A method and system for constructing a global optimization solver based on a trust region method

Abstract

The application discloses a kind of construction method and system of global optimization solver based on trust region method, comprising: through data structure and algorithm module, sequence quadratic programming and quadratic programming subproblem solving of equality constraint are realized, to optimize the calculation efficiency of algorithm;Dynamic adjustment step in optimization process is carried out using interior point method, improve global search ability;Then, the system is divided into data processing, algorithm implementation, architecture design, pre-processing, test case, third-party library calling and other modules by modular design, ensure that each module is efficiently coordinated, reduce redundant calculation;Finally, introduce TikTak multi-start optimization algorithm, generate initial point by Sobol sequence Uniformly cover parameter space, avoid local optimal solution, improve the success rate of global optimal solution.The application significantly reduces the computational complexity when dealing with high-dimensional and complex optimization problems, improves the global search ability, and provides an efficient and stable optimization solution.

Description

Technical Field

[0001] This invention relates to the fields of computer science and software engineering, and in particular to a method for constructing a global optimization solver based on the trust region method, a global optimization solver system, and applications of the global optimization solver. Background Technology

[0002] In the field of optimization, the research and application of solvers has become an important research direction. The current state of research on optimization problem solvers both domestically and internationally indicates that while research on optimization solvers is relatively mature internationally, it started relatively late in China.

[0003] An optimization solver is a computational tool used to solve complex optimization problems, finding the optimal solution to the objective function through numerical computation. Optimization solvers based on the trust region method have wide applications in engineering, science, and finance, effectively handling non-convex optimization problems with multiple local extrema, improving the accuracy and efficiency of problem solving.

[0004] Due to the invisibility of algorithms within optimization solvers, developing and debugging them is often a highly challenging task. Algorithm optimization and improvement require a deep understanding of mathematical theory and extensive experimental verification, which increases the difficulty of algorithm development. Therefore, finding more efficient algorithms and methods has become one of the important directions in optimization solver research.

[0005] In engineering modeling, complex operating conditions often lead to optimization getting stuck in local optima. Multi-starting-point optimization algorithms, as highly successful global optimization algorithms, offer significant advantages. By optimizing from multiple different starting points, multi-starting-point optimization algorithms effectively avoid local optima, thus improving the globality and reliability of the optimization results. This method is particularly suitable for dynamically changing environments in industrial production, enabling the finding of better solutions under complex and variable conditions.

[0006] Trust region (TFR) is a numerical optimization method commonly used for nonlinear optimization problems. Its core idea is to gradually approximate the optimal solution within a specific trust region. During the optimization process, TFR dynamically adjusts the optimization step size by comparing the actual improvement of the objective function with the model's predicted improvement, thus achieving efficient optimization. Besides the algorithm, modular development is also crucial in optimization solvers. Through modular development, the entire solver system can be divided into multiple modules, each responsible for a specific function, facilitating individual development, testing, and maintenance. Modular development not only improves development efficiency but also facilitates the expansion and optimization of the solver system.

[0007] Prior art related to this invention

[0008] Chinese invention patent, application number: CN201611254005.2, title: A method for solving logistic regression analysis based on the tangent single-piece method using the trust region. This method utilizes the fitting function of linear regression and the function to construct a predictive fitting function, derives the cost function through maximum likelihood estimation, and then obtains the objective of the logistic regression analysis. Specific steps include constructing a trust region model subproblem, solving the trust region model subproblem using the tangent single-piece method, and obtaining the optimal numerical solution.

[0009] Compared to the commonly used classical gradient descent method, this method exhibits faster local convergence and more ideal overall convergence. By utilizing a quadratic model to calculate the correction, the descent of the objective function becomes more efficient than linear search methods. Furthermore, this method incorporates an improved tangent-single-line algorithm, further enhancing computational efficiency.

[0010] Disadvantages of existing technology 1

[0011] Compared to the commonly used classical gradient descent method, while it offers faster local convergence and more ideal overall convergence, it still has some drawbacks. First, using a quadratic model to calculate the correction factor can increase computational complexity, especially when dealing with large-scale data. Second, although the improved tangent-single-segment method enhances computational efficiency, it may still fail to reach the optimal solution in non-convex cases, potentially leading to local optima. Therefore, despite its advantages, this existing technique still has room for improvement and limitations. Summary of the Invention

[0012] To address the shortcomings of existing technologies, this invention provides a method and system for constructing a global optimization solver based on the trust region method.

[0013] To achieve the above-mentioned objectives, the technical solution adopted by the present invention is as follows:

[0014] A method for constructing a global optimization solver based on the trust region method includes the following steps:

[0015] S1. Construction of Data Structures and Algorithms:

[0016] Constructing a mathematical model for the optimization problem:

[0017] The equality_constrained_sqp algorithm is used to implement a sequential quadratic programming algorithm with equality constraints, which is used for the core computation of optimization problems.

[0018] The qp_subproblem module is designed to solve quadratic programming subproblems and provide necessary subproblem solving support in optimization algorithms.

[0019] Implement the `projections` module to perform various projection operations and ensure that the solution is within the constraints.

[0020] By combining the tr_interior_point module and using the in-trust region point method, the optimal solution can be found quickly.

[0021] S2, Architecture Design Module Construction:

[0022] Overall architecture design:

[0023] Implement the _minimize_constraint module, design and implement the overall optimization solution architecture, and ensure that the algorithm can work normally under various constraints.

[0024] S3, Pre-processing module construction:

[0025] Input processing: Implement the _canonical_constraint module to normalize the input constraints and convert them into a standard form for easier subsequent processing.

[0026] S4, Test Case and Application Module Construction:

[0027] Test case writing and execution: Write various test cases to cover functionality and boundary conditions.

[0028] Apply the solver to real-world problems and evaluate its applicability and stability.

[0029] S5, third-party library calling module construction:

[0030] Calling external libraries:

[0031] Implement the _numdiff module, call the _numdiff library to perform numerical differentiation calculations, and provide high-precision derivative information.

[0032] Implement the _constraints module, call the _constraints library to handle complex constraints, and enhance the solver's versatility and flexibility.

[0033] Furthermore, the global optimization solver also introduces a multi-starting-point global optimization strategy, including:

[0034] Pre-test: Generate and evaluate N initial points using the Sobol' sequence, and select the N* points with the lowest function values ​​as seed points.

[0035] Local search: Starting from each seed point, the in-trust-region point method is applied to find a local optimum. The starting point for the next local search is a convex combination of the current optimum and the next seed point.

[0036] Stopping condition: The algorithm stops when the absolute difference between two consecutive different values ​​is small enough, and returns the point with the lowest function value among all local optima as the global optimum.

[0037] This invention also discloses a method for applying the above-mentioned global optimization solver, including the following steps:

[0038] Establish a mathematical model: Establish a nonlinear optimization model, including the objective function and constraints.

[0039] Data preprocessing:

[0040] Use the _canonical_constraint module to normalize the constraints.

[0041] Use the numdiff module for numerical differentiation calculations.

[0042] Model relaxation and solution:

[0043] The piecewise relaxation method is used to handle inequality optimization problems.

[0044] The trust region in-point method is used to solve the convex relaxation problem on segments.

[0045] By combining a multi-starting-point global optimization strategy, the globally optimal solution can be found.

[0046] Architecture design and solution:

[0047] The overall optimization solution architecture is designed using the _minimize_constraint module.

[0048] Use the qp_subproblem module to solve quadratic programming subproblems.

[0049] Testing and Verification:

[0050] Write test cases to verify the solver's functionality and stability.

[0051] The global optimization solver was applied to evaluate a real-world industrial optimization problem.

[0052] This invention also discloses a global optimization solver system, which can be used to implement the above-mentioned global optimization solver, specifically including:

[0053] Data Structures and Algorithms Module: Responsible for building mathematical models of optimization problems and providing solution algorithms.

[0054] The components include: equality_constrained_sqp, qp_subproblem, projections, and tr_interior_point;

[0055] Architecture design module: Design the overall optimized solver architecture to ensure efficient collaboration among various algorithms and modules.

[0056] The components include: _minimize_constraint;

[0057] Preprocessing module: Processes system input to ensure that the solver can accurately reflect the actual situation.

[0058] The component includes: _canonical_constraint.

[0059] Test cases and application modules: Write and execute test cases to verify the solver's performance and accuracy.

[0060] The components include: tests.

[0061] Third-party library calling module: Calls external libraries to provide additional functionality support.

[0062] The components include: _numdiff and _constraints.

[0063] Furthermore, the global optimization solver system also includes a multi-starting-point global optimization strategy module, which is used to introduce multi-starting-point global optimization strategies to improve global search capabilities.

[0064] The present invention also discloses a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the aforementioned global optimization solver when executing the program.

[0065] The present invention also discloses a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the aforementioned global optimization solver.

[0066] Compared with the prior art, the advantages of the present invention are as follows:

[0067] 1. Reduced Computational Complexity: Through modular development and optimized computational processes, this invention significantly improves the computational efficiency of the trust region method. The implementation of `equality_constrained_sqp` and `qp_subproblem` in the data structure and algorithm modules optimizes the computation process and reduces redundant calculations. This optimization reduces the computational complexity when dealing with high-dimensional problems and shortens the optimization solution time. Actual tests show that compared to general open-source optimization solvers, the computational efficiency of this invention is improved by approximately 20%.

[0068] 2. Enhanced Global Search Capability: By introducing the interior-point method (tr_interior_point) and a multi-starting-point algorithm, the global search capability of the algorithm is significantly improved. These improvements enable the algorithm to more effectively avoid getting trapped in local optima when dealing with problems with multiple local optima, thereby improving the global optimality of the final optimization result. Furthermore, this adjustment mechanism significantly reduces the difficulty of parameter tuning and secondary development, enhancing the algorithm's intelligence and adaptability. This invention reduces the time spent on parameter tuning and secondary development by approximately 20%. Attached Figure Description

[0069] Figure 1 This is a module relationship diagram of the optimization solver based on the trust region method in an embodiment of the present invention;

[0070] Figure 2 This is a diagram of the TikTak multi-launch algorithm according to an embodiment of the present invention;

[0071] Figure 3 These are three-dimensional plots and isoline plots of the Griewank function according to embodiments of the present invention;

[0072] Figure 4 This is a three-dimensional graph and isoline graph of the Levi No. 13 function in an embodiment of the present invention. Detailed Implementation

[0073] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and examples.

[0074] like Figure 1 As shown, the optimization solver based on the trust region method consists of the following modules: data structure and algorithm module, architecture design module, preprocessing module, test case and application module, and third-party library calling module. These modules work together to achieve an efficient optimization solution process.

[0075] By combining and collaborating the above modules, the optimization solver of this invention can effectively solve complex optimization problems, has good convergence and global search capabilities, and is suitable for various practical application scenarios.

[0076] (1) Data Structures and Algorithms Module

[0077] Includes: equality_constrained_sqp, qp_subproblem, projections, tr_interior_point.

[0078] Function Description: This module is responsible for establishing mathematical models of optimization problems and providing solution algorithms.

[0079] Specific functions:

[0080] equality_constrained_sqp: Implements a sequential quadratic programming algorithm with equality constraints, used for the core computation of optimization problems.

[0081] qp_subproblem: Solves quadratic programming subproblems, providing necessary subproblem solving support in optimization algorithms.

[0082] projections: Perform various projection operations to ensure that the solution is within the constraints.

[0083] tr_interior_point: Combines the trust region in-point method to quickly find the optimal solution.

[0084] (2) Architecture Design Module

[0085] Includes: _minimize_constraint.

[0086] Function Description: This module is used for overall architecture design to ensure that various algorithms and modules can collaborate efficiently.

[0087] Specific functions:

[0088] _minimize_constraint: Design and implement the overall optimization solution architecture to ensure that the algorithm can work properly under various constraints.

[0089] (3) Preprocessing module

[0090] Includes: _canonical_constraint.

[0091] Function Description: This module is used to process system inputs to ensure that the solver accurately reflects the actual situation.

[0092] Specific functions:

[0093] _canonical_constraint: Normalizes the input constraints, converting them into a standard form for easier subsequent processing.

[0094] (4) Test cases and application modules

[0095] Includes: tests.

[0096] Function Description: Used for writing and executing test cases to verify the solver's performance and accuracy.

[0097] Specific functions:

[0098] Write various test cases to cover functionality and boundary conditions.

[0099] Apply the solver to real-world problems and evaluate its applicability and stability.

[0100] (5) Third-party library calling module

[0101] Includes: _numdiff, _constraints.

[0102] Function Description: Calls external third-party libraries to provide additional functional support.

[0103] Specific functions:

[0104] _numdiff: Calls the _numdiff library to perform numerical differentiation calculations, providing high-precision derivative information.

[0105] _constraints: Call the _constraints library to handle complex constraints, enhancing the solver's versatility and flexibility.

[0106] Through the coordinated work of the above modules, this invention can achieve efficient solutions to complex optimization problems, with good performance and broad application prospects. It provides an efficient and stable solution for solving optimization problems, thereby significantly improving optimization efficiency and quality.

[0107] like Figure 2 As shown, TikTak belongs to the multi-starting-point algorithm class. This type of algorithm first selects a point in the parameter space and performs local optimization at that point until a local optimum is found. Then, the algorithm selects the next starting point and repeats the local optimization to find a new local optimum. This process is repeated many times. Finally, the algorithm returns the point with the lowest function value among all local optima as the global optimum. The TikTak algorithm is designed to balance reliability (high success rate) and efficiency (low computational cost), and it is optimized for complex and uncertain environments.

[0108] Algorithm process

[0109] 1. Global Phase

[0110] Pre-test

[0111] First, the objective function is evaluated in the parameter space using quasi-random variables designed to cover the parameter space as uniformly as possible. TikTak uses Sobol' sequences. [3] These variables are generated because of their ideal properties in high-dimensional space. The specific steps are as follows:

[0112] Evaluate N Sobol' points: Generate and evaluate N Sobol' points in the parameter space, and calculate the function value for each point.

[0113] Select N* seed points: From the N Sobol' points evaluated, select N* seed points (s1,...,sN*) with the lowest (optimal) function values. These seed points will serve as the initial points for the local search. Typically, N* is relatively small, for example, 1% to 10% of N.

[0114] Discard the remaining Sobol' points: discard the unselected Sobol' points because the regions they are located in are unlikely to contain the global optimum.

[0115] 2. Local search

[0116] The second step involves the algorithm performing a local search sequentially from the selected N* seed points:

[0117] Perform a local search from N* starting points: starting from each seed point, apply a local optimization algorithm to find the local optimum.

[0118] Choose the next starting point: The starting point for the next local search is the next Sobol's seed point s. j+1 Compared with the best minimum value found in the previous j local searches A convex combination. The specific formula is:

[0119]

[0120] Where, θ j It is a hybrid weighting method, where smaller values ​​are chosen in the early stages of the algorithm to broadly search the parameter space, and the values ​​are gradually increased as the algorithm progresses to focus the search on the region containing the best local minimum.

[0121] Adjust θ j As local search information accumulates, θ j Gradually increase the size to more thoroughly explore the most promising parts of the parameter space.

[0122] 3. Stopping conditions

[0123] when When the absolute difference between the last two distinct values ​​is sufficiently small, the algorithm stops and returns the point with the lowest function value among all local optima as the global optimum.

[0124] in conclusion

[0125] The TikTak algorithm provides an efficient method for finding the global optimum in uncertain and complex environments by combining extensive and dense searches in the parameter space. This algorithm leverages the superior performance of the Sobol' sequence in high-dimensional spaces to ensure that the initial points are selected extensively and uniformly cover the parameter space. Simultaneously, by adjusting the mixing weights θ... jThis balances the breadth and depth of the search, improving the reliability and efficiency of the algorithm.

[0126] The Griewank and Levi No.13 functions are then solved to verify the efficiency and reliability of the optimized solver.

[0127] Griewank function:

[0128]

[0129] constraint:

[0130]

[0131] In this embodiment, the selected parameter a is 200, and the focus of the study is defined within a hypercube where x lies in the range [-100, 100]^n. The global minimum of the function is x = (0, ..., 0), at which point the function value reaches f(0, ..., 0) = 1. Figure 3 The Griewank function is presented in both 3D views and contour plots. In the 3D view, semi-transparent areas represent regions that do not meet the boundary conditions, while shaded areas in the contour plot indicate that they do. Overall, the function exhibits a significant peak-like shape due to the combined influence of the quadratic term and the boundary conditions, with the minimum value hidden within the valleys. Simultaneously, due to the cumulative effect of the cosine term, the function's surface is covered with numerous tiny fluctuations, particularly noticeable in the contour plot, forming numerous local minima. These local minima are represented by points within closed curves in the plot, and are numerous in number. These characteristics are already quite evident in a two-dimensional plane; however, in three-dimensional or higher-dimensional spaces, the complexity of the function and the difficulty of visualizing its shape further increase.

[0132] Levi No.13 function:

[0133]

[0134] constraint:

[0135]

[0136] In this embodiment, the domain of the variable x is [-10, 10]^n. The global minimum of the function is located at x = (1, ..., 1), where the function value is f(1, ..., 1) = 1. Figure 4 This illustrates the shape of the Levi function in a two-dimensional plane. The overall shape of the Levi function resembles a bowl, making the location of the global minimum easily identifiable. However, the function has a series of deep valleys along the x2 axis, each containing a distinct local minimum. These valleys... Figure 4The contour plot clearly illustrates this. Because the function values ​​change drastically from the valley edges to the bottom, the color variations in the contour plot are very concentrated. Narrow regions between valleys are represented by vertical white stripes in the contour plot, pointing to lower objective function values. The larger white circle in the center marks the location of the global minimum; this region has a flatter function shape, adding an extra challenge to finding the optimal solution.

[0137] The algorithm samples 100 randomly selected initial points under the same initialization conditions. A strict performance tolerance of 10⁻⁶ is set for the algorithm's success, and to avoid infinite iterations, a maximum of 2000 iterations is defined.

[0138] To enhance global search capabilities, this embodiment also introduces the TikTak multi-starting point optimization algorithm. The specific process of this algorithm is as follows:

[0139] Pre-test: Generate and evaluate N initial points using the Sobol' sequence, and select the N* points with the lowest function values ​​as seed points.

[0140] Local search: Starting from each seed point, the in-trust-region point method is applied to find a local optimum. The starting point for the next local search is a convex combination of the current optimum and the next seed point.

[0141] Stopping condition: The algorithm stops when the absolute difference between two consecutive different values ​​is small enough, and returns the point with the lowest function value among all local optima as the global optimum.

[0142] By using the TikTak algorithm, this embodiment can effectively avoid local optima traps and enhance global optimization capabilities in high-dimensional and complex environments.

[0143] Solution results:

[0144] In this embodiment, the developed optimization solver was used to solve the Griewank function, and the results are as follows:

[0145] Global Minimum: Through optimization algorithm, the global minimum of the function was successfully found, located at x = (0,...,0), and the function value is f(0,...,0) = 1.

[0146] Robustness and reliability: The algorithm successfully found the global optimum in multiple experiments, verifying its robustness and reliability in handling high-dimensional and complex problems.

[0147] In this embodiment, the Levi No.13 function was solved using the developed optimization solver, and the results are as follows:

[0148] Global Minimum: Through optimization algorithm, the global minimum of the function was successfully found, located at x = (1,...,1), and the function value is f(1,...,1) = 0.

[0149] Robustness and reliability: The algorithm successfully found the global optimum in multiple experiments, verifying its robustness and reliability in handling high-dimensional and complex problems.

[0150] In summary, this embodiment demonstrates the efficiency and reliability of the optimized solver of the present invention by showing in detail the solution process and results of the Levi No.13 function and the Griewank function.

[0151] In the examples, the developed solution algorithm exhibits good performance. By employing multi-starting-point optimization and trust-region optimization algorithms, the overall success rate is significantly improved, avoiding local optimization traps. The algorithm achieved a 100% success rate in both test cases, fully demonstrating its significant advantages in global optimization. This result not only verifies the algorithm's robustness in handling high-dimensional and complex problems but also demonstrates its reliability and practicality in real-world applications.

[0152] Trust-region-based global optimization solvers have been widely applied in various fields, especially in dealing with optimization problems with complex constraints and non-convex objective functions. Below are some of the main application areas and their specific application scenarios:

[0153] 1. Engineering Design and Optimization

[0154] Structural optimization: In fields such as aerospace, automotive, and civil engineering, structural design is optimized to improve performance, reduce weight, or lower costs. The trust region method can handle a variety of constraints, such as strength, stability, and material limitations, ensuring that the design meets all engineering requirements.

[0155] Control system design: Optimizing the parameters of the control system to improve its stability and response speed. The trust region method is used to handle complex nonlinear system models and constraints, ensuring that the designed controller performs well in practical applications.

[0156] 2. Financial and Economic Modeling

[0157] Portfolio optimization: In finance, portfolio optimization aims to maximize returns and minimize risk. The trust region approach can handle complex risk constraints and return prediction models, helping investors find the optimal portfolio.

[0158] Economic forecasting and strategy optimization: used for economic policy formulation and market strategy optimization, to formulate effective economic policies or market strategies through accurate modeling and optimization.

[0159] 3. Machine Learning and Data Mining

[0160] Model parameter optimization: When training a machine learning model, optimizing the algorithm's hyperparameters (such as learning rate, regularization parameters, etc.) improves the model's predictive performance. Trust region methods can handle complex loss functions and constraints, ensuring that the model performs well on various datasets.

[0161] Feature selection: In data mining, the efficiency and accuracy of a model are improved by optimizing the selection of the most relevant features. Trust region methods can handle feature selection problems in high-dimensional data, ensuring the global optimality of the feature selection process.

[0162] 4. Energy and Environment

[0163] Energy system optimization: Optimizing energy production and distribution systems, such as power grids and renewable energy systems, to ensure maximum energy utilization and minimum environmental impact. The trust region method can be used to handle complex energy demand forecasting and resource allocation models.

[0164] Environmental monitoring and management: In environmental science, optimizing the layout of environmental monitoring networks and pollution control strategies is crucial for achieving environmental protection goals. The trust region method can handle complex environmental models and constraints, ensuring the effectiveness of optimization solutions.

[0165] 5. Biomedicine and Health

[0166] Drug design: Optimizing the structure and properties of drug molecules to improve drug efficacy and safety. Trust region methods are used to handle complex molecular models and optimization objectives, helping drug developers find the optimal drug formulation.

[0167] Medical image analysis: In medical image processing and analysis, image processing algorithms are optimized to improve diagnostic accuracy and image quality. Trust region methods can be used to process high-dimensional image data and complex analytical models.

[0168] 6. Automation and Robotics

[0169] Robot path planning: In robot control and automation systems, optimizing robot paths to achieve efficient task execution. Trust region methods are used to handle complex motion models and environmental constraints, ensuring that robots can navigate smoothly in real-world environments.

[0170] Manufacturing process optimization: Optimizing production line layout and manufacturing processes to improve production efficiency and product quality. The trust region method can handle various process constraints and optimization objectives, helping the manufacturing industry improve production capacity.

[0171] The global optimization solver of this invention not only possesses unique advantages in algorithm design and system construction, but also demonstrates superior performance in practical applications. The global optimization solver plays a crucial role in multiple industrial fields, particularly in complex nonlinear optimization problems, such as:

[0172] 1. Production Scheduling: Optimize the scheduling of production lines to ensure efficient operation of each production link and maximize output and efficiency.

[0173] 2. Supply Chain Management: Through global optimization, resources are rationally allocated to reduce logistics costs and improve the overall efficiency of the supply chain.

[0174] 3. Energy Management: Optimize energy allocation and use, reduce energy consumption, and improve energy efficiency.

[0175] 4. Chemical process optimization: In the chemical production process, optimize reaction conditions and process parameters to improve product quality and production efficiency.

[0176] Specific application steps

[0177] 1. Establish a mathematical model:

[0178] Based on actual needs, a nonlinear optimization model is established.

[0179] The model includes objective functions (such as cost minimization and profit maximization) and constraints (such as quality requirements and equipment capacity).

[0180] 2. Data preprocessing:

[0181] The _canonical_constraint module is used to normalize the input constraints, converting them into a standard form for easier subsequent processing.

[0182] The _numdiff module performs numerical differentiation calculations, providing high-precision derivative information to ensure the accuracy of the optimized solution.

[0183] 3. Model relaxation and solution:

[0184] By using a piecewise relaxation method, the inequality optimization problem is relaxed into an equality optimization problem.

[0185] The convex relaxation problem is solved on each segment using the trust region in-point method (tr_interior_point module), which quickly finds the local optimum.

[0186] By combining a multi-starting-point global optimization strategy, multiple initial points are generated and evaluated through the Sobol' sequence. The best seed point is selected for local search, and finally the global optimal solution is obtained.

[0187] 4. Architecture Design and Solution:

[0188] The overall optimization solution architecture is designed and implemented through the _minimize_constraint module to ensure that the algorithm works normally under various constraints.

[0189] The qp_subproblem module is used to solve quadratic programming subproblems, providing necessary support for solving subproblems.

[0190] 5. Testing and Verification:

[0191] Write various test cases to cover functionality and boundary conditions, and verify the applicability and stability of the solver.

[0192] The solver is applied to real-world industrial optimization problems to evaluate its performance in production.

[0193] This invention provides a global optimization solver capable of handling complex nonlinear and nonconvex optimization problems. It offers high-precision derivative information and relaxation techniques, improving both efficiency and accuracy. Supporting multiple programming interfaces and platforms, it facilitates application in various environments. This solver is independent of initial values, avoiding the initial value dependency problem of local optima algorithms. Theoretically, it guarantees global convergence, enhancing the reliability of the solution results. Capable of handling large-scale optimization problems, it is suitable for practical industrial applications, exhibiting particularly outstanding performance in complex domains. These features and advantages enable it to effectively solve complex nonlinear optimization problems, improve production efficiency and optimization effectiveness, and provide strong technical support for various industrial production and management processes.

[0194] In another embodiment of the present invention, a global optimization solver system is provided, which can be used to implement the above-described global optimization solver, specifically including:

[0195] 1. Data Structures and Algorithms Module

[0196] Function: Responsible for establishing mathematical models of optimization problems and providing solution algorithms.

[0197] Components:

[0198] equality_constrained_sqp: A sequential quadratic programming algorithm that implements equality constraints.

[0199] qp_subproblem: Solve a quadratic programming subproblem.

[0200] projections: Perform projection operations to ensure that the solution is within the constraints.

[0201] tr_interior_point: Combines the trust region in-point method to quickly find the optimal solution.

[0202] 2. Architecture Design Module

[0203] Function: Design an overall optimized solver architecture to ensure efficient collaboration among various algorithms and modules.

[0204] Component_minimize_constraint: Designs and implements the overall optimization solution architecture.

[0205] 3. Preprocessing module

[0206] Function: Processes system input to ensure that the solver accurately reflects the actual situation.

[0207] The component _canonical_constraint: performs normalization processing on the input constraints.

[0208] 4. Test cases and application modules

[0209] Function: Write and execute test cases to verify the solver's performance and accuracy.

[0210] Component tests: Write test cases, apply them to real-world problems, and evaluate the applicability and stability of the solver.

[0211] 5. Third-party library calling module

[0212] Functionality: Calls external libraries to provide additional functionality support.

[0213] Components:

[0214] _numdiff: Performs numerical differentiation calculations and provides high-precision derivative information.

[0215] _constraints: Handles complex constraints, enhancing the solver's versatility and flexibility.

[0216] 6. Multi-starting point global optimization strategy module

[0217] Function: Introduces a multi-starting-point global optimization strategy to improve global search capabilities.

[0218] In another embodiment of the present invention, a terminal device is provided, comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions to achieve a corresponding method flow or corresponding function. The processor described in this embodiment can be used to optimize the operation of the solver.

[0219] In another embodiment of the present invention, a storage medium is provided, specifically a computer-readable storage medium (Memory). This computer-readable storage medium is a memory device in a terminal device used to store programs and data. It is understood that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and extended storage media supported by the terminal device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, this storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more computer programs (including program code). It should be noted that the computer-readable storage medium here can be high-speed RAM or non-volatile memory, such as at least one disk storage device.

[0220] One or more instructions stored in a computer-readable storage medium can be loaded and executed by a processor to implement the operation of the optimization solver in the above embodiments; one or more instructions in the computer-readable storage medium are loaded and executed by a processor.

[0221] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0222] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0223] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0224] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0225] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the implementation methods of the present invention, and should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of the present invention.

Claims

1. A method for constructing a global optimization solver based on the trust region method, characterized in that, Includes the following steps: S1. Data Structure and Algorithm Module Construction: Constructing a mathematical model for the optimization problem: The equality-constrained sqp algorithm is used to implement a sequential quadratic programming algorithm for optimization problems. The qp_subproblem module is designed to solve quadratic programming subproblems and provide necessary subproblem solving support in optimization algorithms. Implement the projections module to perform various projection operations and ensure that the solution is within the constraints. By combining the tr_interior_point module and using the trust region in-point method, the optimal solution can be found quickly. S2, Architecture Design Module Construction: Overall architecture design: Implement the _minimize_constraint module, design and implement the overall optimization solution architecture, and ensure that the algorithm can work normally under various constraints; S3, Pre-processing module construction: Input processing: Implement the _canonical_constraint module to normalize the input constraints and convert them into a standard form for easier subsequent processing; S4, Test Case and Application Module Construction: Test case writing and execution: Write various test cases to cover functionality and boundary conditions; Apply the solver to a real-world problem and evaluate its applicability and stability; S5, third-party library calling module construction: Calling external libraries: Implement the _numdiff module, call the _numdiff library to perform numerical differentiation calculations, and provide high-precision derivative information; Implement the _constraints module, call the _constraints library to handle complex constraints, and enhance the solver's versatility and flexibility; In the trust region in-point method, the optimization step size is dynamically adjusted by comparing the actual improvement of the objective function with the model prediction improvement during the optimization process.

2. The global optimization solver construction method according to claim 1, characterized in that: It also introduces a multi-starting-point global optimization strategy, including: Pre-test: Generate and evaluate N initial points using the Sobol' sequence, and select the N* points with the lowest function values ​​as seed points; Local search: Starting from each seed point, the in-trust region method is applied to find the local optimum; the starting point of the next local search is the convex combination of the current optimum and the next seed point; Stopping condition: The algorithm stops when the absolute difference between two consecutive different values ​​is small enough, and returns the point with the lowest function value among all local optima as the global optimum.

3. The application method of the global optimization solver according to claim 1 or 2, characterized in that, include: Establish a mathematical model: Establish a nonlinear optimization model, including the objective function and constraints; Data preprocessing: The _canonical_constraint module is used to normalize the constraints; the numdiff module is used to perform numerical differentiation calculations. Model relaxation and solution: The piecewise relaxation method is used to handle inequality optimization problems; the trust region in-point method is used to solve convex relaxation problems on pieces; and a global optimal solution is found by combining a multi-starting point global optimization strategy. Architecture Design and Solution: The overall optimization solution architecture is designed using the _minimize_constraint module; Use the qp_subproblem module to solve quadratic programming subproblems; Testing and Verification: Write test cases to verify the solver's functionality and stability; The global optimization solver is applied to evaluate real-world industrial optimization problems, including converting optimization parameters into equipment control commands.

4. A global optimization solver system, characterized in that: This system can be used to implement the global optimization solver as described in claim 1 or 2, specifically including: Data Structures and Algorithms Module: Responsible for establishing mathematical models of optimization problems and providing solution algorithms; The components include: equality_constrained_sqp, qp_subproblem, projections, and tr_interior_point; Architecture design module: Design the overall optimized solver architecture to ensure efficient collaboration among various algorithms and modules; The components include: _minimize_constraint; Preprocessing module: processes system input to ensure that the solver can accurately reflect the actual situation; The components include: _canonical_constraint; Test cases and application modules: Write and execute test cases to verify the solver's performance and accuracy; The components include: tests; Third-party library calling module: Provides additional functionality support by calling external libraries; The components include: _numdiff and _constraints; An industrial control interface is used to convert optimization results into equipment control command outputs.

5. The global optimization solver system according to claim 4, characterized in that: The global optimization solver system also includes a multi-starting-point global optimization strategy module, which is used to introduce multi-starting-point global optimization strategies.

6. A computer device, characterized in that: It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the global optimization solver as described in claim 1 or 2.

7. A computer-readable storage medium, characterized in that: It stores a computer program that, when executed by a processor, implements the global optimization solver as described in claim 1 or 2.

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