Online Large-Scale Garbage Collection and Transportation Scheduling Method Based on the Divide and Conquer Method

Abstract

An online large-scale garbage collection and transportation scheduling method based on the divide-and-conquer method. After collecting relevant data of garbage stations and vehicles, data preprocessing is carried out to generate an initial problem model. Then, the initial problem is equivalently partitioned by the hierarchical clustering algorithm (AHC) to obtain several initial clusters. Then, after fine-tuning the initial clusters through cluster refinement (CR), the sub-collection and transportation problems are solved and summarized to obtain the total collection and transportation scheduling plan. Through the hierarchical clustering algorithm Pie, the present invention decomposes a super-large-scale problem into a set of small-scale and easily solvable sub-problems as equivalently as possible, and uses the algorithm solver LKH-3 for solving the vehicle scheduling problem with capacity constraints to solve the sub-problems after splitting of the present invention, thereby effectively reducing the overall garbage collection and transportation cost and the algorithm running time.

Description

Technical Field

[0001] The present invention relates to a technology in the field of urban environmental sanitation, specifically an online large-scale garbage collection and transportation scheduling method based on the divide-and-conquer method. Background Art

[0002] The main existing technologies for classified garbage collection and transportation and their corresponding problems are as follows: Traditional garbage collection and transportation problems are usually carried out manually, unable to make real-time adjustments according to the amount of garbage, and manpower often cannot make the optimal choice. For existing technical methods, the garbage collection and transportation problem is summarized as a vehicle routing problem with capacity constraints (CVRP). For such a problem, the problem existing in the best technical methods in the world is that they cannot solve the problem of urban scale. The scale of garbage stations in a city is in the thousands, and such problems are NP-complete problems that are proven by computers to be unsolvable in polynomial time. Therefore, when the problem scale becomes larger, various methods will be difficult to solve, manifested in too long solution time and too poor results. To reduce the increasing operating costs, large cities often need better online garbage collection and transportation scheduling schemes. However, as an NP-complete problem, the garbage collection and transportation problem cannot be solved in polynomial time. When the number of garbage points is very large, this solution time is unacceptable. Summary of the Invention

[0003] In view of the above deficiencies of the prior art, the present invention proposes an online large-scale garbage collection and transportation scheduling method based on the divide-and-conquer method. By using the hierarchical clustering algorithm Pie, the ultra-large-scale problem is decomposed as equivalently as possible into a group of small-scale and easily solvable sub-problems, and the algorithm solver LKH-3 for solving the vehicle scheduling problem with capacity constraints is used to solve the sub-problems after splitting of the present invention, thereby effectively reducing the overall garbage collection and transportation cost and the algorithm running time.

[0004] The present invention is realized through the following technical solutions:

[0005] The present invention relates to an online large-scale garbage collection and transportation scheduling method based on the divide-and-conquer method. After collecting the data related to garbage stations and vehicles, data preprocessing is carried out to generate an initial problem model; then the initial problem is equivalently dissected by the hierarchical clustering algorithm (AHC) to obtain several initial clusters; and then the initial clusters are finely adjusted through cluster refinement (CR), and the sub-collection and transportation problems are solved and summarized to obtain the total collection and transportation scheduling scheme.

[0006] The data related to garbage stations and vehicles include: the location and garbage amount information of each garbage station and the initial starting point, and the load information of each vehicle.

[0007] The data preprocessing mentioned above refers to: obtaining the travel distance between any two points from the previous garbage points through GPS map information or given data, and obtaining all the required data in the following problem model.

[0008] The initial problem model is as follows: Given n stations arbitrarily distributed geographically, denoted as S = {S i, i ∈ [1, n]}, where each station s i has the amount of garbage q i accumulated at that station. In addition, the s0 station is specially taken out as the origin of the problem, and all collection vehicles will depart from here and finally return to the origin. There are p garbage collection vehicles in the model, forming a fleet, denoted as V = {v j, j ∈ [1, p]}, where each vehicle has a given maximum load capacity called C. The problem requires using these p vehicles to collect all the garbage at n stations and each vehicle cannot be overloaded. On this premise, optimize the collection route to minimize the total cost (the travel distance in this problem), and abstract the initial problem into a standard mathematical model:

[0009] The defined optimization objective is to minimize the total distance traveled by all vehicles while satisfying the following constraints

[0010] s.t.

[0011] Each vehicle needs to leave each station it enters

[0012] Each station is visited only once by one of all the vehicles

[0013] Each vehicle starts from the origin, i.e., the garage, and finally returns to the starting point s0.

[0014] Each vehicle cannot be overloaded.

[0015] Where: d ij is the distance between s i and s j ; x ijk is whether v k goes from s i to s j ; When the amount of garbage at a station is greater than the available capacity of the predetermined vehicle, the station can be divided into multiple virtual stations to meet the definition of the CVRP problem. Therefore, the garbage collection problem can be expressed as a classical vehicle routing problem with capacity constraints, which is an NP-complete problem.

[0016] The described hierarchical clustering algorithm includes: initializing each site defined in the problem description into a single cluster, and then merging adjacent clusters according to the positional relationship between points and the amount of garbage between points (merging clusters that can save the number of collection and transportation vehicles and are the closest), and stopping when there is no cluster to merge.

[0017] The described cluster refinement (CR) fine-tuning includes: starting from the farthest cluster, considering whether the amount of garbage in each cluster is exactly an integer multiple of the load of the collection and transportation vehicle. If not, put the nearest site into this cluster for fine-tuning, and iterate through each cluster until the collection and transportation can be carried out with the least number of vehicles.

[0018] The described solution to the self-collection and transportation problem means: using the LKH-3 algorithm to solve the sub-problems obtained by hierarchical clustering segmentation (solving in parallel or serially), and obtaining multiple collection and transportation routes and the total driving distance of each sub-problem.

[0019] The described summarization includes: summarizing the collection and transportation routes of each sub-problem obtained by the solution, adding up the driving distances, and obtaining the final result of the original problem.

[0020] The present invention relates to a system for implementing the above method, including: an original data acquisition unit, a hierarchical clustering algorithm unit, a cluster fine-tuning algorithm unit, a sub-problem solving unit, and a sub-problem result summarization unit. Among them: the original data acquisition unit accesses the map interface or relevant database according to the input problem information to obtain the real-time passing distance information between points, and obtains the complete input data. The hierarchical clustering algorithm unit performs hierarchical clustering on the original problem according to the complete data information obtained by the previous unit to divide it into several sub-problems. The cluster fine-tuning unit performs fine-tuning processing on each cluster according to the information of several roughly divided sub-problems, so that the collection and transportation can be carried out with the least number of vehicles, and obtains the final sub-problem division result. The sub-problem solving unit uses the LKH-3 algorithm to solve according to the sub-problem input information, and obtains several collection and transportation routes and the total collection and transportation distance of each sub-problem. The summarization unit summarizes the sub-problem information to obtain all the recommended collection and transportation routes and the total collection and transportation distance of the original problem.

[0021] Technical effects

[0022] The present invention can split the initial large-scale CVRP problem into sub-problems with as little loss as possible. This clustering method that considers both capacity and distance can solve a large number of vehicle routing problems, and can obtain a relatively optimal solution to the large-scale CVRP problem in a short time, and the solution effect exceeds all existing methods. Brief description of the drawings

[0023] Figure 1 It is a flowchart of the present invention;

[0024] Figure 2Schematic diagram of the relationship between collection cost and the maximum number of vehicles in a sub-cluster in the embodiment;

[0025] Figure 3 Schematic diagram of the visual difference between the clustering results of the prior art and this embodiment. Detailed implementation manners

[0026] As Figure 1 shown, this embodiment relates to an online large-scale garbage collection and transportation scheduling method based on the divide-and-conquer method. After collecting the data related to garbage sites and vehicles, data preprocessing is performed to generate an initial problem model; then, the initial problem is equivalently dissected by using the hierarchical clustering algorithm to obtain several initial clusters; and then, after fine-tuning the initial clusters, the sub-collection problems are solved and summarized to obtain the total collection and transportation scheduling scheme.

[0027] The described hierarchical clustering algorithm (AHC) iteratively merges sites into clusters, making the amount of garbage in each cluster close to an integer multiple of the capacity of the collection vehicle, and at the same time minimizing the collection cost of each cluster. All clusters are sorted from far to near according to the distance between each cluster and the departure location, and the cluster merging is gradually iterated starting from the farthest cluster. In each iteration, when the distance between the target cluster and the source cluster is within a preset threshold and the total amount of garbage on the merged cluster requires fewer vehicles for collection, the source cluster is merged with the target cluster. This process will be iteratively repeated until the size of the cluster reaches a predefined standard.

[0028] In this embodiment, the size of the cluster is limited by defining the maximum number of vehicles that can be calculated within a cluster (that is, defining the total amount of garbage that the cluster can carry). When it is found in a round of iteration that no clusters can be merged, the iterative hierarchical clustering program will end.

[0029] The described hierarchical clustering algorithm includes:

[0030] Step 1: Initialize all initial points into several initial clusters;

[0031] Step 2: Starting from the farthest site, judge the relationship between each cluster and other adjacent clusters. When, as described above, the total number of collection vehicles can be reduced after the two clusters are merged (2.2 + 1.2 -> 3.4, one vehicle can be saved less), or the collection range has a large coverage (geographical location), the merging standard is met. Merge the cluster that meets the collection standard and is the closest to this cluster among the clusters. When there are no new clusters that can be merged after one round, go to Step 3, otherwise loop Step 2.

[0032] Step 3: Obtain the sub-problems with coarse-grained partitioning.

[0033] The described cluster refinement (CR) fine-tunes the amount of garbage in each initial cluster to be closer to an integer multiple of the capacity of the collection vehicle, so that the capacity of the collection vehicle in this sub-problem can be utilized as much as possible. That is, the sites in each cluster are redistributed within a small range, and the garbage that is collected by some extra integer vehicles is assigned to other neighboring clusters that are not full for collection. Specifically, the present invention starts from the cluster farthest away. When the amount of garbage in this cluster does not reach an integer multiple of the load capacity of the collection vehicle, the present invention transfers some sites from a neighboring cluster to the target cluster for collection, and then freezes this cluster, and searches from far to near in turn. In this way, it can be ensured that the total collection amount of each cluster meets the theoretical setting requirements of the present invention before.

[0034] The described cluster refinement includes:

[0035] Step a: Start from the cluster farthest from the origin, and determine whether the amount of garbage in this cluster has reached an integer multiple of the volume of the collection vehicle. If not, go to step b. Otherwise, go to the next cluster. After traversing all clusters, go to step c.

[0036] Step b: Select the garbage site that is closest to this cluster and will not cause the amount of garbage in this cluster to exceed the current number of required collection vehicles from the clusters that have not yet been adjusted (i.e., the clusters closer to the origin), and add it to this cluster until the amount of garbage in this cluster reaches an integer multiple of the capacity of the collection vehicle or cannot be added. Go back to step a.

[0037] Step c: Obtain several sub-problems divided.

[0038] After specific actual experiments, experimental computational simulations were carried out on a desktop computer equipped with an Intel i7-9800X 16-core CPU and 128GB of memory, using real-world datasets. That is, 2200 garbage points distributed in Xuhui District, Shanghai, denoted as Xuh2200, and the parcel distribution datasets of five cities in Belgium, namely Leuven, Antwerp, Ghent, Brussels, and Flanders. The customer locations in the parcel distribution datasets were regarded as the garbage sites in this problem, including the distribution vehicles and their distribution capabilities regarded as garbage collection vehicles and garbage carrying capacities. For each city in the Belgium dataset, there were two datasets with different departure locations, vehicle capacities, and target site distributions, and the corresponding datasets were represented by the abbreviation of the city name and the number of target sites. For example, the Leu3000 dataset contains 3000 target sites in the city of Leuven. Table 1 lists all 11 datasets used in the experimental simulations. According to the number of sites, this embodiment further divided these 11 datasets into three categories, namely large datasets including Xuh2200, Leu3000, Leu4000, Ant6000, and Ant7000, extra-large datasets including Ghe10000, Ghe11000, Bru15000, and Bru16000, and extremely large datasets including Fla20000 and Fla30000.

[0039] The prior arts compared with the method of this embodiment include:

[0040] LKH-3: This algorithm transforms the CVRP into a standard symmetric traveling salesman problem and uses neighborhood exchange to gradually improve the solution, which requires a long running time to obtain the state-of-the-art performance on large-scale datasets.

[0041] The LKH-3 algorithm with special optimization for the extra-large datasets in Belgium: This algorithm is based on LKH-3 and optimizes the algorithm running time and running results by selecting the best algorithm parameters, and is specially customized for the Belgium datasets.

[0042] CC-CVRP: This algorithm first uses a k-means-based clustering method to divide the site set of each vehicle, and then uses a 2-opt local search algorithm to solve the TSP problem of each sub-problem.

[0043] Pie+LKH-3: This embodiment proposes to first use Pie to decompose the extremely large-scale CVRP problem into a set of tractable small-scale sub-problems, and then use the LKH-3 optimization solver to solve each sub-problem.

[0044] This embodiment considers the following two performance metrics:

[0045] Collection cost. The cost of collecting all the garbage from all locations (e.g., total driving distance). Since the coordinates used in the dataset of this embodiment are normalized unitless values, this embodiment calculates the normalized distance (n.d.) as the distance cost of collection and transportation.

[0046] Running time. The running time required for the candidate algorithm to formulate collection and transportation routes for all vehicles.

[0047] In this embodiment, N is varied from 20 vehicles to 100 vehicles with a scale interval of 10 vehicles, and the collection costs of all 11 datasets are examined. As Figure 2 shown, the relationship between the collection and transportation costs obtained by the original LKH-3 (i.e., directly applying LKH-3 without clustering) and Pie+LKH-3 and the maximum clustering scale of the agreed sub-clusters for all datasets. Two conclusions can be intuitively drawn from the experimental results. First, the collection and transportation costs obtained by the original LKH-3 are greater than those calculated by Pie+LKH-3. Second, the collection and transportation cost results obtained by Pie+LKH-3 under different maximum cluster scales of sub-problems are quite stable. This means that the Pie clustering method can effectively decompose the original CVRP problem equivalently into a set of small-scale sub-problems with almost no performance loss. It is found from the experiment that LKH-3 seems to be able to find better solutions for small-scale CVRP problems. Through equivalent decomposition, Pie+LKH-3 can obtain a smaller collection cost than the original LKH-3.

[0048] This method selects the parameter that allows a maximum of 20 vehicles in the sub-cluster for all datasets. For all algorithms related to LKH-3, according to the suggestions in the official documentation of the LKH-3 optimization solver, for a given CVRP problem, the LKH-3 algorithm is run ten times and the best result is selected. For each algorithm run, a scheduling plan is obtained after 10,000 iterations starting from the initial solution. Table 1 lists the collection costs and running times of all candidate methods obtained on all datasets.

[0049] Table 1 Comparison of the results and running times of this method and other excellent algorithms

[0050]

[0051] As shown in Table 1, it can be seen that Pie+LKH-3 can achieve the minimum collection and transportation cost on all datasets. By observing and analyzing the three sizes of datasets classified before this embodiment respectively, it can be seen that for large datasets, the average collection and transportation cost obtained by Pie+LKH-3 is reduced by about 1.95%, 1.25% and 16.15% respectively compared with LKH-3, LKH-3 specially optimized for the Belgian city dataset, and CC-CVRP. For extra-large datasets, the average collection and transportation cost is reduced by about 3.89%, 1.95% and 11.56% respectively. For extremely large datasets, the average collection cost can be reduced by about 6.07%, 1.32%, and 7.65%.

[0052] As Figure 3 shown, it is the visual difference between the clustering results of the CC-CVRP algorithm based on kmeans and this method. Because both distance and garbage volume information are considered simultaneously, clustering will not cause the result to be worse than the original problem. And because clustering brings the advantage of divide-and-conquer solution, the time is also optimized.

[0053] Secondly, the running time of Pie+LKH-3 on most datasets is much lower than that of other methods. Even when the algorithm is executed on a single CPU core (i.e., serially), this method also has a certain time advantage. A core advantage of Pie+LKH-3 is that because this embodiment uses the hierarchical clustering method to split the original problem, and there is no mutual dependence between sub-problems, the decomposed sub-problems can be executed in parallel on multiple CPU cores (i.e., parallel execution), which can greatly reduce the running time of the algorithm. For example, for the first type of large dataset, the average running time obtained by Pie+LKH-3 is 1.5 hours. Compared with the LKH-3 algorithm, the LKH-3 algorithm specially optimized for the Belgian city dataset, and the CC-CVRP algorithm, the execution time of parallel LKH-3 is reduced by 22.3 times, 5.1 times and 4 times respectively. For the second type of extra-large dataset, compared with the LKH-3 algorithm specially optimized for the Belgian dataset and the CC-CVRP algorithm, the average running time of the Pie+LKH-3 algorithm is reduced by about 15.3 times and 11 times respectively. At this time, the running time of the LKH-3 algorithm is too long, so this embodiment no longer includes it in the comparison range. For the third type of extremely large dataset, compared with the LKH-3 algorithm optimized for the Belgian dataset and the CC-CVRP algorithm, the average parallel running time of the Pie+LKH-3 algorithm is reduced by about 21.4 times and 17.5 times respectively.

[0054] In contrast, for the latter two types of datasets, LKH-3 takes more than a day to complete the calculation.

[0055] Compared with the prior art, the solution time and solution effect of this method for this type of problem are better than those of the prior art.

[0056] The above specific embodiments can be locally adjusted in different ways by those skilled in the art without departing from the principles and purposes of the present invention. The protection scope of the present invention is subject to the claims and is not limited by the above specific embodiments. All implementation solutions within its scope are subject to the present invention.

Claims

1. An online large-scale garbage collection and transportation scheduling method based on the divide-and-conquer method, characterized in that, After collecting the data related to garbage sites and vehicles, data preprocessing is carried out to generate an initial problem model; then the initial problem is equivalently segmented by the hierarchical clustering algorithm AHC to obtain several initial clusters; Then, the initial clusters are fine-tuned by the cluster refinement CR to solve the sub-collection and transportation problems and summarize them to obtain the total collection and transportation scheduling plan; The data related to the garbage sites and vehicles include: the location and garbage volume information of each garbage site and the initial starting point, and the load information of each vehicle; The described initial problem model is as follows: Given n sites arbitrarily distributed geographically, denoted as S = {S i, i ∈ [1, n]}, where each site s i has the amount of garbage q i accumulated at that site. Additionally, the s0 site is specifically selected as the origin of the problem, and all collection vehicles will depart from and ultimately return to this origin. There are p garbage collection vehicles in the model, forming a fleet, denoted as V = {v j, j ∈ [1, p]}, where each vehicle has a given maximum load capacity called C. The problem requires using these p vehicles to collect all the garbage from the n sites without overloading any vehicle. On this premise, the collection routes are optimized to minimize the total cost. The initial problem is abstracted into a canonical mathematical model, that is, the defined optimization objective is to minimize the total distance traveled by all vehicles , while satisfying the following constraints Each vehicle needs to leave every site it enters ; Each station is visited only once by one of all the vehicles ; Each vehicle starts from the origin, i.e., the garage, and finally returns to the starting point s0. ; Each vehicle cannot be overloaded, , where: , , d ij is the distance between s i and s j ; x ijk is whether v k goes from s i to s j ; When the amount of garbage at a site is greater than the available capacity of a predetermined vehicle, the site is divided into multiple virtual sites to meet the definition of the CVRP problem; The solution to the sub-collection and transportation problem refers to: using the LKH-3 algorithm to solve the sub-problems obtained by hierarchical clustering segmentation to obtain multiple collection and transportation routes and the total driving distance of each sub-problem.

2. The online large-scale garbage collection and transportation scheduling method based on the divide-and-conquer method according to claim 1, characterized in that The data preprocessing refers to: obtaining the passing distance between any two points from the previous garbage points through GPS map information or given data to obtain all the required data in the following problem model.

3. The online large-scale garbage collection and transportation scheduling method based on the divide-and-conquer method according to claim 1, characterized in that, The hierarchical clustering algorithm includes: initializing each site defined in the problem description into a single cluster, and then merging adjacent clusters according to the positional relationship between points and the garbage volume relationship between points to save the number of collection and transportation vehicles and the nearest cluster, and stopping when there is no merge.

4. The online large-scale garbage collection and transportation scheduling method based on the divide-and-conquer method according to claim 1, characterized in that, The cluster refinement fine-tuning includes: starting from the farthest cluster, considering whether the garbage volume of each cluster is exactly an integer multiple of the load of the collection and transportation vehicle. If not, the nearest site is put into this cluster for fine-tuning, and each cluster is iterated until the collection and transportation is carried out with the least number of vehicles.

5. The online large-scale garbage collection and transportation scheduling method based on the divide-and-conquer method according to claim 1, characterized in that The summarization includes: summarizing the collection and transportation routes of each sub-problem obtained by the solution, adding the driving distances, and obtaining the final result of the original problem.

6. The online large-scale garbage collection and transportation scheduling method based on the divide-and-conquer method according to claim 1 or 3, characterized in that, The hierarchical clustering algorithm specifically includes: Step 1: Initialize all initial points into several initial clusters; Step 2: Starting from the farthest site, judge the relationship between each cluster and other adjacent clusters. When the total number of collection and transportation vehicles can be reduced or the collection and transportation coverage can be increased after two clusters are merged, the merging standard is met; merge the cluster that meets the collection and transportation standard and is the nearest to this cluster. When there are no new clusters that can be merged after one round, go to Step 3, otherwise loop Step 2; Step 3: Obtain the sub-problems with coarse-grained partitioning.

7. The online large-scale garbage collection and transportation scheduling method based on the divide-and-conquer method according to claim 1 or 4, characterized in that, The cluster refinement includes: Step a: Starting from the cluster farthest from the origin, if the current cluster does not reach the situation where the garbage volume is exactly an integer multiple of the volume of the collection and transportation vehicle, enter Step b; otherwise, go to the next cluster and enter Step c after traversing all clusters; Step b: Select the garbage site that is the nearest to this cluster and will not cause the garbage volume of this cluster to exceed the current number of required garbage trucks from the clusters that have not been adjusted to the cluster, that is, the clusters closer to the origin, and add it to this cluster until the garbage volume of this cluster reaches an integer multiple of the garbage truck capacity or cannot be added, and then return to Step a; Step c: Obtain several sub-problems obtained by the partitioning.

8. A system for implementing the online large-scale garbage collection and transportation scheduling method based on the divide-and-conquer method according to any one of claims 1-7, characterized in that, Include: The original data acquisition unit, hierarchical clustering algorithm unit, cluster fine-tuning algorithm unit, sub-problem solving unit, and sub-problem result summarization unit, where: The original data acquisition unit accesses the map interface or relevant database according to the input problem information to obtain the real-time travel distance information between points and obtains the complete input data; The hierarchical clustering algorithm unit performs hierarchical clustering on the original problem according to the complete data information obtained by the previous unit and divides it into several sub-problems; The cluster fine-tuning unit performs fine-tuning processing on each cluster according to the information of several roughly divided sub-problems to minimize the number of vehicles used for collection and transportation and obtains the final sub-problem division result; The sub-problem solving unit uses the LKH-3 algorithm to solve according to the sub-problem input information and obtains several collection and transportation routes and the total collection and transportation distance for each sub-problem; The summarization unit summarizes the sub-problem information to obtain all the recommended collection and transportation routes and the total collection and transportation distance of the original problem.

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