Multi-robot storage scheduling optimal scheme screening method based on dynamic density clustering
By using dynamic density clustering and genetic algorithm optimization, a high-quality multi-robot warehouse scheduling scheme is generated, which solves the problem of difficult diversity maintenance and achieves efficient and balanced scheduling scheme selection.
Patent Information
- Application Number
- CN202511313427.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-15
- Publication Date
- 2026-01-02
AI Technical Summary
Existing multi-objective optimization algorithms face diverse maintenance difficulties in multi-robot warehouse scheduling, leading to problems such as unbalanced robot load, frequent conflicts, and congestion. The scheduling scheme selection efficiency is low and the effect is poor.
A multi-robot warehouse scheduling method based on dynamic density clustering is adopted. By combining dynamic density clustering and reference point generation with genetic algorithm optimization, a high-quality scheduling scheme is generated, which improves population diversity and convergence.
It significantly improves the efficiency of multi-robot warehouse scheduling scheme selection, realizes a scheduling scheme with short path, low time consumption, few conflicts and balanced distribution, and solves the problems of unbalanced robot load and frequent conflicts.
Smart Images
Figure CN121258024A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the technical field of multi-robot warehouse scheduling, and particularly relates to a multi-robot warehouse scheduling optimal scheme screening method based on dynamic density clustering. BACKGROUND
[0002] The multi-robot warehouse scheduling problem designs the cross fusion of multiple fields, including task allocation, path planning, obstacle avoidance strategy, traffic control, resource scheduling and the like, and is essentially a highly coupled multi-objective optimization problem, and has the following significant features: 1) multi-objective: such as minimizing the total task time, energy consumption, collision probability and the like; 2) multi-constraint: such as robot number limit, path obstacle limit, time window and the like; 3) large scale: the number of robots in a large warehouse system is huge, and a traditional heuristic search algorithm is difficult to take into account multiple optimization objectives, and has poor adaptability in the face of a complex warehouse environment. In comparison, a multi-objective optimization algorithm is widely applied to the field due to its advantages of not requiring gradient information, strong parallel search capability and good adaptability to complex constraints.
[0003] Specifically, in the multi-robot warehouse scheduling, the scheduling process can be modeled as a multi-objective optimization problem, and the task allocation, path planning and conflict avoidance are designed and coded through the design of a fitness function, and are optimized, so as to achieve a global optimal solution or an approximate solution under limited resources.
[0004] However, the current multi-objective optimization algorithm can have the problem of difficulty in maintaining diversity, although the population seems to be distributed between different objectives, but part of the solution is easy to fall into local optimum, thereby causing the search space to be too localized, and the diversity between solutions is poor. And in the warehouse scheduling, multiple non-dominated solutions can tend to assign high-priority tasks to the same few robots, causing uneven robot load and serious system bottleneck. Or lack of path diversity causes robots to frequently collide in certain areas (such as main channels and intersections), causing congestion, obstacle avoidance failure or even deadlock. This requires improving the congestion calculation method and reselecting new non-dominated solutions.
[0005] To sum up, the prior art has the problem of low screening efficiency and poor effect of the scheduling scheme when multiple optimization objectives conflict in a complex problem background. SUMMARY
[0006] The application aims to provide a multi-robot warehouse scheduling optimal scheme screening method based on dynamic density clustering, and solves the problem of low screening efficiency and poor effect of the optimal scheduling scheme in the prior art in a complex background.
[0007] The technical scheme adopted by the application is: a multi-robot warehouse scheduling optimal scheme screening method based on dynamic density clustering, comprising: Step 1: Obtain multi-robot warehouse scheduling data, randomly initialize the scheduling scheme for each robot, and obtain the initial population; Step 2: Calculate the minimum objective function value for each individual in the initial population, including the total robot path length, the maximum robot completion time, and the number of robot collisions; Step 3: Based on the objective function results, perform non-dominated sorting on the initial population and construct a mating pool to generate the next generation of individuals; Step 4: Perform dynamic density clustering on the next generation of individuals and generate reference points; Step 5: Environmental selection based on reference points to form new populations; Step 6: Iterative optimization, outputting the final population as the optimal solution for multi-robot warehouse scheduling.
[0008] The invention is further characterized in that, Step 1 specifically includes the following steps: Step 1.1: Obtain the robot's initial position coordinates, target position coordinates, map boundary information, and obstacle coordinate set; Step 1.2: Using spatiotemporal coding, a legal path is randomly generated for each robot. The path satisfies the following constraints: each step of the path is within the map boundary, the path does not pass through obstacle nodes, the starting point and ending point of the path correspond to the initial position coordinates and target position coordinates in Step 1.1, and adjacent time steps can only move one grid up, down, left, or right or remain stationary. Step 1.3: Combine the paths of all robots into a chromosome to form an individual scheduling scheme; Step 1.4: Repeat steps 1.2 and 1.3 until an initial population of the preset size is generated.
[0009] In step 2, the objective function is constructed with the goals of minimizing the total robot path length, minimizing the maximum robot completion time, and minimizing the number of robot collisions. The total robot path length, maximum robot completion time, and number of robot collisions are calculated sequentially using formulas (1), (2), and (3): (1) In equation (1), N This represents the total number of robots; P i It is the first i The complete path of the robot; The path length is calculated as the number of steps on the path. If the path is... ,but , For individuals The Manhattan distance between step t and step t+1; (2) In formula (2), T i is the number of time steps required for the first i robot to reach the target point; (3) In formula (3), is the number of position conflicts occurring at the first t step, is the number of exchange conflicts occurring at the first t step, is the maximum length of all paths.
[0010] Step 3 specifically includes the following steps: Step 3.1, based on the total length of the robot path, the maximum completion time of the robot, and the number of robot conflicts obtained in step 2, perform non-dominated sorting on the initial population to obtain the non-dominated front; Step 3.2, use binary tournament selection to select parent individuals to build a parent pool: randomly select two individuals from the population, compare their non-dominated front ranks, and select the individual with the better rank into the mating pool. If the ranks are the same, randomly select one into the mating pool; repeat the selection process until the parent pool is full. Step 3.3, apply genetic algorithm crossover and mutation operators to the parent individuals in the mating pool to generate the next generation of individuals and form a new generation of population.
[0011] Step 4 specifically includes the following steps: Step 4.1, for the next generation of individuals, perform normalization scaling to the [0, 1] interval for the total length of the robot path, the maximum completion time of the robot, and the number of robot conflicts, respectively; Step 4.2, calculate the Euclidean distance between each individual and its Knn nearest neighbors to obtain the Knn nearest distance set, sort the Knn nearest distance set in ascending order, and take the distance corresponding to the 75% position as the clustering radius ε; Step 4.3, perform density clustering on the normalized individuals with ε as the radius and Minpts as the threshold to obtain the clustering result; Step 4.4, calculate the mean of the normalized target values of all individuals in each valid cluster to obtain the reference point. If the number of reference points is less than the preset value, add the extreme value solution and the random solution to the reference point set in turn until the preset number is met.
[0012] Step 5 specifically includes the following steps: Step 5.1, perform non-dominated sorting on the next generation of individuals obtained in step 3 again; Step 5.2, place all individuals in the non-dominated sorting except the last layer directly into the set P ; if the setP the number of individuals in the set N , then the following operations are performed on the individuals in the last layer: Step 5.2.1, calculate the Euclidean distance of each individual to all reference points obtained in step 4, and sort in ascending order of distance; Step 5.2.2, the individual with the closest distance is added to the set as the first layer t1 P ; Step 5.2.3, for high-density clusters with the number of individuals ≥ Minpts, calculate the number of individuals to be selected again according to the following formula l :
[0013] In the formula, k is the number of reference points, E is the number of extreme points, N c is the number of high-density clusters; After sorting in ascending order of distance from the reference points in the high-density cluster, the first l individuals are selected and marked as the second layer t2 and added to the set P ; For low-density clusters with the number of individuals < Minpts, randomly select individuals to add to the set P ; Step 5.3, repeat steps 5.2.1 to 5.2.3 until the number of individuals in the set P is equal to the population size N , the set P is the new population.
[0014] In step 4, Knn is set to 5, and Minpts in step 4 and step 5 is set to 3.
[0015] Step 6 is: judging whether the current iteration number reaches the preset maximum number of iterations, if the maximum number of iterations is reached, the new population obtained in step 5 is output as the final population, which is the optimal scheme of multi-robot warehouse scheduling; if the maximum number of iterations is not reached, the new population obtained in step 5 is returned to step 2 for continuous execution.
[0016] The beneficial effects of the present application are: the multi-robot warehouse scheduling optimal scheme screening method based on dynamic density clustering of the present application can guide the evolution direction of the population through the generated reference points, can significantly identify the high-density area in the population by high-density clustering, and can significantly improve the diversity of the population by combining the environment selection strategy associated with the reference points and the high-density clustering, thereby effectively solving the problems of poor diversity, unbalanced robot load, frequent conflicts, congestion, failure and even deadlock of robots in specific areas (such as main channels and intersections) in traditional multi-objective algorithms for multi-robot warehouse scheduling, and thereby effectively screening out high-quality scheduling schemes with short path, low time consumption, few conflicts and balanced distribution. BRIEF DESCRIPTION OF DRAWINGS
[0017] Figure 1 is a flowchart of the multi-robot warehouse scheduling optimal scheme screening method based on dynamic density clustering of the present application; Figure 2 is a schematic diagram of generating reference points in a two-dimensional space in the multi-robot warehouse scheduling optimal scheme screening method based on dynamic density clustering of the present application; Figure 3 is a schematic diagram of the robot transportation route in the optimal set obtained by the multi-robot warehouse scheduling optimal scheme screening method based on dynamic density clustering of the present application. DETAILED DESCRIPTION
[0018] The present application will be described in detail below in combination with the drawings and specific embodiments.
[0019] Embodiment 1 The present application provides a multi-robot warehouse scheduling optimal scheme screening method based on dynamic density clustering, which comprises obtaining multi-robot warehouse scheduling data; based on the scheduling data, combining the three objectives of the shortest total length of the multi-robot path, the shortest completion time and the least number of conflicts, constructing a multi-robot warehouse scheduling model that can be divided into demands; and obtaining the optimal delivery path according to the density clustering algorithm. Figure 1 As shown in the figure, the method comprises the following steps: Step 1: randomly initializing the multi-robot warehouse scheduling multi-objective optimization model to obtain an initial population.
[0020] Step 2: calculating the objective functions (total length of the robot path, maximum completion time of the robot, and number of robot conflicts) of the population.
[0021] Step 3: constructing a mating pool to generate the next generation of individuals.
[0022] Step 4: generating reference points. Performing adaptive density clustering radius, and based on the radius, implementing the adaptive process of the reference points.
[0023] Step 5: Based on the reference points generated above, perform the association process. Conduct an environment selection process based on a label-based hierarchical strategy until the number of individuals in the next generation of the population reaches the population size.
[0024] Step 6: Optimize the multi-robot warehouse scheduling scheme to reach the set maximum number of generations. Optimization complete. If the multi-robot warehouse scheduling scheme population has not reached the maximum number of generations, repeat steps 2 to 5 until the maximum number of generations is reached.
[0025] The data for the robot consortium includes: the initial position information of the multiple robots, the target position information, and the coordinates of obstacles on the path.
[0026] The problem model for the selection method of multi-robot warehouse scheduling scheme with divisible demand includes three objective functions, as shown in formulas (1), (2), and (3).
[0027] (1) (2) (3) In formula (1), N The total number of robots P i It is the first i The complete path of the robot The path length is calculated as the number of steps on the path. If the path is... ,but:
[0028] in, For individuals The Manhattan distance at step t and step t+1.
[0029] In formula (2), T i It is the first i The number of steps required for a robot to reach the target point.
[0030] In formula (3), It is the first t The number of positional conflicts that occur (multiple robots standing in the same position). It is the first t The number of exchange conflicts that occur in a step (referring to the number of times two robots switch positions). It is the maximum length of all paths.
[0031] Formula (1) indicates that the total path length of all robots is the shortest, Formula (2) indicates that the completion time of the last robot is the shortest, and Formula (3) indicates that the number of conflicts among all robots is the minimum.
[0032] The demand divisible multi-robot warehouse scheduling scheme screening method problem model includes constraint conditions, such as formulas (4)-(17): (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) Formula (4) represents the map boundary constraint, meaning that the robot must be within the map boundary at each step. If it exceeds the map boundary, the path is invalid. Formula (5) represents the obstacle avoidance point constraint, meaning that the robot cannot enter an obstacle node at any time. Formula (6) means that the robot's starting point and ending point must be the specified coordinates. Formula (7) means that the robot can only move one grid distance in one of the four directions (up, down, left, or right) within the grid path, and cannot move diagonally or jump. Formulas (5), (6), and (7) together constitute the robot path legality constraint. Formula (8) represents the vertex conflict, meaning that at any time, two robots cannot be on the same grid or vertex to prevent them from colliding. Formula (9) represents the exchange conflict, meaning that two robots exchange positions in adjacent time steps. Formulas (8) and (9) together constitute robot conflict constraints. In the objective of formula (3), the number of these two types of conflicts should be minimized as much as possible. Formula (10) represents time synchronization and path alignment, that is, all robots should be extended to the synchronized length. If a robot has reached the destination, it should wait at the destination for other robots to complete until all robots have completed their tasks. Formula (11) represents reachability constraints, that is, the robot must have an effective path from the starting point to the destination without passing through any obstacles. Formula (12) is the legality constraint of genetic operations, that is, the path of the offspring individuals generated by the parents must also satisfy all basic feasibility conditions. Formula (13) is the time window constraint. Each robot must complete its task within a specified time to control the total task time. Formula (14) is a path smoothness constraint, meaning that the robot should minimize the number of turns and limit the number of turns to a specified number. Formula (15) is for diversity maintenance, to avoid most robots going to a dense area, which would make the path problem difficult to optimize and cause the algorithm to stagnate. Formula (16) prohibits the robot from terminating early, meaning that the robot must not stop at the end point unless it has reached the last time step. Formula (17) is a backtracking redundancy constraint, which prevents the robot from going back or going on a circular path, thereby avoiding low algorithm efficiency or dead loops.
[0033] in, R For the number of robots, r For specific robot labels, r =1, 2, ..., R , For the first r The path length (time steps) of each robot. T This represents the maximum number of time steps for all robots. T It equals the path length (time steps) of the last robot to complete the task. For the first r The robot in the first tPosition coordinates at that moment , for x Axis coordinates for y Axis coordinates. for r The starting point of a robot, For the first r The endpoint of the robot. O Here are the coordinates of the obstacles, representing the coordinates of all impassable grid points. M , N These represent the number of rows and columns of the map, respectively. M * N Grid. It represents the crowding distance of an individual in the target space. This represents the Manhattan distance, which is the distance between grid coordinate points. This is an indicator function; it returns 1 if the condition inside the parentheses is true, and 0 otherwise.
[0034] Example 2 This invention provides a method for selecting the optimal solution for multi-robot warehouse scheduling based on dynamic density clustering. Based on multi-robot warehouse scheduling data and a multi-robot warehouse scheduling model, the optimal delivery path is obtained using a density clustering algorithm. The specific steps are as follows: Step 1: Randomly initialize the multi-robot warehouse scheduling model to obtain the initial population.
[0035] This invention employs a "spatiotemporal coding" method for scheduling multiple robots, specifically: For each robot, its chromosome represents the robot's movement path during scheduling. The specific encoding of the chromosome is as follows: chromosome =
[0036] Each of them Path_i It is the sequence of the robot's positions at each time step, that is:
[0037] Using this spatiotemporal encoding, restrictions must be placed on the position sequence of each time step. For adjacent time steps of each chromosome, the following conditions must be met:
[0038] That is, in adjacent time steps, the robot is guaranteed to move one step in the up, down, left, or right direction, or remain stationary. Using a space-time encoding scheme, it is helpful to highly integrate task assignment and path conflict control, and provide a clear and evaluable solution space structure for multi-objective optimization algorithms. Combined with appropriate mutation operators, conflict repair mechanisms and diversity guiding strategies, the quality, feasibility and diversity of solutions can be significantly improved, and it is an advanced and practical encoding strategy in current warehouse robot scheduling research.
[0039] Step 2, the population is calculated for the objective function (total length of robot path, maximum completion time of robot, number of robot conflicts).
[0040] The application mainly constructs the objective function aiming at minimizing the total length of path, minimizing the maximum completion time and minimizing the number of conflicts: 1) Minimize the total length of path:
[0041] Wherein, N The total number of robots is P i The complete path of the first robot is i The path length is calculated as the path step number, if the path is Then:
[0042] Wherein, The Manhattan distance of the individual In the t step and t+1 step.
[0043] 2) Minimize the maximum completion time:
[0044] T i The time step number required for the first robot to reach the target point is i
[0045] 3) Minimize the number of conflicts:
[0046] Wherein, The number of position conflicts (multiple robots standing at the same position) occurring in the first step is t The number of exchange conflicts (two robots exchanging positions) occurring in the first step is The maximum length of all paths is t
[0047] Step 3, construct a mating pool to generate the next generation of individuals.
[0048] After calculating the objective function of the population, the population will be sorted according to the target value. The non-dominated sorting will divide the population into different frontiers. For different frontiers, the individual with smaller non-dominated frontier number is selected to better optimize the population. Therefore, the sorting result will be used when selecting the parent. In the population, binary tournament is used to construct the parent individual, that is, two individuals are randomly selected from the population. Compare their convergence, and select the individual with good convergence as the parent. If they are non-dominated, a random individual is selected as the parent individual. After constructing the mating pool, GA operators are used to generate the next generation of individuals.
[0049] Step 4, generate reference points. Perform adaptive density clustering radius calculation, and based on the obtained radius, implement the reference point adaptive process.
[0050] The present application is based on a dynamic density clustering process. The radius of the clustering is calculated by adaptive parameters. Adaptive calculation of the density clustering radius can more flexibly adapt to the characteristics of different data sets, and improve the robustness and accuracy of the algorithm.
[0051] Step 5, based on the generated reference points, implement the association process. Perform environment selection process based on the label hierarchical strategy until the number of next generation individuals of the population reaches the population size.
[0052] After the reference point adaptive calculation, the present application will perform the label hierarchical strategy according to the number of reference points and the encoding.
[0053] Step 6, optimize the multi-robot warehouse scheduling scheme to reach the set maximum number of generations, and the optimization is completed. If the multi-robot warehouse scheduling scheme population does not reach the maximum number of generations, repeat steps 2 to 5. Until the maximum number of generations is reached.
[0054] Example 3 The present application provides a multi-robot warehouse scheduling optimal scheme screening method based on dynamic density clustering. Based on example 2, the process of calculating the dynamic density clustering radius is as follows: A1: Perform a normalization process on the remaining solutions that need to be selected.
[0055] The normalization operation eliminates the dimensional differences between the objectives by scaling each objective value to a uniform scale, making different solutions comparable in the solution space, which helps to improve the accuracy of evaluation and thus more effectively assists the screening and decision-making of the optimal solution. The calculation method of the normalization of the present application is as follows:
[0056] Wherein, f i is thei the target value of each solution, Z min and Z max are the minimum and maximum values on the current target respectively.
[0057] A2: Calculate the Euclidean distance between each pair of points in the data set.
[0058] A3: Calculate the dynamic density clustering radius.
[0059] The Euclidean distance of each individual to the Knn-th nearest neighbor is recorded as the Knn-neighbor distance. In the present application, Knn is set to 5. Knn=5 is based on empirical results. It can balance the recognition of local density and noise interference to some extent, thereby improving the accuracy and stability of clustering. Then the Knn-neighbor distances of all individuals are taken as a set. Denoted as And the set is sorted in ascending order, and the distance corresponding to the 75th position after sorting is selected as the density clustering radius ε. Selecting the distance corresponding to the 75th position can ensure that the distances of individuals in most dense regions are calculated, thereby avoiding excessive expansion of the radius due to individuals in individual sparse regions. At the same time, excluding the last 25% of individuals can avoid unnecessary effects of extremely sparse individuals on radius calculation and prevent outliers from interfering with the expansion of the clustering radius.
[0060] Example 4 The present application provides a multi-robot warehouse scheduling optimal scheme screening method based on dynamic density clustering. Based on example 2, after calculating the dynamic density clustering radius, the present application performs adaptive calculation of the dynamic density clustering reference point based on the generated radius. The reference point is set as a representative spatial position in the cluster, which can guide population evolution. The calculation process of the reference point is as follows: A1: When performing dynamic density clustering, each cluster should include at least Minpts individuals to ensure the effectiveness of the cluster. In the present application, Minpts is set to 3. That is, each valid cluster should include at least three points. The adaptive reference point calculation formula is as follows:
[0061] wherein, C j is the number of individuals in the cluster, is the individual x i The target value after normalization is obtained by summing the target value mean to obtain the reference point r j , the reference point rj is clustering C j geometric center in the normalized target space. As shown in Figure 2 , after clustering is done in two-dimensional space, three clusters are obtained, and the reference points are obtained by calculating the geometric center of the individuals in the cluster.
[0062] A2: After calculating the reference points, it is necessary to ensure that the number of reference point sets satisfies the pre-defined number of reference point sets. If the number of reference point sets is insufficient, it needs to be supplemented, at which time the solution in the extreme value solution set is added to the reference point set for supplementation.
[0063] A3: If the number of reference point sets is still insufficient, a random solution will be selected and added to the reference point set.
[0064] Embodiment 5 The present application provides a multi-robot warehouse scheduling optimal scheme screening method based on dynamic density clustering. On the basis of embodiment 2, the steps of the marking hierarchical strategy are as follows: A1: Non-dominated sorting is performed, and all individuals except the last layer in the population are put into set P , A2: If the number of individuals in set P is less than N , the following operations are performed on each solution in the last layer of the population: B1: First, calculate the distance of each individual to the reference point and sort it.
[0065] B2: The individual closest to the reference point is selected as the first layer t1, and t1 is added to set P .
[0066] B3: For the selection of the second layer, the following strategy is used.
[0067] If the number of individuals in the cluster is greater than or equal to the set minimum point threshold, the layer is recorded as a high-density cluster. The number of high-density clusters is recorded as N c . The number of individuals to be selected is calculated by the following formula:
[0068] Where the number of individuals to be selected is l , k is the number of reference points, E is the number of extreme points, N cis the number of high-density clusters, according to the calculated l, the distance of individuals within the high-density cluster from the reference point is sorted in ascending order, and the first l individuals are selected to divide into the second layer, marked as t2.
[0069] B4: If the number of individuals in the cluster is less than the set minimum point threshold, random selection is performed.
[0070] Repeat process A2 until the number of next generations reaches the population size N .
[0071] Example 6 As Figure 3 shown, the partial configuration information of the robot transportation path preferred in the population in the embodiment of the application is as follows: Total number of robots: 6, total route distance of robot operation: 126 Robot 1 path: (0,2)->(0,3)->(0,4)->(0,5)->(0,6)->(0,7)->(1,7)->(1,8)->(1,9)->(1,10)->(1,11)->(2,11)->(3,11)->(3,12)->(3,13)->(4,13)->(4,14)->(4,15)->(4,16)->(4,17)->(4,18)->(5,18)->(6,18)->(7,18)->(8,18)->(9,18)->(10,18)->(11,18)->(12,18)->(13,18)->(14,18)->(15,18)->(16,18)->(17,18)->(18,18)->(19,18) Robot 2 path: (5,18)->(5,17)->(5,16)->(5,15)->(6,15)->(7,15)->(8,15)->(9,15)->(10,15)->(11,15)->(12,15)->(12,14)->(12,13)->(12,12)->(12,11)->(12,10)->(12,9)->(13,9)->(14,9)->(15,9)->(15,8)->(15,7)->(15,6)->(15,5)->(15,4)->(15,3)->(15,2) Robot 3 path: (10,5) -> (10,6) -> (10,7) -> (10,8) -> (10,9) -> (10,10) -> (9,10) -> (8,10) -> (7,10) -> (6,10) -> (5,10) Robot 4 path: (15,1) -> (14,1) -> (14,2) -> (14,3) -> (13,3) -> (12,3) -> (11,3) -> (10,3) -> (9,3) -> (8,3) -> (8,4) -> (8,5) -> (8,6) -> (8,7) -> (8,8) -> (8,9) -> (7,9) -> (6,9) -> (5,9) -> (4,9) -> (4,10) -> (4,11) -> (4,12) -> (3,12) Robot 5 path: (19,19) -> (18,19) -> (17,19) -> (17,18) -> (17,17) -> (17,16) -> (17,15) -> (17,14) -> (17,13) -> (16,13) -> (16,12) -> (16,11) -> (16,10) -> (16,9) -> (16,8) -> (16,7) -> (16,6) -> (16,5) -> (16,4) -> (16,3) -> (16,2) -> (15,2) Robot 6 path: (13,17) -> (13,16) -> (12,16) -> (11,16) -> (10,16) -> (9,16) -> (8,16) -> (8,15) -> (8,14) -> (7,14) -> (6,14) -> (5,14)
Claims
1. A method for selecting the optimal multi-robot warehouse scheduling scheme based on dynamic density clustering, characterized in that, include: Step 1: Obtain multi-robot warehouse scheduling data, randomly initialize the scheduling scheme for each robot, and obtain the initial population; Step 2: Calculate the minimum objective function value for each individual in the initial population, including the total robot path length, the maximum robot completion time, and the number of robot collisions; Step 3: Based on the objective function results, perform non-dominated sorting on the initial population and construct a mating pool to generate the next generation of individuals; Step 4: Perform dynamic density clustering on the next generation of individuals and generate reference points; Step 5: Environmental selection based on reference points to form new populations; Step 6: Iterative optimization, outputting the final population as the optimal solution for multi-robot warehouse scheduling.
2. The method for selecting the optimal multi-robot warehouse scheduling scheme based on dynamic density clustering as described in claim 1, characterized in that, Step 1 specifically includes the following steps: Step 1.1: Obtain the robot's initial position coordinates, target position coordinates, map boundary information, and obstacle coordinate set; Step 1.2: Using spatiotemporal coding, a legal path is randomly generated for each robot. The path satisfies the following constraints: each step of the path is within the map boundary, the path does not pass through obstacle nodes, the starting point and ending point of the path correspond to the initial position coordinates and target position coordinates in Step 1.1, and adjacent time steps can only move one grid up, down, left, or right or remain stationary. Step 1.3: Combine the paths of all robots into a chromosome to form an individual scheduling scheme; Step 1.4: Repeat steps 1.2 and 1.3 until an initial population of the preset size is generated.
3. The method for selecting the optimal multi-robot warehouse scheduling scheme based on dynamic density clustering as described in claim 1, characterized in that, In step 2, objective functions are constructed with the goals of minimizing the total robot path length, minimizing the maximum robot completion time, and minimizing the number of robot collisions. The total robot path length, maximum robot completion time, and number of robot collisions are calculated sequentially using formulas (1), (2), and (3): （1） In equation (1), N This represents the total number of robots; P i It is the first i The complete path of the robot; The path length is calculated as the number of steps on the path. If the path is... ,but , For individuals The Manhattan distance between step t and step t+1; （2） In equation (2), T i It is the first i The number of steps required for a robot to reach the target point; （3） In equation (3), It is the first t The number of positional conflicts that occurred in the step. It is the first t The number of swapping collisions that occur in each step It is the maximum length of all paths.
4. The method for selecting the optimal multi-robot warehouse scheduling scheme based on dynamic density clustering as described in claim 1, characterized in that, Step 3 specifically includes the following steps: Step 3.1: Based on the total robot path length, maximum robot completion time, and number of robot conflicts obtained in Step 2, perform non-dominated sorting on the initial population to obtain the non-dominated front. Step 3.2: Use a binary tournament to select parent individuals to build a parent pool: Randomly select two individuals from the population, compare their non-dominant frontier levels, and select the individual with the higher level to enter the mating pool. If the two individuals have the same level, randomly select one to enter the mating pool. Repeat the selection process until a full parent pool is built. Step 3.3: Apply the genetic algorithm crossover and mutation operators to the parent individuals in the mating pool to generate the next generation of individuals, forming a new generation population.
5. The method for selecting the optimal multi-robot warehouse scheduling scheme based on dynamic density clustering as described in claim 1, characterized in that, Step 4 specifically includes the following steps: Step 4.1: For the next generation of individuals, normalize and scale the total robot path length, maximum robot completion time, and number of robot collisions to the [0,1] interval. Step 4.2: Calculate the Euclidean distance between each individual and its Knn-th nearest neighbor to obtain the Knn-th nearest neighbor set. Sort the Knn-th nearest neighbor set in ascending order and take the distance corresponding to the 75th position as the cluster radius ε. Step 4.3: Perform density clustering on the normalized individuals with ε as the radius and Minpts as the threshold to obtain the clustering results; Step 4.4: Calculate the mean of the normalized target value of all individuals in each valid cluster to obtain reference points. If the number of reference points is less than the preset value, add the extreme value solution and the random solution to the reference point set in turn until the preset number is met.
6. The method for selecting the optimal multi-robot warehouse scheduling scheme based on dynamic density clustering as described in claim 5, characterized in that, Step 5 specifically includes the following steps: Step 5.1: Perform non-dominated sorting again on the next generation of individuals obtained in Step 3; Step 5.2: Directly add all individuals from the non-dominated sort except for the last level into the set. P If set P The number of individuals is insufficient to reach the population size. N Then perform the following operations on the individuals in the last layer: Step 5.2.1: Calculate the Euclidean distance from each individual to all reference points obtained in Step 4, and sort them in ascending order by distance; Step 5.2.2: Add the nearest individual to the set as the first layer t1. P ; Step 5.2.3: For high-density clusters with a number of individuals ≥ Minpts, calculate the number of individuals to be selected using the following formula. l : In the formula, k It is the number of reference points. E It is the number of extreme points. N c It is the number of high-density clusters; Then, within the high-density clusters, sort them in ascending order by distance from the reference point, and select the top... l Each individual is marked as being added to the set at the second layer t2. P ; For low-density clusters with the number of individuals within the cluster less than <Minpts>, randomly select individuals to add to the set P ; Step 5.3: Repeat steps 5.2.1 to 5.2.3 until a set is obtained. P The number of individuals equals the population size. N ,gather P This constitutes a new population.
7. The method for selecting the optimal multi-robot warehouse scheduling scheme based on dynamic density clustering as described in claim 6, characterized in that, In step 4, Knn is set to 5, and in steps 4 and 5, Minpts is set to 3.
8. The method for selecting the optimal multi-robot warehouse scheduling scheme based on dynamic density clustering as described in claim 1, characterized in that, Step 6 specifically involves: determining whether the current iteration count has reached the preset maximum number of generations. If the maximum number of generations has been reached, the new population obtained in step 5 is used as the final population output, which is the optimal solution for multi-robot warehouse scheduling. If the maximum number of generations has not been reached, the new population obtained in step 5 is returned to step 2 to continue execution.