Urban underground cable wiring method based on double-layer multi-fidelity search optimization framework

Abstract

The application discloses a kind of urban underground cable wiring methods based on double-layer multi-fidelity search optimization framework, comprising: S1, establishes double-layer optimization model, with the sum of road excavation cost and cable procurement cost minimization as unified goal;S2, through mixed genetic search optimization upper substation connection topology, obtain initial feasible solution, and based on improved A algorithm planning initial cable path, generate initial scheme satisfying engineering constraint;S3, design adaptive multi-neighborhood search algorithm to carry out upper iteration exploration;S4, construct three-layer progressive lower layer evaluation mechanism;S5, introduce adaptive K value adjustment mechanism based on rank correlation, calculate the Spearman rank correlation coefficient of first layer and second layer sorting result, dynamically adjust candidate solution screening threshold through hypothesis test, ensure that high-fidelity optimizer does not miss high-quality candidate.The application realizes the close coupling and collaborative optimization of substation connection topology decision and specific cable wiring path.

Description

Technical Field

[0001] This invention relates to the field of cable cabling technology, and more specifically, to a method for urban underground cable cabling based on a two-layer multi-fidelity search optimization framework. Background Technology

[0002] With the acceleration of urbanization and the increasing demand for power system reliability, urban core areas are undergoing a large-scale transformation from overhead power distribution lines to underground cable networks to mitigate the impact of extreme weather and ensure power supply continuity and security. Underground cable routing planning, as a crucial aspect of urban medium-voltage power distribution network construction, directly affects project costs, system reliability, and subsequent operation and maintenance efficiency. However, cable routing planning in urban environments faces complex technical bottlenecks. First, spatial constraints and path complexity: Cable laying is strictly limited by the urban road network topology, making straight-line laying impossible; it must rely on existing roads. Compared to Euclidean distance calculations, the actual path length needs to be determined based on the specific road network, significantly increasing the complexity of the routing. Second, the nonlinear nature of the cost structure: Cable construction costs consist of road excavation costs and cable procurement costs, with excavation costs often exceeding three times the procurement costs. This asymmetry creates significant optimization opportunities: parallel laying of multiple cables on the same road segment allows for shared excavation costs, making some "non-shortest paths" the "lowest cost" solutions. Third, network topology constraints: urban medium-voltage distribution networks must adopt a topology configuration of closed-loop construction and open-loop operation to meet the power supply continuity requirements under N-1 fault conditions.

[0003] Existing technologies have significant shortcomings in addressing this problem: First, model simplification is disconnected from engineering. Current research often employs simplified relational models, optimizing only the substation topology while neglecting actual cable routing constraints and the cost effects of shared excavation for parallel cables, leading to significant deviations between the planned scheme and actual engineering needs. Second, phased optimization leads to local optima. Traditional methods use a serial decomposition strategy of "first determining connection relationships, then planning routing paths," where early optimization decisions severely constrain the later search space, easily trapping the problem in local optima. Third, algorithm design lacks specificity. Traditional precise algorithms struggle to handle ultra-large-scale combinatorial optimization spaces, while existing heuristic methods often employ single neighborhood operators or simple multi-neighborhood mechanisms, failing to effectively coordinate the optimization of two tightly coupled decision objects, resulting in low search efficiency and poor stability.

[0004] In summary, existing technologies struggle to address the three core issues of road constraints, precise cost control, and large-scale adaptability within the same framework. There is an urgent need for a method that can integrate the coupling relationship between modeling topology and wiring, jointly optimize through a multi-neighborhood collaborative mechanism, and accelerate the process with efficient evaluation. Summary of the Invention

[0005] The purpose of this invention is to provide a method for urban underground cable routing based on a two-layer multi-fidelity search optimization framework, so as to overcome the defects of the existing technology.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: The urban underground cable routing method based on a two-layer multi-fidelity search optimization framework includes the following steps: S1. Establish a two-level optimization model. The upper-level decision variables of the two-level optimization model represent the connection topology between substations. The lower-level decision variables of the two-level optimization model include road excavation decisions and the number of parallel cable laying. The two-level optimization model takes minimizing the sum of road excavation costs and cable procurement costs as its unified objective. S2. Optimize the upper-level substation connection topology through hybrid genetic search to obtain an initial feasible solution, and then improve the solution based on the A... The algorithm plans the initial cable path and generates an initial solution that meets engineering constraints; S3. Design an adaptive multi-neighborhood search algorithm for upper-level iterative exploration. This adaptive multi-neighborhood search algorithm integrates seven complementary neighborhood operators, including node insertion, node exchange, arc exchange, chain relocation, cross exchange, substation redistribution, and feeder merging and splitting. Through an adaptive weight adjustment mechanism, the exploration effect of each operator is balanced, and the neighborhood size is dynamically adjusted according to the search stagnation situation. S4. Construct a three-layer progressive lower-level evaluation mechanism. The first layer uses Euclidean distance approximation to filter all candidate solutions. The second layer utilizes the mapping relationship between the upper and lower layers to perform A evaluation only on node pairs whose connection relationship has changed. Replanning, retaining the unchanged path, obtains evaluation at a moderate computational cost. The third layer, based on the second layer, iteratively optimizes the cable routing through destruction-repair iteration to obtain a high-fidelity solution. S5. An adaptive K-value adjustment mechanism based on rank correlation is introduced to calculate the Spearman rank correlation coefficient between the first and second layer ranking results. The candidate solution screening threshold is dynamically adjusted through hypothesis testing to ensure that the high-fidelity optimizer does not miss high-quality candidates.

[0007] Furthermore, the formula for the two-layer optimization model in step S1, with the unified objective of minimizing the sum of road excavation cost and cable procurement cost, is as follows:

[0008] In the formula, A collection of road segments. Cost per unit of excavation For the unit cable cost, The length of the road segment is (km). For road section excavation decision variables, This refers to the number of parallel cables in the road segment; The upper-level decision variables Indicates feeder Is it directly connected to the substation? and The upper-level constraints of this upper-level decision variable include: Network topology constraints: Each feeder forms a ring network or interconnected structure, starting from the high-voltage substation and returning to the high-voltage substation; Feeder capacity constraints: ,in For connecting to the feeder A collection of medium-voltage substations, It is a substation peak power, This refers to the maximum power capacity of a single feeder. Coverage constraint: Each medium-voltage substation is assigned exactly one feeder; The lower-level decision variables are given the upper-level topology. Optimize road excavation Parallel number of cables The lower-level constraints of this lower-level decision variable include: Connectivity constraint: There must be a path along the road network between each corresponding substation; Cable capacity constraints: This indicates the number of cables laid in parallel along the same section of road. It cannot exceed the predetermined upper limit. ; Consistency constraint: Cables can only be laid on excavated sections of road.

[0009] Furthermore, the specific steps in step S2 to optimize the upper-level substation connection topology through hybrid genetic search to obtain an initial feasible solution are as follows: The upper-level problem is transformed into a multi-warehouse capacity-constrained vehicle routing problem using the MD-VRP auxiliary model, with the objective of minimizing the Euclidean distance:

[0010] In the formula, Indicates substation and The Euclidean distance between them is solved using a hybrid genetic search in this stage. Through population initialization, crossover, mutation, and selection operations, an initial connection set that satisfies capacity and topological constraints is generated. The improved A The algorithm plans the initial cable path and generates an initial solution that satisfies engineering constraints in the following steps: Based on improved A Algorithm, in city road map In, for each abstract connection The specific path is planned, and the heuristic function is designed as follows:

[0011] In the formula, Using Manhattan distance, Integrate road excavation costs with cable costs, and prioritize road sections where parallel laying is feasible.

[0012] Furthermore, the seven complementary neighborhood operators in step S3 specifically include: node insertion. Remove a substation and reconnect other feeders; node switching. : Substations that exchange two feeders; arc-segment switching : Swap the ends of the two feeders after a random cut point; chain relocation : Moving a sequence of 1-3 consecutive substations; cross-switching Simultaneous switching of internal segments of two feeders; substation redistribution. : Changing the substation allocation of feeders; merging and splitting feeders Merge or split feeders, dynamically adjust the number of feeders; The steps of balancing the exploration effects of each operator through an adaptive weight adjustment mechanism and dynamically adjusting the neighborhood size according to the search stagnation are as follows: For each operator Maintain weight ;

[0013] During the exploration phase, all operators are applied in a random order; during the development phase, they are applied using normalized weights. Sampling, rebalancing every 20 iterations: ; If the search stalls for more than 10 iterations, adjust the size of the neighborhood search. :

[0014] In the formula, It represents the initial neighborhood search size.

[0015] Furthermore, in step S4: The first layer uses Euclidean distance approximation. The steps for screening all candidate solutions are: only calculate the sum of Euclidean distances, without performing the next layer optimization, to initially screen all candidate solutions; The second layer utilizes the mapping relationship between the upper and lower layers to perform A only on node pairs whose connection relationship has changed. The replanning process, preserving invariable paths, and obtaining an evaluation at a moderate computational cost involves: utilizing the mapping relationship between upper and lower layers for efficient local updates; and re-updating the solution from the upper layer. arrive The perturbation involves the following steps: identifying the set of node pairs whose connectivity has changed; applying A only to these changed edge pairs. The algorithm replans the path; retains the original path with unchanged connections; and recalculates the total cost. The third layer, building upon the second layer, iteratively optimizes the cable routing through a destruction-repair iteration to obtain a high-fidelity solution. The steps are as follows: Perform destruction-repair iteration based on the second layer: randomly select and remove some routing paths; use A... The algorithm replans these paths; iterates repeatedly until convergence.

[0016] Furthermore, step S5 specifically includes: Calculate the Spearman rank correlation coefficient between the first and second level ranking results:

[0017] In the formula, For the first The two-level ranking differences of the candidates were analyzed to test the null hypothesis. The test statistic is:

[0018] if ,but ;if ,but In other cases ( The value of p is: ; Based on the assessment coverage Adjust the significance threshold:

[0019] In the formula, , , It refers to population size; when When the difference between the Top-K ranking of the first layer and the second layer is significant, K is conservatively increased to retain more candidates; when At this time, the sorting consistency is sufficient, the screening of the first layer is reliable, and K remains unchanged to concentrate computing resources on high-quality solutions.

[0020] Compared with existing technologies, the advantages of this invention are as follows: This invention addresses the core needs of underground cable routing planning for urban medium-voltage distribution networks, aiming to minimize the total cost of road excavation and cable procurement. Under multiple engineering conditions, including network topology ring / interconnection constraints, feeder capacity constraints, and physical limitations on parallel cable laying, it achieves tight coupling and collaborative optimization of substation connection topology decisions and specific cable routing paths. This invention can be directly applied to practical engineering scenarios such as urban power engineering planning and design, and the upgrading and transformation of medium-voltage distribution networks. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This is a flowchart illustrating the overall framework of the urban underground cable routing method based on a two-layer multi-fidelity search optimization framework of the present invention. Figure 2 This is a schematic diagram of the seven neighborhood operators for upper-level adaptive multi-neighborhood search in this invention. Detailed Implementation

[0023] The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, so that the advantages and features of the present invention can be more easily understood by those skilled in the art, thereby providing a clearer and more explicit definition of the scope of protection of the present invention.

[0024] See Figure 1 As shown, this embodiment discloses a method for urban underground cable routing based on a two-layer multi-fidelity search optimization framework, including the following steps: Step S1: Establish a two-layer optimization model. The upper-layer decision variable of the two-layer optimization model represents the connection topology (feeder allocation scheme) between substations. The lower-layer decision variables of the two-layer optimization model include road excavation decisions and the number of parallel cable laying. The two-layer optimization model takes minimizing the sum of road excavation costs and cable procurement costs as a unified objective, and clarifies multiple conditions such as network topology, feeder capacity, and parallel cable constraints.

[0025] In this embodiment, the formula for the two-layer optimization model with the unified objective of minimizing the sum of road excavation cost and cable procurement cost is as follows:

[0026] In the formula, A collection of road segments. The cost per unit of excavation (million yuan / km). Cost per unit cable (million yuan / km). The length of the road segment is (km). For road section excavation decision variables, This refers to the number of parallel cables in the road segment.

[0027] The upper-level decision variables Indicates feeder Is it directly connected to the substation? and The upper-level constraints of this upper-level decision variable include: Network topology constraints: Each feeder forms a ring network or interconnected structure, starting from and returning to the high-voltage substation; Feeder capacity constraints: ,in For connecting to the feeder A collection of medium-voltage substations, It is a substation peak power, It is the upper limit of the power capacity of a single feeder; coverage constraint: each medium-voltage substation is assigned exactly one feeder.

[0028] The lower-level decision variables are given the upper-level topology. Optimize road excavation Parallel number of cables The lower-level constraints of this lower-level decision variable include: Connectivity constraint: There must be a path along the road network between each corresponding substation; Cable capacity constraint: This indicates the number of cables laid in parallel along the same section of road. It cannot exceed the predetermined upper limit. Consistency constraint: Cables can only be laid on excavated sections of road.

[0029] Step S2: Optimize the upper-level substation connection topology through hybrid genetic search to obtain an initial high-quality feasible solution, and then improve the solution based on the A... The algorithm plans the initial cable path and generates an initial solution that meets engineering constraints.

[0030] In this embodiment, the specific steps for optimizing the upper-level substation connection topology through hybrid genetic search to obtain an initial feasible solution are as follows: The upper-level problem is transformed into a multi-warehouse capacity-constrained vehicle routing problem (MD-CVRP) using an MD-VRP auxiliary model, with the objective of minimizing the Euclidean distance:

[0031] In the formula, Indicates substation and The Euclidean distance between them is determined by a hybrid genetic search, which generates an initial set of connections that satisfies capacity and topological constraints through population initialization, crossover, mutation, and selection operations.

[0032] The improved A The algorithm plans the initial cable path and generates an initial solution that satisfies engineering constraints in the following steps: Based on improved A Algorithm, in city road map In, for each abstract connection The specific path is planned, and the heuristic function is designed as follows:

[0033] In the formula, Using Manhattan distance, Integrate road excavation costs with cable costs, and prioritize road sections where parallel laying is feasible.

[0034] Step S3: Design an adaptive multi-neighborhood search algorithm for upper-level iterative exploration. This adaptive multi-neighborhood search algorithm integrates seven complementary neighborhood operators, including node insertion, node exchange, arc exchange, chain relocation, cross exchange, substation redistribution, and feeder merging and splitting. Through an adaptive weight adjustment mechanism, the exploration effect of each operator is balanced, and the neighborhood size is dynamically adjusted according to the search stagnation situation.

[0035] In this embodiment, see Figure 2 As shown, the seven complementary neighborhood operators are: node insertion Remove a substation and reconnect other feeders; node switching. : Substations that exchange two feeders; arc-segment switching : Swap the ends of the two feeders after a random cut point; chain relocation : Moving a sequence of 1-3 consecutive substations; cross-switching Simultaneous switching of internal segments of two feeders; substation redistribution. : Changing the substation allocation of feeders; merging and splitting feeders : Merge or split feeders, dynamically adjust the number of feeders.

[0036] The steps of balancing the exploration effects of each operator through an adaptive weight adjustment mechanism and dynamically adjusting the neighborhood size according to the search stagnation are as follows: For each operator Maintain weight (Initial value 1.0):

[0037] During the exploration phase, all operators are applied in a random order; during the development phase, they are applied using normalized weights. Sampling, rebalancing every 20 iterations: ; If the search stalls for more than 10 iterations, adjust the size of the neighborhood search. :

[0038] In the formula, It represents the initial neighborhood search size.

[0039] Step S4: Construct a three-layer progressive lower-level evaluation mechanism (LS1-LS2-LS3). The first layer, LS1 (fast estimation), uses Euclidean distance approximation to filter all candidate solutions. The second layer, LS2 (local replanning), utilizes the mapping relationship between the upper and lower layers to perform A* evaluation only on node pairs whose connection relationships have changed. Replanning, retaining the unchanged path, obtains evaluation under moderate computational cost. The third layer LS3 (synthesis optimization) builds on the second layer LS2 and iteratively optimizes the cable routing through destruction-repair iteration to obtain a high-fidelity solution.

[0040] In this embodiment, the first layer LS1 (fast estimation) only calculates the sum of Euclidean distances and does not perform lower-level optimization; it is used to initially screen all candidate solutions. The second layer, LS2 (Local Replanning), utilizes the mapping relationship between upper and lower layers to perform efficient local updates, for solutions from the upper layer... arrive The perturbation involves the following steps: identifying the set of node pairs whose connectivity has changed; applying A only to these changed edge pairs. The algorithm replans the path; retains the original path with unchanged connections; and recalculates the total cost. Layer 3 LS3 (Synthesis Optimization): Based on Layer 2, perform a break-repair iteration: randomly select and remove some routing paths; use A... The algorithm replans these paths; iterates repeatedly until convergence.

[0041] The computational cost of a three-layer optimizer is approximately [percentage missing]. .

[0042] Step S5: Introduce an adaptive K-value adjustment mechanism based on rank correlation, calculate the Spearman rank correlation coefficient between the first and second layer ranking results, and dynamically adjust the candidate solution screening threshold through hypothesis testing to ensure that the high-fidelity optimizer does not miss high-quality candidates.

[0043] The goal is to dynamically adjust the number K of candidate solutions selected from LS1 to enter LS2 based on the consistency of the ranking between the first-level LS1 and the second-level LS2. Calculate the Spearman rank correlation coefficient between the ranking results of the first-level LS1 and the second-level LS2:

[0044] Testing the null hypothesis The test statistic is:

[0045] if ,but ;if ,but In other cases ( The value of p is: ; Based on the assessment coverage Adjust the significance threshold:

[0046] In the formula, , , It refers to population size; when When the difference between the Top-K ranking of the first layer and the second layer is significant, K is conservatively increased to retain more candidates; when At this time, the sorting consistency is sufficient, the screening of the first layer is reliable, and K remains unchanged to concentrate computing resources on high-quality solutions.

[0047] This invention integrates an adaptive multi-neighborhood search and multi-fidelity evaluation into a two-layer coupled optimization framework, which breaks through the local optimum trap caused by traditional staged optimization and achieves close collaboration between upper-layer topology decision-making and lower-layer path planning. This invention constructs a three-layer progressive multi-fidelity evaluation mechanism, which makes full use of the mapping relationship in the problem structure and realizes efficient computation of local replanning in a medium-fidelity optimizer, breaking the stereotype that high-fidelity evaluation inevitably leads to high computational cost. This invention introduces an adaptive K-value adjustment mechanism based on rank correlation. Through hypothesis testing and dynamic significance levels, it achieves intelligent coordination between low-fidelity screening and high-fidelity optimization, ensuring a dynamic balance between the quality of candidate solutions and search efficiency.

[0048] Although embodiments of the present invention have been described in conjunction with the accompanying drawings, the patent owner may make various modifications or alterations within the scope of the appended claims, as long as they do not exceed the protection scope described in the claims of the present invention, they shall be within the protection scope of the present invention.

Claims

1. A method for urban underground cable routing based on a two-layer multi-fidelity search optimization framework, characterized in that, Includes the following steps: S1. Establish a two-level optimization model. The upper-level decision variables of the two-level optimization model represent the connection topology between substations. The lower-level decision variables of the two-level optimization model include road excavation decisions and the number of parallel cable laying. The two-level optimization model takes minimizing the sum of road excavation costs and cable procurement costs as its unified objective. S2. Optimize the upper-level substation connection topology through hybrid genetic search to obtain an initial feasible solution, and then improve the solution based on the A... The algorithm plans the initial cable path and generates an initial solution that meets engineering constraints; S3. Design an adaptive multi-neighborhood search algorithm for upper-level iterative exploration. This adaptive multi-neighborhood search algorithm integrates seven complementary neighborhood operators, including node insertion, node exchange, arc exchange, chain relocation, cross exchange, substation redistribution, and feeder merging and splitting. Through an adaptive weight adjustment mechanism, the exploration effect of each operator is balanced, and the neighborhood size is dynamically adjusted according to the search stagnation situation. S4. Construct a three-layer progressive lower-level evaluation mechanism. The first layer uses Euclidean distance approximation to filter all candidate solutions. The second layer utilizes the mapping relationship between the upper and lower layers to perform A evaluation only on node pairs whose connection relationship has changed. Replanning, retaining the unchanged path, obtains evaluation at a moderate computational cost. The third layer, based on the second layer, iteratively optimizes the cable routing through destruction-repair iteration to obtain a high-fidelity solution. S5. An adaptive K-value adjustment mechanism based on rank correlation is introduced to calculate the Spearman rank correlation coefficient between the first and second layer ranking results. The candidate solution screening threshold is dynamically adjusted through hypothesis testing to ensure that the high-fidelity optimizer does not miss high-quality candidates.

2. The urban underground cable routing method based on a two-layer multi-fidelity search optimization framework according to claim 1, characterized in that, The formula for the two-layer optimization model in step S1, with the unified objective of minimizing the sum of road excavation cost and cable procurement cost, is as follows: In the formula, A collection of road segments. Cost per unit of excavation For the unit cable cost, The length of the road segment is (km). For road section excavation decision variables, This refers to the number of parallel cables in the road segment; The upper-level decision variables Indicates feeder Is it directly connected to the substation? and The upper-level constraints of this upper-level decision variable include: Network topology constraints: Each feeder forms a ring network or interconnected structure, starting from the high-voltage substation and returning to the high-voltage substation; Feeder capacity constraints: ,in For connecting to the feeder A collection of medium-voltage substations, It is a substation peak power, This refers to the maximum power capacity of a single feeder. Coverage constraint: Each medium-voltage substation is assigned exactly one feeder; The lower-level decision variables are given the upper-level topology. Optimize road excavation Parallel number of cables The lower-level constraints of this lower-level decision variable include: Connectivity constraint: There must be a path along the road network between each corresponding substation; Cable capacity constraints: This indicates the number of cables laid in parallel along the same section of road. It cannot exceed the predetermined upper limit. ; Consistency constraint: Cables can only be laid on excavated sections of road.

3. The urban underground cable routing method based on a two-layer multi-fidelity search optimization framework according to claim 1, characterized in that, The specific steps in step S2 to optimize the upper-level substation connection topology through hybrid genetic search and obtain an initial feasible solution are as follows: The upper-level problem is transformed into a multi-warehouse capacity-constrained vehicle routing problem using the MD-VRP auxiliary model, with the objective of minimizing the Euclidean distance: In the formula, Indicates substation and The Euclidean distance between them is solved using a hybrid genetic search in this stage. Through population initialization, crossover, mutation, and selection operations, an initial connection set that satisfies capacity and topological constraints is generated. The improved A The algorithm plans the initial cable path and generates an initial solution that satisfies engineering constraints in the following steps: Based on improved A Algorithm, in city road map In, for each abstract connection The specific path is planned, and the heuristic function is designed as follows: In the formula, Using Manhattan distance, Integrate road excavation costs with cable costs, and prioritize road sections where parallel laying is feasible.

4. The urban underground cable routing method based on a two-layer multi-fidelity search optimization framework according to claim 1, characterized in that, The seven complementary neighborhood operators in step S3 are specifically: node insertion. Remove a substation and reconnect other feeders; node switching. : Substations that exchange two feeders; arc-segment switching : Swap the ends of the two feeders after a random cut point; chain relocation : Moving a sequence of 1-3 consecutive substations; cross-switching Simultaneous switching of internal segments of two feeders; substation redistribution. : Changing the substation allocation of feeders; merging and splitting feeders Merge or split feeders, dynamically adjust the number of feeders; The steps of balancing the exploration effects of each operator through an adaptive weight adjustment mechanism and dynamically adjusting the neighborhood size according to the search stagnation are as follows: For each operator Maintain weight ; During the exploration phase, all operators are applied in a random order; during the development phase, they are applied using normalized weights. Sampling, rebalancing every 20 iterations: ; If the search stalls for more than 10 iterations, adjust the size of the neighborhood search. : In the formula, It represents the initial neighborhood search size.

5. The urban underground cable routing method based on a two-layer multi-fidelity search optimization framework according to claim 1, characterized in that, In step S4: The first layer uses Euclidean distance approximation. The steps for screening all candidate solutions are: only calculate the sum of Euclidean distances, without performing the next layer optimization, to initially screen all candidate solutions; The second layer utilizes the mapping relationship between the upper and lower layers to perform A only on node pairs whose connection relationship has changed. The replanning process, preserving invariable paths, and obtaining an evaluation at a moderate computational cost involves: utilizing the mapping relationship between upper and lower layers for efficient local updates; and re-updating the solution from the upper layer. arrive The perturbation involves the following steps: identifying the set of node pairs whose connectivity has changed; applying A only to these changed edge pairs. Algorithm replans path; Preserve the original path without altering the connection; Recalculate the total cost; The third layer, building upon the second layer, iteratively optimizes the cable routing through a destruction-repair iteration to obtain a high-fidelity solution. The steps are as follows: Perform destruction-repair iteration based on the second layer: randomly select and remove some routing paths; use A... The algorithm replans these paths; iterates repeatedly until convergence.

6. The urban underground cable routing method based on a two-layer multi-fidelity search optimization framework according to claim 1, characterized in that, Step S5 specifically includes: Calculate the Spearman rank correlation coefficient between the first and second level ranking results: In the formula, For the first The two-level ranking differences of the candidates were analyzed to test the null hypothesis. The test statistic is: if ,but ;if ,but In other cases ( The value of p is: ; Based on the assessment coverage Adjust the significance threshold: In the formula, , , It refers to population size; when When the difference between the Top-K ranking of the first layer and the second layer is significant, K is conservatively increased to retain more candidates; when At this time, the sorting consistency is sufficient, the screening of the first layer is reliable, and K remains unchanged to concentrate computing resources on high-quality solutions.

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