record Coding order On P1, random adjustment exist and The encoding position between them is P′1=(2,12,4,14,6,8,16,18,9,19,10,20). p , then P″1=P′1;

[0147] Step 2: Randomly select the storage task 18 in P″1 and change its position. Based on the nearest neighbor principle, Coding order Established on P″1. Random adjustment exist The subsequent encoding positions give C1 = (2, 12, 4, 14, 6, 8, 18, 16, 9, 19, 10, 20), C1∈Ω p .

[0148] 3) Based on the BPSO fusion algorithm framework, the coordinates of the particles are defined as the binary vectors of the mapping task selection strategy, and the fitness of the particles is the optimal (or near-optimal) solution of the DAGDTSP model under this strategy. In this algorithm framework, the solution method of the DAGDTSP model is called the inner optimization component (such as IGA). Figure 1 As shown in Figure 2, according to the selection strategy scale of the executed tasks, the BPSO fusion framework adaptively adopts an exhaustive strategy or a strategy based on the BPSO algorithm, and finally outputs the optimal (or near-optimal) scheduling solution.

[0149] In order to evaluate the optimization effect of the path planning algorithm designed in this invention, a transport distance optimization evaluation index is designed. The transport distance optimization evaluation index F is used to represent the transport distance optimization effect of the optimized scheduling scheme compared with the benchmark scheduling scheme. The higher the F value, the better the optimization effect. Under a given task set, S is used to represent the transport distance optimization effect of the optimized scheduling scheme compared with the benchmark scheduling scheme. basic is the total transport distance of AGV under the benchmark scheduling scheme, S optimal is the total AGV transportation distance under the optimization strategy, and the transportation distance optimization evaluation index F is defined as follows:

[0150] F=(S basic -S optimal ) / S basic

[0151] like Figure 6 As shown in the figure, a test problem with 160 outbound tasks is designed. The outbound tasks in the problem are numbered from 1 to 160, and each task is represented by a triple (task number, transportation starting point, arrival time (seconds)). Taking this problem as an example, in the optimization solution solved by the BPSO fusion framework, the task is represented by a five-tuple (task number, transportation starting point, transportation end point, start execution time (seconds), task execution duration (seconds)). The start execution time of each task is no earlier than the arrival time of the task. The specific information is as follows: Figure 7 In the baseline scheduling scheme and the optimized scheduling scheme, the status of each task is as follows: Figure 8 、 Figure 9As shown. In the task status diagram, the outbound task is represented by a green rectangle, and the inbound task is represented by a red rectangle. The arrival time and completion time of the task determine the length of the rectangle. The period from the arrival of the task to the start of execution is defined as the waiting stage. Compared with the benchmark scheduling scheme, the optimized scheduling scheme solved by the BPSO fusion framework increases the waiting time from the arrival to the completion of some tasks, effectively reducing the total AGV transportation distance, and the transportation distance optimization evaluation index F = 0.0588. This is because the AGV extends the waiting time of some tasks and switches to perform other tasks that are closer during this period. Figure 9 For example, task 311 arrives after task 151 starts executing, and then starts executing after tasks 303 and 158 are completed. The starting time is expressed as That is, the moment when the previous task is completed. Figure 10 is an example illustrating the detailed timing relationship between tasks 151, 311, 158, and 318, where

Claims

1. A single-carrier automated guided vehicle workshop path planning method based on directed acyclic graph modeling is characterized by: The following steps are involved: Constructing a task selection strategy model based on the shop floor layout and a dynamic distance traveling salesman problem model based on directed acyclic graph modeling; Obtaining the number of task selection strategies based on the task selection strategy model; The solution strategy is determined according to the number of task selection strategies, and the dynamic distance traveling salesman problem model based on directed acyclic graph modeling is solved under different task selection strategies: when the number of task selection strategies is less than the threshold, the exhaustive strategy is used to traverse and solve the optimal scheduling scheme under each task selection strategy, and the one with the shortest total AGV driving distance is selected; otherwise, the strategy based on the BPSO algorithm is used to obtain the optimal scheduling scheme of the global optimal particle.

2. The method for single-carrier automated guided vehicle workshop path planning based on directed acyclic graph modeling according to claim 1 is characterized in that: The workshop layout includes: The points in the warehouse area are divided into five categories: working points, preparation points, high-speed points, obstacle points, and charging points. According to the needs of business logic, the warehouse area includes unloading area, finished product storage area and empty pallet area. When the AGV transports the pallet carrying the workpiece in the unloading area to the finished product storage area, the AGV completes an outbound task; when the AGV transports the empty pallet in the empty pallet area to the unloading area, the AGV completes an inbound task.

3. The method for single-carrier automated guided vehicle workshop path planning based on directed acyclic graph modeling according to claim 1 is characterized in that: The task selection strategy model is as follows: For the task selection strategy model space Ω * , the number of task selection strategies is |Ω * |: Among them, r is the number of working points in the unloading area; C is the maximum capacity of the pallet; R i is the number of tasks that have reached the i-th work point.

4. The method for single-carrier automated guided vehicle workshop path planning based on directed acyclic graph modeling according to claim 1, characterized in that: The dynamic distance traveling salesman problem model based on directed acyclic graph modeling is as follows: Among them, X v is the shortest effective path for total transport distance, D(·) represents the distance function between nodes; p c Indicates the charging point, Ω v represents the valid path space, Represents Ω v The i-th path in , the path is used to characterize the task execution order, express The first mission transportation starting point, express The starting point of the j-th task transportation, express The transport destination of the jth task, express The transport destination of the j+1th task; P H is the set of high-speed points in the warehouse, and p is P H At a certain point in the graph, M is the number of outbound tasks being executed; a node represents an executed task, and an edge represents the execution order between two tasks; The edges in the path need to satisfy the following constraints, including: The first constraint is the execution order constraint between the outbound task and the inbound task; The second constraint is the execution order constraint between outbound tasks; The third constraint is the order of the completion time of the outbound task and the arrival time of the inbound task; Each node is visited once, and the path that meets the first and second constraints is defined as a possible path; the possible path that meets the third constraint is defined as a valid path; and the possible path that does not meet the third constraint is defined as an invalid path.

5. The method for single-carrier automated guided vehicle workshop path planning based on directed acyclic graph modeling according to claim 1 is characterized in that: The genetic algorithm is used to solve the dynamic distance traveling salesman problem model based on directed acyclic graph modeling under a fixed task selection strategy, including the following steps: 1.1) Chromosome representation: direct representation is used to encode the possible paths into chromosomes; 1.2) Population initialization: Multiple random topological sortings obtained by the Kahn algorithm are used as alternative scheduling schemes; 1.3) Fitness: When the chromosome corresponds to the effective path space Ω v The fitness of the path in is the total transportation distance; When a chromosome corresponds to an invalid path, the fitness is a fixed penalty value, which is greater than the total transport distance of all corresponding valid paths in the current population; 1.4) Through selection, crossover and mutation operations, the optimal scheduling solution under the fixed task selection strategy is obtained.

6. The method for single-carrier automated guided vehicle workshop path planning based on directed acyclic graph modeling according to claim 1, characterized in that: The strategy based on the BPSO algorithm is used to obtain the optimal scheduling solution for the global optimal particles, including the following steps: 2.1) Particle Representation: The task selection strategy is expressed by the position vector of the particle. The position vector space of the particle is the task selection strategy model space Ω * ; 2.2) Particle swarm initialization: The process of randomly generating a particle's position vector is as follows: Generate the task selection strategy model space Ω * The subspace of Ω, that is, the vector space Ω i ,1≤i≤r, r is the number of working points in the blanking area; Then, randomly select a vector from each subspace; Finally, the selected vectors are sequentially concatenated; 2.3) Fitness: For each particle, a genetic algorithm is used to find the optimal scheduling solution under a fixed task selection strategy by mapping the particle's position vector to the task selection strategy. The fitness of a particle is: When the optimal scheduling scheme of the particle corresponds to the effective path space Ω v The fitness of the path in is the total transportation distance; When the particle's optimized scheduling plan corresponds to an invalid path, the fitness is a fixed penalty value that is greater than the total transport distance of all corresponding valid paths in the current population; 2.4) Update the particle's velocity and position through each iteration: In the kth iteration of the BPSO algorithm, the N-dimensional position vector of the i-th particle in the population is recorded as The velocity vector is The iterative update calculation formula of the particle in the dth dimension is as follows: Among them, w represents the inertia coefficient, C1 and C2 are called learning factors, represents the historical optimal position of the individual particle, Represents the position of the global optimal particle, rand() is a random number in the interval [0,1]; If the updated calculated Not in Ω * In the process, correction calculation is performed so that The details are as follows: The corresponding position vector if Updated to until 1≤j≤r. 2.5) After reaching the number of iterations, the optimization scheduling plan corresponding to the position vector of the global optimal particle is output.

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