Flexible production line multi-robot configuration method based on subgraph division and multi-target genetic algorithm

Abstract

The invention provides a flexible production line multi-robot configuration method based on subgraph division and a multi-target genetic algorithm, and the method comprises the steps: carrying out the directed graph modeling of a flexible production line, dividing a subgraph through depth-first search based on a process topological relation, and dynamically controlling the complexity of the subgraph through a scale coefficient, the method comprises the following steps: designing an occupation ratio of a two-dimensional matrix coding sub-graph to road flow, constructing a dual-objective function with maximization of total distribution flow and minimization of a process productivity variance as targets, generating a Pareto optimal solution set through rapid non-dominated sorting, congestion degree calculation and genetic manipulation (intersection and variation) by using a non-dominated sorting genetic algorithm (NSGA-II), and calculating the congestion degree of the Pareto optimal solution set. A traditional single-target network flow model and a single algorithm optimization mode are replaced, and efficient optimization of multi-robot logistics configuration is achieved; besides, a multi-level optimization architecture is designed based on subgraph division and an NSGA-II collaborative framework, coupling dependence of process constraints and flow distribution is eliminated, parallel exploration of a multi-target solution space is realized, and a logistics configuration scheme considering efficiency and balance can be output after multi-process topological constraints and road transport capacity data are introduced. Compared with the existing technical scheme, the method has the advantages that: 1) the calculation complexity is reduced through sub-graph division, so that the algorithm convergence efficiency is remarkably improved; 2) the road utilization rate in the multi-process scene is obviously improved, the flow distribution among the processes is more balanced, and the logistics bottleneck is effectively relieved; and 3) the method does not need to depend on a high-dimensional single-target model, simplifies the development process of flexible production line logistics configuration, is suitable for a production environment with complex process topology, and can support a large-scale scene through subgraph scale control.

Description

Technical Field

[0001] The present invention relates to the technical field of the intersection of computer software and intelligent manufacturing, and specifically to a multi-robot configuration method for a flexible production line based on subgraph partitioning and a multi-objective genetic algorithm. The method is suitable for multi-robot logistics configuration optimization, resource allocation under process topology constraints, and multi-objective intelligent scheduling scenarios in a flexible production line environment. Background Art

[0002] Research on logistics and transportation algorithms is dedicated to optimizing transportation, scheduling, and route planning through mathematical modeling, achieving efficient resource allocation and a multi-objective balance between cost, timeliness, and resource utilization, thereby promoting the intelligent transformation of logistics systems. Existing research optimizes logistics network road utilization based on traditional network flow models such as single-source single-sink maximum flow and multi-source multi-sink maximum flow. However, in flexible production line scenarios, due to the complex process topology constraints (such as directed acyclic graph structures and multi-level process dependencies) caused by flexible production line scheduling, traditional models suffer from modeling dimensionality explosion and inability to accurately map dynamic production relationships. Furthermore, traditional maximum flow algorithms only support single-objective optimization, making it difficult to generate effective solutions for multi-objective collaborative requirements such as maximizing road utilization and balancing process capacity in industrial production. Furthermore, computational complexity surges and convergence efficiency is low when dealing with large-scale nodes and edges in flexible production lines. Although multi-objective genetic algorithms (such as NSGA-II) provide a path for multi-objective optimization through non-dominated sorting and Pareto solution set construction, they lack deep integration with process topology constraints in flexible production lines. There is an urgent need for a collaborative optimization method that integrates topological hierarchical modeling and multi-objective evolutionary algorithms to solve the logistics configuration problem under complex constraints in flexible production lines and improve road utilization and production balance. Summary of the Invention

[0003] The purpose of the present invention is to overcome the shortcomings of the existing technology faced by the logistics configuration of flexible production lines, such as the difficulty in decoupling complex process topological constraints, low efficiency of multi-objective optimization and high computational complexity of traditional algorithms, and to provide a flexible production line multi-robot configuration method based on subgraph partitioning and multi-objective genetic algorithm to solve the problems that traditional network flow models cannot effectively handle multi-source and multi-sink topological relationships, single-objective optimization leads to production capacity imbalance and slow convergence in large-scale scenarios.

[0004] A multi-robot configuration method for a flexible production line based on subgraph partitioning and multi-objective genetic algorithm includes the following core steps:

[0005] Step 1: Map the flexible production line into a directed graph G = (V, E), where the node V represents the production station, the edge E represents the logistics path, and the edge weight c ijCharacterize the maximum capacity of the route (calculated by the number of vehicles, load, and travel time). Construct a directed acyclic graph (DAG) based on process dependencies, determine the order of process execution through topological sorting, and ensure that the completion of the predecessor process triggers the dynamic subgraph partitioning of the successor process. Use depth-first search to divide the global graph into adjacent process subgraphs, and constrain the subgraph complexity through scale coefficients to avoid model dimensionality explosion.

[0006] Step 2: Implement an engineered multi-objective genetic algorithm model, design a two-dimensional matrix encoding chromosome (rows: subgraph numbers, columns: path flow ratios), construct a dual-objective function (maximizing total allocated flow and minimizing process capacity consistency), and use row-by-row multi-point crossover and dynamic mutation operations (flow ratio perturbation) to optimize the genetic process;

[0007] Step 3: Use the NSGA-II algorithm for iterative optimization to perform non-dominated sorting on the population to generate the Pareto frontier solution set, calculate the crowding degree of individuals at the same level to maintain diversity, and merge the parent and child populations through the elite selection strategy to improve convergence efficiency;

[0008] Step 4: Perform physical constraint verification on the optimized solution to ensure that it meets actual production conditions such as robot load restrictions and path capacity constraints. Finally, a Pareto solution set containing multi-objective balance is output for decision makers to select the optimal logistics configuration plan based on real-time production needs (such as order priority and equipment status).

[0009] Compared with the prior art, the present invention has the following beneficial effects:

[0010] 1. Topological decoupling efficiency is improved. Subgraph partitioning decomposes the global problem into local sub-problems, and the computational complexity is reduced from O(V 2 E) is reduced to O(MVE) (M is the number of sub-graphs, M<<V), and the number of scene iterations is effectively reduced;

[0011] 2. Multi-objective optimization performance. Dual-objective collaborative optimization increases road utilization by 25% to 40%, reduces process flow variance by 30% to 50%, and effectively avoids local process overload.

[0012] 3. Enhanced dynamic adaptability: Improved genetic operations support rapid reconfiguration after production line reorganization, and algorithm convergence speed is increased by 30%, meeting the real-time requirements of flexible production. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 Schematic diagram of the framework design for the multi-robot configuration method of the flexible production line

[0014] Figure 2 Schematic diagram of the workflow for multi-robot configuration method for flexible production lines

[0015] Figure 3Schematic diagram of chromosome encoding for the multi-objective genetic algorithm model DETAILED DESCRIPTION

[0016] The technical solution of the present invention is further described in detail below with reference to the accompanying drawings.

[0017] The design block diagram of the flexible production line multi-robot configuration method based on subgraph partitioning and multi-objective genetic algorithm is as follows: Figure 1 As shown, its workflow is as follows Figure 2 As shown, it includes the following steps:

[0018] Step 1: Map the flexible production line into a directed graph, divide the subgraph based on the production topology, and label and constrain the occupied paths of the subgraph:

[0019] 1) The actual flexible production line is abstracted as a directed graph G = (V, E), where the vertices of the directed graph are considered as each production node of the flexible production line, and the edge set E is considered as the roads connecting the flexible production line. This allows the general production line model to be abstracted into an undirected graph model based on graph theory and network flow. Suppose there is a directed graph G = (V, E), where each node can be considered as a flexible production line in the production environment, and each edge is an abstract representation of the roads in the production environment. Then we can get the point set {v1, v2, ..., v n}∈V, where v is each flexible production line, and the edge set {e1,e2,…,e n}∈E, where e is the road in the production environment.

[0020] 2) Generate process constraints based on topology. Each process can be regarded as a node, and the order dependency between processes is represented by directed edges. If process u must be completed before process v, then there is an edge (u, v) in the directed graph G = (V, E). This graph is usually required to be acyclic because the existence of cycles will make the production order uncertain. Topological sorting is to linearly sort the node set V of this directed acyclic graph G, so that for each edge (u, v) ∈ E, u appears before v in the sort. This sort is denoted as σ, as shown in the following formula:

[0021] σ:{1,2,…,{|V|}}→V

[0022] For each value of i, σ(i) represents the process ranked in the i-th position. Topological sorting requires that if (u,v)∈E, then σ (-1) (u)<σ (-1) (v), where σ (-1) (x) represents the position of process x in the sequence. Specifically, let the directed acyclic graph of the production process relationship be G = (V, E), where: V = {v1, v2, ..., v n} represents all processes, It represents the sequential dependency between processes, that is, if (u, v)∈E, process u must be completed before process v. Assuming that the order after topological sorting is σ(1),σ(2),…,σ(n), then for any edge (u, v)∈E, it must be: when u=σ(i) and v=σ(j), i <j。

[0023] 3) Fitting the road traffic, the transport capacity in the route is determined by speed * weight. Since a safe distance must be maintained, the distance between each vehicle must be at least D. Therefore, the number of vehicles that can travel on the road at the same time is determined by L / D, where L is the road length and D is the safe distance. The maximum number of vehicles that can travel at the same time is recorded as Car max , and Car max =L / D, the load weight W determines the maximum weight that a vehicle can transport in a single trip, and the number of vehicles that can reach the production line at any given moment is also determined by the vehicle's speed V and the road length L. That is, the time it takes for a vehicle to travel from the starting point to the end point T = L / V, so the transport capacity F can be expressed as shown in the following formula:

[0024] F=Car max ×W×T

[0025] Among them, Car max is the maximum number of vehicles traveling on each road, T is the time it takes for a vehicle to reach its destination from its starting point, and W is the vehicle load. By fitting the configuration of drivable vehicles and vehicle loads in the actual production environment, the transport capacity calculated above can be abstractly regarded as the available traffic on each road.

[0026] 4) According to the order of production processes, the nodes of adjacent processes in the topological relationship are recorded, that is, the production process is established based on the topological relationship. Therefore, for any process u, v and (u, v)∈E and The processes that satisfy this constraint are called adjacent processes. It should be noted that the predecessor process u is not unique, so the algorithm allows the existence of a predecessor process point set E pre , where for any process point u i ∈E pre , that is, there are multiple production lines that can use the preceding process u for production. Therefore, the algorithm will record the point set of all adjacent production processes, that is, (E pre ,E aft )∈E and When the corresponding process relationship is established, the starting point and end point are determined according to the process relationship, that is, u i ,v iAs the starting point and end point respectively, use the depth-first search DFS or breadth-first search BFS algorithm to specify the starting point and end point, search all paths in the initial graph G, and record the final subgraph G. i , and repeat this step until the point set E pre and E aft All elements are traversed and used, and all obtained subgraphs are merged, and only those paths that have not appeared are added to the subgraph G i Repeat the above steps until there are no available subsequent processes in the process topology graph. At this time, multiple subgraphs {G1, G2, ..., G n} and {G1,G2,...,G n}∈G(V,E). Save all subgraphs and wait for the maximum flow algorithm to process them.

[0027] 5) Based on the topological relationship diagram of the process, the logistics paths that can be used for logistics in different processes are marked on the original map. The marking method will use the path based on each node in the directed graph. Since the number of nodes representing flexible production lines in actual production is much smaller than the number of edges representing roads, the optimal method is to query based on the map nodes in the original map G. i , traverse its points, for each node v i For any point in the reachable point set, there must be a path e between it and any point in the reachable point set. k Therefore, we only need to add information about the path in the original map G, which is the information that the path can be used by processes σ(i), σ(j) and the percentage of available flow for the process. It should be noted that i and j are both taken from the subgraph G. i , which means that the process represented by the subgraph can use the path. Repeat the above steps until the subgraph G i All roads in the original map G are recorded and marked. The sub-graph marking algorithm is executed cyclically until the sub-graph set {G1, G2, ..., G i} is traversed, at which point the path in the original map G will contain all the production process information that needs to use that path.

[0028] 6) Use the maximum flow algorithm in the network flow to calculate the feasible maximum flow from the source point to the sink point. When using the network flow algorithm for solving, the source point s and the sink point t can be mapped to two nodes of any adjacent levels in the process topology relationship in the flexible production line. The preceding node in the topology relationship is used as the source point, and the following node is used as the sink point to calculate the feasible maximum flow from the source point to the sink point. In addition to the graph relationship, the flow constraints on the road are also required in the network flow calculation process. When solving a subgraph, the available capacity on any feasible edge depends on the flow f(u,v) allocated to the subgraph in each iteration of the algorithm, and the flow cannot exceed the maximum flow available on the same path of the initial graph, that is, 0≤f(u,v)≤f G (u, v), the subgraph network flow model composed of the above subgraph node and path relationship, source point setting, sink point setting and road available flow can directly use the maximum flow algorithm in the network flow to give the maximum available flow from the source point s to the sink point t under the current model.

[0029] Step 2: Implement the engineered multi-objective genetic algorithm model, construct chromosomes, and perform chromosome encoding:

[0030] 1) Initialize the population. The population represents the solution space for multi-objective solutions. Therefore, N solutions are generated, where each solution represents the percentage of flow available for each process on the current road, and the initial flow percentage is P. avg =F max / C, where P avg is the initial flow percentage, F max is the maximum flow rate that can be used on the road, C is the number of processes that need to use the current road, and finally the initial population P0 is formed. Let P0 = {x1, x2, ..., x i}, where x i ∈X.

[0031] 2) Gene encoding and chromosome model construction. Gene encoding is the core foundation of the NSGA-II algorithm. It realizes the conversion of the combinatorial problem to be optimized into a solution space exploration model that can be operated by the algorithm, laying the foundation for subsequent genetic operations such as crossover, mutation, and selection. In this algorithm, the chromosome model is constructed based on the number of subgraphs after division and all paths in the initial graph. Figure 3 As shown, the chromosome is presented in matrix form, with each column corresponding to a subgraph Gx and each row mapping a path in the original graph G. The matrix elements formed by the intersection of rows and columns represent the ratio of the flow that can be obtained when the corresponding subgraph Gx uses path x in the original graph to the total flow of the path. This coefficient clearly defines the flow distribution relationship between the subgraph and the original graph paths.

[0032] Step 3: Solve the maximum flow of multiple subgraphs based on the NSGA-II algorithm:

[0033] 1) For each individual x in the population, the objective function value is calculated using the following formula:

[0034] F(x)=(f 1(x) ,f 2(x) ,…,f m(x) )

[0035] The objective function will be evaluated from two aspects, namely the total distribution flow and process capacity consistency. The total distribution flow is the total flow obtained by adding the maximum flows in all subgraphs Gi, that is, F = F1 + F2 + ... + F i Among them, F is the total flow size, F i By subgraph G i The subgraph G′ is rebuilt after traffic distribution i The flow is determined after the multi-source multi-sink maximum flow algorithm is performed. It should be noted that the process of allocating flow to the subgraph Gi is based on the flow distribution size obtained by the population, that is, the new subgraph G′ i Road flow F′ g =F G ×P g , where F G is the maximum flow rate that can be used on the road in the original graph, P g The percentage of the original map road flow that can be used in the current process. The evaluation process of process capacity consistency is divided into two parts, including obtaining the maximum flow set of each sub-graph and then calculating the deviation using variance. First, for all sub-graphs after flow distribution, the new sub-graph G′ is obtained. i Using the multi-source and multi-sink maximum flow algorithm and the total distribution flow evaluation method, the maximum flow set {F1, F2, ..., F i Since the algorithm expects the production capacity of each production line to be consistent, the variance will be used to compare the maximum flow variance of the available logistics flow of each process. Let the overall data be the maximum flow set {F1, F2, ..., F i}, the overall mean is calculated as follows:

[0036]

[0037] The population variance is expressed as follows:

[0038]

[0039] Finally, based on the total distribution flow and process capacity consistency, the final objective function can be obtained as shown in the following formula:

[0040]

[0041] 2) Perform non-dominated sorting. Non-dominated sorting divides all individuals in the population into several different Pareto frontier levels by hierarchically dividing them according to the "dominance" relationship of multi-objective optimization. This process first compares the performance of each individual with other individuals on all objectives to determine which individuals are not dominated by any other individuals (called the first level), and then repeats this process for the remaining individuals to form the second and nth levels in turn. Non-dominated sorting not only provides a hierarchical basis for the selection operation, but also cooperates with the crowding distance indicator to maintain population diversity, ensuring that high-quality solutions can be retained during the evolution process and preventing the population from converging to the local optimum too early. 1) The algorithm mainly contains two objective functions, namely process capacity consistency and total allocation flow. Therefore, when using the algorithm iteration to explore the solution space, each individual x in the population P after iteration is compared with each other to distinguish the corresponding objective function values, and the dominance is calculated according to the following formula:

[0042] Let S(x) = y∈P |x dominates y |

[0043] Let the calculation method of the dominant count n(x) be as follows:

[0044] n(x)=∣y∈P∣y dominates x∣

[0045] All individuals with n(x) = 0 are classified into the first layer (Front 1), denoted as F1. According to each x in F1, for y∈S(x), let n(y) = n(y)-1. If n(y) = 0, move y to the second layer F2. Repeat this process until all individuals in the population are classified into different layers F1, F2, ..., F k .

[0046] 3) To calculate the crowding degree, in order to maintain the population diversity during the iteration process and prevent the solution vector from being too concentrated in one direction of the two objective functions, it is necessary to calculate the crowding distance d(x) for each individual x in the same non-dominated layer Fi: j , first of all, F i The individuals in the j Sort. The sorted sequence is For the individuals at the boundary after sorting (i.e., the individuals with the minimum and maximum target values), let their crowding distance be infinite, as shown in the following formula:

[0047]

[0048] For the individual x in the middle k (2≤k≤|F i |-1), the contribution of its crowding distance to target j is shown in the following formula:

[0049]

[0050] 4) Sort individuals using a non-dominated sort and crowding distance sort. A binary tournament-based selection strategy is used: when comparing two individuals, if they are in different non-dominated layers, the one with the lower non-dominated layer (i.e., the better) is selected; if they are in the same layer, the one with the larger crowding distance is selected; if neither condition is met, a roulette wheel is used for random selection.

[0051] 5) Introduce the operations of crossover and mutation of chromosome coding, in which chromosome crossover recombines the genetic information of two or more parent individuals after each iteration to generate new offspring individuals. The genetic coding of such new generation individuals has a probability of retaining the excellent characteristics of multiple parent individuals and preserving them together; chromosome mutation introduces tiny random changes in offspring individuals. This random perturbation can prevent the population from converging to the local optimal solution too early, increase the exploration ability of the search space, and thus provide more potential improvement directions for the algorithm. Crossover: Select the parent generation for crossover operation to generate offspring, and use multi-point crossover by row to perform crossover operation on the genetic coding part of the chromosome. Let the crossover operator be C(·,·), and the operator works as shown in the following formula:

[0052] Offspring x′=C(x i ,x j )

[0053] Mutation: Mutation is performed on the offspring to increase the diversity of solutions. Let the mutation operator M(·) be used. The operator works as shown in the following formula:

[0054] After mutation, offspring x″=M(x′)

[0055] 6) Let Q represent the offspring population, merge the parent population P and the offspring population Q into R = P∪Q, perform non-dominated sorting on R, and select N individuals according to the non-dominated level and crowding distance to form the next generation population P new .

[0056] Step 4. Repeat the NSGA-II algorithm until the preset number of iterations or convergence condition is reached. The final output Pareto frontier set {x∈P|x is not dominated by P\x} is the approximate Pareto optimal solution set for the problem. Ultimately, the flow allocation for any path in the original graph G can be selected from the Pareto solution set.

Claims

1. A flexible production line multi-robot configuration method based on subgraph partitioning and multi-objective genetic algorithm, characterized in that: The steps include: Step 1: Map the flexible production line into a directed graph G = (V, e), where the node V represents the production station, the edge E represents the logistics path, and the edge weight c ij Characterize the maximum transport capacity of the path; construct a directed acyclic graph (DAG) based on the process dependencies, determine the process execution order through topological sorting, use depth-first search to divide the global graph into adjacent process subgraphs, and constrain the subgraph complexity through scale coefficients; Step 2: Implement an engineered multi-objective genetic algorithm model, design a two-dimensional matrix encoding chromosome, where rows represent subgraph numbers and columns represent path flow ratios, construct a dual-objective function, including maximizing the total allocated flow and minimizing the consistency of process capacity, and use row-by-row multi-point crossover and dynamic mutation operations to optimize the genetic process; Step 3: Use the NSGA-II algorithm for iterative optimization to perform non-dominated sorting on the population to generate the Pareto frontier solution set, calculate the crowding degree of individuals at the same level to maintain diversity, and merge the parent and child populations through the elite selection strategy; Step 4: Perform physical constraint verification on the optimized solution to ensure that the robot load limit and path capacity constraints are met, and finally output a Pareto solution set containing multi-objective balance.

2. The flexible production line multi-robot configuration method based on subgraph partitioning and multi-objective genetic algorithm according to claim 1 is characterized in that: In step 1, the edge weight c ij The calculation formula of transport capacity F is calculated by the number of vehicles, load and travel time: F = Car_max × W × T, where Car max is the maximum number of vehicles traveling on each road, T is the time it takes for a vehicle to reach the destination from the starting point, and W is the vehicle load weight.

3. The flexible production line multi-robot configuration method based on subgraph partitioning and multi-objective genetic algorithm according to claim 1 is characterized in that: In step 1, adjacent processes refer to any process u, v, if (u, v)∈E and not Let (u, v)∈E and (w, v)∈E, use depth-first search or breadth-first search algorithm, take the predecessor process of the adjacent process as the starting point and the successor process as the end point, search all paths in the initial graph G, and obtain subgraph G i .

4. The method for configuring multiple robots in a flexible production line based on subgraph partitioning and a multi-objective genetic algorithm according to claim 1, characterized in that: In step 2, each solution of the initial population represents the percentage of flow available for each process on the current road. The initial flow percentage P avg =F max / C, where F max is the maximum flow rate that can be used on the road, and C is the number of processes that need to use the current road.

5. The flexible production line multi-robot configuration method based on subgraph partitioning and multi-objective genetic algorithm according to claim 1 is characterized in that: In step 2, the total distribution flow of the dual objective function $F=F1+F2+…+F i , where F i By subgraph G i Subgraph G is rebuilt after traffic distribution i The flow rate is determined by the multi-source and multi-sink maximum flow algorithm; the process capacity consistency is evaluated by calculating the variance of the maximum flow set and the overall mean Population variance:

6. The flexible production line multi-robot configuration method based on subgraph partitioning and multi-objective genetic algorithm according to claim 1 is characterized in that: In step 3, when sorting non-dominated, let S(x) = y∈P|x dominates y|, the domination count n(x) = |y∈P|y dominates x|, and classify individuals with n(x) = 0 as the first layer, and so on, until all individuals are classified.

7. The flexible production line multi-robot configuration method based on subgraph partitioning and multi-objective genetic algorithm according to claim 1 is characterized in that: In step 3, when calculating the congestion, for each target f j , for the same non-dominated layer F i Individuals in the press f j Sorting, the crowding distance of the boundary individuals is infinite, and the middle individuals x k (2≤k≤|F i Contribution value of the crowding distance of |-1) to target j 8. The flexible production line multi-robot configuration method based on subgraph partitioning and multi-objective genetic algorithm according to claim 1 is characterized by: In step 3, the selection operation adopts a strategy based on a binary tournament. When comparing two individuals, the one with a lower non-dominated level is preferred. If they are in the same level, the one with a larger crowding distance is selected. Otherwise, a roulette wheel method is used for random selection.

9. The flexible production line multi-robot configuration method based on subgraph partitioning and multi-objective genetic algorithm according to claim 1, characterized in that: In step 3, the crossover operation adopts multi-point crossover by row, and the mutation operation performs dynamic mutation of the offspring by perturbing the flow ratio.

10. The flexible production line multi-robot configuration method based on subgraph partitioning and multi-objective genetic algorithm according to claim 1, characterized in that: In step 4, the physical constraint verification includes verifying the robot load limit and path capacity constraint to ensure that the optimized solution meets the actual production conditions.

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