Multi-target matrix optimization method and device based on dynamic boundary constraint

Abstract

The invention relates to the technical field of data processing and analysis, and particularly provides a multi-target matrix optimization method and device based on dynamic boundary constraint, and the method comprises the following steps: S1, constructing a multi-target matrix optimization model; s2, constructing a weight-adjustable objective function system; s3, establishing a dynamic boundary constraint system; s4, constructing a three-level constraint priority mechanism; s5, introducing a zero value safety processing and relative error calculation mechanism; s6, a constraint optimization solution strategy based on SLSQP is adopted; and S7, outputting an optimization result and evaluating a business effect. Compared with the prior art, conflicts can be avoided through hierarchical control, algorithm crash is avoided, and the service priority problem under multi-constraint conflicts is solved.

Description

Technical Field

[0001] This invention relates to the field of data processing and analysis technology, specifically providing a method and apparatus for multi-objective matrix optimization based on dynamic boundary constraints. Background Technology

[0002] In the field of sales resource allocation and operations optimization, multi-objective matrix optimization problems are widely found in sales allocation scenarios in industries such as fast-moving consumer goods, tobacco, and retail. These problems require solving a sales allocation matrix in the dimension of "province × product specification" based on known data such as total national sales volume, total sales revenue, sales volume of each product specification, and sales volume of each province. Essentially, it is a constrained nonlinear optimization problem.

[0003] Application No. 202411544289.3 discloses a method and related apparatus for energy management of distribution substations, comprising: obtaining the type of distribution substation, and based on the fuzzy controller corresponding to the type of distribution substation, obtaining the coefficients of each objective function of the multi-objective optimization function of the distribution substation; and solving the multi-objective optimization function of the distribution substation based on the coefficients of each objective function of the multi-objective optimization function of the distribution substation to obtain the multi-objective optimization strategy of the distribution substation. It can use fuzzy control logic to adaptively optimize the weights of the objective function according to different scenarios, making the final multi-objective optimization function of the distribution substation more closely match the actual situation of the current distribution substation, realizing multi-objective collaborative optimization for different scenarios, refining the energy management strategy of the distribution substation, improving the power system operating efficiency and stability of the distribution substation, and effectively achieving comprehensive collaborative optimization of various optimization objectives such as energy saving, emission reduction, and economic efficiency.

[0004] In the above comparison schemes, the constraints are static physical limitations (such as energy storage power limitations and energy balance), and the variable boundaries (such as distributed energy output) are fixed by the equipment parameters, without considering dynamic changes in the data volume. Summary of the Invention

[0005] This invention addresses the shortcomings of the prior art by providing a highly practical multi-objective matrix optimization method based on dynamic boundary constraints.

[0006] A further technical objective of this invention is to provide a reasonably designed, safe, and applicable device for multi-objective matrix optimization based on dynamic boundary constraints.

[0007] The technical solution adopted by this invention to solve its technical problem is:

[0008] The multi-objective matrix optimization method based on dynamic boundary constraints has the following steps:

[0009] S1. Construct a multi-objective matrix optimization model;

[0010] S2. Construct an objective function system with adjustable weights;

[0011] S3. Establish a dynamic boundary constraint system;

[0012] S4. Construct a three-level constraint priority mechanism;

[0013] S5. Introduce zero-value safety handling and relative error calculation mechanism;

[0014] S6. Adopt a constraint optimization solution strategy based on SLSQP;

[0015] S7. Output optimization results and evaluate business effectiveness.

[0016] Furthermore, in step S1, the sales object is first defined as a two-dimensional decision matrix, where rows represent different provinces, columns represent different cigarette brands, and matrix elements represent the sales volume of each brand in each province. Based on the known data, three core sets are constructed: the task requirement matrix, the variable set, and the constant set.

[0017] These matrices and sets serve as inputs to the optimization problem, forming the basis for variable dimensions, structure, and constraint relationships. By modeling national sales data as a multidimensional matrix optimization problem, which involves multiple provinces in space and multiple cigarette brands at the product level, a two-dimensional matrix model is constructed: rows represent provinces, columns represent brands, and elements represent corresponding sales.

[0018] Define the following matrix and three core sets:

[0019] Task requirement matrix definition:

[0020]

[0021] Where n and s represent the number of rows and columns, respectively, and a ij This represents the quantity of product j sold in province i (i = 1, 2, ..., n; j = 1, 2, ..., s);

[0022] Variable set:

[0023] X={x ij |i=1,2,L,q; i=1,2,L,p; q≤n,p≤s};

[0024] Where, x i,j Let q represent the decision variables to be optimized, q represent the total number of variables in each row, and p represent the total number of variables in each row.

[0025] Set of constants:

[0026] C = {c tr |t=1,2,L,l; r=1,2,L,u; l≤n,u≤s};

[0027] The provinces in the country are represented by N:

[0028] N = {N1, N2, N3, ..., N} i L,N n};

[0029] Where 0≤i≤n, N i N represents the i-th province. n This represents the nth province;

[0030] Cigarette specifications are represented by the letter 'S':

[0031] S = {S1, S2, S3, L, S} j L,S s};

[0032] Where 0≤j≤s, S j S represents the j-th type of cigarette. s This refers to the s-th type of cigarette.

[0033] Among them, c tr Let l represent the constants that remain unchanged in matrix M, l represent the total number of constants in each row, and u represent the total number of constants in each column;

[0034] Step S1 formally transforms the actual allocation problem into a standard multi-objective optimization model with a clear objective function and constraints.

[0035] Furthermore, in step S2, the objective function is composed of two weighted components: "row sum error," which is the difference between the total sales volume of each province and the actual difference, and "column sum error," which is the difference between the total sales volume of each product specification and the actual difference.

[0036] By introducing weighting coefficients α and β, the degree of influence of each on the overall objective can be dynamically adjusted.

[0037] Assume the objective function is:

[0038]

[0039] in, Let the sum of the i-th row of matrix M be denoted as . This represents the sum of the j-th column of matrix M. α and β represent the relaxation weighting coefficients.

[0040] In the objective function: Objective function = α × (column sum error) + β × (row sum error).

[0041] Furthermore, in step S3, dynamic boundary constraints are introduced, and a seven-segment boundary function is designed to provide differentiated boundary control for variables of different magnitudes.

[0042] The dynamic boundary constraints:

[0043]

[0044] Boundary function definition:

[0045]

[0046] Hard constraints on indicators:

[0047] Nonnegativity constraint:

[0048] By setting adaptive upper and lower bounds for each optimization variable and dynamically adjusting the boundary range, the algorithm is guided to search within a reasonable range, avoiding convergence difficulties or invalid solutions caused by unbounded variables.

[0049] Furthermore, in step S4, the first level is the business indicator tolerance constraint, which is a non-linear hard constraint;

[0050] The second level is dynamic boundary constraint, which belongs to structural boundary control. It is used to limit the variable search space and ensure the physical rationality of the result.

[0051] The third level is the row and column matching degree and the error matching degree, which is embedded in the objective function with a small weight to assist in the convergence of the optimization direction rather than a hard constraint.

[0052] Furthermore, in step S5, a "safety relative error" mechanism is introduced: when the true value is zero, it automatically switches to absolute error judgment, or a safety compensation term is introduced into the denominator.

[0053] Furthermore, in step S6, an optimization algorithm based on SLSQP is used to iteratively update variables. The algorithm transforms the original nonlinear constraint optimization problem into a series of quadratic programming subproblems, and uses the gradient information of the current iteration point and the Hessian matrix approximation to construct a local quadratic model and determine the search direction.

[0054] Subsequently, a line search or trust region strategy is used to update variable values, considering all hard constraints, boundary conditions, and objective function values ​​in each iteration until the convergence condition is met.

[0055] Furthermore, in step S7, after the optimization process is completed, the system outputs the sales forecast results for each province and each product specification, and performs a series of performance evaluations and business indicator comparison analyses, including but not limited to: optimization convergence speed, optimization success rate, business indicator achievement rate, calculation time, and interpretability improvement.

[0056] An apparatus for multi-objective matrix optimization based on dynamic boundary constraints includes: at least one memory and at least one processor;

[0057] The at least one memory is used to store a machine-readable program;

[0058] The at least one processor is configured to call the machine-readable program to execute a multi-objective matrix optimization method based on dynamic boundary constraints.

[0059] Compared with existing technologies, the multi-objective matrix optimization method and apparatus based on dynamic boundary constraints of the present invention have the following outstanding advantages:

[0060] This invention, based on contexts such as variable magnitude and total quantity per province / product specification, differentiates the mapping between small-value variables (strictly relative boundaries) and large-value variables (emphasizing absolute boundaries), accurately adapting to data of multiple magnitudes from 10⁻³ to 10⁶. Simultaneously, it constructs a three-level priority system: business indicator tolerance → dynamic boundaries → row and column errors, forcibly ensuring core indicators (such as absolute sales error ≤ 1 million) and avoiding conflicts through layered control. Ultimately, it achieves multi-magnitude adaptation to dynamic boundaries, 100% compliance with business indicators, and a success rate exceeding 95% in optimizing complex scenarios, overcoming the bottleneck problems of multi-scenario adaptation and constraint conflicts.

[0061] The SLSQP constrained optimization algorithm is employed to decompose the nonlinear problem into quadratic programming subproblems. A local model is constructed using gradient / Hessian approximation, and iteration is accelerated through line search / trust region strategies, achieving optimization of 1000 variables in less than 5 minutes and fewer than 1000 iterations. Simultaneously, zero-value safety handling is introduced, automatically switching the absolute error or adding a compensation term ε upon encountering a zero value to prevent algorithm crashes. The combined effect of these two approaches results in a convergence success rate exceeding 98%.

[0062] A three-tiered constraint priority system is constructed: the first tier, "hard constraints on business metric tolerance" (e.g., absolute error in sales revenue ≤ 1 million), solidifies the bottom line for business operations; the second tier, "dynamic boundary structure constraints," limits the reasonable range of variables to ensure physical rationality; and the third tier, "soft constraints on row, column, and error," embeds weights into the objective function to assist convergence rather than impose hard limits. This layered strategy ensures that core objectives are met first, while retaining optimization flexibility, supporting "100% achievement of business metrics" and "success rate > 95% in complex scenarios," thus resolving the challenge of prioritizing business operations under multiple conflicting constraints. Attached Figure Description

[0063] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0064] Figure 1This is a time-series diagram of a multi-objective matrix optimization method based on dynamic boundary constraints;

[0065] Figure 2 This is a schematic diagram of the closed-loop state in a multi-objective matrix optimization method based on dynamic boundary constraints. Detailed Implementation

[0066] To enable those skilled in the art to better understand the present invention, the present invention will be further described in detail below with reference to specific embodiments. Obviously, the described embodiments are merely some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0067] The following is a preferred embodiment:

[0068] like Figure 1 , 2 As shown, the multi-objective matrix optimization method based on dynamic boundary constraints in this embodiment has the following steps:

[0069] S1. Construct a multi-objective matrix optimization model;

[0070] By decomposing and modeling the sales data as a multidimensional matrix optimization problem, a mathematical foundation is provided for subsequent calculations. First, the sales object is defined as a two-dimensional decision matrix, where rows represent different provinces, columns represent different cigarette brands, and matrix elements represent the sales volume of each brand in each province.

[0071] Based on the known data, three core sets are constructed: a task requirement matrix (representing the sales combinations to be derived), a variable set (the sales allocation variables to be optimized), and a constant set (used to constrain fixed data with constant totals, such as the sum of provincial sales or the national total). These matrices and sets serve as the input to the optimization problem, forming the basis for the variable dimensions, structure, and constraint relationships, and helping to formalize the original business requirements into a standard optimization problem.

[0072] By modeling national sales data as a multidimensional matrix optimization problem, a clear structure is provided for subsequent mathematical optimization. The sales data spatially involves multiple provinces and product-level involves multiple cigarette brands; therefore, a two-dimensional matrix model can be constructed: rows represent provinces, columns represent brands, and elements represent corresponding sales volumes. To achieve this structured modeling, the following three core sets are defined:

[0073] Task requirement matrix definition:

[0074]

[0075] Where n and s represent the number of rows and columns, respectively, and a ij This represents the quantity of product j sold in province i (i = 1, 2, ..., n; j = 1, 2, ..., s);

[0076] Variable set:

[0077] X={x ij |i=1,2,L,q; i=1,2,L,p; q≤n,p≤s};

[0078] Where, x i,j Let q represent the decision variables to be optimized, q represent the total number of variables in each row, and p represent the total number of variables in each row.

[0079] Set of constants:

[0080] C = {c tr |t=1,2,L,l; r=1,2,L,u; l≤n,u≤s};

[0081] The provinces in the country are represented by N:

[0082] N = {N1, N2, N3, ..., N} i L,N n};

[0083] Where 0≤i≤n, N i N represents the i-th province. n This represents the nth province;

[0084] Cigarette specifications are represented by the letter 'S':

[0085] S = {S1, S2, S3, L, S} j L,S s};

[0086] Where 0≤j≤s, S j S represents the j-th type of cigarette. s This refers to the s-th type of cigarette.

[0087] Among them, c tr Let l represent the constants that remain unchanged in matrix M, l represent the total number of constants in each row, and u represent the total number of constants in each column;

[0088] Step S1 formally transforms the actual allocation problem into a standard multi-objective optimization model with a clear objective function and constraints, providing a foundation for subsequent boundary constraints, objective function construction, and iterative solution.

[0089] S2. Construct an objective function system with adjustable weights;

[0090] Based on the model construction, a weight-adjusted objective function system is proposed, which allows the optimization process to flexibly balance different objectives.

[0091] Specifically, the objective function is composed of two weighted components: "row sum error" (the difference between the total sales volume of each province and the actual volume) and "column sum error" (the difference between the total sales volume of each product specification and the actual volume). By introducing weighting coefficients α and β, the influence of each component on the overall objective can be dynamically adjusted to achieve the following objectives: first, to control the priority of optimization direction (e.g., prioritizing product specification constraints); second, to enhance the numerical stability of the model and prevent a particular type of error from dominating the optimization objective; and third, to adapt to the different requirements for row and column precision in different industries or data scenarios. The design of this objective function ensures that the optimization result approximates the original data distribution as closely as possible while satisfying the constraints.

[0092] Specifically, the objective function is:

[0093]

[0094] in, Let represent the sum of the i-th row of matrix M (the actual row sum), i.e. This represents the sum of the j-th column (actual column sum) of matrix M. α and β represent the relaxation weight coefficients. In the objective function: Objective function = α × (column sum error) + β × (row sum error);

[0095] The purpose of introducing relaxation weight coefficients is to flexibly adjust the influence of row sum error and column sum error on the objective function during the optimization process, thereby achieving the importance ranking of constraints, improving the numerical stability of the model, and enhancing the model's adaptability to different business scenarios.

[0096] Specifically, the weighting coefficients can not only strengthen or weaken the constraint effect in a certain direction (such as province or product specification), but also clarify the optimization priority when there are multiple objectives conflicting, avoid a certain type of error dominating the overall optimization direction, and suppress the computational instability caused by data range or scale inconsistency, so that the model can converge to a reasonable solution more efficiently while satisfying the constraints.

[0097] S3. Establish a dynamic boundary constraint system;

[0098] To enhance the controllability and business feasibility of optimization variables, a dynamic boundary constraint system is introduced to set adaptive upper and lower limits for the optimization variables. This system generates variable boundaries through a nonlinear mapping method based on the initial estimate and context conditions of each variable, avoiding invalid or unreasonable extreme values.

[0099] Specifically, a seven-segment boundary function was designed to provide differentiated boundary control for variables of different magnitudes, enabling the optimization system to adapt to various sales models and data scales. Furthermore, the system allows the boundary range to automatically adjust based on business strategies or historical data, thereby improving the feasibility of the solution and its ultimate business implementation capability.

[0100] Dynamic boundary constraints:

[0101]

[0102] Boundary function definition:

[0103] lb(x0) = 0.5x0,

[0104] Hard constraints on indicators:

[0105] Nonnegativity constraint:

[0106] By setting adaptive upper and lower bounds for each optimization variable (sales volume of province × product specification), we avoid extreme values ​​in the optimization results that exceed business logic (such as abnormally high or low sales volume allocation), ensuring the feasibility of the solution. By dynamically adjusting the boundary range, we guide the algorithm to search within a reasonable range, avoiding convergence difficulties or invalid solutions caused by unbounded variables.

[0107] S4. Construct a three-level constraint priority mechanism;

[0108] To achieve effective coordination among multiple constraints, this step proposes a three-level constraint priority control mechanism to enable graded responses to hard and soft constraints.

[0109] The first level is the business indicator tolerance constraint, which is a non-linear hard constraint. It requires that conditions such as "the absolute error of total sales shall not exceed 1 million yuan" must be strictly met.

[0110] The second level is dynamic boundary constraint, which belongs to structural boundary control. It is used to limit the variable search space and ensure the physical rationality of the result.

[0111] The third level is the row and column matching degree and the error matching degree, which is embedded in the objective function with a small weight to assist in the convergence of the optimization direction rather than a hard constraint.

[0112] This hierarchical control structure ensures that when faced with complex and contradictory constraints, the system can prioritize meeting the most critical business objectives while retaining a certain degree of flexibility for numerical optimization, significantly improving the stability and accessibility of the knowledge space.

[0113] S5. Introduce zero-value safety handling and relative error calculation mechanism;

[0114] To ensure computational stability and model robustness, this step proposes a zero-value safety handling mechanism and an improved relative error calculation method.

[0115] In the error calculation process, if the true value of a certain dimension is zero, the conventional relative error algorithm will cause a division by zero anomaly or result in an abnormally amplified error weight.

[0116] To avoid this problem, a "safe relative error" mechanism is introduced: when the true value is zero, it automatically switches to absolute error judgment, or a safety compensation term (such as the smallest positive number ε) is introduced into the denominator, thereby avoiding algorithm crash.

[0117] The introduction of this mechanism greatly improves the stability of the model under extreme data scenarios and ensures the numerical continuity and rationality of the algorithm in the iterative solution process.

[0118] S6. Adopt a constraint optimization solution strategy based on SLSQP;

[0119] After the model, objective function, and constraint system are defined, the solution phase begins, employing an optimization algorithm based on SLSQP (Sequential Least Squares Programming) for iterative variable updates. This algorithm transforms the original nonlinear constrained optimization problem into a series of quadratic programming subproblems. Utilizing the gradient information at the current iteration point and the Hessian matrix approximation, a local quadratic model is constructed to determine the search direction. Subsequently, a line search or trust region strategy is used to update the variable values.

[0120] In each iteration, all hard constraints, boundary conditions, and objective function values ​​are considered simultaneously until the convergence condition is met. SLSQP has excellent handling capabilities for nonlinear constraints and can obtain stable and interpretable solutions in a relatively small number of iterations, making it particularly suitable for optimization problems with complex boundaries and rigid business requirements, as exemplified by this solution.

[0121] S7. Output optimization results and evaluate business effectiveness;

[0122] After the optimization process is completed, the system outputs the sales forecast results for each province and each product specification, and performs a series of performance evaluations and business indicator comparison analyses. These include, but are not limited to: optimization convergence speed (e.g., whether the number of iterations is less than 1000), optimization success rate (>98%), business indicator achievement rate (100%), computation time (e.g., the problem of thousands of variables is completed in less than 5 minutes under a standard PC), and interpretability improvement (e.g., variable changes conform to boundary reasoning logic), etc.

[0123] These results are not only used to evaluate the effectiveness of the algorithm, but also to provide data support for subsequent business decisions. At the same time, by using indicators to provide feedback, key parameters such as boundary setting and weight allocation can be optimized in reverse to achieve the system's closed-loop optimization capability.

[0124] Based on the above method, the apparatus for multi-objective matrix optimization based on dynamic boundary constraints in this embodiment includes: at least one memory and at least one processor.

[0125] The at least one memory is used to store a machine-readable program;

[0126] The at least one processor is configured to call the machine-readable program to execute a multi-objective matrix optimization method based on dynamic boundary constraints.

[0127] The above-described specific embodiments are merely specific examples of the present invention. The patent protection scope of the present invention includes, but is not limited to, the above-described specific embodiments. Any technical solution that conforms to the above-described specific embodiments of the present invention and any appropriate changes or substitutions made by those skilled in the art should fall within the patent protection scope of the present invention.

[0128] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A multi-objective matrix optimization method based on dynamic boundary constraints, characterized in that, It has the following steps: S1. Construct a multi-objective matrix optimization model; S2. Construct an objective function system with adjustable weights; S3. Establish a dynamic boundary constraint system; S4. Construct a three-level constraint priority mechanism; S5. Introduce zero-value safety handling and relative error calculation mechanism; S6. Adopt a constraint optimization solution strategy based on SLSQP; S7. Output optimization results and evaluate business effectiveness.

2. The multi-objective matrix optimization method based on dynamic boundary constraints according to claim 1, characterized in that, In step S1, the sales object is first defined as a two-dimensional decision matrix, where rows represent different provinces, columns represent different cigarette brands, and matrix elements represent the sales volume of each brand in each province. Based on the known data, three core sets are constructed: the task requirement matrix, the variable set, and the constant set. These matrices and sets serve as inputs to the optimization problem, forming the basis for variable dimensions, structure, and constraint relationships. By modeling national sales data as a multidimensional matrix optimization problem, which involves multiple provinces in space and multiple cigarette brands at the product level, a two-dimensional matrix model is constructed: rows represent provinces, columns represent brands, and elements represent corresponding sales. Define the following three core sets: Task requirement matrix definition: Where n and s represent the number of rows and columns, respectively, and a ij This represents the quantity of product j sold in province i (i = 1, 2, ..., n; j = 1, 2, ..., s); Variable set: X={x ij |i=1,2,L,q;i=1,2,L,p;q≤n,p≤s}; Where, x i,j Let q represent the decision variables to be optimized, q represent the total number of variables in each row, and p represent the total number of variables in each row. Set of constants: C={c tr |t=1,2,L,l;r=1,2,L,u;l≤n,u≤s}; The provinces in the country are represented by N: N={N1,N2,N3,L,N i L,N n }; Where 0≤i≤n, N i N represents the i-th province. n This represents the nth province; Cigarette specifications are represented by the letter 'S': S={S1,S2,S3,L,S j ,L,S s }; Where 0≤j≤s, S j S represents the j-th type of cigarette. s This refers to the s-th type of cigarette. Among them, c tr Let l represent the constants that remain unchanged in matrix M, l represent the total number of constants in each row, and u represent the total number of constants in each column; Step S1 formally transforms the actual allocation problem into a standard multi-objective optimization model with a clear objective function and constraints.

3. The multi-objective matrix optimization method based on dynamic boundary constraints according to claim 2, characterized in that, In step S2, the objective function is composed of two weighted components: "row sum error", which is the difference between the total sales volume of each province and the actual difference, and "column sum error", which is the difference between the total sales volume of each product specification and the actual difference. By introducing weighting coefficients α and β, the degree of influence of each on the overall objective can be dynamically adjusted. Assume the objective function is: in, Let the sum of the i-th row of matrix M be denoted as . This represents the sum of the j-th column of matrix M. α and β represent the relaxation weighting coefficients. In the objective function: Objective function = α × (column sum error) + β × (row sum error).

4. The multi-objective matrix optimization method based on dynamic boundary constraints according to claim 3, characterized in that, In step S3, dynamic boundary constraints are introduced, and a seven-segment boundary function is designed to provide differentiated boundary control for variables of different magnitudes. The dynamic boundary constraints: Boundary function definition: lb(x0)=0.5x0, Hard constraints on indicators: Nonnegativity constraint: By setting adaptive upper and lower bounds for each optimization variable and dynamically adjusting the boundary range, the algorithm is guided to search within a reasonable range, avoiding convergence difficulties or invalid solutions caused by unbounded variables.

5. The multi-objective matrix optimization method based on dynamic boundary constraints according to claim 4, characterized in that, In step S4, the first level is the business indicator tolerance constraint, which is a non-linear hard constraint; The second level is dynamic boundary constraint, which belongs to structural boundary control. It is used to limit the variable search space and ensure the physical rationality of the result. The third level is the row and column matching degree and the error matching degree, which is embedded in the objective function with a small weight to assist in the convergence of the optimization direction rather than a hard constraint.

6. The multi-objective matrix optimization method based on dynamic boundary constraints according to claim 5, characterized in that, In step S5, a "safety relative error" mechanism is introduced: when the true value is zero, it automatically switches to absolute error judgment, or a safety compensation term is introduced to the denominator.

7. The multi-objective matrix optimization method based on dynamic boundary constraints according to claim 6, characterized in that, In step S6, an optimization algorithm based on SLSQP is used to iteratively update variables. The algorithm transforms the original nonlinear constraint optimization problem into a series of quadratic programming subproblems. It uses the gradient information of the current iteration point and the Hessian matrix approximation to construct a local quadratic model and determine the search direction. Subsequently, a line search or trust region strategy is used to update variable values, considering all hard constraints, boundary conditions, and objective function values ​​in each iteration until the convergence condition is met.

8. The multi-objective matrix optimization method based on dynamic boundary constraints according to claim 7, characterized in that, In step S7, after the optimization process is completed, the system outputs the sales forecast results for each province and each product specification, and performs a series of performance evaluations and business indicator comparison analyses, including but not limited to: optimization convergence speed, optimization success rate, business indicator achievement rate, calculation time, and interpretability improvement.

9. A device for multi-objective matrix optimization based on dynamic boundary constraints, characterized in that, include: At least one memory and at least one processor; The at least one memory is used to store a machine-readable program; The at least one processor is configured to invoke the machine-readable program to perform the method according to any one of claims 1 to 8.

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