A site selection and routing optimization method considering the impact of obstacles

Abstract

The present invention relates to a site selection and path optimization method that takes into account the influence of obstacles and obstructions, and belongs to the field of engineering construction management technology. It solves the problem that a large number of path planning processes become increasingly difficult as the number of target points increases. The information of obstacles on the plane is extracted and predicted; the information of obstacle impact distance includes the area of ​​the obstacle, the shape of the obstacle, the Euclidean distance, and the centroid offset distance; based on the information of obstacle impact distance, combined with the information of the target point, the vehicle capacity, and the plane information, the site of the distribution center is selected, the path from the distribution center to the target point is planned, and a mathematical model is constructed; it is determined whether there is obstacle information on several paths from the distribution center to several target points, and a prediction model is constructed. The obstacle impact distance is predicted by Gaussian process regression learning to achieve rapid estimation of the obstacle impact distance between different target points, and the material storage location and distribution path are rationally planned in a blocked environment based on HO-NSGAⅡ.

Description

Technical Field

[0001] The invention relates to a site selection path optimization method and belongs to the technical field of engineering construction management. Background Art

[0002] During the construction process, assembly work needs to be carried out on several target points at the same time. During the assembly process, materials need to be stored and distributed according to demand. If the material storage location and subsequent distribution route are not selected properly, it is easy to cause on-site congestion, construction delays and other problems.

[0003] Prior art document 1 “A multiple ant colony optimization algorithm for the capacitated location routing problem”, Ting et al., International Journal of Production Economics, 2013, 141(1): 33-44, “A multiple ant colony optimization algorithm for the capacitated location routing problem” proposes a multiple ant colony optimization algorithm to solve the location routing problem with capacity constraints for vehicles and warehouses, decomposing the capacity location routing problem into a facility location problem and a multi-station vehicle routing problem, but does not consider the impact of obstacles on the distribution route; Document 2 “Integrating Location-Routing with Task and Motion Planning”, Warsame et al., IEEE International Conference on Automation Science and Engineering, 2020, 329–334, “Integrating Location-Routing Task and Motion Planning” combines the location routing problem with motion planning, and applies the existing path planning method to output an obstacle avoidance route map. This method can solve the location routing problem in a simple obstacle environment. However, this method requires a large amount of path planning processing, and the processing difficulty increases with the increase in the number of target points. Therefore, further research is needed on the site-routing problem that takes into account the impact of obstacles.

[0004] Therefore, it is urgent to propose a site selection-path optimization method that takes into account the impact of obstacles to solve the above technical problems. Summary of the Invention

[0005] The present invention aims to overcome the shortcomings of the prior art by proposing a site selection and routing optimization method that takes into account the effects of obstacles. A brief overview of the present invention is provided below to provide a basic understanding of certain aspects of the present invention. It should be understood that this overview is not an exhaustive overview of the present invention. It is not intended to identify key or important aspects of the present invention, nor is it intended to limit the scope of the present invention.

[0006] The technical solution of the present invention:

[0007] The location-route optimization method considering the impact of obstacles includes the following steps:

[0008] Step 1: Extract obstacle information on the plane and predict the distance affected by the obstacle. The information on the distance affected by the obstacle includes the area, shape, Euclidean distance, and centroid offset distance of the obstacle.

[0009] Step 2: Based on the obstacle information, combined with the target point information, the vehicle capacity of the distribution center, and the plane information, the distribution center is located, and the path from each distribution center to one or more target points is planned to construct a mathematical model;

[0010] Step 3: Determine whether there are obstacle information on several paths from each distribution center to several target points, and build a prediction model.

[0011] Preferred: In step 1, information about the distance affected by obstacles is selected for prediction. This information is processed based on Gaussian process regression. Gaussian process regression is a kernel function machine learning method based on statistical learning and Bayesian theory. As a non-parametric regression method, it organizes data in a way that ensures that any given subset of the data always follows a Gaussian distribution. This method is used to handle regression problems with small samples and has strong learning and generalization capabilities. The specific Gaussian process regression is as follows:

[0012] For a set of training data sets D:(x,y), f(x i )=y i , and assume that they all obey multivariate joint Gaussian distribution; among them, x, x i is the characteristic data, y, y i is the target data;

[0013] f(X)=[f(x1),f(x2),f(x3),f(x4)]-GP[μ(x),∑(x)] (1)

[0014] Y=f(X)+ε-N[μ(x),∑(x)+σ 2 E] (2)

[0015] μ(x)=[μ(x1),μ(x2),μ(x3),μ(x4)] (3)

[0016]

[0017] Where: x1 is the area of ​​the obstacle; x2 is the shape of the obstacle; x3 is the Euclidean distance; x4 is the centroid offset distance; f(X) is the prediction function; GP is the multivariate Gaussian distribution; Y is the predicted value; N[μ(x),∑(x)+σ 2 E] is used to represent the mean and variance; ε is the noise prediction value; σ is the standard deviation; E is the unit matrix; μ(x) is f(x1), f(x2), ..., f(x n ) is a vector composed of the mean of ∑(x), K is its covariance matrix;

[0018] The x to be predicted i The set is defined as X * =(x1 * ,x2 * ,x3 * ,x4 * ), the corresponding predicted value is:

[0019] y * =f(x * )+ε (5)

[0020] Where f(x * ) is the prediction function; if ε is 0, it is a noise-free prediction, and if it is not 0, it is a noisy prediction.

[0021] Preferably, in step 2, a target optimization mathematical model is constructed, with dual objectives, including minimizing the delivery distance and the number of vehicles; the objective function is:

[0022]

[0023]

[0024] Where, F1 is the number of delivery vehicles; F2 is the delivery distance; K k For vehicle service objects, K k =1 means the vehicle has a service object, otherwise K k = 0, k∈K; k is the vehicle number, K is the set of cars; X ijkn =1 if vehicle k is on the nth path from the distribution center or destination point i to j, otherwise, X ijkn =0,i,j∈I∪J,k∈K,n∈R k ; i is the number of the distribution center; I is the set of distribution centers; j is the number of the target point; J is the set of target points; n is the number of the distribution path; Rk is the set of delivery routes; D ij is the distance between distribution center i or target point, i,j∈I∪J; ij is the obstacle influence coefficient, i,j∈I∪J.

[0025] Preferably, in step 3, the HO-NSGAⅡ algorithm is designed to solve the problem, including the following steps:

[0026] Step 3.1: Barriers and obstacles affect processing;

[0027] Step 3.2: Encoding method;

[0028] Step 3.3: Generation of initial solution;

[0029] Step 3.4: Non-dominated sorting and congestion calculation;

[0030] Step 3.5: Selection, crossover, and mutation operations.

[0031] Preferably: in step 3.1, the coordinates of all target points, distribution center coordinates, and obstacle coordinates are entered, and a centroid offset distance matrix is ​​introduced (this matrix indicates that the centroid offset distance is recorded in a matrix manner in the subsequent practical application process) to determine whether there are obstacles between the distribution center and the target point, and between the target points; by reading the coordinate information of the target point, distribution center, and obstacle on the plane map, a centroid offset distance matrix for each obstacle between the distribution center and the target point, and between the target points is formed, and then saved in the form of a matrix.

[0032] Preferably: in step 3.2, integer codes are used to represent individuals, each of which includes one or more delivery paths, with delivery centers and target points on the delivery paths; each delivery path includes several target points and a delivery center, and the vehicles of the delivery center depart from the delivery center and complete the delivery tasks in the order of distance from the target points from near to far; for example: given 4 candidate delivery centers and 10 cabin points, a feasible solution code for the problem is given through step 3.1, and the feasible solution consists of 3 delivery paths. The vehicle on path 1 departs from delivery center No. 12, completes the delivery to target point 6-3-2, and then returns to delivery center No. 12, and so on; delivery center 13 does not appear in the code of the feasible solution, indicating that it is not open.

[0033] Preferred: In step 3.3, first randomly select a target point, then build a set of time nodes that the current target point is allowed to visit according to the time limit, and then select the next target point, accumulate the demand for the target point set, terminate the current path when the vehicle capacity limit is reached, and assign distribution centers to other target points.

[0034] Preferably: in step 3.4, the population is divided into different non-dominated levels according to the dominance relationship; the crowding calculation is used to represent the distance between individuals in the same non-dominated level, and is used in the algorithm to ensure the diversity of individuals in the population and avoid falling into a local optimal solution.

[0035] Preferably: in step 3.5, after performing the non-dominated sorting and crowding calculation of the population, the top 80% of the best individuals are selected according to the elite strategy to form a mating pool, and then perform subsequent crossover and mutation operations.

[0036] The present invention has the following beneficial effects:

[0037] A site selection and route optimization method that takes into account the impact of obstacles and blockages was invented. The obstacle impact distance was predicted through Gaussian process regression learning, and the obstacle impact distance between different target points was quickly estimated. On this basis, a mathematical model was constructed, and a hybrid obstacle blockage processing HO-NSGAⅡ algorithm was designed. Compared with the traditional NSGAⅡ algorithm, it solves the disadvantage of its inability to reflect the real obstacle impact. Based on this algorithm, the material storage location and distribution route are reasonably planned in a blocked environment, achieving site selection and route optimization that takes into account the impact of obstacles and blockages. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 Flowchart of the location-route optimization method considering the impact of obstacles.

[0039] Figure 2 Plot of predicted responses from trained models for Gaussian process regression learning.

[0040] Figure 3 This is a diagram of the solution using the traditional NSGAⅡ algorithm;

[0041] Figure 3 Including corrected routes, where DC represents the distribution center, the solid line represents the delivery path, and the dotted line represents the corrected delivery path.

[0042] Figure 4 This is a solution diagram for the location-path optimization method that takes into account the impact of obstacles;

[0043] Figure 4 Including corrected routes, where DC represents the distribution center, the solid line represents the delivery path, and the dotted line represents the corrected delivery path.

[0044] Figure 5 Schematic diagram of centroid offset distance and impact.

[0045] In the figure: 1-distribution center, 2-target point, 3-obstacle, 4-plane, Euclidean distance, Centroid deviation distance. DETAILED DESCRIPTION

[0046] To make the objectives, technical solutions, and advantages of the present invention more clearly apparent, the present invention is described below using specific embodiments shown in the accompanying drawings. However, it should be understood that these descriptions are merely illustrative and are not intended to limit the scope of the present invention. In addition, in the following description, descriptions of well-known structures and technologies are omitted to avoid unnecessary confusion of the concepts of the present invention.

[0047] Specific implementation method 1: Combination Figure 1-5 This embodiment describes a method for optimizing a site and a path in consideration of the impact of obstacles, including the following steps:

[0048] Step 1: Extract obstacle information on the plane and predict the obstacle impact distance information; the obstacle impact distance information includes the obstacle area, obstacle shape, Euclidean distance (the distance between the obstacle's two endpoints in space), and centroid offset distance (the distance from the obstacle's centroid to the distribution center and the target point);

[0049] Step 2: Extract target point information on the plane. Based on the obstacle information, combined with target point information (location, construction time), vehicle capacity of each distribution center (every distribution center has the same vehicle capacity), and plane information (the length and width of the plane), select a distribution center site, set one or more distribution centers, and plan a path from each distribution center to one or more target points. This path is the shortest straight line path from the distribution center to the target point, and a mathematical model is constructed. The present invention predicts the obstacle impact distance based on Gaussian process regression learning, achieving rapid estimation of the obstacle impact distance between different target points, and constructing a mathematical model on this basis. The present invention considers the constraints of actual plane map obstacles, avoiding the errors caused by applying Euclidean distance in traditional problems and the impact of errors on solution design.

[0050] Step 3: Determine whether there are obstacles on the paths from each distribution center to several target points. For paths with obstacles, replan the paths based on the centroid offset distance, bypass the obstacles based on the area, shape, and Euclidean distance, and build a prediction model.

[0051] Specific implementation method 2: Combination Figure 1-5This embodiment describes a site selection and path optimization method that takes into account the impact of obstacles. In step one, information on obstacle impact distances is selected for prediction. This information is processed based on Gaussian process regression. Based on probability theory in statistical learning, it is used to model unknown functions, thereby predicting unknown output values ​​using known data points. The extracted obstacle impact distance information is used as four types of feature data for Gaussian process regression. A training set for the Gaussian process regression model is constructed using 50 sets of measured data. The model is trained using a five-fold cross-validation method using exponential kernel functions, square exponential kernel functions, and Matern5 / 2 kernel functions to obtain corresponding prediction models. The prediction results under different kernel functions are then compared to select a more appropriate kernel function for subsequent obstacle impact distance prediction. Gaussian process regression is a kernel function machine learning method based on statistical learning and Bayesian theory. As a non-parametric regression method, it organizes data in a way that any given subset of the data always follows a Gaussian distribution. It is used to handle regression problems with small samples and has strong learning and generalization capabilities. As a non-parametric regression method, Gaussian process regression is specifically described as follows:

[0052] For a set of training data sets D:(x,y), f(x i )=y i , and assume that they all obey multivariate joint Gaussian distribution; among them, x, x i is the characteristic data, y, y i is the target data;

[0053] f(X)=[f(x1),f(x2),f(x3),f(x4)]-GP[μ(x),∑(x)] (1)

[0054] Y=f(X)+ε-N[μ(x),∑(x)+σ 2 E] (2)

[0055] μ(x)=[μ(x1),μ(x2),μ(x3),μ(x4)] (3)

[0056]

[0057] Where: x1 is the area of ​​the obstacle; x2 is the shape of the obstacle; x3 is the Euclidean distance; x4 is the centroid offset distance; f(X) is the prediction function; GP is the multivariate Gaussian distribution; Y is the predicted value; N[μ(x),∑(x)+σ 2 E] is used to represent the mean and variance; ε is the noise prediction value; σ is the standard deviation; E is the unit matrix; μ(x) is f(x1), f(x2), ..., f(x n ) is a vector composed of the mean of ∑(x), K is its covariance matrix;

[0058] The x to be predicted i The set is defined as X * =(x1 * ,x2 * ,x3 * ,x4 * ), the corresponding predicted value is:

[0059] y * =f(x * )+ε (5)

[0060] Where f(x * ) is the prediction function; if ε is 0, it is a noise-free prediction, and if it is not 0, it is a noisy prediction.

[0061] Specific implementation method three: Combination Figure 1-5 This embodiment is described. The site selection and route optimization method of this embodiment takes into account the influence of obstacles. In step 2, the distribution center site is selected based on the information of several target points. While avoiding some obstacles, the sum of the straight-line paths from each delivery center to the corresponding target points is minimized. If a vehicle delivers to two or more target points at the same time and then returns to the distribution center, the sum of the shortest straight-line paths from the distribution center to the corresponding target points and from the target points to the target points is the shortest, which is the minimized delivery distance. The vehicle departs from the distribution center, transports the materials to each target point, and then returns to the distribution center with the shortest distance. The purpose is to design a logistics network that avoids obstacles as much as possible through the site selection of the distribution center and the optimization of the vehicle route, so as to maximize the utilization rate of the distribution center. Therefore, a target optimization mathematical model is constructed. The target is a dual-objective objective, which includes minimizing the delivery distance and the number of vehicles. The objective function is:

[0062]

[0063]

[0064] Where, F1 is the number of delivery vehicles; F2 is the delivery distance; K k For vehicle service objects, K k =1 means the vehicle has a service object, otherwise K k = 0, k∈K; k is the vehicle number, K is the set of cars; X ijkn =1 if vehicle k is on the nth path from the distribution center or destination point i to j, otherwise, X ijkn =0,i,j∈I∪J,k∈K,n∈R k ; i is the number of the distribution center; I is the set of distribution centers; j is the number of the target point; J is the set of target points; n is the number of the distribution path; R k is the set of delivery routes; D ijis the distance between distribution center i or target point, i,j∈I∪J; ij is the obstacle influence coefficient, i,j∈I∪J.

[0065] Specific implementation method four: Combination Figure 1-5 This embodiment describes the location selection and path optimization method that takes into account the influence of obstacles. In step 3, the HO-NSGAⅡ algorithm (non-dominated sorting genetic algorithm with hybrid obstacle processing) is designed to solve the problem and reduce the processing difficulty. The method includes the following steps:

[0066] Step 3.1: Barriers and obstacles affect processing;

[0067] Step 3.2: Encoding method;

[0068] Step 3.3: Generation of initial solution;

[0069] Step 3.4: Non-dominated sorting and congestion calculation;

[0070] Step 3.5: Selection, crossover, and mutation operations.

[0071] Specific implementation method five: Combination Figure 1-5 This embodiment describes the site selection-path optimization method that takes into account the influence of obstacles. In step 3.1, the coordinates of all target points, distribution center coordinates, and obstacle coordinates are entered into the program, and a centroid offset distance matrix is ​​introduced (this matrix indicates that the centroid offset distance is recorded in a matrix form in the subsequent practical application process) to determine whether there are obstacles between the distribution center and the target point, and between the target points. By reading the coordinate information of the target points, distribution centers, and obstacles on the plane map, the distance between the connecting lines between each distribution center and the target point and each obstacle is calculated (specifically calculated by the program) to form a centroid deviation distance matrix between the distribution center and the target point, and between the target points for each obstacle, and then save it in the form of a matrix as a new set of distribution paths. According to Figure 5If the centroid offset distance between the distribution center and the target point is greater than the coverage range of the obstacle, it means that there is no obstacle between them. If it is less than the obstacle coverage range, it means that there is an obstacle between them. For example: there are 30 distribution center and target point coordinates, which is a 30 by 30 matrix. The (1, 3) data represents the centroid offset distance between target point 1 and distribution center 3 to the obstacle. Then, by judging whether the centroid offset distance exceeds the coverage range of different obstacles, the obstacle blocking coefficient matrix between the distribution center and each target point is constructed. After the centroid offset distance matrix of each obstacle is completed, it is judged that if the centroid offset distance between the two points is less than the maximum radius of the obstacle, there is an obstacle between the two points. The obstacle blocking coefficient matrix is ​​used to integrate the judgment of distribution. Are there any obstacles between the center and the target point, and between the target points, and what obstacles are there? Based on the Gaussian process regression in the first step, a set of data sets is established, and the required feature data and target data are provided through actual measurement. The prediction model is constructed according to formulas (1) to (5); the centroid offset distance matrix and the obstacle blocking coefficient matrix are both data provided by the Gaussian process regression program. By directly inputting the data into the prediction model, the required prediction data can be obtained, and the required feature data can be provided for the subsequent obstacle impact distance prediction processing. Finally, the distance matrix required by the actual problem is obtained, which solves the problem that the existing NSGAⅡ algorithm (non-dominated sorting genetic algorithm) can only calculate the Euclidean distance through the position coordinates when processing distance, and cannot reflect the actual situation affected by obstacles.

[0072] Specific implementation method six: combination Figure 1-5 This embodiment describes the location selection and route optimization method that takes into account the impact of obstacles. In step 3.2, integer codes are used to represent individuals. Each individual includes one or more delivery paths, and there are delivery centers and target points on the delivery paths. Each delivery path includes several target points and a delivery center. Vehicles from the delivery center depart from the delivery center and complete the delivery task in order of distance from the target points from near to far. For example, given a system with 4 candidate delivery centers and 10 cabin points, a feasible solution code for the problem is given by step 3.1. The feasible solution consists of 3 delivery paths. The vehicle on path 1 departs from delivery center No. 12, completes the delivery to target point 6-3-2, and then returns to delivery center No. 12, and so on. Delivery center 13 does not appear in the code of the feasible solution, indicating that it is not open. Coding example: chromosome: 63212|41911|5871014.

[0073] Specific implementation method seven: combination Figure 1-5This embodiment describes the site selection-path optimization method that takes into account the influence of obstacles. In step 3.3, a target point is first randomly selected, and then a set of time nodes that the current target point is allowed to access is constructed based on the time window limit. Then, the next target point is selected, and the demand for the target point set is accumulated. When the vehicle capacity limit is reached, the current path is terminated, and another distribution center vehicle is allocated to other target points; that is, a target point is randomly selected, and according to the delivery time requirement of the target point, the target points to be delivered after it are selected to form a set of nodes that are allowed to be accessed, and selection is made among them, and then the operation is repeated. Through such a decoding method, the quality of the initial solution can be effectively improved, the population can converge quickly, and the situation where the initial solution has an infeasible solution can be avoided; this specific embodiment introduces the decoding method of a path, and the same is true for the remaining paths of the chromosome.

[0074] Specific implementation method eight: combination Figure 1-5 This embodiment describes a location-route optimization method that takes into account the impact of obstacles. In step 3.4, the population is divided into different non-dominated hierarchies based on dominance relationships. In population P, the non-dominated rank of the individuals with the current Pareto optimal solution is 1. These individuals with rank 1 are then removed to form a new population P*. The optimal solution in this new population P* has a non-dominated rank of 2. This is repeated for all individuals in population P. The congestion degree calculation represents the distance between individuals with the same non-dominated rank. It is used in the algorithm to ensure diversity within the population and avoid falling into local optimal solutions. The congestion degree calculation requires sorting the population in ascending order of the objective function values. For example, if a first-level non-dominated layer is obtained, it is sorted by the magnitude of the objective function before the congestion degree is calculated.

[0075] Specific implementation method nine: Combination Figure 1-5 This embodiment describes the location selection and path optimization method that takes into account the influence of obstacles. In step 3.5, after performing the non-dominated sorting and crowding calculation of the population, the top 80% of the best individuals are selected according to the elite strategy to form a mating pool for subsequent crossover and mutation operations.

[0076] For example, the crossover operation is to recombine a certain number of genes from two parent individuals to create a new individual. Usually, it is necessary to not destroy the genes that express good traits, but to generate good new individuals.

[0077] Randomly select a position of the parent chromosome gene and cross-exchange the genes at the two positions; if the constraints are met, output the solution after the exchange; if the constraints are not met, output the initial solution;

[0078] Before crossover:

[0079] Chromosome 1: 63212|41911|5871014

[0080] Chromosome 2: 53911|101213|678414

[0081] After crossover:

[0082] Chromosome 1: 63212|41211|5871014

[0083] Chromosome 2: 53911|101913|678414

[0084] The mutation operation can prevent the population from falling into the local optimum and increase the diversity of chromosomes. The present invention selects two methods: swap mutation and reverse mutation.

[0085] Swap mutation: randomly select two positions on a chromosome and perform swap mutation;

[0086] Before mutation:

[0087] Chromosome 1: 63212|41911|5871014

[0088] After mutation:

[0089] Chromosome 1: 63212|41914|5871011

[0090] Reverse mutation: Randomly select two positions from the chromosome encoding arrangement and reverse the sequence of the elements between the two positions.

[0091] Before mutation:

[0092] Chromosome 1: 63212|41911|5871014

[0093] After mutation:

[0094] Chromosome 1: 63212|4198511|71014

[0095] After the whole process is completed, the parent and offspring populations are merged, and the fast non-dominated sort is performed again to select the best individuals to enter the next generation.

[0096] Example 1:

[0097] The construction process of large cruise ships is a typical complex, customized, and giant system project, which is recognized as a major challenge for the shipbuilding industry. One of the difficulties in building large cruise ships is the assembly of thousands of cabins. Cruise ship cabins are divided into prefabricated cabins and bulk cabins. Prefabricated cabins are assembled in advance and transported to the corresponding deck as a whole by elevators, while bulk cabins require materials to be transported in batches to temporary storage locations on the ship and then assembled on-site on the deck. The assembly process of bulk cabins can be regarded as a site selection-path problem. Cabin construction, as the focus of cruise ship interior decoration, has a huge impact on the construction process of the entire cruise ship. Therefore, the present invention takes into account the impact of obstacles commonly present in the deck environment, optimizes the temporary storage location on the deck and the subsequent distribution path of bulk cabin materials and components, which is of great significance to saving construction time and resources for large cruise ships. Setting the target point as the cruise ship cabin and the plane as the cruise ship deck, the following steps are included:

[0098] Step 1: Predict the information of obstacle impact distance; the information of obstacle impact distance includes the area of ​​the obstacle, the shape of the obstacle, the Euclidean distance, and the centroid offset distance;

[0099] In step 1, we select the information about the distance affected by the obstacle for prediction. The specific Gaussian process regression is as follows:

[0100] For a set of training data sets D:(x,y), f(x i )=y i , and assume that they all obey multivariate joint Gaussian distribution; among them, x, x i is the characteristic data, y, y i is the target data;

[0101] f(X)=[f(x1),f(x2),f(x3),f(x4)]-GP[μ(x),∑(x)] (1)

[0102] Y=f(X)+ε-N[μ(x),∑(x)+σ 2 E] (2)

[0103] μ(x)=[μ(x1),μ(x2),μ(x3),μ(x4)] (3)

[0104]

[0105] Where: x1 is the area of ​​the obstacle; x2 is the shape of the obstacle; x3 is the Euclidean distance; x4 is the centroid offset distance; f(X) is the prediction function; GP is the multivariate Gaussian distribution; Y is the predicted value; N[μ(x),∑(x)+σ 2 E] is used to represent the mean and variance; ε is the noise prediction value; σ is the standard deviation; E is the unit matrix; μ(x) is f(x1), f(x2), ..., f(xn ) is a vector composed of the mean of ∑(x), K is its covariance matrix;

[0106] The x to be predicted i The set is defined as X * =(x1 * ,x2 * ,x3 * ,x4 * ), the corresponding predicted value is:

[0107] y * =f(x * )+ε (5)

[0108] Where f(x * ) is the prediction function; if ε is 0, it is a noise-free prediction, and if it is not 0, it is a noisy prediction;

[0109] Step 2: Based on the impact range of obstacles, combined with the cabin information, the vehicle capacity of the distribution center, and the deck information, the distribution center is located. The path from each distribution center to one or more cabins is planned and a mathematical model is constructed.

[0110] like Figure 4 As shown, a part of the cruise ship deck is selected for example verification. The area is 100m long and 35m wide, with 4 obstacles, 25 cabins to be delivered, and 5 optional delivery centers.

[0111] Construct a mathematical model for target optimization with dual objectives, including minimizing the delivery distance and the number of vehicles; the objective function is:

[0112]

[0113]

[0114] Where, F1 is the number of delivery vehicles; F2 is the delivery distance; K k For vehicle service objects, K k =1 means the vehicle has a service object, otherwise K k = 0, k∈K; k is the vehicle number, K is the set of cars; X ijkn =1 if vehicle k is on the nth path from the distribution center or destination point i to j, otherwise, X ijkn =0,i,j∈I∪J,k∈K,n∈R k ; i is the number of the distribution center; I is the set of distribution centers; j is the number of the target point; J is the set of target points; n is the number of the distribution path; R k is the set of delivery routes; D ijis the distance between distribution center i or target point, i,j∈I∪J; ij is the obstacle influence coefficient, i,j∈I∪J; according to the trained mathematical model, an obstacle influence distance matrix is ​​provided for subsequent solution; Figure 4 The lines connecting the middle target point and the target point, and the target point and the distribution center are the delivery paths, represented by solid lines. There are obstacles on two delivery paths, 10 delivery vehicles, and a delivery distance of 432.3m.

[0115] Step three includes the following steps:

[0116] The coordinates of 25 cabins, 5 distribution centers, and 4 obstacles are entered, and the centroid offset distance matrix is ​​introduced to determine whether there are obstacles between the distribution center and the cabin, and between cabins. By reading the coordinate information of the cabin, distribution center, and obstacles on the deck map, the centroid offset distance matrix between the distribution center and the cabin, and between cabins for each obstacle is formed. This step extracts typical obstacle information based on the map, provides eigenvalues ​​for Gaussian process regression learning, and then saves it in the form of a matrix. Based on the Gaussian process regression in the first step, a set of data sets is established. The required feature data and target data are provided through actual measurement, and a prediction model is constructed according to formulas (1) to (5).

[0117] Individuals are represented by integer codes. Each individual consists of one or more delivery routes, which include delivery centers and cabins. Each delivery route consists of several cabins and a delivery center. Vehicles from the delivery center depart from the delivery center and complete delivery tasks in the order of their distance from the cabins from closest to farthest.

[0118] First, a cabin is randomly selected. Then, a set of time nodes that the current cabin is allowed to visit is constructed based on the time window limit. Then, the next cabin is selected and the demand for the cabin set is accumulated. When the vehicle capacity limit is reached, the current path is terminated and distribution centers are assigned to other cabins.

[0119] The population is divided into different non-dominated levels according to the dominance relationship; the crowding calculation is used to express the distance between individuals in the same non-dominated level. It is used in the algorithm to ensure the diversity of individuals in the population and avoid falling into local optimal solutions.

[0120] After performing the non-dominated sorting and crowding calculation of the population, the top 80% of the best individuals are selected according to the elite strategy to form a mating pool for subsequent crossover and mutation operations;

[0121] Crossover is the process of recombining a certain number of genes from two parent individuals to create a new individual. This usually requires that genes that express good traits should not be damaged while still producing good new individuals.

[0122] The machine selects a position of the parent chromosome gene and cross-exchanges the genes at the two positions; if the constraints are met, the exchanged solution is output; if the constraints are not met, the initial solution is output;

[0123] The HO-NSGAⅡ algorithm designed in this paper was used to solve the problem. The relevant parameters were as follows: population size (popsize) = 400, maximum number of iterations (genmax) = 500, crossover probability (crossp) = 0.9, and mutation probability (mutp) = 0.05. The algorithm first constructed an initial solution based on the encoding rules. Then, when evaluating the delivery distance metric, it introduced the obstacle impact distance as a correction. Selection, crossover, and mutation were then performed, and the final solution was obtained after iterative optimization. The two affected delivery routes were replaced with new ones, represented by dashed lines.

[0124] To illustrate the beneficial effects of the method of the present invention, a comparative test is conducted between the method of the present invention and the existing NSGAⅡ algorithm. When the number of delivery vehicles is the same, the delivery distance calculated by the method of the present invention can be reduced by 3.5%-21.9% compared with the NSGAⅡ algorithm, and the delivery route is more reasonable. Figure 3 、 4 As shown;

[0125] Attachment Figure 3 As shown, 5 of the delivery routes are affected by obstacles, with 12 delivery vehicles and a delivery distance of 486.1m;

[0126] Attachment Figure 4 The figure shows the solution obtained by the method of the present invention, in which only two delivery routes are affected by obstacles, there are 10 delivery vehicles, and the delivery distance is 432.3m.

[0127] It should be noted that in the above embodiments, as long as the technical solutions are not contradictory, they can be permuted and combined. Those skilled in the art can exhaust all possibilities based on the mathematical knowledge of permutations and combinations. Therefore, the present invention will no longer describe the technical solutions after permutations and combinations one by one, but it should be understood that the technical solutions after permutations and combinations have been disclosed by the present invention.

[0128] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A site selection and path optimization method taking into account the impact of obstacles, characterized by: The following steps are involved: Step 1: Extract the information of the obstacle (3) on the plane (4) and predict the information of the obstacle impact distance; the information of the obstacle impact distance includes the area of ​​the obstacle (3), the shape of the obstacle (3), the Euclidean distance, and the centroid offset distance; the centroid offset distance is the distance from the centroid of the obstacle to the distribution center and the target point; Information about the distance affected by obstacles is selected for prediction and processed using Gaussian process regression. Gaussian process regression is a kernel function machine learning method based on statistical learning and Bayesian theory. The specific Gaussian process regression is as follows: For a set of training data , ,in, 、 is the characteristic data, 、 is the target data; (1) (2) (3) (4) Where: is the area of ​​obstacle (3); is the shape of the obstacle (3); is the Euclidean distance; is the centroid offset distance; is the prediction function; is a multivariate Gaussian distribution; is the predicted value; Used to represent mean and variance; is the noise prediction value; is the standard deviation; is the identity matrix; for The vector consisting of the means of ; 、 is its covariance matrix; The forecast required The set is defined as , then the corresponding predicted value is: (5) In the formula is the prediction function; If it is 0, it is a noise-free prediction, if it is not 0, it is a noisy prediction; Step 2: Based on the information of the obstacle (3), combined with the information of the target point (2), the vehicle capacity of the distribution center (1), and the plane (4) information, the distribution center (1) is located, and the path from each distribution center (1) to one or more target points (2) is planned to construct a mathematical model; Build an optimization model with the following objectives: (6) (7) Where, is the number of delivery vehicles; is the delivery distance; For vehicle service objects, For vehicles with service objects, otherwise , ; is the vehicle number, For the collection of cars; For vehicles In the From the path arrive ,otherwise, , , ; is the number of the distribution center (1); is the set of distribution centers (1); is the number of the target point (2); is the set of target points (2); Number the delivery route; is the set of delivery routes; For distribution centers (1) or the distance between target points (2), ; is the obstacle influence coefficient, ; Step 3: Determine whether there is an obstacle (3) information on each path and build a prediction model; The HO-NSGAⅡ algorithm is designed to solve the problem, including the following steps: Step 3.1: Barriers and obstacles affect processing; The coordinates of all target points, distribution centers, and obstacles are entered into the program. A centroid offset distance matrix is ​​introduced to determine whether there are obstacles between distribution centers and target points, and between target points. By reading the coordinate information of target points, distribution centers, and obstacles on the plane map, the distance between each distribution center and each target point and each obstacle is calculated to form a centroid offset distance matrix for each obstacle between distribution centers and target points, and between target points. The matrix is ​​then saved as a new set of distribution routes. If the centroid offset distance between distribution centers and target points is greater than the obstacle coverage range, it means there is no obstacle between them. If it is less than the obstacle coverage range, it means there is an obstacle between them. Step 3.2: Encoding method; Step 3.3: Generation of initial solution; Step 3.4: Non-dominated sorting and congestion calculation; Step 3.5: Selection, crossover, and mutation operations.

2. The method for site selection and route optimization taking into account the impact of obstacles according to claim 1, characterized in that: In step 3.2, integer codes are used to represent individuals. Each individual includes one or more delivery routes, and there are delivery centers (1) and target points (2) on the delivery routes. Each delivery route includes several target points (2) and one delivery center (1). The vehicles of the delivery center (1) depart from the delivery center (1) and complete the delivery task in the order of distance from the target points (2) from near to far.

3. The site selection and path optimization method taking into account the impact of obstacles according to claim 2 is characterized in that: In step 3.3, a target point (2) is randomly selected, and a set of time nodes that the current target point (2) is allowed to visit is constructed according to the time limit. The next target point (2) is selected, and the demand for the target point (2) set is accumulated. When the vehicle capacity limit is reached, the current path is terminated, and distribution centers (1) are assigned to other target points (2).

4. The method for site selection and route optimization taking into account the impact of obstacles according to claim 3, characterized in that: In step 3.4, the population is divided into different non-dominated levels according to the dominance relationship; the crowding calculation is used to represent the distance between individuals in the same non-dominated level.

5. The method for site selection and route optimization taking into account the influence of obstacles according to claim 4, characterized in that: In step 3.5, after performing the non-dominated sorting and crowding calculation of the population, the top 80% of the best individuals are selected according to the elite strategy to form a mating pool for subsequent crossover and mutation operations; The crossover operation is to recombine a certain number of genes from two parent individuals to create a new individual; Randomly select a position of the parent chromosome gene and cross-exchange the genes at the two positions; if the constraints are met, output the solution after the exchange; if the constraints are not met, output the initial solution; Mutation operations include swap mutation and reverse mutation; Swap mutation: randomly select two positions on a chromosome and perform swap mutation; Reverse mutation: Randomly select two positions from the chromosome encoding arrangement and reverse the sequence of the elements between the two positions.

Images