High-dimension aggregation algorithm for solving multi-target site selection problem

Abstract

The invention discloses a high-dimensional aggregation algorithm for solving a multi-target site selection problem, and provides a new algorithm for solving the problems that a traditional site selection algorithm is poor in universality and complex in target function processing during new energy facility site selection. According to the algorithm, a place in a region is taken as a decision variable, a sub-objective function is calculated and projected as a high-dimensional space demand point, and a place difference is reflected by an Euclidean distance. The method comprises the following steps: firstly, using an improved 2-DFPSA to find a high-dimensional Pareto median point, then using n-DFPSA to find a high-dimensional Pareto median point, empowering a facility according to a distance, finally projecting the facility to a two-dimensional plane, and using the improved 2-DFPSA to find a plane weighted Steiner point to determine site selection. In industrial and commercial energy storage station site selection cases, compared with an NSGA2 algorithm, the n-DFPSA algorithm is better in Euclidean distance, average profile factor and other indexes, the calculation efficiency is improved by nearly 46%, and the stability is better. The algorithm can effectively solve the new energy facility site selection problem, is suitable for scenes with high requirements for site selection precision, efficiency and stability, and provides an effective way for new energy facility layout and multi-target site selection.

Description

Technical Field

[0001] The present invention relates to a high-dimensional aggregation algorithm for solving multi-objective site selection problems. Background Art

[0002] With the growing global demand for clean energy, the rational layout of new energy facilities has become a key research direction. However, traditional site selection algorithms perform poorly when faced with complex multi-objective optimization problems, especially when considering multiple important factors such as construction cost, transmission efficiency, and power demand. Existing advanced aggregation operators, such as the Interval Neutral Weighted Average (INNWA) and Interval Neutral Weighted Geometric (INNWG), can effectively handle data ambiguity. However, their aggregation accuracy decreases significantly when encountering special values ​​(such as "0" or "1"), affecting the final site selection results.

[0003] To overcome these challenges, researchers have proposed a variety of improvement strategies, including but not limited to using different distance metrics (such as Manhattan distance, Euclidean distance, and Chebyshev distance) to evaluate the differences between different options. Although some progress has been made, existing solutions still have limitations in practical applications, especially in processing high-dimensional data and improving computational efficiency. Summary of the Invention

[0004] This paper provides a high-dimensional clustering algorithm for solving multi-objective site selection problems. This algorithm processes fuzzy information onto a two-dimensional plane and combines it with a plant growth simulation algorithm to find the optimal clustering point. This method enables precise site selection for new energy facility nodes (such as charging stations and backup stations). This method is particularly suitable for solving multi-attribute group decision-making problems in complex environments, such as emergency response and enterprise solution decision-making.

[0005] The technical solutions adopted in the present invention are:

[0006] A high-dimensional aggregation algorithm for solving a multi-objective site selection problem includes the following steps:

[0007] S1) Constructing a high-dimensional demand point space:

[0008] Each candidate facility location and its corresponding n objective function values ​​in the multi-objective location selection problem are constructed as an objective function vector, with each dimension corresponding to a sub-objective function. The objective function vector is then mapped to a point in a high-dimensional space. The difference between the objective function vectors is quantified using Euclidean distance to construct a high-dimensional demand point space.

[0009] S2) Solve the high-dimensional Pareto median point:

[0010] Based on the L-system growth rule, the step size and rotation angle are dynamically adjusted in the high-dimensional demand point space, and the probability density function is used to guide the screening of candidate points to find the high-dimensional Pareto median point. The high-dimensional Pareto median point is initialized, and candidate directions are generated through the L-system. The sum of the differences between the candidate point and all demand points in the high-dimensional demand point space is evaluated. If the high-dimensional Pareto median point is not updated after several consecutive iterations, the current high-dimensional Pareto median point is output as the final result.

[0011] S3) Planar weighted Steiner point positioning:

[0012] Projecting the high-dimensional Pareto median point into a two-dimensional geographic space, mapping the latitude and longitude and weight of the candidate location onto a two-dimensional plane to form a demand point, and constructing a weight-coordinate mapping relationship based on the weight information in the high-dimensional demand point space;

[0013] The weight information is normalized, and the plane weighted Steiner point is solved by an improved 2-DFPSA algorithm to ultimately determine the optimal site location.

[0014] Furthermore, in S1), the objective function vector is expressed as:

[0015] F(x k )=[f1(x k ),f2(x k ),f3(x k )];

[0016] Among them, f i (x k ) represents the objective function value corresponding to the kth candidate facility location, i = 1, 2, …, n, where n is an integer greater than or equal to 2;

[0017] The difference between the objective function vectors is quantified by the Euclidean distance, and its formula is:

[0018]

[0019] Among them, x l is another candidate facility location, Q(x k ,x l ) represents the Euclidean distance between the kth candidate facility location and the lth candidate facility location in the objective function space.

[0020] Furthermore, in S2), the high-dimensional Pareto median point is found based on the L-system growth rule, specifically:

[0021] (21) Initialize the Pareto median point xα0 and randomly generate an initial point as xα0;

[0022] (22) Set the growth step λ and rotation angle θ, λ = l / 2000, where l is the average axis length of the demand point space;

[0023] (23) Taking xα0 as the starting point, rotate by an angle θ in an alternating clockwise and counterclockwise manner to generate a new candidate point;

[0024] (24) For each candidate point, calculate the sum of its differences with all demand points in the demand point space Q min , and select the new median point according to the probability formula;

[0025] (25) Select the candidate point with the smallest sum of differences as the new Pareto median point;

[0026] (26) Repeat the process (21)-(25) until the Pareto median point is no longer updated in several consecutive iterations. The Pareto median point x is obtained at this time. * This is the optimal solution.

[0027] Furthermore, the sum of the differences Q min The calculation formula is:

[0028]

[0029] Where: x α0 Indicates the current median point;

[0030]

[0031] Where: m is the number of feasible solutions, n is the total number of objective functions;

[0032] f j (x α0 ) is the jth objective function in the feasible solution x α0 The value at

[0033] f j (x i ) The jth objective function is in the feasible solution x i The value at .

[0034] Furthermore, the probability formula is:

[0035]

[0036] Among them, Qx α Represents the sum of the differences between the candidate point and all demand points; select the candidate point with the largest probability as the new Pareto median point x * .

[0037] Furthermore, in S3), the normalization processing formula of the weight information is:

[0038]

[0039] in: is the weight coefficient of the kth candidate facility location;

[0040] Q(x k ,x*) is the kth candidate facility location x k and the high-dimensional Pareto median point x * the differences between;

[0041] Q(x j ,x*) represents the jth candidate facility location x j and the high-dimensional Pareto median point x * the differences between;

[0042] N represents the total number of candidate facility locations.

[0043] Furthermore, in S3), a weight-coordinate mapping relationship is constructed, specifically:

[0044] The location of each candidate facility includes the latitude N k With longitude E k The geographical coordinates and the corresponding weight coefficient ω k Combined, a triple (Nk, Ek, ωk) is formed.

[0045] Furthermore, in S3), the improved 2-DFPSA algorithm solves the plane weighted Steiner point, specifically:

[0046] In two-dimensional geographic space, the improved 2-DFPSA algorithm is used to find the Steiner point that minimizes the sum of weighted distances. The calculation formula is:

[0047]

[0048] Among them: Qxα0 represents the sum of weighted distances;

[0049] M is the total number of candidate facility locations;

[0050] ωi is the weight coefficient of the i-th candidate facility location;

[0051] Nxα0 and Exα0 are the latitude and longitude of the current high-dimensional Pareto median point xα0;

[0052] Nxi and Exi: represent the latitude and longitude of the location of the i-th candidate facility;

[0053] The improved 2-DFPSA algorithm gradually optimizes the search path through a multi-resolution search strategy and ultimately determines the optimal address location.

[0054] The present invention has the following beneficial effects:

[0055] (1) The sum of the weighted Hamming distances between the optimal preference aggregation matrix constructed by the present invention and the decision maker’s preference matrix is ​​smaller, and the sum of the correlations is larger. Therefore, the optimal preference aggregation matrix constructed by the IVNPPA algorithm is more accurate in describing the decision maker’s comprehensive preference information.

[0056] (2) The present invention is insensitive to the special value of the interval neutrinometry. When solving the multi-objective site selection problem of actual new energy facilities, the aggregation accuracy is prioritized, thereby improving the accuracy of site selection decisions.

[0057] (3) The present invention not only solves the problems of insufficient versatility and accuracy in existing technologies, but also achieves precise site selection optimization through efficient allocation and optimization strategies, providing a practical and effective solution for the rational layout of new energy facilities. In addition, the present invention has broad application prospects and can be applied to the site selection planning of various new energy facilities.

[0058] Through the above technical solutions, the present invention demonstrates significant advantages in the field of new energy facility site selection, and provides a highly versatile and efficient optimization path for future multi-objective site selection problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a schematic diagram of the spatial construction of demand points.

[0060] Figure 2 This is a schematic diagram of random point selection.

[0061] Figure 3 This is a schematic diagram of finding the weighted Steiner point in a plane.

[0062] Figure 4 This is a schematic diagram of finding the optimal high-dimensional Pareto median point.

[0063] Figure 5 This is a schematic diagram of finding the weighted Steiner point in a plane. DETAILED DESCRIPTION

[0064] The present invention will be further described below with reference to the accompanying drawings.

[0065] The present invention proposes a high-dimensional aggregation algorithm to analyze the objective function in multi-objective site selection and use it to solve the new energy facility site selection problem, which specifically includes the following steps:

[0066] Step 1: Construct a high-dimensional demand point space

[0067] All candidate facilities in the region are defined as decision variables, and the sub-objective function values ​​corresponding to each facility (such as power generation efficiency, transmission cost, power demand, etc.) are calculated.

[0068] The decision variables and objective function values ​​of each facility are projected into high-dimensional demand points in n-dimensional space (each dimension corresponds to a sub-objective function).

[0069] The comprehensive differences of different facilities in a multi-objective optimization environment are quantified by the Euclidean distance between high-dimensional demand points, and a high-dimensional demand point space is constructed. Figure 1 shown.

[0070] Step 2: Solve the high-dimensional Pareto median point

[0071] Randomly generate an initial median point and calculate the sum of its Euclidean distances to all high-dimensional demand points;

[0072] Generate multi-directional search paths based on the L-system, and dynamically adjust the step size (λ = l / 2000) and rotation angle (θ = 22.5°);

[0073] The probability model is used to screen candidate points and the spherical region division mechanism is used to avoid local optimality, such as Figure 2 shown.

[0074] Iterate the optimization until convergence (100 iterations without updating) to obtain the Pareto median point that minimizes the total distance.

[0075] Step 3: Spatial weighting of facility points

[0076] Generate weight coefficients through normalization Weight formula:

[0077]

[0078] Output a weighted facility geographic coordinate set (a triplet of latitude N, longitude E, and weight ω).

[0079] Step 4: Solve the plane weighted Steiner point

[0080] Project the weighted facility coordinates into two-dimensional geographic space;

[0081] Improve the 2-DFPSA algorithm and introduce a weight factor in the distance calculation:

[0082]

[0083] The Steiner point that minimizes the sum of weighted distances is determined by a multi-resolution search strategy. This point is the optimal location. The weighted Steiner point search process is as follows: Figure 3 shown.

[0084] Step 5: Algorithm Performance Verification

[0085] Establishing an evaluation system:

[0086] 1. Euclidean distance (difference quantification);

[0087] 2. Mean profile factor MPF (layout balance);

[0088] 3. Computational efficiency (CE) (35s vs 65s for NSGA2);

[0089] 4. Stability σ (0.0266 vs 0.0395).

[0090] Furthermore, step one is as follows:

[0091] Define the decision variables and set the candidate facility location set in the region as x=(x1,x2,...,x 50 ), each candidate facility location x k , containing geographic coordinates (latitude N k , precision E k ).

[0092] Construct the objective function vector, for each candidate facility location x k , calculate three sub-objective functions: where f1(x k ) is the power generation efficiency function, f2(x k ) is the transmission line construction cost function, f3(x k ) is the electricity demand function.

[0093] The objective function vector is:

[0094] F(x k )=[f1(x k ),f2(x k ),f3(x k )]

[0095] Map the objective function value to a three-dimensional space point and calculate the Euclidean distance.

[0096] The objective function vector F(x k ), projected into three-dimensional space, forming a three-dimensional point x k =(f1(x k ),f2(x k ),f3(x k )), calculate two candidate positions x k and x l Difference in objective function space:

[0097]

[0098] Furthermore, step 2 is as follows:

[0099] Initialize the parameters, set the step size λ = l / 2000, (l is the average axis length of the three-dimensional space), the rotation angle θ = 22.5°, the initial median point Randomly generated.

[0100] Generate alternative sites Calculating the total difference is to calculate the sum of the Euclidean distances from all high-dimensional demand points:

[0101]

[0102] Filter new median points based on the probability formula:

[0103]

[0104] When Q min , no longer updated, output the final Pareto median point x * .

[0105] Furthermore, step three is as follows:

[0106] The weight of each candidate position for:

[0107]

[0108] Combine the weight with the geographic coordinates to form a weighted point x k =(N k ,E k ,ω k )

[0109] Furthermore, step four is as follows:

[0110] The longitude and latitude of the candidate location (N k ,E k ) and weight ω k Mapped to a two-dimensional plane, forming demand points:

[0111] p k =(N k ,E k ,ω k ).

[0112] Find the midpoint p of the plane * =(N * ,E * ), so that the total weighted distance is minimized:

[0113]

[0114] Furthermore, step five is as follows:

[0115] 1. Euclidean distance (difference measure):

[0116]

[0117] 2. Mean Profile Factor (MPF):

[0118]

[0119] 3. Computational efficiency: Comparison between the time required for the present invention to select the optimal address and the time required by NSGA-II

[0120] 4. Stability (σ):

[0121]

[0122] Among them, x k represents the kth candidate point, x * represents the optimal candidate point, f j (x k ) The jth objective function is in the feasible solution x k The value at f j (x * ) indicates that at the optimal candidate point x * The value of D j (x k ,x * ) represents x k with x * The Euclidean distance between k represents the weight of the candidate point, σ F Indicates stability.

[0123] Application of this invention to the site selection of new energy facilities:

[0124] District B, located in City A, a national key pilot zone for new energy industries, was selected as the research target for a new energy facility site selection case study. The goal was to plan an industrial and commercial energy storage station to store electricity generated by the district's photovoltaic power generation equipment. The PV equipment within the district is primarily located in residential communities, commercial centers, public spaces, and new energy parks. These locations were analyzed as part of the feasible solution vector to assess the optimality of their site selection.

[0125] Suppose these places constitute a feasible solution vector x=(x1,x2,...,x 50 ), the objective function value vector is:

[0126] F(x k )=[f1(x k ),f2(x k),f3(x k )],

[0127] where f1(x k ) is the power generation efficiency function, f2(x k ) is the transmission line construction cost function, f3(x k ) is the electricity demand function, as shown in Table 1. The site selection of industrial and commercial energy storage stations should meet the requirements of being as close as possible to places with high power generation efficiency, while reducing the cost of transmission line construction and ensuring that they are close to places with high power demand.

[0128] Table 1. Objective function vector values

[0129]

[0130]

[0131] The coordinates of the high-dimensional Pareto median point of the optimal position calculated through steps one and two are [0.53614, 0.46649, 0.50906]. The process of finding the high-dimensional Pareto median point of the optimal position is as follows: Figure 4 shown.

[0132] Through steps three and four, the final feasible solution vector is calculated, as shown in Table 2:

[0133] Table 2. Weighted feasible solution vectors

[0134]

[0135]

[0136] Finally, the coordinates of the optimal location are obtained by the plane weighted Steiner point method, which is [31.55927, 119.6756]. The plane weighted Steiner point search process is as follows Figure 5 shown.

[0137] Through step five, various indicators are calculated and compared. The specific indicators are shown in Table 3.

[0138] Table 3 Comparison indicators

[0139]

[0140] This method demonstrates significant advantages in comparisons of new energy facility site selection. It outperforms NSGA2 in both Euclidean distance and average profile factor, demonstrating that it can more effectively meet spatial layout requirements and avoid local optima. Furthermore, its computational efficiency is nearly 46% higher, and its stability is improved, resulting in less fluctuation in results and higher reliability. Therefore, this method is particularly suitable for applications requiring high site selection accuracy, efficiency, and stability.

[0141] The above description is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements can be made without departing from the principles of the present invention. These improvements should also be regarded as the scope of protection of the present invention.

Claims

1. A high-dimensional aggregation algorithm for solving multi-objective site selection problems, characterized by: The following steps are involved: S1) Constructing a high-dimensional demand point space: Each candidate facility location and its corresponding n objective function values ​​in the multi-objective location selection problem are constructed as an objective function vector, and the objective function vector is mapped to a point in a high-dimensional space. The difference between the objective function vectors is quantified by Euclidean distance to construct a high-dimensional demand point space; S2) Solve the high-dimensional Pareto median point: Based on the L-system growth rule, the step size and rotation angle are dynamically adjusted in the high-dimensional demand point space, and the probability density function is combined to guide the candidate point screening to find the high-dimensional Pareto median point; Initialize the high-dimensional Pareto median point, generate candidate directions through the L-system, evaluate the sum of the differences between the candidate point and all demand points in the high-dimensional demand point space, and if the high-dimensional Pareto median point is not updated after several consecutive iterations, output the current high-dimensional Pareto median point as the final result; S3) Planar weighted Steiner point positioning: Projecting the high-dimensional Pareto median point into a two-dimensional geographic space, mapping the latitude and longitude and weight of the candidate location onto a two-dimensional plane to form a demand point, and constructing a weight-coordinate mapping relationship based on the weight information in the high-dimensional demand point space; The weight information is normalized, and the plane weighted Steiner point is solved by an improved 2-DFPSA algorithm to ultimately determine the optimal site location.

2. The high-dimensional aggregation algorithm for solving the multi-objective site selection problem according to claim 1, characterized in that: In S1), the objective function vector is expressed as: F(x k )=[f1(x k ),f2(x k ),f3(x k )]; Among them, x k represents the kth candidate facility location, f i (x k ) represents the objective function value corresponding to the kth candidate facility location, i = 1, 2, …, n, where n is an integer greater than or equal to 2; The difference between the target function vectors is quantified by the Euclidean distance, and its formula is: Among them, x l is another candidate facility location, Q(x k ,x l ) represents the Euclidean distance between the kth candidate facility location and the lth candidate facility location in the objective function space.

3. The high-dimensional aggregation algorithm for solving the multi-objective site selection problem according to claim 1, characterized in that: In S2), the high-dimensional Pareto median point is found based on the L-system growth rule, specifically: (21) Initialize the Pareto median point xα0 and randomly generate an initial point as xα0; (22) Set the growth step λ and rotation angle θ, λ = l / 2000, where l is the average axis length of the demand point space; (23) Taking xα0 as the starting point, rotate by an angle θ in an alternating clockwise and counterclockwise manner to generate a new candidate point; (24) For each candidate point, calculate the sum of its differences with all demand points in the demand point space Q min , and select the new median point according to the probability formula; (25) Select the candidate point with the smallest sum of differences as the new Pareto median point; (26) Repeat the process (21)-(25) until the Pareto median point is no longer updated in several consecutive iterations. The Pareto median point x is obtained at this time. * This is the optimal solution.

4. The high-dimensional aggregation algorithm for solving the multi-objective site selection problem according to claim 3, characterized in that: The sum of the differences Q min The calculation formula is: Where: x α0 Indicates the current median point; Where: m is the number of feasible solutions, n is the total number of objective functions; f j (x α0 ) is the jth objective function in the feasible solution x α0 The value at f j (x i ) The jth objective function is in the feasible solution x i The value at .

5. The high-dimensional aggregation algorithm for solving the multi-objective site selection problem according to claim 3, characterized in that: The probability formula is: Among them, Qx α Represents the sum of the differences between the candidate point and all demand points; select the candidate point with the largest probability as the new Pareto median point x * .

6. The high-dimensional aggregation algorithm for solving the multi-objective site selection problem according to claim 1, characterized in that: In S3), the normalization processing formula of the weight information is: in: is the weight coefficient of the kth candidate facility location; Q(x k ,x*) is the kth candidate facility location x k and the high-dimensional Pareto median point x * the differences between; Q(x j ,x*) represents the jth candidate facility location x j and the high-dimensional Pareto median point x * the differences between; N represents the total number of candidate facility locations.

7. The high-dimensional aggregation algorithm for solving the multi-objective site selection problem according to claim 1, characterized in that: In S3), a weight-coordinate mapping relationship is constructed, specifically: The location of each candidate facility includes the latitude N k With longitude E k The geographical coordinates and the corresponding weight coefficient ω k Combined, a triple (Nk, Ek, ωk) is formed.

8. The high-dimensional aggregation algorithm for solving the multi-objective site selection problem according to claim 1, characterized in that: In S3), in the two-dimensional geographic space, the improved 2-DFPSA algorithm is used to find the Steiner point that minimizes the sum of weighted distances. The calculation formula is: Among them: Qxα0 represents the sum of weighted distances; M is the total number of candidate facility locations; ωi is the weight coefficient of the i-th candidate facility location; Nxα0 and Exα0 are the latitude and longitude of the current high-dimensional Pareto median point xα0; Nxi and Exi: represent the latitude and longitude of the location of the i-th candidate facility; The improved 2-DFPSA algorithm gradually optimizes the search path through a multi-resolution search strategy and ultimately determines the optimal address location.

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