Cost income tradeoff analysis method based on improved population algorithm

Abstract

The invention discloses a cost income tradeoff analysis method based on an improved group algorithm. The method comprises the following steps: S1, generating an initial data set; s2, constructing a multi-objective optimization model according to the analysis requirements of the financial cost and the income; s3, performing population initialization based on statistical characteristics of the initial data set, and generating an initial search range and a solution set of an optimization algorithm through initialized individual distribution; s4, improving the global search capability of a hunter prey optimization algorithm, expanding the search range, preliminarily optimizing the optimization objective function in the global range, and updating the solution set according to the optimization objective function value; s5, optimizing the quality and convergence speed of the solution; s6, outputting an optimized final solution set; and S7, mapping the final solution set to a financial cost income analysis scene, and generating a multi-target tradeoff analysis result. The method is suitable for a complex and multi-target financial cost income trade-off analysis scene, and provides powerful technical support for enterprise financial management.

Description

Technical Field

[0001] The present invention relates to the field of financial technology, and in particular to a cost-benefit trade-off analysis method based on an improved group algorithm. Background Art

[0002] With the development of intelligent optimization algorithms, the financial field has gradually introduced intelligent tools to assist cost control and benefit evaluation. Financial cost-benefit trade-off analysis is a core issue in corporate financial management. The analysis results can directly affect the accuracy of resource allocation, budget allocation and benefit forecasting. In traditional financial optimization and analysis methods, there are still many technical difficulties in the balance analysis between cost and benefit.

[0003] At present, most companies and institutions still use methods based on static models or empirical decisions to conduct trade-off analysis on financial costs and benefits. Financial data is usually processed manually or through simple linear analysis models, and then decisions are made based on the experience of managers. Although traditional methods can meet the needs of some simple scenarios, they have significant limitations when faced with complex multi-objective financial scenarios.

[0004] In recent years, some intelligent optimization algorithms have begun to be applied in the field of financial analysis, such as optimization models based on genetic algorithms, particle swarm optimization, and ant colony algorithms. Intelligent optimization algorithms simulate natural group behavior to find the optimal solution, which improves the efficiency and accuracy of financial analysis to a certain extent. Existing intelligent optimization technologies have exposed the following problems in practical applications: First, most existing algorithms are general models, lacking specific optimization designs for financial scenarios, and are difficult to quickly converge to effective solutions under complex multi-objective conditions; second, the performance of many optimization algorithms significantly decreases when the data scale is large or the dynamic constraints change frequently, and cannot adapt to the real-time and dynamic requirements of financial data; third, existing intelligent optimization methods usually ignore the multi-level structural characteristics of financial data and cannot fully explore the potential correlation between data, resulting in a lack of depth and insight in the analysis results.

[0005] In summary, existing technologies have significant shortcomings when dealing with complex, multi-objective financial cost-benefit trade-off analysis, including static models, low efficiency, poor dynamic adaptability and insufficient intelligent optimization means. The defects of existing technologies directly affect the resource allocation efficiency and financial decision-making quality of enterprises. A new method is urgently needed to solve the above problems. Summary of the invention

[0006] One purpose of the present invention is to propose a cost-benefit trade-off analysis method based on an improved swarm algorithm. The present invention is applicable to complex, multi-objective financial cost-benefit trade-off analysis scenarios and provides powerful technical support for enterprise financial management.

[0007] A cost-benefit trade-off analysis method based on an improved swarm algorithm according to an embodiment of the present invention comprises the following steps:

[0008] S1. Obtain a multi-dimensional financial data set, pre-process the financial data set to generate a structured financial data set, and extract key parameters related to cost and benefit to generate an initial data set;

[0009] S2. Construct a multi-objective optimization model based on the analysis requirements of financial costs and benefits;

[0010] S3. Initialize the population based on the statistical characteristics of the initial data set, and generate the initial search range and solution set of the optimization algorithm through the initialized individual distribution;

[0011] S4. By improving the global search capability of the hunter-prey optimization algorithm, the search range is expanded, the optimization objective function is preliminarily optimized in the global range, and the solution set is updated according to the value of the optimization objective function;

[0012] S5. Based on the high potential solutions obtained in the exploration phase, narrow the search scope and conduct fine development to optimize the quality and convergence speed of the solution;

[0013] S6. Further optimize the local area based on the solution set optimized in the development phase, and output the optimized final solution set;

[0014] S7. Map the final solution set to the financial cost-benefit analysis scenario, generate multi-objective trade-off analysis results, and output optimized financial decision recommendations.

[0015] Optionally, the S1 includes the following steps:

[0016] S11. Obtain multi-dimensional financial data from the financial information system, and preliminarily organize the obtained multi-dimensional financial data to generate a financial data matrix:

[0017] M raw =[D c ,D r ,D a ,D k ];

[0018] Among them, D c Represents the time series data of historical financial costs, D r represents the time series data of historical returns, D a represents the resource allocation ratio or the set of budget allocation parameters, D k Represents a set of dynamic constraints;

[0019] S12. Preliminary sorting of financial data matrix M rawStatistical methods are used to eliminate abnormal data points that exceed the set range, and the financial data matrix is ​​normalized by minimum-maximum normalization to obtain a normalized financial data matrix;

[0020] S13. Use principal component analysis to reduce the dimension of the normalized financial data matrix and extract the main eigenvectors F related to cost and benefit pca , construct the initial data set for input optimization algorithm:

[0021] M input =[F pca,1 ,F pca,2 ,…,F pca,n ];

[0022] Among them, F pca,n It represents the nth extracted main feature vector, where n is the number of main features.

[0023] Optionally, S2 includes the following steps:

[0024] S21. According to the analysis requirements of financial costs and benefits, a dynamic weighted multi-objective optimization function is constructed to minimize the short-term financial cost objective function f c (x) and the long-term financial benefit maximization objective function f r (x) are dynamically combined into a unified objective function f total (x):

[0025] f total (x) = α(t)·f c (x)-β(t)·f r (x);

[0026] in, x i and x j represent the financial decision variables related to cost and benefit, respectively, c i represents the coefficient associated with the ith cost variable, r j represents the coefficient associated with the jth benefit variable, n and m represent the total number of cost and benefit variables, respectively, α(t) and β(t) represent dynamically adjusted weight functions, and t is the current time;

[0027] S22. Based on the actual needs of the financial field, define the dynamic budget constraint, return on investment fluctuation control constraint and cash flow stability constraint of the scenario:

[0028] Dynamic Budget Constraints:

[0029]

[0030] Where B(t) represents the dynamic budget value that changes with time;

[0031] ROI Fluctuation Control:

[0032]

[0033] Among them, σ R is the allowable fluctuation range of investment return rate, and R is the minimum return rate threshold;

[0034] Cash flow stability constraints:

[0035]

[0036] Among them, δ represents the maximum fluctuation rate of cash flow, f k (x) is the financial liquidity function within a preset time period;

[0037] S23. Decompose the multi-objective optimization model into two levels: short-term optimization and long-term optimization. Optimize the short-term objective function f according to the current budget and revenue situation. c (x), while meeting budget constraints and reducing the risk of cost fluctuations, and giving priority to allocating efficient resources, determine the short-term cost variable x i The best allocation plan:

[0038]

[0039] in, represents the time change rate of the i-th cost, which is used to evaluate the cost fluctuation in the short term. λ1 and λ2 are weight coefficients used to adjust the priority of cost volatility and budget constraints. B(t) represents the dynamic budget threshold, and γ is the budget pressure control parameter.

[0040] On the basis of achieving short-term goals, optimize the long-term objective function f r (x), maximize the long-term return variable x j Configuration ratio:

[0041]

[0042] Among them, σ j represents the volatility of the jth return variable, represents the rate of change of the return variable over time, μ1 and μ2 are weight coefficients used to control the priority of risk and return stability;

[0043] S24. Combine the short-term optimization and long-term optimization results to form an improved multi-objective optimization model

[0044] Among them, g k(x, t) represents the kth constraint, ensuring that the optimized solution meets the scenario requirements, and η is the penalty factor.

[0045] Optionally, S3 includes the following steps:

[0046] S31. According to the input data set M input and feature vectors, combined with the dynamic weighted multi-objective optimization function f total (x) expression, generating the initial solution P of the population init :

[0047] x i,0 =μ F,i +σ F,i ·Z i ,i=1,2,…,N;

[0048]

[0049] Among them, x i,0 is the initial position of the i-th individual in the population, x j,0 is the initial position of the jth individual in the population, μ F,i and σ F,i The eigenvectors F pca,i The mean and standard deviation of Z i is a random number generated from a standard normal distribution, f total (x i,0 ) Calculate the dynamic weighted objective function value through the initial solution to evaluate the quality of the initial solution;

[0050] S32. Combine the short-term optimization function and the long-term optimization function to optimize the distribution of hunters and prey in the population. Through the adaptive distribution optimization strategy, the hunter individuals tend to reduce the short-term cost, while the prey individuals tend to increase the long-term benefits, and adjust the initial position to x respectively. hunter,i and x prey,i :

[0051]

[0052]

[0053] Among them, x hunter,i and x prey,i Represent the optimized positions of hunter and prey individuals, λ h and λ p are adaptive learning rates, used for hunter and prey optimization respectively, and is the gradient of the objective function with respect to the individual position;

[0054] S33. Combine the optimized hunter and prey individuals to generate a complete population solution set Popt , and determine the initial search range R search :

[0055] P opt ={x hunter,i ,x prey,i |i=1,2,…,N};

[0056]

[0057] Optionally, S4 includes the following steps:

[0058] S41. According to the population solution set P opt , combined with the dynamic weighted multi-objective optimization function f total (x) gradient information, dynamically adjust the search step length Δx of the hunter and prey individuals hunter,i and Δx prey,i :

[0059]

[0060] Among them, η h and η p is the step size adjustment coefficient, corresponding to the hunter and prey respectively, and Provide individual search directions for the gradients of the short-term optimization objective function and the long-term optimization objective function to the position, ∈ h and ∈ p is the random perturbation coefficient, which is used to enhance the global search capability. i Random numbers generated for standard normal distribution;

[0061] S42. Update the positions of the hunter and prey according to the dynamically adjusted search step size and

[0062]

[0063] S43. In each iteration, the objective function values ​​corresponding to the updated positions of the hunter and prey individuals are calculated, and high potential solutions are recorded. The screening rule is:

[0064] x best =arg min(α(t)·f short (x,t)-β(t)·f long (x,t));

[0065] Among them, x best Indicates the solution with the best objective function value in the current iteration, recorded in the high potential solution set P high ;

[0066] S44. According to the high potential solution set Phigh Dynamic update solution set and search scope

[0067]

[0068] in, is the updated population solution set, including the current solution and high potential solution, is the updated search range for the next iteration.

[0069] Optionally, S5 includes the following steps:

[0070] S51. In the updated population solution set and search scope Based on the local analysis of the objective function, high potential solutions are screened out and the search range is narrowed to screen the highest potential solution set P focus The rules are:

[0071]

[0072] Among them, θ is the search range reduction factor, which is used to limit the proportion of high potential solutions;

[0073] Based on the highest potential solution set P focus Redefine the local search range R focus :

[0074]

[0075] Among them, R focus To narrow down the search scope;

[0076] S52. In the narrowed search range R focus Dynamically adjust the weight of the objective function to achieve a dynamic balance between cost and benefit;

[0077] S53. In the optimization process of high potential solutions, the global convergence ability is enhanced through information sharing and collaboration among hunters;

[0078] S54. By enhancing the avoidance mechanism of prey individuals near high potential solutions, we guide them to explore new solutions. Through avoidance updates, prey individuals avoid local extreme points, optimizing the diversity and global search ability of the population.

[0079] S55. Dynamically update the solution set P according to the optimized positions of the hunter and prey individuals developed and the local search range R developed .

[0080] Optionally, the S6 includes the following steps:

[0081] S61. Based on the updated solution set P developed and the local search range R developed , filter out the candidate solution set P in the local area candidate and the optimization range R candidate ;

[0082] S62. For the candidate solution set P candidate Perform a fine search in the local range, optimize the solution by introducing small adjustment operations, and update the solution position to:

[0083]

[0084] in, represents the position of the i-th candidate solution after optimization, ξ is the fine-tuning step size, which is used to control the adjustment amplitude of the solution. is the gradient of the objective function with respect to the position, which is used to guide the optimization direction, x best represents the optimal solution in the current local range, γ1 is the position similarity control parameter, which is used to limit the fine-tuning range of the solution;

[0085] S63. Determine the optimized solution based on the dynamic convergence criterion Whether the optimal conditions are met, the criterion formula is:

[0086]

[0087] Wherein, ∈1 is the gradient threshold, which is used to determine whether the objective function value has reached stability, and δ1 is the position difference threshold, which is used to determine whether the solution converges to the local optimal point. If the stop condition is met, the optimization ends and the current solution set is output; otherwise, return to step S62 to continue local optimization;

[0088] S64. When the dynamic convergence criterion is met, the optimized final solution set P is output final :

[0089]

[0090] Optionally, the S7 includes the following steps:

[0091] S71. Based on the final solution set obtained by optimization, the cost and benefit parameters of each solution are mapped to the financial scenario, combined with the actual financial cost indicators and benefit targets, to form a multi-objective trade-off result set for analysis, and the total cost value and total benefit value of each solution are extracted during the mapping process;

[0092] S72. Perform a multi-objective trade-off analysis on the mapping results to determine the relative relationship between the total cost value and the total benefit value in the solution set, generate a trade-off solution set that reflects the optimal cost-benefit balance relationship by screening the analysis results, and select solutions that meet both low cost and high benefit through trade-off analysis to form an optimal solution set that meets financial optimization requirements;

[0093] S73. Present the trade-off analysis results in a visual form;

[0094] S74. Based on the results of the multi-objective trade-off analysis, output optimization decision recommendations including the following:

[0095] The optimal resource allocation scheme optimizes resource allocation by selecting the scheme with a higher cost-benefit ratio than the preset one in the trade-off solution set;

[0096] Budget allocation strategy, providing budget recommendations based on the cost distribution of the optimal solution set;

[0097] Forecast future earnings and combine optimization results to provide earnings performance trends in dynamic financial scenarios.

[0098] The beneficial effects of the present invention are:

[0099] (1) The present invention significantly improves the algorithm's multi-objective optimization capability by constructing a dynamic weighted multi-objective optimization function and combining a multi-level optimization structure that minimizes short-term costs and maximizes long-term benefits. Traditional intelligent optimization algorithms usually optimize a single objective or a simple weighted objective with a fixed weight, which makes it difficult to take into account the dynamic balance between multiple conflicting objectives. The present invention adaptively adjusts the weight strategy to enable the algorithm to dynamically respond to changes in objective priorities in financial scenarios, thereby achieving an accurate balance between costs and benefits. By enhancing the collaboration mechanism between hunters and the avoidance mechanism of prey, the algorithm's search efficiency and global convergence capability are optimized, avoiding falling into the local optimum.

[0100] (2) The present invention introduces scenario-specific optimization constraints such as dynamic budget constraints, return on investment fluctuation control, and cash flow stability constraints in view of the dynamic changing characteristics of financial data, so that the algorithm can flexibly adapt to the needs of different financial scenarios. Compared with the fixed constraints of traditional static models, dynamic constraints can adjust the search scope and trade-off strategy in the optimization process in real time, so as to quickly generate the optimal solution that meets the current financial needs when the budget changes or the income fluctuates. Through the dynamic screening of population solutions and regional fine-tuning strategies, it demonstrates stronger adaptability and stability in dynamic financial scenarios, and the optimization results are more in line with actual business needs. BRIEF DESCRIPTION OF THE DRAWINGS

[0101] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0102] Figure 1 This is a flow chart of a cost-benefit trade-off analysis method based on an improved swarm algorithm proposed by the present invention. DETAILED DESCRIPTION

[0103] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, which only illustrate the basic structure of the present invention in a schematic manner, and therefore only show the components related to the present invention.

[0104] refer to Figure 1 , a cost-benefit trade-off analysis method based on an improved swarm algorithm, comprising the following steps:

[0105] S1. Obtain a multi-dimensional financial data set, pre-process the financial data set to generate a structured financial data set, and extract key parameters related to cost and benefit to generate an initial data set;

[0106] S2. Construct a multi-objective optimization model based on the analysis requirements of financial costs and benefits;

[0107] S3. Initialize the population based on the statistical characteristics of the initial data set, and generate the initial search range and solution set of the optimization algorithm through the initialized individual distribution;

[0108] S4. By improving the global search capability of the hunter-prey optimization algorithm, the search range is expanded, the optimization objective function is preliminarily optimized in the global range, and the solution set is updated according to the value of the optimization objective function;

[0109] S5. Based on the high potential solutions obtained in the exploration phase, narrow the search scope and conduct fine development to optimize the quality and convergence speed of the solution;

[0110] S6. Further optimize the local area based on the solution set optimized in the development phase, and output the optimized final solution set;

[0111] S7. Map the final solution set to the financial cost-benefit analysis scenario, generate multi-objective trade-off analysis results, and output optimized financial decision recommendations.

[0112] In this implementation, S1 includes the following steps:

[0113] S11. Obtain multi-dimensional financial data from the financial information system, and preliminarily organize the obtained multi-dimensional financial data to generate a financial data matrix:

[0114] M raw =[Dc ,D r ,D a ,D k ];

[0115] Among them, D c Represents the time series data of historical financial costs, D r represents the time series data of historical returns, D a represents the resource allocation ratio or the set of budget allocation parameters, D k Represents a set of dynamic constraints;

[0116] S12. Preliminary sorting of financial data matrix M raw Statistical methods are used to eliminate abnormal data points that exceed the set range, and the financial data matrix is ​​normalized by minimum-maximum normalization to obtain a normalized financial data matrix;

[0117] S13. Use principal component analysis to reduce the dimension of the normalized financial data matrix and extract the main eigenvectors F related to cost and benefit pca , construct the initial data set for input optimization algorithm:

[0118] M input =[F pca,1 ,F pca,2 ,…,F pca,n ];

[0119] Among them, F pca,n It represents the nth extracted main feature vector, where n is the number of main features.

[0120] In this implementation, S2 includes the following steps:

[0121] S21. According to the analysis requirements of financial costs and benefits, a dynamic weighted multi-objective optimization function is constructed to minimize the short-term financial cost objective function f c (x) and the long-term financial benefit maximization objective function f r (x) are dynamically combined into a unified objective function f total (x):

[0122] f total (x) = α(t)·f c (x)-β(t)·f r (x);

[0123] in, x i and x j represent the financial decision variables related to cost and benefit, respectively, c i represents the coefficient associated with the ith cost variable, r jrepresents the coefficient associated with the jth benefit variable, n and m represent the total number of cost and benefit variables, respectively, α(t) and β(t) represent dynamically adjusted weight functions, and t is the current time;

[0124] S22. Based on the actual needs of the financial field, define the dynamic budget constraint, return on investment fluctuation control constraint and cash flow stability constraint of the scenario:

[0125] Dynamic Budget Constraints:

[0126]

[0127] Where B(t) represents the dynamic budget value that changes with time;

[0128] ROI Fluctuation Control:

[0129]

[0130] Among them, σ R is the allowable fluctuation range of investment return rate, and R is the minimum return rate threshold;

[0131] Cash flow stability constraints:

[0132]

[0133] Among them, δ represents the maximum fluctuation rate of cash flow, f k (x) is the financial liquidity function within a preset time period;

[0134] S23. Decompose the multi-objective optimization model into two levels: short-term optimization and long-term optimization. Optimize the short-term objective function f according to the current budget and revenue situation. c (x), while meeting budget constraints and reducing the risk of cost fluctuations, and giving priority to allocating efficient resources, determine the short-term cost variable x i The best allocation plan:

[0135]

[0136] in, represents the time change rate of the i-th cost, which is used to evaluate the cost fluctuation in the short term. λ1 and λ2 are weight coefficients used to adjust the priority of cost volatility and budget constraints. B(t) represents the dynamic budget threshold, and γ is the budget pressure control parameter.

[0137] On the basis of achieving short-term goals, optimize the long-term objective function f r (x), maximize the long-term return variable x j Configuration ratio:

[0138]

[0139] Among them, σ j represents the volatility of the jth return variable, represents the rate of change of the return variable over time, μ1 and μ2 are weight coefficients used to control the priority of risk and return stability;

[0140] S24. Combine the short-term optimization and long-term optimization results to form an improved multi-objective optimization model

[0141] Among them, g k (x, t) represents the kth constraint, ensuring that the optimized solution meets the scenario requirements, and η is the penalty factor.

[0142] In this implementation, S3 includes the following steps:

[0143] S31. According to the input data set M input and feature vectors, combined with the dynamic weighted multi-objective optimization function f total (x) expression, generating the initial solution P of the population init :

[0144] x i,0 =μ F,i +σ F,i ·Z i ,i=1,2,…,N;

[0145]

[0146] Among them, x i,0 is the initial position of the i-th individual in the population, x j,0 is the initial position of the jth individual in the population, μ F,i and σ F,i The eigenvectors F pca,i The mean and standard deviation of Z i is a random number generated from a standard normal distribution, f total (x i,0 ) Calculate the dynamic weighted objective function value through the initial solution to evaluate the quality of the initial solution;

[0147] S32. Combine the short-term optimization function and the long-term optimization function to optimize the distribution of hunters and prey in the population. Through the adaptive distribution optimization strategy, the hunter individuals tend to reduce the short-term cost, while the prey individuals tend to increase the long-term benefits, and adjust the initial position to x respectively. hunter,i and x prey,i :

[0148]

[0149] Among them, x hunter,i and x prey,i Represent the optimized positions of hunter and prey individuals, λ h and λ p are adaptive learning rates, used for hunter and prey optimization respectively, and is the gradient of the objective function with respect to the individual position;

[0150] S33. Combine the optimized hunter and prey individuals to generate a complete population solution set P opt , and determine the initial search range R search :

[0151] P opt ={x hunter,i ,x prey,i |i=1,2,…,N};

[0152]

[0153] In this implementation, S4 includes the following steps:

[0154] S41. According to the population solution set P opt , combined with the dynamic weighted multi-objective optimization function f total (x) gradient information, dynamically adjust the search step length Δx of the hunter and prey individuals hunter,i and Δx prey,i :

[0155]

[0156] Among them, η h and η p is the step size adjustment coefficient, corresponding to the hunter and prey respectively, and Provide individual search directions for the gradients of the short-term optimization objective function and the long-term optimization objective function to the position, ∈ h and ∈ p is the random perturbation coefficient, which is used to enhance the global search capability. i Random numbers generated for standard normal distribution;

[0157] S42. Update the positions of the hunter and prey according to the dynamically adjusted search step size and

[0158]

[0159] S43. In each iteration, the objective function values ​​corresponding to the updated positions of the hunter and prey individuals are calculated, and high potential solutions are recorded. The screening rule is:

[0160] x best =argmin(α(t)·f short (x,t)-β(t)·f long (x,t));

[0161] Among them, x best Indicates the solution with the best objective function value in the current iteration, recorded in the high potential solution set P high ;

[0162] S44. According to the high potential solution set P high Dynamic update solution set and search scope

[0163]

[0164] in, is the updated population solution set, including the current solution and high potential solution, is the updated search range for the next iteration.

[0165] In this implementation, S5 includes the following steps:

[0166] S51. In the updated population solution set and search scope Based on the local analysis of the objective function, high potential solutions are screened out and the search range is narrowed to screen the highest potential solution set P focus The rules are:

[0167]

[0168] Among them, θ is the search range reduction factor, which is used to limit the proportion of high potential solutions;

[0169] Based on the highest potential solution set P focus Redefine the local search range R focus :

[0170]

[0171] Among them, R focus To narrow down the search scope;

[0172] S52. In the narrowed search range R focus Dynamically adjust the weight of the objective function to achieve a dynamic balance between cost and benefit;

[0173] S53. In the optimization process of high potential solutions, the global convergence ability is enhanced through information sharing and collaboration among hunters;

[0174] S54. By enhancing the avoidance mechanism of prey individuals near high potential solutions, we guide them to explore new solutions. Through avoidance updates, prey individuals avoid local extreme points, optimizing the diversity and global search ability of the population.

[0175] S55. Dynamically update the solution set P according to the optimized positions of the hunter and prey individuals developed and the local search range R developed .

[0176] In this implementation, S6 includes the following steps:

[0177] S61. Based on the updated solution set P developed and the local search range R developed , filter out the candidate solution set P in the local area candidate and the optimization range R candidate ;

[0178] S62. For the candidate solution set P candidate Perform a fine search in the local range, optimize the solution by introducing small adjustment operations, and update the solution position to:

[0179]

[0180] in, represents the position of the i-th candidate solution after optimization, ξ is the fine-tuning step size, which is used to control the adjustment amplitude of the solution. is the gradient of the objective function with respect to the position, which is used to guide the optimization direction, x best represents the optimal solution in the current local range, γ1 is the position similarity control parameter, which is used to limit the fine-tuning range of the solution;

[0181] S63. Determine the optimized solution based on the dynamic convergence criterion Whether the optimal conditions are met, the criterion formula is:

[0182]

[0183] Wherein, ∈1 is the gradient threshold, which is used to determine whether the objective function value has reached stability, and δ1 is the position difference threshold, which is used to determine whether the solution converges to the local optimal point. If the stop condition is met, the optimization ends and the current solution set is output; otherwise, return to step S62 to continue local optimization;

[0184] S64. When the dynamic convergence criterion is met, the optimized final solution set P is output final :

[0185]

[0186] In this implementation, S7 includes the following steps:

[0187] S71. Based on the final solution set obtained by optimization, the cost and benefit parameters of each solution are mapped to the financial scenario, combined with the actual financial cost indicators and benefit targets, to form a multi-objective trade-off result set for analysis, and the total cost value and total benefit value of each solution are extracted during the mapping process;

[0188] S72. Perform a multi-objective trade-off analysis on the mapping results to determine the relative relationship between the total cost value and the total benefit value in the solution set, generate a trade-off solution set that reflects the optimal cost-benefit balance relationship by screening the analysis results, and select solutions that meet both low cost and high benefit through trade-off analysis to form an optimal solution set that meets financial optimization requirements;

[0189] S73. Present the trade-off analysis results in a visual form;

[0190] S74. Based on the results of the multi-objective trade-off analysis, output optimization decision recommendations including the following:

[0191] The optimal resource allocation scheme optimizes resource allocation by selecting the scheme with a higher cost-benefit ratio than the preset one in the trade-off solution set;

[0192] Budget allocation strategy, providing budget recommendations based on the cost distribution of the optimal solution set;

[0193] Forecast future earnings and combine optimization results to provide earnings performance trends in dynamic financial scenarios.

[0194] The present invention significantly improves the multi-objective optimization capability of the algorithm by constructing a dynamic weighted multi-objective optimization function and combining a multi-level optimization structure that minimizes short-term costs and maximizes long-term benefits. Traditional intelligent optimization algorithms usually optimize single objectives or simple weighted objectives with fixed weights, and it is difficult to take into account the dynamic balance between multiple conflicting objectives. The present invention adaptively adjusts the weight strategy to enable the algorithm to dynamically respond to changes in target priorities in financial scenarios, thereby achieving an accurate balance between costs and benefits. By enhancing the collaboration mechanism between hunters and the avoidance mechanism of prey, the algorithm's search efficiency and global convergence capability are optimized, avoiding falling into local optimal situations.

[0195] In view of the dynamic changing characteristics of financial data, the present invention introduces scenario-specific optimization constraints such as dynamic budget restrictions, return on investment fluctuation control and cash flow stability constraints, so that the algorithm can flexibly adapt to the needs of different financial scenarios. Compared with the fixed constraints of traditional static models, dynamic constraints can adjust the search scope and trade-off strategy in the optimization process in real time, so as to quickly generate the optimal solution that meets the current financial needs in the event of budget changes or revenue fluctuations. Through dynamic screening of population solutions and regional fine-tuning strategies, it demonstrates stronger adaptability and stability in dynamic financial scenarios, and the optimization results are more in line with actual business needs.

[0196] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A cost-benefit trade-off analysis method based on an improved swarm algorithm, characterized in that: The steps include: S1. Obtain a multi-dimensional financial data set, pre-process the financial data set to generate a structured financial data set, and extract key parameters related to cost and benefit to generate an initial data set; S2. Construct a multi-objective optimization model based on the analysis requirements of financial costs and benefits; S3. Initialize the population based on the statistical characteristics of the initial data set, and generate the initial search range and solution set of the optimization algorithm through the initialized individual distribution; S4. By improving the global search capability of the hunter-prey optimization algorithm, the search range is expanded, the optimization objective function is preliminarily optimized in the global range, and the solution set is updated according to the value of the optimization objective function; S5. Based on the high potential solutions obtained in the exploration phase, narrow the search scope and conduct fine development to optimize the quality and convergence speed of the solution; S6. Further optimize the local area based on the solution set optimized in the development phase, and output the optimized final solution set; S7. Map the final solution set to the financial cost-benefit analysis scenario, generate multi-objective trade-off analysis results, and output optimized financial decision recommendations.

2. The cost-benefit trade-off analysis method based on the improved swarm algorithm according to claim 1, characterized in that: The S1 comprises the following steps: S11. Obtain multi-dimensional financial data from the financial information system, and preliminarily organize the obtained multi-dimensional financial data to generate a financial data matrix: M raw =[D c ,D r ,D a ,D k ]; Among them, D c Represents the time series data of historical financial costs, D r represents the time series data of historical returns, D a represents the resource allocation ratio or the set of budget allocation parameters, D k Represents a set of dynamic constraints; S12. Preliminary sorting of financial data matrix M raw Statistical methods are used to eliminate abnormal data points that exceed the set range, and the financial data matrix is ​​normalized by minimum-maximum normalization to obtain a normalized financial data matrix; S13. Use principal component analysis to reduce the dimension of the normalized financial data matrix and extract the main eigenvectors F related to cost and benefit pca , construct the initial data set for input optimization algorithm: M input =[F pca,1 ,F pca,2 ,…,F pca,n ]; Among them, F pca,n It represents the nth extracted main feature vector, where n is the number of main features.

3. The cost-benefit trade-off analysis method based on the improved swarm algorithm according to claim 1 is characterized in that: The S2 comprises the following steps: S21. According to the analysis requirements of financial costs and benefits, a dynamic weighted multi-objective optimization function is constructed to minimize the short-term financial cost objective function f c (x) and the long-term financial benefit maximization objective function f r (x) Dynamically combine into a unified objective function f total (x): f total (x)=α(t)·f c (x)-β(t)·f r (x); in, x i and x j represent the financial decision variables related to cost and benefit, respectively, c i represents the coefficient associated with the ith cost variable, r j represents the coefficient associated with the jth benefit variable, n and m represent the total number of cost and benefit variables, respectively, α(t) and β(t) represent dynamically adjusted weight functions, and t is the current time; S22. Based on the actual needs of the financial field, define the dynamic budget constraint, return on investment fluctuation control constraint and cash flow stability constraint of the scenario: Dynamic Budget Constraints: Where B(t) represents the dynamic budget value that changes with time; ROI Fluctuation Control: Among them, σ R is the allowable fluctuation range of investment return rate, and R is the minimum return rate threshold; Cash flow stability constraints: Among them, δ represents the maximum fluctuation rate of cash flow, f k (x) is the financial liquidity function within a preset time period; S23. Decompose the multi-objective optimization model into two levels: short-term optimization and long-term optimization. Optimize the short-term objective function f according to the current budget and revenue situation. c (x), while meeting budget constraints and reducing the risk of cost fluctuations, and giving priority to allocating efficient resources, determine the short-term cost variable x i The best allocation plan: in, represents the time change rate of the i-th cost, which is used to evaluate the cost fluctuation in the short term. λ1 and λ2 are weight coefficients used to adjust the priority of cost volatility and budget constraints. B(t) represents the dynamic budget threshold, and γ is the budget pressure control parameter. On the basis of achieving short-term goals, optimize the long-term objective function f r (x), maximize the long-term return variable x j Configuration ratio: Among them, σ j represents the volatility of the jth return variable, represents the rate of change of the return variable over time, μ1 and μ2 are weight coefficients used to control the priority of risk and return stability; S24. Combine short-term optimization and long-term optimization results to form an improved multi-objective optimization model Among them, g k (x, t) represents the kth constraint, ensuring that the optimized solution meets the scenario requirements, and η is the penalty factor.

4. The cost-benefit trade-off analysis method based on the improved swarm algorithm according to claim 1 is characterized in that: The S3 comprises the following steps: S31. According to the input data set M input and feature vectors, combined with the dynamic weighted multi-objective optimization function f total (x) expression, generating the initial solution P of the population init : x i,0 =μ F,i +s F,i ·Z i ,i=1,2,…,N; Among them, x i,0 is the initial position of the i-th individual in the population, x j,0 is the initial position of the jth individual in the population, μ F,i and σ F,i The eigenvectors F pca,i The mean and standard deviation of Z i is a random number generated from a standard normal distribution, f total (x i,0 ) Calculate the dynamic weighted objective function value through the initial solution to evaluate the quality of the initial solution; S32. Combine the short-term optimization function and the long-term optimization function to optimize the distribution of hunters and prey in the population. Through the adaptive distribution optimization strategy, the hunter individuals tend to reduce the short-term cost, while the prey individuals tend to increase the long-term benefits, and adjust the initial position to x respectively. hunter,i and x prey,i : Among them, x hunter,i and x prey,i Represent the optimized positions of hunter and prey individuals, λ h and λ p are adaptive learning rates, used for hunter and prey optimization respectively, and is the gradient of the objective function with respect to the individual position; S33. Combine the optimized hunter and prey individuals to generate a complete population solution set P opt , and determine the initial search range R search : P opt ={x hunter,i ,x prey,i ∣i=1,2,…,N}; 5. The cost-benefit trade-off analysis method based on improved swarm algorithm according to claim 1, characterized in that: The S4 comprises the following steps: S41. According to the population solution set P opt , combined with the dynamic weighted multi-objective optimization function f total (x) gradient information, dynamically adjust the search step length Δx of the hunter and prey individuals hunter,i and Δx prey,i : Among them, η h and η p is the step size adjustment coefficient, corresponding to the hunter and prey respectively, and Provide individual search directions for the gradients of the short-term optimization objective function and the long-term optimization objective function to the position, ∈ h and ∈ p is the random perturbation coefficient, which is used to enhance the global search capability. i Random numbers generated for standard normal distribution; S42. Update the positions of the hunter and prey according to the dynamically adjusted search step size and S43. In each iteration, the objective function values ​​corresponding to the updated positions of the hunter and prey individuals are calculated, and high potential solutions are recorded. The screening rule is: x best =arg min(α(t)·f short (x,t)-β(t)·f long (x,t)); Among them, x best Indicates the solution with the best objective function value in the current iteration, recorded in the high potential solution set P high ; S44. According to the high potential solution set P high Dynamic update solution set and search scope in, is the updated population solution set, including the current solution and high potential solution, is the updated search range for the next iteration.

6. The cost-benefit trade-off analysis method based on the improved swarm algorithm according to claim 1, characterized in that: The S5 comprises the following steps: S51. In the updated population solution set and search scope Based on the local analysis of the objective function, high potential solutions are screened out and the search range is narrowed to screen the highest potential solution set P focus The rules are: Among them, θ is the search range reduction factor, which is used to limit the proportion of high potential solutions; Based on the highest potential solution set P focus Redefine the local search range R focus : Among them, R focus To narrow down the search scope; S52. In the narrowed search range R focus Dynamically adjust the weight of the objective function to achieve a dynamic balance between cost and benefit; S53. In the optimization process of high potential solutions, the global convergence ability is enhanced through information sharing and collaboration among hunters; S54. By enhancing the avoidance mechanism of prey individuals near high potential solutions, we guide them to explore new solutions. Through avoidance updates, prey individuals avoid local extreme points, optimizing the diversity and global search ability of the population. S55. Dynamically update the solution set P according to the optimized positions of the hunter and prey individuals developed and the local search range R developed .

7. The cost-benefit trade-off analysis method based on the improved swarm algorithm according to claim 1 is characterized in that: The S6 comprises the following steps: S61. Based on the updated solution set P developed and the local search range R developed , filter out the candidate solution set P in the local area candidate and the optimization range R candidate ; S62. For the candidate solution set P candidate Perform a fine search in the local range, optimize the solution by introducing small adjustment operations, and update the solution position to: in, represents the position of the i-th candidate solution after optimization, ξ is the fine-tuning step size, which is used to control the adjustment amplitude of the solution. is the gradient of the objective function with respect to the position, which is used to guide the optimization direction, x best represents the optimal solution in the current local range, γ1 is the position similarity control parameter, which is used to limit the fine-tuning range of the solution; S63. Determine the optimized solution based on the dynamic convergence criterion Whether the optimal conditions are met, the criterion formula is: Wherein, ∈1 is the gradient threshold, which is used to determine whether the objective function value has reached stability, and δ1 is the position difference threshold, which is used to determine whether the solution converges to the local optimal point. If the stop condition is met, the optimization ends and the current solution set is output; otherwise, return to step S62 to continue local optimization; S64. When the dynamic convergence criterion is met, the optimized final solution set P is output final :

8. The cost-benefit trade-off analysis method based on the improved swarm algorithm according to claim 1 is characterized in that: The S7 comprises the following steps: S71. Based on the final solution set obtained by optimization, the cost and benefit parameters of each solution are mapped to the financial scenario, combined with the actual financial cost indicators and benefit targets, to form a multi-objective trade-off result set for analysis, and the total cost value and total benefit value of each solution are extracted during the mapping process; S72. Perform a multi-objective trade-off analysis on the mapping results to determine the relative relationship between the total cost value and the total benefit value in the solution set, generate a trade-off solution set that reflects the optimal cost-benefit balance relationship by screening the analysis results, and select solutions that meet both low cost and high benefit through trade-off analysis to form an optimal solution set that meets financial optimization requirements; S73. Present the trade-off analysis results in a visual form; S74. Based on the results of the multi-objective trade-off analysis, output optimization decision recommendations including the following: The optimal resource allocation scheme optimizes resource allocation by selecting the scheme with a higher cost-benefit ratio than the preset one in the trade-off solution set; Budget allocation strategy, providing budget recommendations based on the cost distribution of the optimal solution set; Forecast future earnings and combine optimization results to provide earnings performance trends in dynamic financial scenarios.

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