Reservoir basin dam line site selection method based on improved adaptive variable neighborhood search algorithm

Abstract

A reservoir basin dam line site selection method based on an improved adaptive variable neighborhood search algorithm is realized based on an established dam line site selection optimization target mathematical model, and comprises the following steps: obtaining area DEM data needing site selection, and dividing the area DEM data into four identical sub-areas R1-R4; obtaining an initial parameter of each sub-region boundary, initializing the initial parameter of each sub-region boundary, and generating an initial solution Sol0; the initial solution Sol0 is used as a starting point, an IAVNS algorithm is adopted to solve the optimization target mathematical model, and the optimal solution Solbest of each sub-region is obtained; and outputting a global optimal solution Solbest fullness of the site selection area by using an SHP file, and carrying out visual display on the global optimal solution Solbest fullness. By proposing an IAVNS algorithm and adopting a double-layer collaborative optimization architecture, a dynamic hierarchical variable neighborhood search strategy and a rapid evaluation method based on terrain elevation variance analysis, global exploration, fine local search and multi-target dynamic balance optimization are realized, and fine optimization requirements under complex terrains are met.

Description

Technical Field

[0001] This invention belongs to the field of hydraulic engineering optimization design technology, specifically relating to a reservoir basin dam line location method based on an improved adaptive variable neighborhood search algorithm. Background Technology

[0002] The site selection of the dam line for pumped storage power stations (hereinafter referred to as "reservoir-dam line") is a core issue in the optimal design of water conservancy projects, requiring comprehensive consideration of multiple objectives such as terrain adaptability, reservoir capacity constraints, and engineering economics. In practical applications, the technologies typically used for pumped storage power station dam line site selection are mainly divided into two categories:

[0003] Site selection methods based on GIS spatial analysis, such as the paper "Geographic Information System Algorithms to Locate Prospective Sites for Pumped Hydro Energy Storage" (using STORES software), achieve preliminary screening through high-resolution DEM data and virtual watershed analysis, proposing the "water-to-rock ratio (W / R)" index to optimize energy storage capacity and engineering costs. However, this method relies on fixed terrain feature parameters, such as slope and elevation difference, and does not dynamically optimize for dam line geometry, such as vertex coordinates and convex polygon constraints, making it difficult to break through local optima.

[0004] Algorithm-driven automated site selection methods, such as the patent document CN117273263A entitled "A Method for Site Selection of Pumped Storage Power Stations Based on DEM Data," employ a priority flooding algorithm and mean-variable point analysis to optimize reservoir-basin matching. However, it fails to address multi-objective conflict issues, such as simultaneously minimizing excavation and filling volume and surface area. Its calculation method is simplistic and lacks an adaptive search mechanism, making it prone to getting trapped in local optima. Similarly, the literature "Research on Site Selection Method for Upper and Lower Reservoirs of Pumped Storage Power Stations Based on Satellite Remote Sensing Topographic Data" extracts concave areas through morphological operations. This approach only focuses on macroscopic location selection within the reservoir area and does not model the dam line geometric fine-tuning process, making it difficult to meet the refined optimization needs under complex terrain.

[0005] For example, patent document CN118536657A, based on GIS software, employs Bursa coordinate transformation, priority flooding algorithm, and mean change point analysis to automate the entire process from data preprocessing to reservoir-basin matching. It improves computational efficiency by using dynamic thresholds to ensure the objectivity of river network extraction. However, this technical solution only considers the impact of hydrology on dam site selection and cannot precisely control the geometry, exact location, and three-dimensional spatial shape of the reservoir dam line. Furthermore, it does not consider optimizing the entire region, resulting in a non-globally optimal solution and failing to address the real-time adaptation of dynamic constraints, such as reservoir capacity, reservoir surface area, and dead water level elevation.

[0006] Therefore, it is very important to study a pumped storage reservoir dam line location method that can solve the real-time adaptation problem under dynamic constraints, solve the local optimal solution problem of reservoir dam line selection, and meet the fine optimization needs under complex terrain. Summary of the Invention

[0007] To address the above technical problems, this application provides a reservoir basin dam alignment selection method based on an improved adaptive variable neighborhood search algorithm. This method is implemented based on an established mathematical model for optimizing dam alignment selection and includes the following steps:

[0008] Obtain the DEM data of the area to be selected, and divide the DEM data into four identical sub-regions R1-R4;

[0009] Obtain the initial parameters of the boundary of each sub-region, initialize the initial parameters of the boundary of each sub-region, generate the initial solution Sol0, and perform directional optimization; the initial parameters include reservoir capacity Λ, dam crest elevation h, dead water level H, normal water level ω, similarity ratio k, reservoir capacity error, number of polygon vertices, slope θ, and water depth;

[0010] Starting with the initial solution Sol0, the IAVNS algorithm is used to solve the optimization objective mathematical model to obtain the optimal solution Sol for each sub-region. best子 ;

[0011] Output the globally optimal solution Sol for the selected location region as an SHP file. best全 And visualize it; the global optimal solution Sol best全 The final dam site selection scheme includes the optimal solution Sol for each sub-region. best子 The optimal values ​​for the latitude and longitude coordinates of each vertex of the dam line, as well as the dam crest elevation h, dead water level H, and similarity ratio k.

[0012] Furthermore, the mathematical model for the optimization objective is as follows:

[0013] Objective function:

[0014] Constraint: S = S + +S - , S - =k 2 S + ;

[0015]

[0016]

[0017] Where w1 is the weighting coefficient for the reservoir excavation volume; w2 is the weighting coefficient for the reservoir surface area; μ is the cost per unit area; and r is the grid. Let X be the cut volume of grid r; i and j are any two non-repeating vertices of the polygon on the grid; V is the set of all points, i∈V, j∈V; X ij Let i be the line segment between points i and j. For line segment X ij The set of grids that pass through, R is the set of all grids, r∈R; The fill volume for grid r is given; h is the reservoir depth; S + S represents the surface area of ​​the reservoir. - Let x be the area of ​​the lower surface of the reservoir; U is the uncertain set of the reservoir depth; x i Let be the x-coordinate of point i; y-coordinate of point i. i Let x be the y-coordinate of point i; j Let j be the x-coordinate of point j; y j Let j be the y-coordinate of point j.

[0018] Furthermore, the IAVNS algorithm adopts a two-layer collaborative optimization architecture of an internal search module and an external adjustment module, which iterates repeatedly until the termination condition of the IAVNS algorithm is reached. The termination condition of the IAVNS algorithm is that the number of iterations of the IAVNS algorithm reaches the preset maximum number of iterations MaxIter.

[0019] Furthermore, the internal search module includes the following:

[0020] Preset the neighborhood operator weights and iteration number thresholds, and select the neighborhood operator according to the neighborhood operator selection strategy;

[0021] Based on the selected neighborhood operator, a dynamic hierarchical variable neighborhood search strategy is used to perform a local search to obtain a new solution Sol1;

[0022] By establishing an elevation variance index, a fast evaluation function f is constructed. fast To determine the relative sizes of f(Sol1) and f(Sol0), the specific steps are as follows:

[0023] When f(Sol1) < f(Sol0), update the optimal solution Sol. best子 =Sol1, let Sol0 = Sol1, t = 1; after updating the operator weights, proceed to the next iteration calculation;

[0024] When f(Sol1)≥f(Sol0), determine whether the new solution Sol1 satisfies the simulated annealing acceptance criterion;

[0025] If satisfied, update the optimal solution Sol. best子=Sol1, let Sol0 = Sol1, t = 1; after updating the operator weights, proceed to the next iteration calculation;

[0026] If the condition is not met, the cumulative iteration count is t; then, it is determined whether the stopping criterion is met. If it is met, the iteration stops, and the fitness value of each sub-region is output to the external adjustment module. The fitness value is the optimal solution Sol in each sub-region. best子 The objective function value fit(R) i If the condition is not met, proceed to the next iteration calculation; the stopping criterion is to stop iteration when the cumulative iteration count t reaches the iteration count threshold.

[0027] Furthermore, the external adjustment module includes the following:

[0028] Receive the fitness value fit(R) output by the internal search module i ), calculate the weight of each sub-region;

[0029] According to the fitness value fit(R) i A weighted movement strategy is used to select the fitness value fit(R). i The worst subregion R′ is moved along its boundary, and the search space of the algorithm is changed by adjusting its boundary.

[0030] While maintaining other subregions R i With the boundary unchanged, update the boundary of subregion R′, R i ≠R′, and serves as a prerequisite for the next iteration of the internal search module.

[0031] Furthermore, the neighborhood operators include a two-dimensional up shift operator K1, a two-dimensional down shift operator K2, a two-dimensional left shift operator K3, a two-dimensional right shift operator K4, a rotation operator K5, a three-dimensional up shift operator G1, a three-dimensional down shift operator G2, and a geometric deformation operator V1.

[0032] Furthermore, the dynamic hierarchical variable neighborhood search strategy is as follows:

[0033] In the early stages of iteration, when iter / Iter max ≤0.6, the algorithm focuses on planar position optimization, executes the operator set Φ1={K1,K2,K3,K4,K5,G1,G2,V1}, and introduces an adaptive probability selection mechanism;

[0034] In the middle of the iteration, when 0.6 < iter / Iter max ≤0.9, the algorithm integrates the co-optimization of planar position and height, constructs a hybrid operator space Φ2=Φ1∪{G1,G2}, and introduces an adaptive probability selection mechanism;

[0035] In the later stages of iteration, when iter / Iter max >0.9, execute deformation operator V1, and change the height h and the shape of the bottom surface of the reservoir by fine-tuning the similarity ratio k, thereby optimizing the internal search process;

[0036] Where iter represents the current iteration number, Iter max This indicates the maximum number of iterations.

[0037] Furthermore, the adaptive probability selection mechanism specifically includes the following:

[0038] Record the historical improvement count S for each operator. i (t) and the number of calls N i (t), calculate the success probability of the i-th operator in the t-th iteration:

[0039] The success rate is mapped to the selection probability using the softmax function:

[0040] Furthermore, the fast evaluation function f fast The construction method is as follows:

[0041] Obtain the set of coordinates P of the vertices on the upper surface of the reservoir corresponding to the current solution. top ={p i (x i ,y i For each vertex coordinate set of the upper base, m sampling points are generated by random sampling within the set of vertex coordinates of the upper base.

[0042] The elevation value z of the sampling point is obtained based on the DEM data. j The elevation variance of the sampling points is calculated as an index of terrain flatness.

[0043] Construct a fast evaluation function f fast :f fast =ασ 2 ;

[0044] Where α is the topographic influence coefficient.

[0045] Furthermore, the weighted movement strategy is to not move the sub-region R′ with a low probability, to move the sub-region R′ randomly with a moderate probability, and to perform regular movement on the sub-region R′ with a high probability.

[0046] The beneficial effects of this invention are as follows: It proposes an improved adaptive variable neighborhood search algorithm, namely the IAVNS algorithm, which achieves global exploration, refined local search, and multi-objective dynamic balance optimization by adopting a two-layer collaborative optimization architecture, a dynamic hierarchical variable neighborhood search strategy, a fast evaluation method based on terrain elevation variance analysis, and an external sub-region optimization mechanism. This improves the accuracy of site selection, meets the fine optimization requirements under complex terrain, and provides a high-precision, fully automated solution for dam line site selection under complex terrain conditions. It has significant engineering application value and socio-economic benefits. Attached Figure Description

[0047] Figure 1 This is a flowchart of the reservoir basin dam line location method based on the improved adaptive variable neighborhood search algorithm provided by the present invention;

[0048] Figure 2 This is a schematic diagram of the Delaunay convex hull detection algorithm provided by the present invention;

[0049] Figure 3 This is a schematic diagram of the IAVNS algorithm provided by the present invention;

[0050] Figure 4 This is a schematic diagram of the up-shift operator and the down-shift operator provided by the present invention;

[0051] Figure 5 These are schematic diagrams of the left shift operator and the right shift operator provided by this invention;

[0052] Figure 6 This is a schematic diagram of the rotation operator provided by the present invention;

[0053] Figure 7 This is a schematic diagram of the initialization parameter input provided by the present invention;

[0054] Figure 8 This is the visualization effect provided by the present invention. Figure 1 ;

[0055] Figure 9 This is the visualization effect provided by the present invention. Figure 2 ;

[0056] Figure 10 This is a schematic diagram of a reservoir simulation as a multi-faceted truncated pyramid provided by the present invention;

[0057] Figure 11 This is a schematic diagram of the polygonal dam line provided by the present invention;

[0058] Figure 12 This is an example diagram of polygon encoding provided by the present invention. Detailed Implementation

[0059] The technical solution of the present invention is further described below, but the scope of protection is not limited to what is described.

[0060] This invention provides a reservoir basin dam alignment selection method based on an improved adaptive variable neighborhood search algorithm, implemented based on an established mathematical model for dam alignment selection optimization objectives, such as... Figure 1 As shown, it includes the following steps:

[0061] Step S100: Obtain the DEM data of the area to be selected, and divide the DEM data of the area into four identical sub-areas R1-R4;

[0062] Step S200: Obtain the initial parameters of the boundary of each sub-region, initialize the initial parameters of the boundary of each sub-region, generate an initial solution Sol0, and perform directional optimization; the initial parameters include reservoir capacity Λ, dam crest elevation h, dead water level H, normal water level ω, similarity ratio k, reservoir capacity error, number of polygon vertices, slope θ, and water depth; the initialization parameter input is as follows: Figure 7 As shown;

[0063] Existing intelligent optimization algorithms typically employ iterative improvement strategies, such as genetic algorithms, simulated annealing, and variable neighborhood search, which start from the current solution and gradually optimize it through neighborhood search or mutation operations.

[0064] Without an initial solution Sol0, the algorithm would need to randomly generate a large number of candidate solutions, leading to a waste of computational resources and potentially failing to find a feasible solution within a reasonable timeframe. The purpose of the initial solution Sol0 is to provide a reasonable starting point, enabling the algorithm to perform targeted optimization rather than a completely random search.

[0065] In intelligent algorithms, the initial solution Sol0 is typically constructed in two ways: random generation or heuristic generation. Variable neighborhood search algorithms have relatively low dependence on the initial solution Sol0; therefore, this invention will use random generation to construct the initial solution Sol0. During the random generation of the initial solution Sol0, a convex hull algorithm is used to ensure that the initial solution satisfies convex polygon constraints and library capacity constraints. The convex hull algorithm is the Delaunay convex hull detection algorithm, such as... Figure 2 As shown.

[0066] Step S300: Using the initial solution Sol0 as the starting point, the IAVNS algorithm is used to solve the optimization objective mathematical model to obtain the optimal solution Sol for each sub-region. best子 ;

[0067] In this embodiment, as Figure 3As shown, the IAVNS algorithm adopts a two-layer collaborative optimization architecture of internal search module and external adjustment module, which iterates until the termination condition of the IAVNS algorithm is reached. The termination condition of the IAVNS algorithm is that the number of iterations of the IAVNS algorithm reaches the preset maximum number of iterations MaxIter.

[0068] The internal search module includes the following:

[0069] Preset the neighborhood operator weights and iteration number thresholds, and select the neighborhood operator according to the neighborhood operator selection strategy;

[0070] Based on the selected neighborhood operator, a dynamic hierarchical variable neighborhood search strategy is used to perform a local search to obtain a new solution Sol1;

[0071] The quality of local search algorithms is a key factor determining the overall performance of an algorithm. For the same solution, different neighborhood operators may find solutions of varying quality. Similarly, for the same neighborhood operator, different neighborhood selection strategies may also lead to solutions of different quality. To improve the global search capability of the algorithm, this paper designs a series of neighborhood operators and employs an efficient neighborhood selection strategy, taking into account the characteristics of the dam site selection problem and the encoding method used. This invention designs eight neighborhood operators and combines them with a dynamic hierarchical adaptive search strategy for local search.

[0072] The neighborhood operator includes:

[0073] a. Two-dimensional upward shift operator K1 and two-dimensional downward shift operator K2: By increasing or decreasing the Y-coordinate of the current solution by a random step size, the vertical translation adjustment of the solution in the two-dimensional plane is achieved. The two-dimensional upward shift operator K1 and the two-dimensional downward shift operator K2 are as follows... Figure 4 As shown;

[0074] b. Two-dimensional left shift operator K3 and two-dimensional right shift operator K4: By increasing or decreasing the X-coordinate of the current solution by a random step, the solution can be translated and adjusted in the left and right directions in the two-dimensional plane. The two-dimensional left shift operator K3 and the two-dimensional right shift operator K4 are as follows... Figure 5 As shown;

[0075] c. Rotation operator K5; This operator applies a rotation matrix with a random angle to the X and Y coordinates of the current solution, thereby achieving a rotation transformation of the solution. Rotation operator K5, such as... Figure 6 As shown;

[0076] d. Three-dimensional upward shift operator G1: In the current solution, a displacement step size Δh is randomly generated, and the dam crest elevation and dead water level elevation are increased by Δh simultaneously to ensure that the reservoir capacity constraint is still satisfied after the solution is changed.

[0077] e. Three-dimensional downward displacement operator G2: In the current solution, a displacement step size Δh is randomly generated, and the dam crest elevation and dead water level elevation are reduced by Δh simultaneously to ensure that the reservoir capacity constraint is still satisfied after the solution is changed.

[0078] f. Geometric deformation operator V1. The reservoir's geometric shape is adjusted by perturbing the similarity parameter k of the lower base. While maintaining the geometric features of the upper base, the shape parameters of the lower base and the reservoir height are simultaneously optimized based on the volume constraint of the frustum, ensuring that the reservoir capacity requirements are strictly met. When perturbing the similarity k, to ensure that the reservoir capacity constraint is met, both the shape of the lower base of the frustum and the height of the reservoir need to be adjusted simultaneously. Its mathematical essence is to achieve geometric deformation while preserving volume by controlling the similarity transformation parameters. The calculation formula is V = 1 / 3S(1 + k + k) 2 ).

[0079] To fully exploit the algorithm's local optimization capabilities, this invention employs a best-improvement neighborhood search strategy. In each neighborhood search process, all neighborhood solutions of the current solution are traversed, and the optimal solution is selected as the optimal solution for this neighborhood search.

[0080] Extensive experiments have demonstrated that traditional variable neighborhood search strategies result in significant fluctuations and slow convergence during the algorithm's convergence process. To address the three-dimensional characteristics of the dam site selection optimization problem, this invention employs a dynamic hierarchical variable neighborhood search strategy. This method dynamically adjusts the combination of neighborhood operators through iteration cycles; that is, based on the role of each neighborhood operator, specific neighborhood operators are used for local searching at different iteration periods.

[0081] The dynamic hierarchical variable neighborhood search strategy is as follows:

[0082] In the early stages of iteration, when iter / Iter max ≤0.6, the algorithm focuses on planar position optimization, executes the operator set Φ1={K1,K2,K3,K4,K5,G1,G2,V1}, and introduces an adaptive probability selection mechanism;

[0083] In the middle of the iteration, when 0.6 < iter / Iter max ≤0.9, the algorithm integrates the co-optimization of planar position and height, constructs a hybrid operator space Φ2=Φ1∪{G1,G2}, and introduces an adaptive probability selection mechanism;

[0084] In the later stages of the iteration, when iter / Iter max If the value is greater than 0.9, execute the deformation operator V1 to change the height h and the shape of the bottom surface of the reservoir by fine-tuning the similarity ratio k, thereby optimizing the internal search process;

[0085] Where iter represents the current iteration number, Itermax This indicates the maximum number of iterations.

[0086] This invention employs an adaptive probability selection mechanism, the core of which lies in constructing a mapping relationship between operator performance evaluation indicators and selection probabilities. The adaptive probability selection mechanism specifically includes the following:

[0087] Record the historical improvement count S for each operator. i (t) and the number of calls N i (t), calculate the success probability of the i-th operator in the t-th iteration:

[0088]

[0089] The success rate is mapped to the selection probability using the softmax function:

[0090]

[0091] Meanwhile, throughout the local search process, the algorithm will follow the best-improvement search strategy, that is, in each neighborhood search process, it will traverse all neighborhood solutions of the current solution and select the best solution as the best solution of this neighborhood search.

[0092] By establishing an elevation variance index, a fast evaluation function f is constructed. fast To determine the relative sizes of f(Sol1) and f(Sol0), the specific steps are as follows:

[0093] When f(Sol1) < f(Sol0), update the optimal solution Sol. best子 =Sol1, let Sol0 = Sol1, t = 1, after updating the operator weights, proceed to the next iteration calculation;

[0094] When f(Sol1)≥f(Sol0), determine whether the new solution Sol1 satisfies the simulated annealing acceptance criterion;

[0095] If satisfied, update the optimal solution Sol. best子 =Sol1, let Sol0 = Sol1, t = 1, after updating the operator weights, proceed to the next iteration calculation;

[0096] If the condition is not met, the cumulative iteration count is t; then, it is determined whether the stopping criterion is met. If it is met, the iteration stops, and the fitness value of each sub-region is output to the external adjustment module. The fitness value is the optimal solution Sol in each sub-region. best子 The objective function value fit(R) i If the condition is not met, proceed to the next iteration calculation; the stopping criterion is to stop iteration when the cumulative iteration count t reaches the iteration count threshold.

[0097] Multiple experiments have shown that during algorithm execution, the objective function value fit(R) of the solution is calculated. i This process consumes significant time and computational resources. To address the issue of time-consuming objective function calculations, this invention proposes a rapid evaluation method based on terrain flatness analysis. This rapid evaluation method is grounded in hydraulic engineering experience—optimal dam sites are often located in areas with minimal terrain fluctuations. Therefore, it establishes an elevation variance index to achieve a rapid evaluation of the solution quality.

[0098] The fast evaluation function f fast The construction method is as follows:

[0099] Obtain the set of coordinates P of the vertices on the upper surface of the reservoir corresponding to the current solution. top ={p i (x i ,y i For each vertex coordinate set of the upper base, m sampling points are generated by random sampling within the set of vertex coordinates of the upper base.

[0100] The elevation value z of the sampling point is obtained based on the DEM data. j The elevation variance of the sampling points is calculated as an index of terrain flatness.

[0101]

[0102] Construct a fast evaluation function f fast :

[0103] f fast =ασ 2 (4);

[0104] Where α is the topographic influence coefficient.

[0105] To prevent the algorithm from getting trapped in a local optimum (Sol) too early during the local search process. best子 This invention adds a criterion for accepting simulated annealing during the local search phase. Specifically, the algorithm does not always accept the best solution during the search process; it also accepts the less optimal solution with a certain probability, thus avoiding the search from getting trapped in a local optimum. best子 The acceptance probability is dynamically adjusted based on the difference between the objective function values ​​of the current solution and the new solution, as well as the temperature parameter.

[0106] The formula for calculating the acceptance probability is as follows:

[0107]

[0108] Where: ΔE=E new -E curr It is the difference in objective function values ​​between the new solution and the current solution, E. new and E currThese are the objective function values ​​for the new solution and the current solution, respectively; T is the current temperature parameter, which gradually decreases as the iteration progresses.

[0109] P(ΔE) is the probability of accepting a worse solution. If ΔE≤0 (i.e., the new solution is better than the current solution), the probability of accepting the new solution is 1; if ΔE>0, the probability of accepting a worse solution is calculated using this formula.

[0110] In this embodiment, since the dam site selection problem typically involves a global optimization search over a large terrain area, to improve search efficiency, the present invention divides the entire topographic map into four sub-regions, and applies the improved Adaptive Variable Neighborhood Search (IAVNS) algorithm separately to find the local optimum Sol within each sub-region. best子 The solution is to find the global optimal solution Sol. best全 It may be located at the intersection of these four sub-regions, therefore it is necessary to dynamically adjust the extent of the sub-regions to ensure that the search covers the entire problem space. To this end, the present invention adds an outer heuristic guidance mechanism, namely the external adjustment module, which aims to optimize the sub-region division to achieve global optimum.

[0111] The external adjustment module includes the following:

[0112] Receive the fitness value fit(R) output by the internal search module i ), calculate the weight of each sub-region;

[0113] According to the fitness value fit(R) i A weighted movement strategy is used to select the fitness value fit(R). i The worst subregion R′ is moved along its boundary, and the search space of the algorithm is changed by adjusting its boundary.

[0114] While maintaining other subregions R i With the boundary unchanged, update the boundary of subregion R′, R i ≠R′, and serves as a prerequisite for the next iteration of the internal search module.

[0115] The weighted movement strategy is to not move the sub-region R′ with a low probability, to move the sub-region R′ randomly with a moderate probability, and to perform regular movement on the sub-region R′ with a high probability.

[0116] Step S400: Output the globally optimal solution Sol for the selected area as an SHP file. best全 And visualize it; the global optimal solution Sol best全 The final dam site selection scheme includes the optimal solution Sol for each sub-region. best子The optimal values ​​of the latitude and longitude coordinates of each vertex of the central dam line, as well as the dam crest elevation h, dead water level H, and similarity ratio k, are visualized as follows: Figure 8 , Figure 9 As shown.

[0117] In this embodiment, the principle and process of establishing the mathematical model for optimizing the dam line location are as follows:

[0118] In a two-dimensional grid space mapped from DEM raster data, there are n points. m ordered vertices are selected from these points to form a convex polygon dam line. The objective of reservoir site selection is to minimize the excavation volume, fill volume, the difference between excavation and fill volumes, and the reservoir surface area. Simultaneously, it must satisfy reservoir capacity constraints and convex polygon constraints.

[0119] Therefore, this invention models the dam line selection problem as a minimization problem, that is, finding a set of optimal dam line vertex coordinates under the conditions of satisfying reservoir capacity constraints and convex polygon constraints, such that the excavation volume... Fill volume Excavation volume and fill volume The difference and the minimum surface area of ​​the reservoir.

[0120] To address the issue of dam site selection optimization, the reservoir is simulated as a multi-faceted truncated pyramid, such as... Figure 10 As shown, the upper and lower bases of the reservoir are similar polygons, both of which are convex polygons. The slope of each side slope is the same and known.

[0121] Seven points are selected within a certain area as the vertices of the dam line, and the dam line polygon is as follows: Figure 11 As shown, an optimization objective mathematical model for dam line site selection is established;

[0122] The mathematical model for the optimization objective is:

[0123] Objective function:

[0124] Constraints:

[0125] S = S + +S - (7);

[0126]

[0127] S - =k 2 S + (9);

[0128]

[0129] Equation (6) is the objective function, which describes the optimization objective of the dam line location problem, namely, minimizing the excavation volume and surface area of ​​the reservoir.

[0130] Equation (7) is the formula for calculating the reservoir area S;

[0131] Equation (8) represents the upper bottom surface S of the reservoir. + The calculation method can be achieved through the vertex coordinates of the polygon;

[0132] Equation (9) gives the area S of the lower base based on the similarity ratio between the upper and lower bases. - The calculation formula;

[0133] Equation (10) is the calculation method for the reservoir volume V, ensuring that the reservoir capacity meets the design requirements;

[0134] Equation (11) specifies the constraints on the utilization rate of cut and fill to ensure the effective utilization of earth and rock.

[0135] Equation (12) restricts the coordinates between any two vertices of a polygon on the mesh from being repeated, in order to avoid redundant or unreasonable geometric configurations;

[0136] Equations (13) and (14) ensure that the out-degree and in-degree of each selected point are equal, and that the sum of the out-degree and in-degree of each point is 1, thus ensuring the connectivity and topological consistency of the dam line polygon.

[0137] Where w1 is the weighting coefficient for the reservoir excavation volume; w2 is the weighting coefficient for the reservoir surface area; μ is the cost per unit area; and r is the grid. Let X be the cut volume of grid r; i and j are any two non-repeating vertices of the polygon on the grid; V is the set of all points, i∈V, j∈V; X ij Let i be the line segment between points i and j. For line segment X ij The set of grids that pass through, R is the set of all grids, r∈R; The fill volume for grid r is given; h is the reservoir depth; S + S represents the surface area of ​​the reservoir. - Let x be the area of ​​the lower surface of the reservoir; U is the uncertain set of the reservoir depth; x i Let be the x-coordinate of point i; y-coordinate of point i. i Let x be the y-coordinate of point i; j Let j be the x-coordinate of point j; y j Let j be the y-coordinate of point j.

[0138] To enable computers and intelligent algorithms to better solve practical problems, it is necessary to encode the solution to the dam line location problem. Encoding is the process of digitizing the practical problem. In this invention, due to the order constraints between polygon nodes, the solution to the dam line location problem is described using sequential encoding. Specifically, each vertex of the dam line is represented by a pair of coordinates (x, y), and the entire dam line is composed of a series of vertices arranged in sequence. To encode this problem, an order vector [x1, x2, ..., x...] is defined. n ,y1,y2,…,y n ,z top ], where n represents the number of vertices of the dam line polygon, z top This represents the height of the polygon. In this encoding scheme, the first n elements of the vector represent the x-coordinate values ​​of the vertices, and the subsequent n elements represent the corresponding y-coordinate values. For example... Figure 12 As shown, an example of polygon encoding with 7 vertices is presented.

[0139] In this embodiment, the improved Adaptive Variable Neighborhood Search (IAVNS) algorithm demonstrates significant technical advantages and application value in the reservoir basin dam line site selection optimization problem. Traditional methods, such as GIS-based spatial analysis or priority flooding algorithms, are mainly limited to terrain preprocessing or single-objective optimization, making it difficult to simultaneously meet multiple requirements such as geometric accuracy, cut-fill balance, and engineering constraints. Furthermore, they are highly dependent on human experience, typically requiring several hours to several days, with an average Intersection over Union (IoU) of less than 40% and a Cut-fill Ratio (CFR) fluctuation greater than 2.0, resulting in low efficiency and unstable solution quality.

[0140] In contrast, the IAVNS algorithm proposed in this invention achieves dynamic balance optimization of multiple objectives, such as cut-fill volume and surface area, through a two-layer collaborative optimization architecture. This combines a directional migration strategy for global exploration with a hierarchical local search mechanism, including position translation, height adjustment, and geometric fine-tuning. Experimental results show that the IAVNS algorithm achieves an intersection-union ratio exceeding 70% in 80% of cases, compared to the previous best of 69.93%. The cut-fill ratio remains stable at 1.7, compared to the previous best of 1.27. The average error of key engineering parameters, such as dam crest elevation, dead water level, and reservoir capacity, is less than 0.15%, and the solution time for a single case is reduced to 500 seconds. These technical benefits reduce cut-fill volume by 15%-20%, significantly lowering engineering costs and decision-making cycles. Furthermore, it provides a high-precision, fully automated solution for dam site selection under complex terrain conditions, demonstrating significant engineering application value and socio-economic benefits.

[0141] The above-disclosed embodiments are merely specific examples of the present invention. However, the present invention is not limited thereto, and any variations that can be conceived by those skilled in the art should fall within the protection scope of the present invention.

Claims

1. A reservoir basin dam alignment selection method based on an improved adaptive variable neighborhood search algorithm, characterized in that, The optimization objective mathematical model based on the established dam line location is implemented, including the following steps: Obtain the DEM data of the area to be selected, and divide the DEM data into four identical sub-regions R1-R4; Obtain the initial parameters of the boundary of each sub-region, initialize the initial parameters of the boundary of each sub-region, generate the initial solution Sol0, and perform directional optimization; the initial parameters include reservoir capacity Λ, dam crest elevation h, dead water level H, normal water level ω, similarity ratio k, reservoir capacity error, number of polygon vertices, slope θ, and water depth; Starting with the initial solution Sol0, the IAVNS algorithm is used to solve the optimization objective mathematical model to obtain the optimal solution Sol for each sub-region. best子 ; Output the globally optimal solution Sol for the selected location region as an SHP file. best全 And visualize it; the global optimal solution Sol best全 The final dam site selection scheme includes the optimal solution Sol for each sub-region. best子 The optimal values ​​for the latitude and longitude coordinates of each vertex of the dam line, as well as the dam crest elevation h, dead water level H, and similarity ratio k.

2. The reservoir basin dam line location method based on the improved adaptive variable neighborhood search algorithm as described in claim 1, characterized in that, The mathematical model for the optimization objective is: Objective function: Constraint: S = S + +S - , S - =k 2 S + ; Where w1 is the weighting coefficient for the reservoir excavation volume; w2 is the weighting coefficient for the reservoir surface area; μ is the cost per unit area; and r is the grid. Let X be the cut volume of grid r; i and j are any two non-repeating vertices of the polygon on the grid; V is the set of all points, i∈V, j∈V; X ij Let i be the line segment between points i and j. Let X be the line segment ij The set of grids that pass through, R is the set of all grids, r∈R; The fill volume for grid r is given; h is the reservoir depth; S + S represents the surface area of ​​the reservoir. - Let x be the area of ​​the lower surface of the reservoir; U is the uncertain set of the reservoir depth; x i Let be the x-coordinate of point i; y i Let x be the y-coordinate of point i; j Let j be the x-coordinate of point j; y j Let j be the y-coordinate of point j.

3. The reservoir basin dam line location method based on the improved adaptive variable neighborhood search algorithm as described in claim 2, characterized in that, The IAVNS algorithm adopts a two-layer collaborative optimization architecture of internal search module and external adjustment module, which iterates until the termination condition of the IAVNS algorithm is reached. The termination condition of the IAVNS algorithm is that the number of iterations of the IAVNS algorithm reaches the preset maximum number of iterations MaxIter.

4. The reservoir basin dam line location method based on the improved adaptive variable neighborhood search algorithm as described in claim 3, characterized in that, The internal search module includes the following: Preset the neighborhood operator weights and iteration number thresholds, and select the neighborhood operator according to the neighborhood operator selection strategy; Based on the selected neighborhood operator, a dynamic hierarchical variable neighborhood search strategy is used to perform a local search to obtain a new solution Sol1; By establishing an elevation variance index, a fast evaluation function f is constructed. fast To determine the relative sizes of f(Sol1) and f(Sol0), the specific steps are as follows: When f(Sol1) < f(Sol0), update the optimal solution Sol. best子 =Sol1, let Sol0 = Sol1, t = 1; after updating the operator weights, proceed to the next iteration calculation; When f(Sol1)≥f(Sol0), determine whether the new solution Sol1 satisfies the simulated annealing acceptance criterion; If satisfied, update the optimal solution Sol. best子 =Sol1, let Sol0 = Sol1, t = 1; After updating the operator weights, proceed to the next iteration calculation; If the condition is not met, the cumulative iteration count is t; then, it is determined whether the stopping criterion is met. If it is met, the iteration stops, and the fitness value of each sub-region is output to the external adjustment module. The fitness value is the optimal solution Sol in each sub-region. best子 The objective function value fit(R) i If the condition is not met, proceed to the next iteration calculation; the stopping criterion is to stop iteration when the cumulative iteration count t reaches the iteration count threshold.

5. The reservoir basin dam line location method based on the improved adaptive variable neighborhood search algorithm as described in claim 4, characterized in that, The external adjustment module includes the following: Receive the fitness value fit(R) output by the internal search module i ), calculate the weight of each sub-region; According to the fitness value fit(R) i A weighted movement strategy is used to select the fitness value fit(R). i The worst subregion R′ is moved along its boundary, and the search space of the algorithm is changed by adjusting its boundary. While maintaining other subregions R i With the boundary unchanged, update the boundary of subregion R′, R i ≠R′, and serves as a prerequisite for the next iteration of the internal search module.

6. The reservoir basin dam line location method based on the improved adaptive variable neighborhood search algorithm as described in claim 5, characterized in that, The neighborhood operators include a two-dimensional up shift operator K1, a two-dimensional down shift operator K2, a two-dimensional left shift operator K3, a two-dimensional right shift operator K4, a rotation operator K5, a three-dimensional up shift operator G1, a three-dimensional down shift operator G2, and a geometric deformation operator V1.

7. The reservoir basin dam line location method based on the improved adaptive variable neighborhood search algorithm as described in claim 4, characterized in that, The dynamic hierarchical variable neighborhood search strategy is as follows: In the early stages of iteration, when iter / Iter max ≤0.6, the algorithm focuses on planar position optimization, executes the operator set Φ1={K1,K2,K3,K4,K5,G1,G2,V1}, and introduces an adaptive probability selection mechanism; In the middle of the iteration, when 0.6 < iter / Iter max ≤0.9, the algorithm integrates the co-optimization of planar position and height, constructs a hybrid operator space Φ2=Φ1∪{G1,G2}, and introduces an adaptive probability selection mechanism; In the later stages of the iteration, when iter / Iter max If the value is greater than 0.9, execute the deformation operator V1 to change the height h and the shape of the bottom surface of the reservoir by fine-tuning the similarity ratio k, thereby optimizing the internal search process; Where iter represents the current iteration number, Iter max This indicates the maximum number of iterations.

8. The reservoir basin dam line location method based on the improved adaptive variable neighborhood search algorithm as described in claim 7, characterized in that, The adaptive probability selection mechanism specifically includes the following: Record the historical improvement count S for each operator. i (t) and the number of calls N i (t), calculate the success probability of the i-th operator in the t-th iteration: The success rate is mapped to the selection probability using the softmax function:

9. The reservoir basin dam line location method based on the improved adaptive variable neighborhood search algorithm as described in claim 4, characterized in that, The fast evaluation function f fast The construction method is as follows: Obtain the set of coordinates P of the vertices on the upper surface of the reservoir corresponding to the current solution. top ={p i (x i ,y i For each vertex coordinate set of the upper base, m sampling points are generated by random sampling within the set of vertex coordinates of the upper base. The elevation value z of the sampling point is obtained based on the DEM data. j The elevation variance of the sampling points is calculated as an index of terrain flatness. Construct a fast evaluation function f fast :f fast =ασ 2 ; Where α is the topographic influence coefficient.

10. The reservoir basin dam line location method based on the improved adaptive variable neighborhood search algorithm as described in claim 5, characterized in that, The weighted movement strategy is to not move the sub-region R′ with a low probability, to move the sub-region R′ randomly with a moderate probability, and to perform regular movement on the sub-region R′ with a high probability.

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