Buckle anchor cable force optimization method based on improved second-generation genetic algorithm

Abstract

The invention relates to the technical field of evolutionary algorithms, in particular to a buckle anchor cable force optimization method based on an improved second-generation genetic algorithm, and the method comprises the following steps: obtaining cable force scheme data, calculating eccentric distance quadratic sum and stress over-limit cubic sum, comparing a dominating relationship and grading, distributing grades for a merged population, and filling a new population. If yes, kernel density estimation screening is called, and finally, new population Gray code coding, crossing and self-adaptive variation are carried out to generate filial generations. According to the method, the operation period eccentric distance quadratic sum and the construction period stress over-limit cubic sum are calculated, a cable force optimized multi-objective function is constructed, the construction safety and the operation performance are balanced, then individuals are screened through a non-dominated sorting mechanism, the population crowding degree is evaluated through a kernel density estimation function, and a diversified solution set is reserved; the algorithm is prevented from falling into local optimum, and finally, the robustness and convergence efficiency of search are enhanced by combining Gray code coding and the adaptive variation rate changing along with iterative generations, and a more balanced anchor cable pre-stress configuration scheme is found.

Description

Technical Field

[0001] This invention relates to the field of evolutionary algorithm technology, and in particular to a method for optimizing anchor cable force based on an improved second-generation genetic algorithm. Background Technology

[0002] The field of evolutionary algorithms encompasses a class of computational methods inspired by natural selection and biological evolution. Core aspects of this field include specific implementations of genetic algorithms, genetic programming, and evolutionary strategies, all of which iteratively search for solutions by simulating selection, crossover, and mutation processes during biological evolution. This technical field is primarily used to handle complex optimization problems, especially finding feasible or optimal solutions in high-dimensional, nonlinear, or multi-peak search spaces. Traditional anchor cable force optimization methods address the problem of determining the magnitude of anchor cable prestress in anchoring projects. In traditional practice, cable force optimization typically relies on established analytical mechanical models or simplified computational models, combined with empirical engineering formulas for estimation. Some methods also employ numerical simulation techniques, such as finite element analysis, to simulate the interaction between the anchor cable and the structure, or use linear programming algorithms to solve for the cable force distribution under given constraints.

[0003] Existing methods for optimizing anchor cable force, especially those relying on simplified mechanical models or linear programming, struggle to effectively handle the nonlinear trade-offs between multiple performance indicators during construction and operation. Their optimization objectives are often oversimplified, making it difficult to balance construction stress control with long-term structural eccentricity. Furthermore, traditional estimation methods or basic numerical simulations are susceptible to getting stuck in local optima when faced with high-dimensional and complex search spaces due to parameter settings. They fail to provide a sufficiently diverse set of high-performance cable force solutions, leading to a final selection that relies too heavily on engineering experience and lacks a global perspective. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by proposing an anchor cable force optimization method based on an improved second-generation genetic algorithm.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: a method for optimizing anchor cable force based on an improved second-generation genetic algorithm, comprising the following steps: S1: Obtain the maximum tensile stress during construction, bending moment during operation, axial force during operation, and the baseline value of the maximum tensile stress allowable upper limit during construction for each individual cable force scheme; calculate the section eccentricity; obtain the sum of squares of eccentricity during operation; calculate the portion exceeding the baseline value of the maximum tensile stress allowable upper limit during construction; obtain the sum of cubic over-limit stress during construction. S2: Based on the sum of squares of eccentricity during the operation period and the sum of cubics of stress exceeding the limit during the construction period, compare the pairwise dominance relationships of the individual cable force schemes, select the set of individuals that are not dominated as the first level, and repeat the selection until a level value is assigned. S3: Assign the level value to the merged population composed of parent and offspring Soli scheme individuals, and fill the new population. When the number of Soli scheme individuals at a certain level exceeds the remaining empty slots, call the kernel density estimation function to obtain the kernel density estimate, and select the one with the lowest kernel density estimate to fill the remaining empty slots. S4: Perform Gray code encoding on the individuals of the Soli scheme in the new population, perform crossover operation to generate offspring numerical sequences, obtain the iteration number, calculate the adaptive mutation rate, and perturb the offspring numerical sequences to generate offspring Soli scheme individuals.

[0006] As a further aspect of the present invention, the sum of squared eccentricities during the operation period specifically refers to the objective function value characterizing the long-term structural eccentricity during the operation period; the sum of cubic stress exceeding the limit during the construction period specifically refers to the penalty function value characterizing the instantaneous stress safety during the construction period; the level value specifically refers to the Pareto front level identifier of the individual cable force scheme; the kernel density estimate specifically refers to the scalar value characterizing the sparsity of the distribution of the individual cable force scheme in the normalized objective space; the offspring numerical sequence specifically refers to the cable force parameter sequence after Gray code encoding and crossover operation combination; the adaptive mutation rate specifically refers to the mutation probability value that decreases with the increase of the iteration generation; and the offspring cable force scheme individual includes a set of initial tension force values ​​of the anchor cable generated after decoding through mutation perturbation.

[0007] As a further aspect of the present invention, the step of obtaining S1 specifically comprises: S101: Obtain the baseline values ​​of the maximum tensile stress during construction, bending moment during operation, axial force during operation, and the allowable upper limit of the maximum tensile stress during construction for each individual cable force scheme. Aggregate the four types of numerical data to establish an initial cable force state matrix. S102: Based on the initial cable force state matrix, call the operating period bending moment value and the operating period axial force value, and for each corresponding section in the individual cable force scheme, perform numerical calculation by dividing the operating period bending moment value by the operating period axial force value to obtain the section eccentricity and generate the section eccentricity vector. S103: For the multiple element values ​​in the cross-sectional eccentricity vector, perform squaring operation one by one to obtain the squared values ​​of the eccentricity of multiple cross-sections, aggregate all the squared values ​​of the eccentricity of the cross-sections, and perform summation calculation on the aggregated result to obtain the sum of squared eccentricities during the operation period; S104: Call the maximum tensile stress value during construction period and the baseline value of the allowable upper limit of the maximum tensile stress during construction period in the initial cable force state matrix, iterate through all the maximum tensile stress values ​​during construction period, perform subtraction operation, determine and extract the stress exceeding the baseline value that exceeds the allowable upper limit of the maximum tensile stress during construction period, perform cube operation on all the stress exceeding the limit values, aggregate all cube operation results and sum them to generate the cube sum of stress exceeding the limit during construction period.

[0008] As a further aspect of the present invention, the step of obtaining the level value specifically includes: S201: Obtain the set of all cable force scheme individuals, and retrieve the sum of squares of the eccentricity during the operation period and the sum of cubics of the stress exceeding the limit during the construction period for each cable force scheme individual, construct the target value matrix of the cable force scheme individuals, traverse the matrix to perform pairwise comparisons between any two cable force scheme individuals, determine the dominance and subordination status between individuals, and generate a set of individual dominance relationship identifiers; S202: Based on the individual dominance relationship identifier set, initialize the level counter to one, retrieve all individuals of the cable force scheme, filter individuals in the individual dominance relationship identifier set that are not dominated by any other individuals of the cable force scheme, establish a first-level set of undominated individuals, assign the level counter value to all individuals of the cable force scheme in the set, and obtain the first-level cable force scheme set. S203: For the remaining cable force scheme individuals outside the first level cable force scheme set, form a set of undetermined levels, increment the level counter value, repeatedly call the individual dominance relationship identifier set to perform filtering within the set of undetermined levels, and assign the incremented level counter value until the set of undetermined levels is empty, establish an index of all cable force scheme individuals and their corresponding level identifiers, and obtain the level value.

[0009] As a further aspect of the present invention, the step of filling the new population specifically includes: S301: Obtain the set of parent generation Soli scheme individuals and the set of child generation Soli scheme individuals, merge the two sets to construct a merged population, and initialize the empty new population and obtain the preset capacity value, which is set as the initial number of remaining empty spaces; S302: For all the cable force scheme individuals in the merged population, call the corresponding sum of squares of eccentricity during the operation period and the sum of cubics of stress exceeding the limit during the construction period, perform pairwise dominance relationship determination, filter the set of undominated individuals, repeat the filtering in the remaining cable force scheme individuals, and incrementally assign the level value to establish a merged population level index. S303: Based on the merged population level index, retrieve individuals in the merged population in ascending order of the level value, determine whether the number of individuals at the current level exceeds the initial remaining empty space, and if not, fill all individuals of the Soli scheme at the level into the empty new population, and subtract the number from the initial remaining empty space to obtain the updated remaining empty space. S304: If the number of individuals at the current level is determined to exceed the number of remaining empty slots for the update, then the kernel density estimation function is called to calculate the kernel density estimate of all individuals of the power scheme within the level. Based on the kernel density estimate, individuals of the power scheme corresponding to the number of remaining empty slots for the update are selected to fill the empty population and obtain a new population.

[0010] As a further aspect of the present invention, the step of obtaining the individual offspring cable force scheme is specifically as follows: S401: Based on the new population, traverse all the individuals of the Soli scheme in the new population, extract the decision variable values ​​of multiple individuals of the Soli scheme, perform Gray code conversion operation for each decision variable value, generate a corresponding binary Gray code encoding sequence, aggregate all the binary Gray code encoding sequences, and establish a Gray code encoding population. S402: Based on the Gray code encoded population, select the parent generation binary Gray code encoded sequence pairs from them according to a preset pairing rule, randomly set crossover points, perform gene fragment exchange of the parent generation binary Gray code encoded sequence pairs after the crossover points, recombine the parent generation binary Gray code encoded sequence pairs, and generate offspring numerical sequences. S403: Obtain the current iteration number and the preset maximum iteration number, perform the ratio operation of the current iteration number divided by the preset maximum iteration number to obtain the iteration process ratio, and substitute the iteration process ratio into the preset nonlinear decreasing function, and calculate the adaptive mutation rate in combination with the initial mutation rate parameter; S404: For the offspring numerical sequence, the adaptive mutation rate is used as the perturbation probability benchmark. All gene sites in the offspring numerical sequence are traversed, site flip perturbation is determined and executed, a mutated numerical sequence is generated, and then the Gray code inverse decoding conversion is performed on the mutated numerical sequence to restore the decision variable values ​​and obtain the offspring Soli scheme individuals.

[0011] As a further aspect of the present invention, the calculation method of the kernel density estimate is as follows: Obtain the sum of squares of the eccentricity during the operation period and the sum of cubics of the stress exceeding the limit during the construction period for all individuals of the cable force scheme within the same level, and form a set of objective function values; The objective function value set is normalized to obtain a normalized objective vector set; For any individual cable force scheme to be calculated, its kernel density estimate is obtained using the formula: Calculated; in, For the first The kernel density estimate of each individual cable force scheme, This represents the total number of individuals with the aforementioned cable force scheme within the current level. and The first The and the first The normalized target vector corresponding to each of the aforementioned cable force schemes. For the preset bandwidth matrix, It is a multivariate Gaussian kernel function. and This is the index identifier for an individual in the Soli scheme within the current level.

[0012] As a further aspect of the present invention, the adaptive mutation rate is specifically calculated as follows: Obtain the current iteration number, the preset maximum iteration number, the preset initial mutation rate, and the preset minimum mutation rate; Substitute the four obtained values ​​into the non-linear decreasing function: Perform calculations to generate the adaptive mutation rate; in, The adaptive mutation rate, The preset initial mutation rate, The preset minimum mutation rate, Let the current iteration algebra be... The preset maximum number of iterations, This is a nonlinear adjustment coefficient used to control the decay rate of the variability rate.

[0013] As a further aspect of the present invention, the criteria for determining the dominance and subjugation states between individuals are specifically as follows: Arbitrarily select a first cable force scheme individual and a second cable force scheme individual from the individual target value matrix of the cable force scheme; Obtain the sum of squares of eccentricity during the first operating period and the sum of cubic stress exceeding the limit during the first construction period for the individual cable force schemes; and obtain the sum of squares of eccentricity during the second operating period and the sum of cubic stress exceeding the limit during the second construction period for the individual cable force schemes. When the sum of squares of eccentricity during the first operating period is less than or equal to the sum of squares of eccentricity during the second operating period, and the sum of cubic stress exceeding the limit during the first construction period is less than or equal to the sum of cubic stress exceeding the limit during the second construction period, the first cable force scheme individual and the second cable force scheme individual are determined to be non-dominant. Furthermore, based on the non-dominance relationship, if the sum of squares of eccentricity during the first operating period is less than the sum of squares of eccentricity during the second operating period, or the sum of cubic stress exceeding the limit during the first construction period is less than the sum of cubic stress exceeding the limit during the second construction period, then it is determined that the first cable force scheme individual dominates the second cable force scheme individual.

[0014] As a further aspect of the present invention, the specific execution method of the cross operation is as follows: Randomly select the first parent binary Gray code encoding sequence and the second parent binary Gray code encoding sequence from the Gray code encoding population; Obtain the sequence length of the first parent binary Gray code encoded sequence, and generate a random integer within the sequence length range as the intersection point; All gene segments following the crossover point of the first parent binary Gray code sequence are exchanged with all gene segments following the crossover point of the second parent binary Gray code sequence; The portion of the first parent binary Gray code sequence before the crossover point is recombined with the exchanged second parent gene fragment to generate the first offspring numerical sequence. The portion of the second parent binary Gray code sequence before the crossover point is recombined with the exchanged first parent gene fragment to generate the second offspring numerical sequence.

[0015] Compared with the prior art, the advantages and positive effects of the present invention are as follows: In this invention, a multi-objective function for cable stress optimization is constructed by calculating the sum of squares of eccentricity during the operation period and the sum of cubic over-limit stress during the construction period, which more accurately balances construction safety and operational performance. Then, a non-dominated sorting mechanism is used to screen individuals, and the population crowding is evaluated using a kernel density estimation function, which effectively preserves the diversity of solution sets and avoids the algorithm getting trapped in local optima. Finally, Gray code encoding and an adaptive mutation rate that changes with the iteration algebra are combined to enhance the robustness and convergence efficiency of the search and find a more balanced anchor cable prestress configuration scheme. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the overall process of the anchor cable force optimization method of the present invention. Figure 2 This is a flowchart illustrating the calculation of the objective function value and the penalty function value in this invention. Figure 3 This is a flowchart of the individual non-dominated sorting process of the cable force scheme of the present invention; Figure 4 This is a flowchart illustrating the novel population filling and elite retention process of this invention. Figure 5 This is a flowchart illustrating the generation process of the offspring cable force scheme of this invention. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the software-based technical solution is described in detail below with reference to system architecture diagrams and embodiments. It should be understood that the specific embodiments described herein are only for explaining the technical solutions of this invention and do not constitute a limitation on the scope of protection.

[0018] In the description of this invention, the system architecture relationships or data processing flows indicated by terms such as "layer," "module," "interface," "data flow," "client," and "server" are all defined based on the architecture diagram or flowchart corresponding to the embodiments. This way of describing is only used to clearly illustrate the logical relationships between the elements in the technical solution, and not to limit the physical deployment form. The term "multiple" includes two or more technical units, including but not limited to multiple data nodes, processing threads, service instances, or functional components and other scalable elements. The specific number is determined according to the actual business scenario and needs to be specifically specified.

[0019] Please see Figure 1 and Figure 2 This invention provides a technical solution: a method for optimizing anchor cable force based on an improved second-generation genetic algorithm, comprising the following steps: S1: Obtain the maximum tensile stress during construction, bending moment during operation, axial force during operation, and the baseline value of the maximum tensile stress allowable upper limit during construction for each individual cable force scheme. Calculate the section eccentricity, obtain the sum of squares of eccentricity during operation, calculate the portion exceeding the baseline value of the maximum tensile stress allowable upper limit during construction, and obtain the sum of cubic stress exceeding the limit during construction. The sum of squared eccentricities during the operating period specifically refers to the objective function value that characterizes the long-term structural eccentricity during the operating period. The cubic value of stress exceeding the limit during construction and the specific value of the penalty function characterizing instantaneous stress safety during construction; The specific steps to obtain S1 are as follows: S101: Obtain the baseline values ​​of the maximum tensile stress during construction, bending moment during operation, axial force during operation, and the allowable upper limit of the maximum tensile stress during construction for each individual cable force scheme. Aggregate the four types of numerical data to establish an initial cable force state matrix. S102: Based on the initial cable force state matrix, call the operational period bending moment value and operational period axial force value, and for each corresponding section in the individual cable force scheme, perform numerical calculation by dividing the operational period bending moment value by the operational period axial force value to obtain the section eccentricity and generate the section eccentricity vector. S103: For multiple element values ​​in the cross-sectional eccentricity vector, perform squaring operation one by one to obtain the squared value of the eccentricity of multiple cross-sections, aggregate all the squared values ​​of the eccentricity of the cross-sections, perform summation calculation on the aggregated result, and obtain the squared eccentricity of the operation period. S104: Call the baseline values ​​of the maximum tensile stress during construction and the allowable upper limit of the maximum tensile stress during construction from the initial cable force state matrix. Iterate through all the maximum tensile stress values ​​during construction, perform subtraction operations, determine and extract the stress exceeding the baseline values ​​that exceed the allowable upper limit of the maximum tensile stress during construction, perform cube operations on all stress exceeding values, aggregate all cube operation results and sum them to generate the cube sum of stress exceeding the limit during construction.

[0020] In S101, a specific cable tension scheme is obtained, denoted as individual P1. Individual P1 contains a set of initial tension values ​​for the anchor cables, set as follows: Its specific value is The unit is kN. A detailed model including the anchor cables, anchorage zone, and main structure is established using structural finite element analysis software (such as ANSYS or ABAQUS). The tension force value of individual component P1 is then input. kN is used as the prestressed load, and corresponding load combinations are applied during the construction and operation phases. Nonlinear calculations are performed to obtain the stress and internal force responses of the key sections (4 sections are set) of the individual P1 under different construction and operation phases.

[0021] The baseline value for the maximum allowable tensile stress during the construction period ( The setting of the tensile strength is based on material properties and relevant design specifications. This embodiment uses 1860MPa grade standard strength prestressed steel strand, commonly used in engineering, with a standard tensile strength value of... That is, 1860 MPa. Based on relevant special working condition design requirements or ultra-high strength material testing standards, the upper limit of the control stress during the construction tensioning stage can be taken as 0.5 times the standard value of tensile strength; therefore, the benchmark value... .

[0022] The analysis results of individual P1 are aggregated with the baseline values ​​to establish an initial cable force state matrix. This matrix aims to structurally collect the key response data (stress, internal forces) generated after finite element analysis of a single cable force scheme, providing a unified data input source for the efficient calculation of the objective function and penalty function in subsequent steps S102 and S104. Specific data are shown in Table 1.

[0023] Table 1: Initial cable force state matrix data for individual P1; In S102, based on the initial cable force state matrix shown in Table 1, the operational bending moment and operational axial force values ​​are retrieved. For section SEC-01, the following steps are executed: The calculation yields the cross-sectional eccentricity. For section SEC-02, execute... The calculation yielded For section SEC-03, execute... The calculation yielded For section SEC-04, execute... The calculation yielded The calculated eccentricity values ​​of the four sections are combined to generate a section eccentricity vector. .

[0024] In S103, regarding the cross-sectional eccentricity vector The first element Perform the squaring operation to get For the second element Perform the squaring operation to get For the third element Perform the squaring operation to get For the fourth element Perform the squaring operation to get Aggregate the squared values ​​of the eccentricities of all sections, and perform a summation calculation on the aggregated results: The value of 0.18799 represents the sum of squared eccentricities during the operating period of individual P1.

[0025] In S104, the maximum tensile stress value during the construction period from Table 1 is called up, along with the baseline value of the allowable upper limit of the maximum tensile stress during the construction period set in S101. Iterate through all maximum tensile stress values ​​during the construction period. For SEC-01, its value is... ,implement Subtraction operation, determine Extracting the numerical values ​​of the stress exceeding the limit For SEC-02, its value is... ,implement Subtraction operation, determine No stress exceeding the limit. For SEC-03, its value is... ,implement Subtraction operation, determine Extracting the numerical values ​​of the stress exceeding the limit For SEC-04, its value is... ,implement Subtraction operation, determine No stress exceeding the limit. The extracted values ​​for all stress exceeding the limit portions. Perform the cube operation one by one: , Sum the results of all cube operations: The value 243.0 represents the sum of the cubic over-limit stresses during the construction period for individual P1.

[0026] Please see Figure 1 and Figure 3 S2: Based on the sum of squares of eccentricity during operation and the sum of cubics of stress exceeding limits during construction, compare the pairwise dominance relationships of individual cable force schemes, select the set of individuals that are not dominated as the first level, and repeat the selection until a level value is assigned. The specific level value is the Pareto front level identifier of the individual Soleil scheme; The specific steps to obtain the level value are as follows: S201: Obtain the set of all individual cable force schemes, and retrieve the sum of squares of eccentricity during the operation period and the sum of cubics of stress exceeding the limit during the construction period for each individual cable force scheme. Construct a target value matrix for individual cable force schemes, traverse the matrix to perform pairwise comparisons between any two individual cable force schemes, determine the dominance and subordination status between individuals, and generate a set of individual dominance relationship identifiers. The specific criteria for determining the dominant and subjugated state between individuals are as follows: Arbitrarily select the first cable force scheme individual and the second cable force scheme individual from the individual target value matrix of the cable force scheme; Obtain the sum of squares of eccentricity during the first operating period and the sum of cubic stress exceeding the limit during the first construction period for the individual cable force scheme; and obtain the sum of squares of eccentricity during the second operating period and the sum of cubic stress exceeding the limit during the second construction period for the individual cable force scheme. When the sum of squares of eccentricity in the first operating period is less than or equal to the sum of squares of eccentricity in the second operating period, and the sum of cubic stress exceeding the limit in the first construction period is less than or equal to the sum of cubic stress exceeding the limit in the second construction period, the individuals of the first cable force scheme and the individuals of the second cable force scheme are determined to be non-dominant. Furthermore, based on the non-dominance relationship, if the sum of squares of eccentricity in the first operating period is less than the sum of squares of eccentricity in the second operating period, or the sum of cubic stress exceeding the limit in the first construction period is less than the sum of cubic stress exceeding the limit in the second construction period, then it is determined that the first cable force scheme individual dominates the second cable force scheme individual.

[0027] S202: Based on the individual dominance relationship identifier set, initialize the level counter to one, retrieve all cable force scheme individuals, filter individuals in the individual dominance relationship identifier set that are not dominated by any other cable force scheme individuals, establish a first-level undominated individual set, assign level counter values ​​to all cable force scheme individuals in the set, and obtain the first-level cable force scheme set; S203: For the remaining cable force schemes outside the first-level cable force scheme set, form a set of undetermined levels, increment the level counter value, repeatedly call the individual dominance relationship identifier set to perform filtering within the undetermined level set, and assign the incremented level counter value until the undetermined level set is empty, establish an index of all cable force schemes and their corresponding level identifiers, and obtain the level value.

[0028] In S201, a set of individual cable force schemes is obtained, containing 5 individual cable force schemes, denoted as P1, P2, P3, P4, and P5. The calculation steps in S1 are called to obtain the sum of squared eccentricities during the operating period for each individual. ) and the cubic meters of stress exceeding the limit during construction and ( Construct the individual target value matrix for the cable force scheme, with specific values ​​as follows: P1: [ , P2: [ , P3: [ , P4: [ , P5: [ , Traverse the matrix and perform pairwise comparisons between any two cable force scheme individuals. Taking P1 and P2 as an example: Select the first cable force scheme individual P1 and the second cable force scheme individual P2. Obtain the sum of squares of eccentricity during the first operating period (0.18799) and the sum of cubic stress exceeding the limit during the first construction period (1165.625) for P1; obtain the sum of squares of eccentricity during the second operating period (0.1750) and the sum of cubic stress exceeding the limit during the second construction period (1300.0) for P2. Determine the dominance relationship between P1 and P2: Execute... (Right now The judgment was negative. Execute. (Right now The determination of ) is yes. Execute. (Right now The judgment is negative. P1 and P2 do not satisfy the precondition of a non-dominant relationship; therefore, P1 and P2 are not mutually dominant. Taking P4 and P1 as an example: Select the first cable force scheme individual P4 and the second cable force scheme individual P1. Obtain the corresponding... and ; Get the corresponding P1 and Determine the dominance relationship between P4 and P1: Execute (Right now The determination of ) is yes. Execute. (Right now The determination is as follows: The basic condition for a non-dominant relationship is met. Next, the determination... (Right now The result is yes; or (Right now The result is yes. The "or" condition is satisfied. P4 dominates P1. Repeat the above comparison process for all individual pairs. P2 vs P3: They do not dominate each other. P2 vs P4: P4 dominates P2. no; yes, No). They do not dominate each other. P2 vs P5: Check if P2 dominates P5: ( ) is, but ( The answer is no, therefore P2 does not dominate P5. Check if P5 dominates P2: ( The answer is no, therefore P5 does not dominate P2. Therefore, P2 and P5 are mutually non-dominant. P3 vs P4: P4 dominates P3. yes, No). P3 dominates P4 ( No). They do not dominate each other. P3 vs P5: P3 dominates P5 ( yes, yes; Yes). P3 dominates P5. P4 vs P5: P4 dominates P5 ( yes, yes; Yes). P4 dominates P5. The final generated set of individual dominance relationship identifiers ( Describes the set of individuals dominated by individual p. (This represents the number of individuals that dominate individual p). , (Dominated by P4) , , , (Note: P4 vs P5 comparison correction) and P4 dominates P5. A comparison and correction of P4 vs. P1 is needed. and , P4 dominates P1. ) , (Dominated by P3 and P4) (Reorganizing the dominance relationship) P4(0.1800, 1150.0) vs P1(0.18799, 1165.625) -> P4 dominates P1 P3(0.1900, 1100.0) vs P1(0.18799, 1165.625) -> No mutual dominance P2(0.1750, 1300.0) vs P1(0.18799, 1165.625) -> No mutual dominance P3(0.1900, 1100.0) 0, 1100.0) vs P4(0.1800, 1150.0) -> no mutual domination P2(0.1750, 1300.0) vs P4(0.1800, 1150.0) -> no mutual domination P2(0.1750, 1300.0) vs P3(0.1900, 1100.0) -> no mutual domination P5(0.1950, 1250.0) vs P1(0.18799, 1165.625) -> P1 dominates P5( yes, yes; Yes) P5 vs P2 (0.1750, 1300.0) -> P2 dominates P5 ( yes, No). They do not dominate each other. P5 vs P3 (0.1900, 1100.0) -> P3 dominates P5 ( yes, yes; Yes) P5 vs P4 (0.1800, 1150.0) -> P4 dominates P5 ( yes, yes; Yes) Domination Relationship Identifier Set ( (Number of individuals dominating p) (by P4), , , , (by P1, P3, P4).

[0029] In S202, the level counter is initialized based on the individual dominance relationship identifier set generated in S201. Retrieve all individuals in the cable-driven scheme {P1, P2, P3, P4, P5}. Filter within the set of individual dominance relationship identifiers. Individuals that are not dominated by any other force-dependent individuals are considered as follows: The selection results are {P2, P3, P4}. A first-level set of undominated individuals is established. . for set Assign a level counter value of 1 to all individual cable force schemes P2, P3, and P4. This yields the first-level cable force scheme set {P2: 1, P3: 1, P4: 1}.

[0030] In S203, for the first-level cable force scheme set The remaining cable force schemes {P1, P5} constitute the undetermined level set. The incrementing level counter value... Iterate through all individuals in the set of undetermined ranks and update their dominated counts: for P1, its... The individual P4 that controls it belongs to Therefore, an update was made. For P5, its The individuals P3 and P4 that dominate it belong to Therefore, an update was made. In the set of undetermined levels {P1, P5}, filter and update the results. The individuals were selected. The screening result was {P1}. A set of second-level undominated individuals was established. . for set All individual cable force schemes P1 are assigned an incremented level counter value of 2. This yields the second-level cable force scheme set {P1: 2}. The process is repeated, and the remaining cable force schemes form the undetermined level set {P5}. The level counter value is then incremented. Within the set of undetermined ranks {P5}, the individual P5's... Subtract from The dominant individual P1 updates .filter The individuals selected were {P5}. A set of third-level undominated individuals was established. . for set Assign an incrementing level counter value of 3 to all individual cable force schemes P5. This yields the third-level cable force scheme set {P5: 3}. At this point, the undetermined level set is empty. Establish indices for all individual cable force schemes and their corresponding level identifiers: {P1: 2, P2: 1, P3: 1, P4: 1, P5: 3}.

[0031] Please see Figure 1 and Figure 4 S3: Assign level values ​​to the merged population composed of parent and offspring Soli scheme individuals, fill the new population. When the number of Soli scheme individuals at a certain level exceeds the number of remaining vacancies, call the kernel density estimation function to obtain the kernel density estimate, and select the one with the lowest kernel density estimate to fill the remaining vacancies. The kernel density estimate is specifically a scalar value that characterizes the sparsity of the distribution of individual members of the sling force scheme in the normalized target space; The specific steps for filling a new population are as follows: S301: Obtain the set of parent generation Soli scheme individuals and the set of child generation Soli scheme individuals, merge the two sets to construct a merged population, and initialize the empty new population and obtain the preset capacity value, which is set as the initial number of remaining empty spaces; S302: For all cable force scheme individuals in the merged population, call the corresponding sum of squares of eccentricity during the operation period and the sum of cubics of stress exceeding the limit during the construction period, perform pairwise dominance relationship determination, filter the set of individuals that are not dominated, repeat the filtering in the remaining cable force scheme individuals, and incrementally assign level values ​​to establish a merged population level index. S303: Based on the merged population level index, retrieve individuals in the merged population in ascending order of level value, determine whether the number of individuals at the current level exceeds the initial remaining empty space, and if not, fill all individuals of the Soli scheme at the level into the empty new population, and subtract the number from the initial remaining empty space to obtain the updated remaining empty space. S304: If the number of individuals at the current level is determined to exceed the number of remaining empty slots for updating, the kernel density estimation function is called to calculate the kernel density estimate of all cable force scheme individuals within the level. Based on the kernel density estimate, individuals are sorted from low to high, and the number of cable force scheme individuals corresponding to the number of remaining empty slots for updating is selected to fill the empty population and obtain a new population.

[0032] The specific method for calculating the kernel density estimate is as follows: Obtain the sum of squares of eccentricity during the operation period and the sum of cubics of stress exceeding the limit during the construction period for all individual cable force schemes within the same level, and form a set of objective function values; The set of objective function values ​​is normalized to obtain a set of normalized objective vectors; For any individual cable force scheme to be calculated, its kernel density estimate is obtained through the formula: Calculated; in, For the first Kernel density estimates for individual cable-driven schemes, This represents the total number of individual cable force schemes within the current level. and The first The and the first The normalized target vector corresponding to each cable force scheme is a preset bandwidth matrix. It is a multivariate Gaussian kernel function. and This is the index identifier for an individual in the Soli scheme within the current level.

[0033] In S301, obtain the set of individual parent cable force schemes. That is, {P1, P2, P3, P4, P5} sorted in S2. Obtain the set of individual child cable force schemes. This set is generated by the crossover and mutation operation of S4, and is assumed to also contain 5 individuals {Q1, Q2, Q3, Q4, Q5}. The two sets are then merged to construct a combined population. The total number is 10. Simultaneously, an empty new population is initialized. and obtain the preset capacity value. Set the initial number of remaining empty spaces. .

[0034] In S302, regarding the merging of populations For all 10 cable-driven schemes, use method S1 to calculate the sum of squared eccentricities during the operating period. With the construction period stress exceeding the limit cubic meter and . Target values: P1(0.18799, 1165.625), P2(0.1750, 1300.0), P3(0.1900, 1100.0), P4(0.1800, 1150.0), P5(0.1950, 1250.0), Q1(0.1700, 1250.0), Q2(0.1850, 1080.0), Q3(0.1820, 1180.0), Q4(0.1920, 1120.0), Q5(0.1780, 1350.0) for merging populations. Perform a non-dominated sort on all 10 individuals and calculate the sorting for each individual. The number of people controlled After comparing all pairs of data, the statistics were... Value (i.e., dominance of individuals) The number of individuals is as follows: (Dominated by P2, P3, P4, Q1, Q2, Q3); (Dominated by Q1 and Q5); (Dominated by Q1, Q2, Q4); (Dominated by Q1, Q2, Q3); (Dominated by P1, P2, P3, P4, Q1, Q2, Q3, Q4); ; ; (Dominated by Q1 and Q2); (Dominated by P3, Q1, Q2, Q3); (Dominated by Q1); Screening Individuals (first level) ): {Q1, Q2}. Filter the second level. (right Individuals, minus those from After the dominance count, Individuals): {Q3, Q5}. Screening for the third level. (right Individuals, minus those from After the dominance count, Individuals): {P2, P4}. Screening for the fourth level. {P3}. Filtering for the fifth level. {P1}. Filtering for the sixth level. {P5}. Establish a merged population hierarchy index: {P1:5, P2:3, P3:4, P4:3, P5:6, Q1:1, Q2:1, Q3:2, Q4:4, Q5:2}.

[0035] In S303, based on the merged population level index of S302, the populations are ranked according to their level values. Incremental search. Search a collection of individuals The current number of individuals at this level is 2. (Judgment) (Right now The result is (not exceeding). All two individuals from the two Optimization schemes {Q1, Q2} are filled into the empty new population. . Subtract the number of empty spaces from the initial remaining number of spaces. Get the updated remaining empty numbers. .

[0036] In S304, retrieval a collection of individuals The current number of individuals at this level is 2. (Judgment) (Right now The result is (not exceeding). All two individuals from the Soleil scheme {Q3, Q5} are added to the empty new population. . Subtract the quantity from the remaining empty spaces. Get the updated remaining empty numbers. .

[0037] Search a collection of individuals The current number of individuals at this level is 2. (Judgment) (Right now The result is (exceeding the limit). The kernel density estimation function is called to calculate... Kernel density estimates for all two individual spurious schemes within the rank. The objective function value set is: P2(0.1750, 1300.0), P4(0.1800, 1150.0). Normalization is performed on the objective function value set. : Min=0.1750, Max=0.1800, Range=0.005 The set of normalized target vectors: Min=1150.0, Max=1300.0, Range=150.0 : For any individual cable force scheme to be calculated, its kernel density estimate is obtained through the formula: Calculated. Formula parameter explanation: For the first The estimated kernel density of each individual. Current level The total number of individuals within, . and The first The and the first The normalized target vector corresponding to each individual. This is the preset bandwidth matrix. It is a multivariate Gaussian kernel function, specifically in the form of: ,in For the target dimension, , . Indicates to Excluding individuals within the level All outside of oneself Individual values ​​are summed. Bandwidth matrix. Setup: Using Silverman's rule of thumb, Here , . of . of .coefficient . . .set up diagonal matrix . . . .calculate Required constant terms . To calculate (correspond For example: , Take {P4}. : . . . . To supplement the calculation process, the calculation is... (correspond ): , Take {P2}. . . . . .right Perform the above calculation on all two individuals to obtain the kernel density estimate: Sort by kernel density estimate from lowest to highest (if values ​​are the same, then individual index order P2 takes precedence over P4): 1. 2. Select to update the remaining empty numbers ( The corresponding number of individuals in the Soleil scheme, i.e., the individual with the lowest kernel density estimate: {P2}. {P2} is then used to fill the empty population. Acquiring new populations .

[0038] Please see Figure 1 and Figure 5 S4: Perform Gray code encoding on individuals of the Soli scheme in the new population, perform crossover operation to generate offspring numerical sequences, obtain the iteration number, calculate the adaptive mutation rate, and perturb the offspring numerical sequences to generate offspring Soli scheme individuals.

[0039] The offspring numerical sequence specifically refers to the sequence of sorghum parameters after Gray code encoding and crossover operations; The adaptive mutation rate specifically refers to the mutation probability value that decreases as the number of iterations increases; Each offspring cable tension scheme includes a set of initial tension values ​​for the anchor cable generated after being decoded by mutation perturbation.

[0040] The specific steps for obtaining offspring cable scheme individuals are as follows: S401: Based on the new population, traverse all individuals of the power scheme in the new population, extract the decision variable values ​​of multiple power scheme individuals, perform Gray code conversion operation for each decision variable value, generate the corresponding binary Gray code encoding sequence, aggregate all binary Gray code encoding sequences, and establish a Gray code encoding population. S402: Based on the Gray code encoded population, select parent binary Gray code encoded sequence pairs from them according to the preset pairing rules, randomly set crossover points, perform gene fragment exchange of the parent binary Gray code encoded sequence pairs after the crossover points, recombine the parent binary Gray code encoded sequence pairs, and generate offspring numerical sequences. The specific execution method of crossover operation is as follows: Randomly select the first parent binary Gray code sequence and the second parent binary Gray code sequence from the Gray code encoded population; Obtain the sequence length of the first parent binary Gray code encoded sequence, and generate a random integer within the sequence length range as the intersection point; All gene segments after the crossover point in the first parent binary Gray code encoded sequence are swapped with all gene segments after the crossover point in the second parent binary Gray code encoded sequence. The portion of the first parent binary Gray code sequence before the crossover point is recombined with the exchanged second parent gene segment to generate the first offspring numerical sequence. The portion of the second parent binary Gray code sequence before the crossover point is recombined with the exchanged first parent gene segment to generate the second offspring numerical sequence.

[0041] S403: Obtain the current iteration algebra and the preset maximum iteration algebra, perform the ratio operation of the current iteration algebra to the preset maximum iteration algebra, obtain the iteration process ratio, substitute the iteration process ratio into the preset nonlinear decreasing function, and calculate the adaptive mutation rate in combination with the initial mutation rate parameter. The adaptive variability rate is calculated as follows: Get the current iteration number, the preset maximum iteration number, the preset initial mutation rate, and the preset minimum mutation rate; Substitute the four obtained values ​​into the non-linear decreasing function: Perform calculations to generate an adaptive variability rate; in, To adapt the mutation rate, To preset the initial mutation rate, To preset the minimum mutation rate, Let the current iteration algebra be... To preset the maximum number of iterations, This is a nonlinear adjustment coefficient used to control the decay rate of the variability rate.

[0042] S404: For the offspring numerical sequence, the adaptive mutation rate is used as the perturbation probability benchmark. All gene loci in the offspring numerical sequence are traversed, the locus flipping perturbation is determined and executed, the mutated numerical sequence is generated, and the Gray code inverse decoding conversion is performed on the mutated numerical sequence to restore the decision variable values ​​and obtain the offspring Soli scheme individuals.

[0043] In S401, a new population was obtained based on S3. Iterate through all 5 individuals with different power strategies in the new population. Taking individual Q1 as an example, extract the values ​​of its decision variables, i.e., the power strategy. Individual Q1 is a progeny introduced in S301, and its decision variable values ​​(i.e., the power-based scheme) are [2010.5, 2030.0, 2065.2, 2100.8] kN. This scheme obtains the target values ​​(0.1700, 1250.0) mentioned in S302 through the analysis and calculation in S1. The range of values ​​for the decision variables is set as follows. kN, accuracy requirement is kN. This range The length of the corresponding integer interval is .need . hour (insufficient), hour Therefore, each decision variable requires 13 bits of binary encoding. For the first decision variable... kN, convert it to an integer encoding: Convert the decimal integer 2105 to 13-bit binary: Perform Gray code conversion on this binary sequence: get The corresponding 13-bit binary Gray code sequence: .right (Integer 2300, binary) ), (Integer 2652, binary) ), (Integer 3008, binary) Perform this operation on all cases to obtain Q1 (denoted as Q1). ) corresponding Bit-bit binary Gray code encoded sequence Aggregate the sequences of all 5 individuals to establish a Gray code-encoded population.

[0044] In S402, based on the Gray code encoded population, parent binary Gray code encoded sequence pairs are selected according to a preset pairing rule. For example, selecting... (from Q1) and (From Q2). To illustrate the calculation process, the decision variable values ​​for individual Q2 are set as follows: kN, after being encoded using the same method as in S401, yields its 52-bit binary Gray code sequence. Get the sequence length 52, and... Generate a random integer within the range as the intersection point, and set the intersection point. .

[0045] Will At the intersection All subsequent gene segments, and At the intersection All subsequent gene segments are exchanged. The part before the intersection and the part after the swap Gene fragment recombination generates the first generation numerical sequence. : Will The part before the intersection and the part after the swap Gene fragment recombination generates second-generation numerical sequences. : .

[0046] In S403, the current iteration number and the preset maximum iteration number are obtained. The ratio of the current iteration number to the preset maximum iteration number is calculated to obtain the iteration progress ratio. This ratio is then substituted into a preset nonlinear decreasing function and combined with the initial mutation rate parameter to generate an adaptive mutation rate. The adaptive mutation rate is calculated as follows: The current iteration number is obtained... Preset maximum number of iterations Obtain the preset initial mutation rate. . Typically set to ( This is the encoding length of 52 or a slightly larger value. It is set here. Obtain the preset minimum mutation rate. Set as Obtain the nonlinear adjustment coefficient. . The settings are based on experimental verification. To determine... ,set up Group 5 The values ​​were run 10 times on the same test problem, and the average convergence algebra and the diversity index of the Pareto front (Hypervolume) were calculated.

[0047] Table 2: Table of the impact of coefficients on algorithm performance; As shown in Table 2 The test results (over-volume index 0.945) meet the preset performance requirements. Therefore, this embodiment sets... The four values ​​obtained and Substitute into the nonlinear decreasing function: Perform calculations to generate an adaptive variability rate; The result This is the adaptive mutation rate generated in the current 80th generation.

[0048] In S404, the offspring numerical sequence generated for S402. Call the adaptive mutation rate As a benchmark for perturbation probability, traverse All 52 gene loci were identified, and site flipping perturbations were performed. The 10th gene ( For example, generate random numbers between 0 and 1. ,determination Perform site flipping. Assume that no other sites have changed. Chinese correspondence The sequence is After mutation, the result is The corresponding sequence Then, perform Gray code reverse decoding on the mutated numerical sequence. sequence For example: The decoded 13-bit binary sequence is obtained. Binary Convert to decimal integer: Finally, restore the values ​​of the decision variables (inverse normalization): kN. (This likely refers to a specific kN value.) The remaining three 13-bit sequences (corresponding to) Perform the same decoding and recovery operations to ultimately obtain the offspring Solaris scheme individual. .

[0049] The above embodiments illustrate preferred embodiments of the present invention. Any equivalent adjustments to the technical solution based on software engineering methods are within the scope of protection, including but not limited to: implementing algorithm logic using different programming languages, refactoring functional modules into services, adjusting data interaction protocols, and optimizing resource scheduling strategies. Any implementation scheme derived from reasonable modifications to the data processing flow, service call chain, or system architecture layer without departing from the core technology of the present invention should be considered within the scope of protection defined by the claims of the present invention.

Claims

1. A method for optimizing anchor cable force based on an improved second-generation genetic algorithm, characterized in that, Includes the following steps: S1: Obtain the maximum tensile stress during construction, bending moment during operation, axial force during operation, and the baseline value of the maximum tensile stress allowable upper limit during construction for each individual cable force scheme; calculate the section eccentricity; obtain the sum of squares of eccentricity during operation; calculate the portion exceeding the baseline value of the maximum tensile stress allowable upper limit during construction; obtain the sum of cubic over-limit stress during construction. S2: Based on the sum of squares of eccentricity during the operation period and the sum of cubics of stress exceeding the limit during the construction period, compare the pairwise dominance relationships of the individual cable force schemes, select the set of individuals that are not dominated as the first level, and repeat the selection until a level value is assigned. S3: Assign the level value to the merged population composed of parent and offspring Soli scheme individuals, and fill the new population. When the number of Soli scheme individuals at a certain level exceeds the remaining empty slots, call the kernel density estimation function to obtain the kernel density estimate, and select the one with the lowest kernel density estimate to fill the remaining empty slots. S4: Perform Gray code encoding on the individuals of the Soli scheme in the new population, perform crossover operation to generate offspring numerical sequences, obtain the iteration number, calculate the adaptive mutation rate, and perturb the offspring numerical sequences to generate offspring Soli scheme individuals.

2. The anchor cable force optimization method based on the improved second-generation genetic algorithm according to claim 1, characterized in that, The sum of squared eccentricities during the operation period specifically refers to the objective function value characterizing the long-term structural eccentricity during the operation period; the sum of cubic stress exceeding the limit during the construction period specifically refers to the penalty function value characterizing the instantaneous stress safety during the construction period; the level value specifically refers to the Pareto front level identifier of the individual cable force scheme; the kernel density estimate specifically refers to the scalar value characterizing the sparsity of the distribution of the individual cable force scheme in the normalized objective space; the offspring numerical sequence specifically refers to the cable force parameter sequence after Gray code encoding and crossover operation; the adaptive mutation rate specifically refers to the mutation probability value that decreases with the increase of the iteration number; and the offspring cable force scheme individual includes a set of initial tension force values ​​of the anchor cable generated after decoding after mutation perturbation.

3. The anchor cable force optimization method based on the improved second-generation genetic algorithm according to claim 2, characterized in that, The specific steps for obtaining S1 are as follows: S101: Obtain the baseline values ​​of the maximum tensile stress during construction, bending moment during operation, axial force during operation, and the allowable upper limit of the maximum tensile stress during construction for each individual cable force scheme. Aggregate the four types of numerical data to establish an initial cable force state matrix. S102: Based on the initial cable force state matrix, call the operating period bending moment value and the operating period axial force value, and for each corresponding section in the individual cable force scheme, perform numerical calculation by dividing the operating period bending moment value by the operating period axial force value to obtain the section eccentricity and generate the section eccentricity vector. S103: For the multiple element values ​​in the cross-sectional eccentricity vector, perform squaring operation one by one to obtain the squared values ​​of the eccentricity of multiple cross-sections, aggregate all the squared values ​​of the eccentricity of the cross-sections, and perform summation calculation on the aggregated result to obtain the sum of squared eccentricities during the operation period; S104: Call the maximum tensile stress value during construction period and the baseline value of the allowable upper limit of the maximum tensile stress during construction period in the initial cable force state matrix, iterate through all the maximum tensile stress values ​​during construction period, perform subtraction operation, determine and extract the stress exceeding the baseline value that exceeds the allowable upper limit of the maximum tensile stress during construction period, perform cube operation on all the stress exceeding the limit values, aggregate all cube operation results and sum them to generate the cube sum of stress exceeding the limit during construction period.

4. The anchor cable force optimization method based on the improved second-generation genetic algorithm according to claim 3, characterized in that, The specific steps for obtaining the level value are as follows: S201: Obtain the set of all cable force scheme individuals, and retrieve the sum of squares of the eccentricity during the operation period and the sum of cubics of the stress exceeding the limit during the construction period for each cable force scheme individual, construct the target value matrix of the cable force scheme individuals, traverse the matrix to perform pairwise comparisons between any two cable force scheme individuals, determine the dominance and subordination status between individuals, and generate a set of individual dominance relationship identifiers; S202: Based on the individual dominance relationship identifier set, initialize the level counter to one, retrieve all individuals of the cable force scheme, filter individuals in the individual dominance relationship identifier set that are not dominated by any other individuals of the cable force scheme, establish a first-level set of undominated individuals, assign the level counter value to all individuals of the cable force scheme in the set, and obtain the first-level cable force scheme set. S203: For the remaining cable force scheme individuals outside the first level cable force scheme set, form a set of undetermined levels, increment the level counter value, repeatedly call the individual dominance relationship identifier set to perform filtering within the set of undetermined levels, and assign the incremented level counter value until the set of undetermined levels is empty, establish an index of all cable force scheme individuals and their corresponding level identifiers, and obtain the level value.

5. The anchor cable force optimization method based on the improved second-generation genetic algorithm according to claim 4, characterized in that, The specific steps for filling the new population are as follows: S301: Obtain the set of parent generation Soli scheme individuals and the set of child generation Soli scheme individuals, merge the two sets to construct a merged population, and initialize the empty new population and obtain the preset capacity value, which is set as the initial number of remaining empty spaces; S302: For all the cable force scheme individuals in the merged population, call the corresponding sum of squares of eccentricity during the operation period and the sum of cubics of stress exceeding the limit during the construction period, perform pairwise dominance relationship determination, filter the set of undominated individuals, repeat the filtering in the remaining cable force scheme individuals, and incrementally assign the level value to establish a merged population level index. S303: Based on the merged population level index, retrieve individuals in the merged population in ascending order of the level value, determine whether the number of individuals at the current level exceeds the initial remaining empty space, and if not, fill all individuals of the Soli scheme at the level into the empty new population, and subtract the number from the initial remaining empty space to obtain the updated remaining empty space. S304: If the number of individuals at the current level is determined to exceed the number of remaining empty slots for the update, then the kernel density estimation function is called to calculate the kernel density estimate of all individuals of the power scheme within the level. Based on the kernel density estimate, individuals of the power scheme corresponding to the number of remaining empty slots for the update are selected to fill the empty population and obtain a new population.

6. The anchor cable force optimization method based on the improved second-generation genetic algorithm according to claim 5, characterized in that, The specific steps for obtaining the offspring cable force scheme individuals are as follows: S401: Based on the new population, traverse all the individuals of the Soli scheme in the new population, extract the decision variable values ​​of multiple individuals of the Soli scheme, perform Gray code conversion operation for each decision variable value, generate a corresponding binary Gray code encoding sequence, aggregate all the binary Gray code encoding sequences, and establish a Gray code encoding population. S402: Based on the Gray code encoded population, select the parent generation binary Gray code encoded sequence pairs from them according to a preset pairing rule, randomly set crossover points, perform gene fragment exchange of the parent generation binary Gray code encoded sequence pairs after the crossover points, recombine the parent generation binary Gray code encoded sequence pairs, and generate offspring numerical sequences. S403: Obtain the current iteration number and the preset maximum iteration number, perform the ratio operation of the current iteration number divided by the preset maximum iteration number to obtain the iteration process ratio, and substitute the iteration process ratio into the preset nonlinear decreasing function, and calculate the adaptive mutation rate in combination with the initial mutation rate parameter; S404: For the offspring numerical sequence, the adaptive mutation rate is used as the perturbation probability benchmark. All gene sites in the offspring numerical sequence are traversed, site flip perturbation is determined and executed, a mutated numerical sequence is generated, and then the Gray code inverse decoding conversion is performed on the mutated numerical sequence to restore the decision variable values ​​and obtain the offspring Soli scheme individuals.

7. The anchor cable force optimization method based on the improved second-generation genetic algorithm according to claim 5, characterized in that, The specific method for calculating the kernel density estimate is as follows: Obtain the sum of squares of the eccentricity during the operation period and the sum of cubics of the stress exceeding the limit during the construction period for all individuals of the cable force scheme within the same level, and form a set of objective function values; The objective function value set is normalized to obtain a normalized objective vector set; For any individual cable force scheme to be calculated, its kernel density estimate is obtained using the formula: Calculated; in, For the first The kernel density estimate of each individual cable force scheme, This represents the total number of individuals with the aforementioned cable force scheme within the current level. and The first The and the first The normalized target vector corresponding to each of the aforementioned cable force schemes. For the preset bandwidth matrix, It is a multivariate Gaussian kernel function. and This is the index identifier for an individual in the Soli scheme within the current level.

8. The anchor cable force optimization method based on the improved second-generation genetic algorithm according to claim 6, characterized in that, The adaptive mutation rate is calculated as follows: Obtain the current iteration number, the preset maximum iteration number, the preset initial mutation rate, and the preset minimum mutation rate; Substitute the four obtained values ​​into the non-linear decreasing function: Perform calculations to generate the adaptive mutation rate; in, The adaptive mutation rate, The preset initial mutation rate, The preset minimum mutation rate, Let the current iteration algebra be... The preset maximum number of iterations, This is a nonlinear adjustment coefficient used to control the decay rate of the variability rate.

9. The anchor cable force optimization method based on the improved second-generation genetic algorithm according to claim 4, characterized in that, The criteria for determining the dominance and subjugation status between individuals are as follows: Arbitrarily select the first cable force scheme individual and the second cable force scheme individual from the individual target value matrix of the cable force scheme; Obtain the sum of squares of eccentricity during the first operating period and the sum of cubic stress exceeding the limit during the first construction period for the individual cable force schemes; and obtain the sum of squares of eccentricity during the second operating period and the sum of cubic stress exceeding the limit during the second construction period for the individual cable force schemes. When the sum of squares of eccentricity during the first operating period is less than or equal to the sum of squares of eccentricity during the second operating period, and the sum of cubic stress exceeding the limit during the first construction period is less than or equal to the sum of cubic stress exceeding the limit during the second construction period, the first cable force scheme individual and the second cable force scheme individual are determined to be non-dominant. Furthermore, based on the non-dominance relationship, if the sum of squares of eccentricity during the first operating period is less than the sum of squares of eccentricity during the second operating period, or the sum of cubic stress exceeding the limit during the first construction period is less than the sum of cubic stress exceeding the limit during the second construction period, then it is determined that the first cable force scheme individual dominates the second cable force scheme individual.

10. The anchor cable force optimization method based on the improved second-generation genetic algorithm according to claim 6, characterized in that, The specific execution method of the crossover operation is as follows: Randomly select the first parent binary Gray code encoding sequence and the second parent binary Gray code encoding sequence from the Gray code encoding population; Obtain the sequence length of the first parent binary Gray code encoded sequence, and generate a random integer within the sequence length range as the intersection point; All gene segments following the crossover point of the first parent binary Gray code sequence are exchanged with all gene segments following the crossover point of the second parent binary Gray code sequence; The portion of the first parent binary Gray code sequence before the crossover point is recombined with the exchanged second parent gene fragment to generate the first offspring numerical sequence. The portion of the second parent binary Gray code sequence before the crossover point is recombined with the exchanged first parent gene fragment to generate the second offspring numerical sequence.

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