A method for optimizing inspection paths of urban pollution sources

Abstract

The invention discloses a method for optimizing the inspection path of urban pollution sources, receiving the inspection task of the area to be inspected and the current position information of each inspector in the area to be inspected; constructing an urban pollution source inspection network in the area to be inspected, wherein the nodes of the urban pollution source inspection network include pollution source nodes and inspector initial nodes corresponding to the current position information of the inspector, and the pollution source nodes include mandatory nodes corresponding to the newly added pollution occurrence sites and selective nodes corresponding to the historical pollution source occurrence sites; according to the urban pollution source inspection network, setting the constraint conditions for generating the optimal inspection route and constructing a mixed integer programming model; solving the mixed integer programming model by using an adaptive large neighborhood search algorithm, obtaining the optimal inspection route corresponding to each inspector, and issuing the inspection task corresponding to the optimal inspection route to the corresponding inspector. The inspection work planning of the inspector is recommended through the path optimization result, thereby improving the inspection efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of urban environmental pollution source management, and in particular to a method for optimizing an urban pollution source inspection path. Background Art

[0002] The supervision and investigation of urban environmental pollution sources have become a key part of urban environmental management. Regulatory measures include environmental protection inspections and routine or on-demand inspections of environmental risk sites to regulate production activities and reduce pollutant emissions. Although the number of air quality sensors has increased dramatically and environmental management information systems have continued to improve, urban environmental pollution management cannot be without routine inspections of thousands or even tens of thousands of pollution hotspots distributed in cities.

[0003] Urban pollution source inspections mainly involve inspectors conducting inspections of production sites, construction sites, parking lots and other places where there is a risk of environmental pollution. When performing these inspections, there are usually two main types of tasks, namely, checking new pollution sources and regularly checking pollution sources that already exist in the database. For the first type of tasks, inspectors are assigned to check emerging environmental pollution incidents from enterprises, factories, construction sites and other locations. Due to regulations aimed at reducing safety risks, two inspectors need to be assigned to jointly carry out the inspection work when completing these inspection tasks. For the second type of tasks, the status of previously inspected pollution sources recorded in the database needs to be regularly checked and updated. In this case, only one inspector is required, as their duty is only to confirm the current status of the pollution source without entering the pollution source plant or site.

[0004] In previous work practices, new incidents are usually assigned to inspectors by dispatchers. After receiving the task, each inspector will first work with another inspector to complete the investigation of all new pollution sources assigned to them. After completing all the first-class tasks, the two-person team will be disbanded, and each inspector will begin to freely investigate and update the status of the pollution sources that have been inspected before. During the inspection process, the order and route of the pollution source investigation are determined by the inspectors and dispatchers based on experience, resulting in inefficient investigation paths such as duplication and round trips. These inefficient paths seriously affect the efficiency of pollution source investigation. Summary of the invention

[0005] The purpose of the present invention is to provide a method for optimizing the inspection path of urban pollution sources, plan the inspection routes of inspectors according to the inspection conditions required by various types of pollution sources, recommend inspectors to plan inspection work through path optimization results, improve inspection efficiency, and complete the inspection work of various types of pollution sources with quality and quantity.

[0006] To achieve the above objectives, this application adopts the following scheme:

[0007] The present invention provides a method for optimizing the inspection path of urban pollution sources, which specifically comprises the following steps:

[0008] S1. Receive the inspection tasks of the area to be inspected and the current location information of each inspector in the area to be inspected. The inspection tasks include the locations of newly added pollution sources and the locations of historical pollution sources to be updated in the database;

[0009] S2. Constructing an urban pollution source inspection network in the area to be inspected, wherein the nodes of the urban pollution source inspection network include pollution source nodes and inspector initial nodes, the pollution source nodes include mandatory nodes and optional nodes, the mandatory nodes correspond to the locations of newly added pollution, the optional nodes correspond to the locations of historical pollution sources, and the inspector initial node corresponds to the current location information of the inspector;

[0010] S3. According to the urban pollution source inspection network, set the constraints for generating the optimal inspection route, use the big M method to transform the constraints into inequality constraints, and construct a mixed integer programming model;

[0011] S4. Use the adaptive large neighborhood search algorithm to solve the mixed integer programming model to obtain the optimal inspection route corresponding to each inspector, and send the inspection work task corresponding to the optimal inspection route to the corresponding inspector.

[0012] In some specific implementation schemes, the method for constructing the urban pollution source inspection network in step S2 is:

[0013] S21, screening the historical pollution source locations to be updated in the database, and selecting the historical pollution source locations within the preset range of the newly added pollution source locations from the database as selective nodes;

[0014] S22, constructing an urban pollution source inspection network based on each mandatory node, optional node and inspector initial node, the urban pollution source inspection network is a complete graph;

[0015] S23. Set the node attributes of each mandatory node and selective node in the urban pollution source inspection network, and set the importance of each selective node in turn according to the length of the time interval between the last inspection time and the current inspection time; unify the importance of all mandatory nodes, and set the importance of mandatory nodes to be greater than the importance of all selective nodes.

[0016] In some specific implementation schemes, the mixed integer programming model uses whether each inspector visits the pollution source node and the order of visiting each pollution source node as decision variables, path constraints, task constraints, time constraints and score constraints as constraints, and optimizes the inspection efficiency as the goal. The objective function is set to maximize the difference between the comprehensive node score and the standard work efficiency score.

[0017] In some specific implementation schemes, the path constraint is to ensure that each inspector starts from the inspector's initial node and returns to the end point, and all inspector's initial nodes and end points are visited only once, and at the same time check the continuity and integrity of the generated inspection route, and the calculation formula is:

[0018]

[0019] in, P Represents the set of pollution source nodes; D represents the inspector's terminal node set, and the travel time from all other nodes to the terminal node is 0; O represents the inspector's initial node set, K Indicates the inspectors are gathering. x i,j,k is a binary variable taking values ​​of 0 or 1, and i≠j If the inspector k Slave Node i Go to Node j ,but x i,j,k =1;

[0020] Task constraints: Ensure that mandatory nodes must be visited and checked by two inspectors, and optional nodes can only be checked by one inspector, as shown in the following formula:

[0021]

[0022] in, P M Represents a mandatory node set, P E represents a selective node set, y i is a binary variable with a value of 0 or 1. If node i is checked by any inspector, y i =1;

[0023] Time constraint: The conditional constraint is converted into an inequality constraint through the Big M method to ensure the correctness of the node inspection completion time, including the travel time, inspection time and waiting time. The calculation formula is:

[0024]

[0025] in, Representation Node j The investigation is time-consuming. t i,j Representation Node i To Node j The travel time, w i Representation Node iThe time when the investigation is completed. w j Representation Node j The time when the investigation is completed. M Represents a preset constant value. V Represents a collection of network nodes, V ={ P M ∪ P E ∪ O ∪ D}, P represents the set of polluted nodes, P ={ P M ∪ P E};

[0026] Score constraint: Determine the actual importance score that a node can obtain based on the node access situation and time constraints. The calculation formula for the importance score that a node can obtain is:

[0027]

[0028] in, p i Representation Node i The importance of setting Indicates access to mandatory nodes i The time threshold, Indicates that when the mandatory node i access timeout The actual importance score that can be obtained when

[0029] In some specific embodiments, the objective function is:

[0030]

[0031] y i Represents a binary variable with a value of 0 or 1. i is visited, then y i =1, q i Representation Node i The actual importance score that can be obtained is w j Representation Node j The time when the investigation is completed. θ Indicates standard work efficiency.

[0032] In some embodiments, all mandatory nodes constitute a mandatory node set P M, all selective nodes constitute the selective node set P E , pollution source node set P ={ P M ∪ P E}, all inspector initial nodes constitute the inspector initial node set O; network node set V ={ P M ∪ P E ∪ O}, each inspector's inspection route consists of nodes in the order of access. The specific process of step S4 is:

[0033] According to the constructed mixed integer programming model, the adaptive large domain search algorithm is used to generate the initial path solution with the greedy insertion algorithm. The initial path solution is iteratively improved by multiple removal and insertion operations. The operation method of the removal and insertion operation of each iteration is dynamically selected through the roulette mechanism. Each iteration is iterated with the objective function as the target, and finally the optimal path solution is obtained. The optimal path solution includes the optimal inspection route corresponding to each inspector.

[0034] During each iteration, an inspector is randomly selected from the initial path solution to check the route, nodes are randomly removed from the check route, and after removal, all available mandatory nodes and randomly selected available optional nodes are reinserted into the initial path solution to obtain a new solution after each iteration. The objective function is used to calculate the target values ​​corresponding to the initial path solution and the new solution after the iteration, and according to the target values ​​corresponding to the initial path solution and the new solution after the iteration, it is determined whether the new solution is accepted as the new iterative path solution according to the simulated annealing criterion.

[0035] In some specific embodiments, the removal operation methods include: random removal, worst removal, continuous removal and synchronous removal, wherein:

[0036] The specific process of random removal is: randomly select a patrolman in the initial path solution and the current inspection route R containing n nodes K (P1, P2, …, Pn), randomly determine the number of nodes that need to be removed from the current inspection route, determine the type of nodes that need to be removed, and when a node is a mandatory node, remove the node from the inspection route of all inspectors;

[0037] The specific process of worst removal is as follows: for the current search route R KFor each node in the current inspection route, calculate the travel time cost from the previous node to the current node, use the travel time cost to evaluate the current node, compare the travel time costs of each node, remove the node with the highest travel time cost from the current inspection route, and determine the type of node to be removed. If the node is a mandatory node, remove the node from the inspection routes of all inspectors.

[0038] The specific process of continuous removal is as follows: a node to be removed is randomly determined from the current inspection route, and according to the position of the node in the current inspection route, a random number of nodes after the node are removed from the current inspection route. At the same time, the type of the node to be removed is determined. If the node is a mandatory node, the node is removed from the inspection routes of all inspectors.

[0039] Synchronous removal: Randomly remove a set number of mandatory nodes from the current inspection route and remove the node from the inspection routes of all inspectors.

[0040] In some specific embodiments, the insertion operation method includes: random insertion and greedy insertion;

[0041] The specific process of random insertion is: S01, calculate the selective node set P E The difference set between the solution of the current path and the solution of the current path is used to obtain the remaining available selective nodes, and a plurality of selective node subsets are randomly selected from the remaining available selective nodes;

[0042] S02, merging the selective node subset and the mandatory nodes removed during the removal operation into a set of nodes to be inserted;

[0043] S03. Select a node from the set of nodes to be inserted. If the node is a mandatory node, randomly insert it into any two paths of the current path solution to obtain the corresponding new solution to be checked. Perform a feasibility check on the new solution to be checked. If the feasibility check passes, keep the new solution to be checked. If the feasibility check fails, use the current path solution as the new solution to be checked. If the node is a selective node, randomly insert it into any one path of the current path solution and keep the new solution to be checked.

[0044] S04. Repeat step S03, and use the new solution to be checked as the current path solution, until all nodes in the set of nodes to be inserted are inserted into the current path solution to obtain a new path solution.

[0045] In some specific implementation schemes, the specific process of generating the initial path solution by greedy insertion is:

[0046] S41. For each inspector, determine the inspector's initial node and the inspector's terminal node, select a random subset from the pollution source node set, and ensure that all mandatory nodes are included in the random subset. There are several positions to be inserted for inserting each node in the random subset in the node access order between each inspector's initial node and the inspector's terminal node.

[0047] S42, calculating the increase in travel time cost of a route formed by randomly inserting a node from the random subset into the position to be inserted, inserting the node into the position to be inserted corresponding to the minimum increase in travel time cost, updating the inspection route of each inspector, and forming the inspection routes of all inspectors into the current path solution;

[0048] S43, performing a feasibility check on the current path solution to determine whether there is a cross-synchronization problem between the positions to be inserted of each mandatory node between the checked routes, and if so, prohibiting the mandatory node from being inserted into the position to be inserted when cross-synchronization occurs;

[0049] S44. Repeat steps S42-S43 until all nodes in the random subset are inserted, and an initial path solution consisting of the inspection routes corresponding to each inspector is obtained.

[0050] In some specific implementation schemes, the specific process of feasibility check is:

[0051] S10, constructing a sequence matrix to record the access order of the mandatory nodes of each screening route in the current path solution in each screening route;

[0052] S20, using the transitive closure method to derive the access order between all mandatory nodes, if there is a pair of mandatory nodes with a bidirectional access order recorded in the sequence matrix, it is determined that there is cross synchronization and the current path solution is not feasible. It is forbidden to insert the pair of mandatory nodes into the current node access order insertion position of the current path solution.

[0053] The present invention has the beneficial effects:

[0054] The present invention proposes a patrol path optimization strategy, models routine patrols in urban pollution source management, and constructs a targeted mixed integer programming model. Different from classic path optimization problems (such as the traveling salesman problem and the vehicle routing problem), this application divides the pollution source locations to be patrolled into mandatory nodes that must be inspected by two patrol officers at the same time and selective nodes that only require one patrol officer to inspect, and constructs an urban pollution source patrol network based on the pollution source nodes and the initial positions of the patrol officers according to the actual needs of pollution source patrol work;

[0055] Based on the urban pollution source inspection network, whether each inspector visits the pollution source node and the order of visits are used as decision variables, path constraints, task constraints, time constraints and score constraints are used as constraints, and a mixed integer programming model is established with the goal of optimizing the inspection efficiency. Then, the mixed integer programming model is solved using an adaptive large neighborhood search algorithm to obtain the optimal inspection route for each inspector. This ensures that the inspection path for historical pollution sources can be flexibly planned while ensuring the completion of the inspection task of new pollution sources, thereby improving the overall inspection efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 A flow chart of a method for optimizing the inspection path of urban pollution sources provided by an embodiment of the present invention;

[0057] Figure 2 A schematic diagram of a synchronous crossover situation provided by an embodiment of the present invention;

[0058] Figure 3 A schematic diagram of a generated troubleshooting route provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0059] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is by no means intended to limit the present invention and its application or use. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0060] The relative arrangement of components and steps, the numerical expressions and numerical values ​​set forth in these embodiments do not limit the scope of the present invention unless specifically stated otherwise.

[0061] At the same time, it should be understood that for the convenience of description, the sizes of the various parts shown in the drawings are not drawn according to the actual proportional relationship.

[0062] Additionally, descriptions of well-known structures, functions, and configurations may be omitted for clarity and conciseness.One of ordinary skill in the art will recognize that various changes and modifications may be made to the examples described herein without departing from the spirit and scope of the present disclosure.

[0063] Technologies, methods, and apparatus known to ordinary technicians in the relevant field may not be discussed in detail, but where appropriate, such technologies, methods, and apparatus should be considered part of the authorization specification.

[0064] In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limiting. Therefore, other examples of the exemplary embodiments may have different values.

[0065] Urban pollution sources include new pollution sources and historical pollution sources. The order of inspection visits of existing inspectors to urban pollution sources is often determined based on the experience of inspectors or dispatchers. However, completing the inspection of new pollution sources has already consumed most of the working time. There are still a large number of pollution sources to be updated in the database. If the inspection route is planned based on experience, it is easy to have unreasonable pollution source task allocation and route planning, and low efficiency. In the process of inspecting new pollution sources, inspectors can simultaneously check and update some pollution sources in the database that need to be inspected, while still ensuring that the inspection task of new pollution sources is completed within the time limit, thereby improving the overall inspection efficiency.

[0066] Among the existing path optimization problems, two types of path optimization problems are widely applicable, namely the Traveling Salesmen Problem (TSP) and the Vehicle Routing Problem (VRP). However, whether it is TSP or VRP, all nodes in the network must be visited, which is not in line with the actual work of urban pollution source inspection. The goal of urban pollution source inspection is to ensure that all new pollution sources are checked within the specified time limit, and at the same time, as many pollution sources in the database as possible are checked, especially those that are more important. It is impractical to include all pollution sources in the database in the inspection path. In addition, it is not reasonable to first select a subset of pollution sources in the database and then establish a TSP or VRP model for path planning, because the selection of subset pollution sources and route planning interact with each other. In this way, it is necessary to repeatedly establish and solve TSP or VRP to obtain the optimal path solution for a single urban environmental pollution source inspection problem.

[0067] There is a relatively less studied path problem and its variants that are very suitable for describing and constructing path optimization problems for urban pollution source inspections. The Orienteering Problem (OP) is a path problem that selects a subset from all available nodes under limited time or distance constraints and determines the order of visits to maximize the scores obtained from the visited nodes. The Team Orienteering Problem (TOP) is a natural extension and variant of the Orienteering Problem. It plans multiple routes, each with time or distance constraints. All routes select their own subset of nodes from the same set of nodes in the same network, and each node can only be visited once at most. The goal is to maximize the sum of the scores obtained from the visited nodes in all routes.

[0068] There are generally two types of methods for solving path optimization problems: exact algorithms and metaheuristic algorithms. As for exact algorithms, there are already several commonly used commercial solvers based on exact algorithms that perform well in solving various optimization problems, such as CPLEX and Gurobi. When the problem scale exceeds the processing limit of commercial solvers, there are also some studies on exact algorithms for solving directional problems, such as branch-pruning pricing algorithms and branch-pricing algorithms. However, in the work of urban pollution source inspection, after receiving the new pollution source event, it is necessary to complete the route planning in real time and send the route planning results to the inspectors. Therefore, it is not feasible to obtain the exact optimal solution for the urban pollution source inspection path optimization problem through exact algorithms. In previous studies, there have been some explorations of metaheuristic algorithms for solving directional problems and their variants, such as using taboo search to solve random directional problems, using ant colony algorithms to solve thief directional problems, and using harmony search algorithms to solve directional problems. In the path optimization problem of urban pollution source inspection, a very tricky problem is the processing of the constraint that two inspectors need to visit the new pollution source simultaneously. In the design of metaheuristic algorithms, dealing with simultaneous access constraints is very complicated. In previous studies, orientation problems with simultaneous access constraints and time window constraints are usually defined as cooperative orientation problems (COPTW). There are few studies that use metaheuristic algorithms to solve cooperative orientation problems. All of them use the Adaptive Large Neighborhood Search (ALNS) algorithm to solve cooperative orientation problems in different scenarios. In addition, there are also some studies that add simultaneous access constraints to the classic VRP problem and use metaheuristic algorithms to solve it, including simulated degradation algorithms, adaptive large neighborhood search algorithms, and artificial bee colony algorithms.

[0069] Therefore, in order to improve the efficiency of urban pollution source inspection tasks, this application models the path optimization problem of urban pollution source inspection work. This path optimization problem is characterized by planning multiple paths at the same time, with mandatory nodes and optional nodes, different nodes have different importance, and mandatory nodes require two inspectors to visit simultaneously and have time constraints. By establishing and solving the path optimization problem of urban pollution source inspection, inspectors can be guided to conduct efficient pollution source inspection. The specific implementation method is as follows:

[0070] Example 1

[0071] like Figure 1 As shown, this embodiment provides a method for optimizing the inspection path of urban pollution sources, which specifically includes the following steps:

[0072] S1. Receive the inspection tasks of the area to be inspected and the current location information of each inspector in the area to be inspected. The inspection tasks include the locations of newly added pollution sources and the locations of historical pollution sources to be updated in the database;

[0073] S2. Constructing an urban pollution source inspection network in the area to be inspected, wherein the nodes of the urban pollution source inspection network include pollution source nodes and inspector initial nodes, the pollution source nodes include mandatory nodes and optional nodes, the mandatory nodes correspond to the locations of newly added pollution, the optional nodes correspond to the locations of historical pollution sources, and the inspector initial node corresponds to the current location information of the inspector;

[0074] The specific process of constructing the urban pollution source inspection network is as follows:

[0075] S21, screening the historical pollution source locations to be updated in the database, and selecting the historical pollution source locations within the preset range of the newly added pollution source locations from the database as selective nodes;

[0076] S22, constructing an urban pollution source inspection network based on each mandatory node, optional node and inspector initial node, the urban pollution source inspection network is a complete graph;

[0077] S23. Set the attributes of each mandatory node and selective node in the urban pollution source inspection network, and set the importance of each selective node in turn according to the length of the time interval between the last inspection time and the current inspection time; unify the importance of all mandatory nodes, and set the importance of mandatory nodes to be greater than the importance of all selective nodes.

[0078] S3. According to the urban pollution source inspection network, set the constraints for generating the optimal inspection route, use the big M method to convert the constraints into inequality constraints, and build a mixed integer programming model;

[0079] The mixed integer programming model takes whether each inspector visits the pollution source node and the order of visiting each pollution source node as decision variables, path constraints, task constraints, time constraints and score constraints as constraints, and optimizes the inspection efficiency as the goal. The objective function is set to maximize the difference between the comprehensive node score and the standard work efficiency score.

[0080] The constraints include:

[0081] Path constraint: ensure that each inspector starts from the inspector's initial node and returns to the end point, and all inspectors' initial nodes and end points are visited only once, and check the continuity and integrity of the generated inspection route. The calculation formula is:

[0082] in, PRepresents the set of pollution source nodes; D represents the inspector's terminal node set, and the travel time from all other nodes to the terminal node is 0; O represents the inspector's initial node set, K Indicates the inspectors are gathering. x i,j,k is a binary variable taking values ​​of 0 or 1, and i≠j If the inspector k Slave Node i Go to Node j ,but x i,j,k =1; the inspector's terminal node has no practical significance and only represents the end of the path. Because the time of the terminal should be the same as the time of the last pollution source node before the terminal, the travel time from all other nodes to the terminal is 0, and the inspection time required at the terminal is also 0.

[0083] Task constraint: Ensure that mandatory nodes must be visited and checked by two inspectors, and optional nodes can only be checked by one inspector at most, as shown in the following formula.

[0084]

[0085] in, P M Represents a mandatory node set, P E represents a selective node set, y i is a binary variable with a value of 0 or 1. If node i is checked by any inspector, y i =1;

[0086] Time constraint: The conditional constraint is converted into an inequality constraint through the Big M method to ensure the correctness of the node inspection completion time, including the travel time, inspection time and waiting time. The calculation formula is:

[0087]

[0088] in, Representation Node j The investigation is time-consuming. t i,j Representation Node i To Node j The travel time, w i Representation Node i The time when the investigation is completed. w j Representation Node j The time when the investigation is completed. MRepresents a preset constant value. V Represents a collection of network nodes, V ={ P M ∪ P E ∪ O ∪ D}, P represents the set of polluted nodes, P ={ P M ∪ P E};

[0089] Score constraint: Determine the actual importance score that a node can obtain based on the node access situation and time constraints. The calculation formula for the importance score that a node can obtain is:

[0090]

[0091] in, p i Representation Node i The importance of setting Indicates access to mandatory nodes i The time threshold, Indicates that when the mandatory node i access timeout The actual importance score that can be obtained when

[0092] In some specific embodiments, the objective function is:

[0093]

[0094] y i Represents a binary variable with a value of 0 or 1. i is visited, then y i =1, q i Representation Node i The actual importance score that can be obtained is w j Representation Node j The time when the investigation is completed. θ Indicates standard work efficiency, where standard work efficiency is a model parameter set based on historical management experience. It can be adjusted according to the effect in the work application. If it is set too large, it may result in fewer historical pollution sources for the recommended path to be checked. If it is set too small, it may result in too many historical pollution sources for the recommended path to be checked.

[0095] S4. Use the adaptive large neighborhood search algorithm to solve the mixed integer programming model to obtain the optimal inspection route corresponding to each inspector, and send the inspection work task corresponding to the optimal inspection route to the corresponding inspector.

[0096] All mandatory nodes constitute the mandatory node set P M , all selective nodes constitute the selective node set P E , pollution source node set P ={ P M ∪ P E}, all inspector initial nodes constitute the inspector initial node set O ; Network node collection V ={ P M ∪ P E ∪ O}, each inspector's inspection route consists of nodes in the order of access. The specific process of step S4 is:

[0097] According to the constructed mixed integer programming model, the adaptive large domain search algorithm is used to generate the initial path solution with the greedy insertion algorithm. The initial path solution is iteratively improved by multiple removal and insertion operations. The operation method of the removal and insertion operation of each iteration is dynamically selected through the roulette mechanism. Each iteration is iterated with the objective function as the target, and finally the optimal path solution is obtained. The optimal path solution includes the optimal inspection route corresponding to each inspector.

[0098] During each iteration, an inspector is randomly selected from the initial path solution to check the route, nodes are randomly removed from the check route, and after removal, all available mandatory nodes and randomly selected available optional nodes are reinserted into the initial path solution to obtain a new solution after each iteration. The objective function is used to calculate the target values ​​corresponding to the initial path solution and the new solution after the iteration, and according to the target values ​​corresponding to the initial path solution and the new solution after the iteration, it is determined whether the new solution is accepted as the new iterative path solution according to the simulated annealing criterion.

[0099] like Figure 3As shown, assuming that there are three inspectors (A, B, C) in the current area to be inspected, selective nodes (1, 2, 4, 6, 7, 8, 9, 10), and mandatory nodes (3, 5), according to the above method, mandatory nodes 3 and 5 must be visited by two inspectors, and the selective nodes near mandatory nodes 3 and 5 are visited by the way. From the final generated inspection route, it can be seen that since the inspection officers A and B have the shortest travel time to reach the mandatory nodes, inspectors A and B can inspect the mandatory node 3 together. Before reaching the mandatory node 3, inspectors A and B respectively inspect the selective nodes 1 and 2 on their routes to the mandatory node 3.

[0100] It can be understood that the removal and insertion operations in the iteration process are essentially searches in the neighborhood of the current path solution. The new solution generated by one iteration is actually a solution in the neighborhood of the current solution. The new solution is judged according to the optimization goal, and whether it is used as a new current solution to generate a new neighborhood solution according to the simulated annealing criterion. Because of the simulated annealing criterion, the iteration is close to the solution that makes the objective function optimal (of course, there will be fluctuations during the iteration process). Even if the neighborhood search is completely random, the solution can be continuously optimized by retaining the better new solution and continuing to search in the neighborhood of the better new solution. Of course, the iteration process can also be accelerated by introducing some information related to the optimization problem during the neighborhood search. The worst removal and greedy insertion in the present invention utilize the peer time information of the nodes in the path to accelerate the iteration to the direction of the shortest path time. Since the waiting time of the inspector at the mandatory node causes a serious decrease in the inspection efficiency, the synchronous removal in the present invention utilizes the information that the pollution source inspection needs to be accessed synchronously, and searches in the neighborhood of the current solution involving synchronous access constraints to accelerate the iteration to the direction of the shortest waiting time.

[0101] In the scenario of pollution source inspection route recommendation, the end point of the iteration is when the algorithm running time reaches the set time limit. After an iteration is completed, if the running time reaches the limit, the iteration is stopped and the optimal path solution is output.

[0102] (1) The removal operation methods include: random removal, worst removal, continuous removal and synchronous removal, among which:

[0103] 1. The specific process of random removal is: randomly select a patrolman in the initial path solution and the current inspection route R containing n nodes K (P1, P2, …, Pn), randomly determine the number of nodes that need to be removed from the current inspection route, determine the type of nodes that need to be removed, and when a node is a mandatory node, remove the node from the inspection route of all inspectors;

[0104] 2. The specific process of worst removal is: for the current search route R KFor each node in the current inspection route, calculate the travel time cost from the previous node to the current node, use the travel time cost to evaluate the current node, compare the travel time costs of each node, remove the node with the highest travel time cost from the current inspection route, and determine the type of node to be removed. If the node is a mandatory node, remove the node from the inspection routes of all inspectors.

[0105] 3. The specific process of continuous removal is: randomly determine a node to be removed from the current inspection route, and according to the position of the node in the current inspection route, remove a random number of nodes after the node from the current inspection route, and determine the type of the node to be removed. If the node is a mandatory node, remove the node from the inspection routes of all inspectors;

[0106] 4. Synchronous removal: Randomly remove a set number of mandatory nodes from the current inspection route, and remove the node from the inspection routes of all inspectors.

[0107] (2) The insertion operation methods include: random insertion and greedy insertion;

[0108] 1. The specific process of random insertion is:

[0109] S01. Calculate the selective node set P E The difference set between the solution of the current path and the solution of the current path is used to obtain the remaining available selective nodes, and a plurality of selective node subsets are randomly selected from the remaining available selective nodes;

[0110] S02, merging the selective node subset and the mandatory nodes removed during the removal operation into a set of nodes to be inserted;

[0111] S03. Select a node from the set of nodes to be inserted. If the node is a mandatory node, randomly insert it into two paths in the current path solution to obtain the corresponding new solution to be checked. Perform a feasibility check on the new solution to be checked. If the feasibility check passes, keep the new solution to be checked. If the feasibility check fails, use the current path solution as the new solution to be checked. If the node is a selective node, randomly insert it into one path in the current path solution and keep the new solution to be checked.

[0112] S04. Repeat step S03, and use the new solution to be checked as the current path solution, until all nodes in the set of nodes to be inserted are inserted into the current path solution to obtain a new path solution.

[0113] 2. The specific process of generating the initial path solution by greedy insertion is:

[0114] S41. For each inspector, determine the inspector's initial node and the inspector's terminal node, select a random subset from the pollution source node set, and ensure that all mandatory nodes are included in the random subset. Insert the initial node and the terminal node of each inspector into the path corresponding to each inspector in the initial path solution.

[0115] S42, select a node from the random subset, calculate the increased travel time cost after the node is inserted into all the positions to be inserted in the current path solution (any two nodes in all paths in the path solution can be used as the position to be inserted into), if the node is a mandatory node, first insert it into the position to be inserted with the smallest increase in travel time cost, then insert it into the position to be inserted with the smallest increase in travel time cost outside the path that has been inserted, if the node is a selective node, insert it into the position to be inserted with the smallest increase in travel time cost;

[0116] S43, when the inserted node is a mandatory node, perform a feasibility check on the current path solution, if the solution is not feasible, immediately prohibit the position to be inserted and reselect. When performing a feasibility check on the current path solution, determine whether there is a cross-synchronization problem between the positions to be inserted for each mandatory node between the checked routes, if so, prohibit the mandatory node from being inserted into the position to be inserted when cross-synchronization occurs;

[0117] S44. Repeat steps S42-S43 until all nodes in the random subset are inserted, and an initial path solution consisting of the inspection routes corresponding to each inspector is obtained.

[0118] During the above insertion operation, due to the existence of synchronous access constraints, cross synchronization problems may occur, resulting in an infeasible solution. Figure 2 As shown in the figure, the horizontal arrows from left to right represent the order in which different inspectors visit the nodes. Assuming that the order of visit to route 1 of inspector 1 is mandatory node 1→mandatory node 2, and the order of visit to route 2 of inspector 2 is mandatory node 2→mandatory node 1, the order of visit to mandatory nodes 1 and 2 of inspector 1 and inspector 2 intersects. Since the inspection routes 1 and 2 intersect, inspector 1 will wait for inspector 2 at mandatory node 1, and inspector 2 will wait for inspector 1 at mandatory node 2. They will never be able to wait for another inspector to complete the inspection together, making the entire path solution infeasible. Therefore, in order to solve the problem of cross synchronization in the path solution, the feasibility of the path solution after each insertion operation is checked. The specific process is as follows:

[0119] S10, constructing a sequence matrix to record the access order of the mandatory nodes of each screening route in the current path solution in each screening route;

[0120] S20. Use the transitive closure method to derive the access order between all mandatory nodes. If there is a pair of mandatory nodes with a bidirectional access order recorded in the sequence matrix, it is determined that cross synchronization exists and the current path solution is infeasible.

[0121] In order to improve the efficiency of urban pollution source inspection, this embodiment calls the above method when the dispatch center decides to assign a new pollution source event to an inspector, and provides the dispatcher and inspector with optimized work tasks and sequence for each inspector. The work tasks include new pollution source events and historical pollution sources in the database that can be updated along the way. In order to recommend inspection routes for urban pollution source management, it is first necessary to model the urban pollution source inspection work.

[0122] 1. Problem Modeling

[0123] (1) Node classification and definition

[0124] The locations in the inspection tasks are regarded as nodes, which are divided into mandatory nodes (new pollution source events that must be investigated by two inspectors at the same time), selective nodes (historical pollution sources that have been recorded in the database and only require one inspector to investigate), and inspector initial nodes (the current location of the inspector at the time of task assignment). Mandatory nodes and selective nodes have importance attributes, where the importance of mandatory nodes is unified as the maximum value, and the importance of each selective node is determined by the interval from the last time the selective node was investigated to the present time.

[0125] (2) Network construction

[0126] The complete urban pollution source inspection network should theoretically include all mandatory nodes and selective nodes, but the actual goal is to visit some selective nodes while completing the mandatory node inspection, so only a network containing all mandatory nodes and selective nodes near these mandatory nodes is constructed. The network is constructed as a complete graph, that is, all nodes are interconnected.

[0127] (3) Mathematical model construction

[0128] The present invention models the urban pollution source inspection path optimization problem as a mixed integer programming model with three subscript decision variables. Table 1 lists the variable symbols used in the model formula and their meanings.

[0129] Table 1 Symbols of variables in model formula

[0130]

[0131] Objective function: The most direct approach is to maximize the importance score collected from nodes per unit time. However, considering that placing the inspection time variable in the denominator is not conducive to accurate algorithm solution, the concept of standard work efficiency is introduced, and the objective function is set to maximize the difference between the sum of node scores and the standard work efficiency score, as shown in the following formula.

[0132]

[0133] Path constraint: ensure that each inspector starts from the initial location and returns to the end point, and all original locations and end points are visited only once, while ensuring the continuity and integrity of the path, as shown in the following formula.

[0134]

[0135] Task constraint: Ensure that mandatory nodes must be visited and checked by two inspectors, and optional nodes can only be checked by one inspector at most, as shown in the following formula.

[0136]

[0137] Time constraint: The conditional constraint is converted into an inequality constraint through the Big M method to ensure the correctness of the node troubleshooting completion time, including travel time, troubleshooting time, and waiting time, as shown in the following formula.

[0138]

[0139] Score constraint: Determine the actual importance score that can be collected by the node based on the node troubleshooting situation and time constraints, as shown in the following formula.

[0140]

[0141] 2. Solution

[0142] (1) Algorithm framework

[0143] This application proposes an algorithm based on adaptive large neighborhood search (ALNS). The algorithm takes the initial solution generated by the greedy insertion algorithm as the starting point and iteratively improves the current solution through a series of removal and insertion operations. In each iteration, a patrolman's route is randomly selected, the number of nodes to be removed is randomly determined, and after removing some nodes, all available mandatory nodes and some randomly selected available optional nodes are reinserted. The removal and insertion operations are dynamically selected through a roulette mechanism based on their past performance, and the newly generated solution is accepted as the new current solution based on the acceptance criteria of the simulated annealing process.

[0144] (2) Removal operation: When a mandatory node is removed, the node is completely removed from all routes to avoid invalid searches, including:

[0145] Random Removal: A patroller's route is randomly selected, a certain number of nodes are randomly removed, and when a mandatory node is removed, the node is completely removed from all routes to avoid invalid searches.

[0146] Worst removal: Evaluate nodes based on the travel time cost from the previous node to the current node, select and remove the most unfavorable nodes (with the highest travel time), which helps to converge quickly to a better solution.

[0147] Continuous Removal: After determining a random position on the route, a random number of nodes are removed continuously.

[0148] Synchronous Removal: Considering the importance and complexity of mandatory synchronous access to nodes, a patroller’s route is randomly selected and a certain number of nodes that require synchronous access are randomly removed.

[0149] (3) Insert operation

[0150] Random insertion: Randomly select a subset of available optional nodes that are not included in the current solution, and randomly insert them into the current solution together with the removed mandatory nodes. During insertion, feasibility needs to be checked to avoid cross-synchronization problems.

[0151] Greedy insertion: Select a random subset from the available node set (make sure it contains all remaining mandatory nodes), calculate the increase in route travel time cost after each node is inserted at each position, and insert the node at the position with the smallest increase in travel time cost. For mandatory nodes, first insert them as described above. If a cross-synchronization problem occurs, the current insertion position is prohibited and greedy insertion is performed again.

[0152] (4) Feasibility check

[0153] Detection method: By constructing a sequence matrix to record the visit order of the mandatory nodes in the current solution in the routes of each inspector, the transitive closure method is used to derive the visit order between all mandatory nodes. If there is a pair of nodes with a bidirectional visit order recorded in the matrix, it means that cross synchronization exists and the solution is not feasible.

[0154] 3. The effects of the method of this embodiment are:

[0155] (1) Innovative patrol route optimization strategy

[0156] The present invention innovatively models routine inspections in urban pollution source management and constructs a targeted mixed integer programming model. Different from classic path optimization problems (such as the traveling salesman problem and the vehicle routing problem), this method incorporates the importance of pollution sources into the path optimization problem according to the actual needs of pollution source inspections, sets some nodes as selective access, and realizes flexible planning of the inspection path for historical pollution sources while ensuring the completion of the new pollution source inspection task, thereby improving the overall inspection efficiency. This is an important innovation in urban pollution source path planning.

[0157] (2) Real-time response and decision support

[0158] The present invention can calculate the optimal patrol route in real time after receiving new pollution source events. This feature provides unprecedented real-time decision support capabilities for urban pollution source management. Patrolmen can immediately start work based on the real-time optimized route, which significantly enhances the ability to respond to sudden pollution events and makes urban pollution source management more flexible and efficient. This is in sharp contrast to traditional pre-planning or empirical decision-making methods, and reflects an innovative breakthrough in decision support.

[0159] (3) Adaptability and flexibility

[0160] The characteristics of the algorithm of the present invention enable it to easily cope with pollution source inspection tasks of different scales and complexities. Whether it is a small-scale local area inspection or a large-scale urban pollution source investigation, the present invention can achieve good results and provide a more universal solution for urban pollution source management.

[0161] For some specific scenarios, the implementation methods are similar, for example:

[0162] 1. When there is a need to inspect both new pollution source incidents and historical pollution sources at the same time.

[0163] Step 1.1: The dispatch center receives a certain number of new pollution source incidents and decides to assign pollution source inspection tasks.

[0164] Step 1.2: Add the historical pollution sources and new pollution sources in the vicinity of the new pollution source event in the database into the work pool, and record the current locations of all inspectors.

[0165] Step 1.3: Call the above method, include all pollution sources in the working pool into the path optimization problem and solve to obtain the recommended pollution source inspection tasks and recommended paths.

[0166] Step 1.4: The dispatch center sends the recommended pollution source inspection tasks and recommended routes to the corresponding inspectors.

[0167] 2. Due to the tight timeline and heavy workload of investigating new pollution source incidents, only new pollution source incidents are investigated.

[0168] Step 2.1: A large number of new pollution source incidents were received during the dispatch process, and it was decided to assign pollution source inspection tasks.

[0169] Step 2.2: Add new pollution source events to the work pool and record the current locations of all inspectors.

[0170] Step 2.3: Call the above method, include all pollution sources in the working pool into the path optimization problem and solve to obtain the recommended pollution source inspection tasks and recommended paths.

[0171] Step 2.4: The dispatch center sends the recommended pollution source inspection tasks and recommended routes to the corresponding inspectors.

[0172] 3. The situation where the working hours have started but no new pollution source incidents have been received.

[0173] Step 3.1: As no new pollution source incidents have been received during dispatch, it is decided to assign a pollution source inspection task.

[0174] Step 3.2: Record the current locations of all inspectors and put the historical pollution source events in the database near the inspector's location into the work pool.

[0175] Step 3.3: Call the above method, include all pollution sources in the working pool into the path optimization problem and solve to obtain the recommended pollution source inspection tasks and recommended paths.

[0176] Step 3.4: The dispatch center sends the recommended pollution source inspection tasks and recommended routes to the corresponding inspectors.

[0177] 4. Test Cases

[0178] To verify the effectiveness of the above method, different numbers of pollution sources (nodes) were randomly selected from a specific urban environmental pollution source database to generate test instances, ranging from 5 to 100, with an interval of 5, for a total of 20 scales. For each scale, different numbers of mandatory nodes (2, 4, 6, 8) and inspectors (2, 4, 6) were set, and the initial positions of the inspectors were randomly set. The mandatory node time constraints were manually set according to actual work experience, the mandatory node scores were unified to 10, and the selective node scores were randomly generated (integers between 1 and 5). The travel time between nodes was calculated based on longitude and latitude (using the Haversine distance multiplied by the appropriate nonlinear coefficient 1.2 and divided by the average vehicle speed of 31.71 km / h in Chengdu). For each test instance, three calculation time limits (1 second, 10 seconds and 100 seconds) were set for the algorithm of the present invention, and multiple tests were performed under different time limits (20 tests under 1 second and 10 second limits, and 10 tests under 100 second limits). At the same time, the commercial solver CPLEX (called in Python through DOcplex) was used for solving, and its calculation time was limited to 1 hour. The solution results of the algorithm of the present invention and CPLEX under different test instances were compared. The experimental results show that in small-scale instances, CPLEX can effectively solve the problem within 1 hour, but as the instance scale increases, its calculation time is too long to meet actual needs. The algorithm of the present invention can quickly obtain solutions close to or equal to CPLEX on small-scale instances. On large-scale instances, when CPLEX cannot provide a feasible solution within 1 hour, the algorithm of the present invention can still obtain a good solution within 10 to 100 seconds, and among the 112 test instances, the algorithm of the present invention achieved the best results on 105 instances, proving the effectiveness and practicality of the present method. The average test results of the first 16 test instances are shown in Table 2.

[0179] Table 2 Average results of the first 16 test instances

[0180]

[0181] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. According to the technical essence of the present invention, within the spirit and principles of the present invention, any simple modification, equivalent replacement and improvement made to the above embodiment still falls within the protection scope of the technical solution of the present invention.

Claims

1. A method for optimizing the inspection path of urban pollution sources, characterized in that: The specific steps include: S1. Receive the inspection tasks of the area to be inspected and the current location information of each inspector in the area to be inspected. The inspection tasks include the locations of newly added pollution sources and the locations of historical pollution sources to be updated in the database; S2. Constructing an urban pollution source inspection network in the area to be inspected, wherein the nodes of the urban pollution source inspection network include pollution source nodes and inspector initial nodes, the pollution source nodes include mandatory nodes and optional nodes, the mandatory nodes correspond to the locations of newly added pollution, the optional nodes correspond to the locations of historical pollution sources, and the inspector initial node corresponds to the current location information of the inspector; S3. According to the urban pollution source inspection network, set the constraints for generating the optimal inspection route, use the big M method to transform the constraints into inequality constraints, and build a mixed integer programming model; S4. Use the adaptive large neighborhood search algorithm to solve the mixed integer programming model to obtain the optimal inspection route corresponding to each inspector, and send the inspection work task corresponding to the optimal inspection route to the corresponding inspector; The mixed integer programming model takes whether each inspector visits the pollution source node and the order of visiting each pollution source node as decision variables, path constraints, task constraints, time constraints and score constraints as constraints, and optimizes the inspection efficiency as the goal. The objective function is set to maximize the difference between the comprehensive node score and the standard work efficiency score.

2. The method for optimizing the inspection path of urban pollution sources according to claim 1, characterized in that: The construction method of the urban pollution source inspection network in step S2 is: S21, screening the historical pollution source locations to be updated in the database, and selecting the historical pollution source locations within the preset range of the newly added pollution source locations from the database as selective nodes; S22, constructing an urban pollution source inspection network based on each mandatory node, optional node and inspector initial node, the urban pollution source inspection network is a complete graph; S23. Set the node attributes of each mandatory node and selective node in the urban pollution source inspection network, and set the importance of each selective node in turn according to the length of the time interval between the last inspection time and the current inspection time; unify the importance of all mandatory nodes, and set the importance of mandatory nodes to be greater than the importance of all selective nodes.

3. The method for optimizing the inspection path of urban pollution sources according to claim 1, characterized in that: The constraints include: Path constraint: ensure that each inspector starts from the inspector's initial node and returns to the end point, and all inspectors' initial nodes and end points are visited only once. At the same time, check the continuity and integrity of the generated inspection route. The calculation formula is: in, P Represents the set of pollution source nodes; D represents the inspector's terminal node set, and the travel time from all other nodes to the terminal node is 0; O represents the inspector's initial node set, K Indicates the inspectors are gathering. x i,j,k is a binary variable with a value of 0 or 1, and i≠j If the inspector k Slave Node i Go to Node j ,but x i,j,k =1; Task constraints: Ensure that mandatory nodes must be visited and checked by two inspectors, and optional nodes can only be checked by one inspector, as shown in the following formula: in, P M Represents a mandatory node set, P E represents a selective node set, y i is a binary variable with a value of 0 or 1. If node i is checked by any inspector, y i =1; Time constraint: The conditional constraint is converted into an inequality constraint through the Big M method to ensure the correctness of the node inspection completion time, including the travel time, inspection time and waiting time. The calculation formula is: in, Representation Node j The investigation is time-consuming. t i,j Representation Node i To Node j The travel time, w i Representation Node i The time when the investigation is completed. w j Representation Node j The time when the investigation is completed. M Represents a preset constant value. V Represents a collection of network nodes, V ={ P M ∪ P E ∪ O ∪ D }, P represents the set of polluted nodes, P ={ P M ∪ P E }; Score constraint: Determine the actual importance score that a node can obtain based on the node access situation and time constraints. The calculation formula for the importance score that a node can obtain is: in, p i Representation Node i The importance of setting Indicates access to mandatory nodes i The time threshold, Indicates that when the mandatory node i access timeout The actual importance score that can be obtained when 4. The method for optimizing the inspection path of urban pollution sources according to claim 3 is characterized in that: The objective function is: y i Indicates that the binary variable value is 0 or 1. If the node i is visited, then y i =1, q i Representation Node i The actual importance score that can be obtained is w j Representation Node j The time when the investigation is completed. θ Indicates standard work efficiency.

5. The method for optimizing the inspection path of urban pollution sources according to claim 2, characterized in that: All mandatory nodes constitute the mandatory node set P M , all selective nodes constitute the selective node set P E , pollution source node set P ={ P M ∪ P E }, all inspector initial nodes constitute the inspector initial node set O ; Network node collection V ={ P M ∪ P E ∪ O }, each inspector's inspection route consists of each node in the order of access. The specific process of step S4 is: According to the constructed mixed integer programming model, the adaptive large domain search algorithm is used to generate the initial path solution with the greedy insertion algorithm. The initial path solution is iteratively improved by multiple removal and insertion operations. The operation method of the removal and insertion operation of each iteration is dynamically selected through the roulette mechanism. Each iteration is iterated with the objective function as the target, and finally the optimal path solution is obtained. The optimal path solution includes the optimal inspection route corresponding to each inspector. During each iteration, an inspector is randomly selected from the initial path solution to check the route, nodes are randomly removed from the check route, and after removal, all available mandatory nodes and randomly selected available optional nodes are reinserted into the initial path solution to obtain a new solution after each iteration. The objective function is used to calculate the target values ​​corresponding to the initial path solution and the new solution after the iteration, and according to the target values ​​corresponding to the initial path solution and the new solution after the iteration, it is determined whether the new solution is accepted as the new iterative path solution according to the simulated annealing criterion.

6. The method for optimizing the inspection path of urban pollution sources according to claim 5, characterized in that: The removal operation methods include: random removal, worst removal, continuous removal and synchronous removal, among which, The specific process of random removal is: randomly select a patrolman in the initial path solution and the current inspection route R containing n nodes K , randomly determine the number of nodes that need to be removed from the current inspection route, determine the type of nodes that need to be removed, and when a node is a mandatory node, remove the node from the inspection routes of all inspectors; The specific process of worst removal is as follows: for the current search route R K For each node in the current inspection route, calculate the travel time cost from the previous node to the current node, use the travel time cost to evaluate the current node, compare the travel time costs of each node, remove the node with the highest travel time cost from the current inspection route, and determine the type of node to be removed. If the node is a mandatory node, remove the node from the inspection routes of all inspectors. The specific process of continuous removal is as follows: a node to be removed is randomly determined from the current inspection route, and according to the position of the node in the current inspection route, a random number of nodes after the node are removed from the current inspection route. At the same time, the type of the node to be removed is determined. If the node is a mandatory node, the node is removed from the inspection routes of all inspectors. Synchronous removal: Randomly remove a set number of mandatory nodes from the current inspection route and remove the node from the inspection routes of all inspectors.

7. The method for optimizing the inspection path of urban pollution sources according to claim 5, characterized in that: The insertion operation methods include: random insertion and greedy insertion. The specific process of random insertion is: S01. Calculate the selective node set P E The difference set between the solution of the current path and the solution of the current path is used to obtain the remaining available selective nodes, and a plurality of selective node subsets are randomly selected from the remaining available selective nodes; S02, merging the selective node subset and the mandatory nodes removed during the removal operation into a set of nodes to be inserted; S03. Select a node from the set of nodes to be inserted. If the node is a mandatory node, randomly insert it into any two paths of the current path solution to obtain the corresponding new solution to be checked. Perform a feasibility check on the new solution to be checked. If the feasibility check passes, keep the new solution to be checked. If the feasibility check fails, use the current path solution as the new solution to be checked. If the node is a selective node, randomly insert it into any one path of the current path solution and keep the new solution to be checked. S04. Repeat step S03, and use the new solution to be checked as the current path solution, until all nodes in the set of nodes to be inserted are inserted into the current path solution to obtain a new path solution.

8. The method for optimizing the inspection path of urban pollution sources according to claim 7, characterized in that: The specific process of generating the initial path solution by greedy insertion is: S41. For each inspector, determine the inspector's initial node and the inspector's terminal node, select a random subset from the pollution source node set, and ensure that all mandatory nodes are included in the random subset. There are several positions to be inserted for inserting each node in the random subset in the node access order between each inspector's initial node and the inspector's terminal node. S42, calculating the increase in travel time cost of a route formed by randomly inserting a node from the random subset into the position to be inserted, inserting the node into the position to be inserted corresponding to the minimum increase in travel time cost, updating the inspection route of each inspector, and forming the inspection routes of all inspectors into the current path solution; S43, performing a feasibility check on the current path solution to determine whether there is a cross-synchronization problem between the positions to be inserted of each mandatory node between the checked routes, and if so, prohibiting the mandatory node from being inserted into the position to be inserted when cross-synchronization occurs; S44. Repeat steps S42-S43 until all nodes in the random subset are inserted, and an initial path solution consisting of the inspection routes corresponding to each inspector is obtained.

9. The method for optimizing the inspection path of urban pollution sources according to claim 8, characterized in that: The specific process of feasibility check is as follows: S10, constructing a sequence matrix to record the access order of the mandatory nodes of each screening route in the current path solution in each screening route; S20. Use the transitive closure method to derive the access order between all mandatory nodes. If there is a pair of mandatory nodes with a bidirectional access order recorded in the sequence matrix, it is determined that cross synchronization exists and the current path solution is infeasible.

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