Global optimization solver construction method and system based on trust region method

Abstract

The invention discloses a method and system for constructing a global optimization solver based on a trust region method.The method comprises the steps that sequential quadratic programming and quadratic programming subproblem solving of equal constraints are achieved through a data structure and an algorithm module, so that the calculation efficiency of an algorithm is optimized; the step length is dynamically adjusted in the optimization process by using an interior point method, and the global search capability is improved; then, the system is divided into a data processing module, an algorithm implementation module, an architecture design module, a pre-processing module, a test case module, a third-party library calling module and the like through modular design, efficient cooperation of the modules is ensured, and redundant calculation is reduced; and finally, introducing a TikTak multi-starting-point optimization algorithm, generating an initial point which uniformly covers a parameter space through a Sobol'sequence, avoiding a local optimal solution, and improving the success rate of a global optimal solution, and according to the method, when high-dimension and complex optimization problems are processed, the calculation complexity is remarkably reduced, the global search capability is improved, and an efficient and stable optimization solution is provided.

Description

Technical Field

[0001] The present invention relates to the technical field of computer science and software engineering, and in particular to a global optimization solver construction method based on a trust region method, a global optimization solver system, and an application of the global optimization solver. Background Art

[0002] In the field of optimization, the research and application of solvers has become an important research direction. The current status of research on solvers for optimization problems at home and abroad shows that although the 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 an objective function through numerical calculations. Optimization solvers based on the trust region method are widely used in engineering, science, and finance. They can effectively handle non-convex optimization problems with multiple local extreme points, 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 challenging task. Optimizing and improving algorithms requires a deep mathematical foundation and extensive experimental verification, which increases the difficulty of algorithm development. Therefore, finding more effective algorithms and methods has become a key research direction in optimization solvers.

[0005] In the field of engineering modeling, complex operating conditions often lead to optimization stuck in local optima. Multi-start optimization algorithms, as global optimization algorithms with a high success rate, offer significant advantages. By optimizing and solving from multiple different starting points, multi-start optimization algorithms effectively avoid local optima, thereby improving the globality and reliability of the optimization results. This approach is particularly well-suited to the dynamic environments of industrial production, enabling the identification of optimal solutions under complex and changing conditions.

[0006] The trust region method is a numerical optimization method commonly used for nonlinear optimization problems. Its core concept is to gradually approach the optimal solution within a specific trust region. During the optimization process, the trust region method dynamically adjusts the optimization step size by comparing the actual improvement in the objective function with the improvement predicted by the model, thereby achieving efficient optimization. In addition to algorithms, modular development is also important in optimization solvers. Through modular development, the entire solver system can be divided into multiple modules, each responsible for a specific function, facilitating independent 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 the present invention

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

[0009] Compared to the commonly used classic gradient descent method, this method has faster local convergence and better overall convergence. By utilizing a quadratic model to determine the correction, the descent of the objective function is more efficient than with linear search methods. Furthermore, this method incorporates an improved algorithm, the tangent single broken line method, further improving computational efficiency.

[0010] Disadvantages of the prior art 1

[0011] Compared to the commonly used classic gradient descent method, although it has faster local convergence and more ideal overall convergence, it still has some problems. First, when this method uses a quadratic model to calculate the correction amount, it may increase the computational complexity, especially when processing large-scale data. Second, although the improved algorithm tangent single broken line method improves computational efficiency, it may still not reach the optimal solution in non-convex cases, which may lead to the problem of local optimal solution. Therefore, although the existing technology has certain advantages, there is still room for improvement and limitations. Summary of the Invention

[0012] In view of the defects of the prior art, the present invention provides a global optimization solver construction method and system based on the trust region method.

[0013] In order to achieve the above object of the invention, the technical solution adopted by the present invention is as follows:

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

[0015] S1. Data structure and algorithm module construction:

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

[0017] Use equality_constrained_sqp to implement the equality-constrained sequential quadratic programming algorithm, which is used for the core calculation of the optimization problem.

[0018] Design the qp_subproblem module to solve quadratic programming subproblems and provide the necessary subproblem solving support in the optimization algorithm.

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

[0020] Combined with the tr_interior_point module, the trust region interior point method is used to quickly find the optimal solution.

[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 properly 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 subsequent processing.

[0026] S4. Test case and application module construction:

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

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

[0029] S5. Third-party library call module construction:

[0030] Calling external libraries:

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

[0032] Implement the _constraints module and call the _constraints library to handle complex constraints, enhancing the versatility and flexibility of the solver.

[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 through the Sobol' sequence, and select the N* points with the lowest function values ​​as seed points.

[0035] Local search: Starting from each seed point, apply the trust region interior point method 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.

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

[0037] The present invention also discloses an application method of the global optimization solver, comprising the following steps:

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

[0039] Data preprocessing:

[0040] Use the _canonical_constraint module to canonicalize constraints.

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

[0042] Model relaxation and solution:

[0043] Using piecewise relaxation methods to deal with inequality optimization problems.

[0044] Solve the piecewise convex relaxation problem using a trust region interior point method.

[0045] Combine the multi-starting point global optimization strategy to find the global optimal solution.

[0046] Architecture design and solution:

[0047] Use the _minimize_constraint module to design the overall optimization solution architecture.

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

[0049] Tested and verified:

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

[0051] The global optimization solver is applied to a real industrial optimization problem for evaluation.

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

[0053] Data structure and algorithm module: responsible for establishing mathematical models of optimization problems and providing solution algorithms.

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

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

[0056] Components include: _minimize_constraint;

[0057] Pre-processing module: processes system input to ensure that the solver can accurately reflect the actual situation.

[0058] Components include: _canonical_constraint.

[0059] Test Cases and Application Modules: Write and execute test cases to verify solver performance and accuracy.

[0060] Components include: tests.

[0061] Third-party library call module: calls external libraries to provide additional functional support.

[0062] 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 a multi-starting point global optimization strategy to improve the global search capability.

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

[0065] The present invention also discloses a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the global optimization solver is realized.

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

[0067] 1. Reduced Computational Complexity: Through modular development and computational process optimization, this paper 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 computational process and reduces redundant calculations. This optimization reduces the computational complexity of high-dimensional problems and shortens the optimization solution time. Actual tests show that compared to general open source optimization solvers, this paper improves computational efficiency by approximately 20%.

[0068] 2. Improved Global Search Capabilities: By introducing the interior point method (tr_interior_point) and a multi-starting point algorithm, the algorithm's global search capabilities are significantly enhanced. These improvements more effectively avoid being trapped in local optima when dealing with problems with multiple local optimal solutions, thereby improving the global optimality of the final optimization result. Furthermore, this adjustment mechanism significantly reduces the difficulty of parameter adjustment and secondary development, enhancing the algorithm's intelligence and adaptability. This invention reduces the time required for parameter adjustment and secondary development by approximately 20%. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0071] Figure 3 3D graph and isoline graph of the Griewank function according to an embodiment of the present invention;

[0072] Figure 4 It is a three-dimensional graph and isoline graph of the Levi No.13 function according to an embodiment of the present invention. DETAILED DESCRIPTION

[0073] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and examples.

[0074] like Figure 1 As shown in Figure 1, the trust region method-based optimization solver is divided into the following modules: data structure and algorithm module, architecture design module, pre-processing module, test case and application module, and third-party library call module. These modules work together to achieve an efficient optimization solution process.

[0075] Through the combination and collaboration of the above modules, the optimization solver of the present 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 structure and algorithm module

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

[0078] Function description: This module is responsible for establishing the mathematical model of the optimization problem and providing a solution algorithm.

[0079] Specific functions:

[0080] equality_constrained_sqp: Implements the equality-constrained sequential quadratic programming algorithm, which is used for the core calculation of the optimization problem.

[0081] qp_subproblem: solves quadratic programming subproblems and provides the necessary subproblem solving support in optimization algorithms.

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

[0083] tr_interior_point: Combines the trust region interior 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) Pre-processing module

[0090] Includes: _canonical_constraint.

[0091] Function description: This module is used to process system input to ensure that the solver can accurately reflect the actual situation.

[0092] Specific functions:

[0093] _canonical_constraint: Normalizes the input constraints and converts them into a standard form for easy subsequent processing.

[0094] (4) Test cases and application modules

[0095] Includes: tests.

[0096] Function description: Used to write and execute test cases to verify solver performance and accuracy.

[0097] Specific functions:

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

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

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

[0101] Includes: _numdiff, _constraints.

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

[0103] Specific functions:

[0104] _numdiff: Calls the _numdiff library to perform numerical differential calculations and provide high-precision derivative information.

[0105] _constraints: Call the _constraints library to handle complex constraints and enhance the versatility and flexibility of the solver.

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

[0107] like Figure 2 As shown in the figure, TikTak belongs to the class of multi-starting point algorithms. These algorithms first select a point in parameter space and perform local optimization at that point until a local optimum is found. The algorithm then selects the next starting point and repeats the local optimization to find a new local optimum. This process is repeated multiple times. Ultimately, 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 to optimize in complex and uncertain environments.

[0108] Algorithm Process

[0109] 1. Global stage

[0110] Pre-test

[0111] First, the objective function is evaluated in the parameter space by quasi-random variables that are designed to cover the parameter space as evenly as possible. TikTak uses the Sobol' sequence [3] To generate these variables, due to their ideal properties in high-dimensional space. The specific steps are as follows:

[0112] Evaluate N Sobol' points: Generates and evaluates N Sobol' points in parameter space, computing the function value at each point.

[0113] Select N* seed points: From the N evaluated Sobol' points, 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, such as 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 optimal solution.

[0115] 2 Local Search

[0116] In the second step, the algorithm performs local searches from the selected N* seed points in sequence:

[0117] Perform local search from N* starting points: Starting from each seed point in turn, apply the local optimization algorithm to find the local optimal value

[0118] Select the next starting point: The starting point of the next local search is the next Sobol' seed point s j+1 The best minimum value found in the previous j local searches The specific formula is:

[0119]

[0120] Among them, θ j is a mixing weight that is chosen small in the early stages of the algorithm to allow a wide search of the parameter space, and gradually increases 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 , thereby exploring the most promising parts of the parameter space more thoroughly.

[0122] 3. Stop Condition

[0123] when When the absolute difference between the last two different values ​​of is small enough, the algorithm stops and returns the point with the lowest function value among all local optimal values ​​as the global optimal value.

[0124] in conclusion

[0125] The TikTak algorithm provides an effective method for finding the global optimal solution in uncertain and complex environments by combining extensive and intensive search in the parameter space. The algorithm uses the superior performance of the Sobol' sequence in high-dimensional space to ensure that the selection of the initial point is extensive and evenly covers the parameter space. At the same time, by adjusting the mixing weight θ j, which balances the breadth and depth of the search and improves the reliability and efficiency of the algorithm.

[0126] Next, we solve the Griewank function and Levi No.13 function to verify the efficiency and reliability of the optimization solver.

[0127] Griewank function:

[0128]

[0129] constraint:

[0130]

[0131] In this example, the parameter a is selected to be 200, and the focus of the study is defined within the hypercube x located in [-100, 100]. 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 a 3D view and as a contour plot. Semi-transparent areas in the 3D view represent regions that do not meet the definition criteria, while shaded areas in the contour plot meet them. Overall, the function exhibits a pronounced peaked shape due to the combined influence of the quadratic term and the definition criteria, with the minimum hidden in the valley. Furthermore, due to the cumulative effect of the cosine term, the function surface is dotted with numerous tiny fluctuations, which are particularly noticeable in the contour plot, forming numerous local minima. These local minima are represented in the figure as points within closed curves, and they are numerous. While these characteristics are already quite obvious in a two-dimensional plane, in three or higher dimensional spaces, the complexity of the function and the difficulty of visualizing its shape increase further.

[0132] Levi No.13 Function:

[0133]

[0134] constraint:

[0135]

[0136] The variable x in this embodiment has a domain of [-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 The figure shows the shape of the Levi function in a two-dimensional plane. The overall shape of the Levi function is similar to a bowl, so the location of the global minimum is easy to identify. However, the function has a series of deep valleys along the x2 axis, and there is a clear local minimum point in each valley. These valleys are Figure 4This is clearly demonstrated in the contour plot. Due to the dramatic change in function value from the edge of the valley to the bottom, the color changes in the contour plot are very concentrated. The narrow regions between the valleys are represented in the contour plot as vertical white stripes, pointing to lower objective function values. The larger white circle in the center marks the location of the global minimum, where the function shape is flatter, adding an additional challenge to finding the optimal solution.

[0137] By sampling 100 randomly selected initial points and implementing the same initialization conditions, a strict performance tolerance level of 10-6 is set for the success criterion of the algorithm. At the same time, to avoid infinite iterations, the maximum number of iterations is capped at 2000.

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

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

[0140] Local search: Starting from each seed point, apply the trust region interior point method 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.

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

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

[0143] Solution:

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

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

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

[0147] In this embodiment, the developed optimization solver is used to solve the Levi No. 13 function, and the results are as follows:

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

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

[0150] In summary, this embodiment fully demonstrates the efficiency and reliability of the optimization 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 practical examples, the developed solution algorithm demonstrated excellent performance. By utilizing a multi-starting point optimization algorithm and a trust region optimization algorithm, the overall solution success rate was significantly improved, avoiding local optimization traps. The algorithm achieved a 100% success rate in both test cases, fully demonstrating its significant advantage in global optimization. This result not only validates 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 are widely used in many fields, especially when dealing with optimization problems with complex constraints and non-convex objective functions. The following 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 designs are optimized to improve performance, reduce weight, or lower costs. Trust region methods can handle multiple constraints, such as strength, stability, and material limitations, ensuring that the design meets all engineering requirements.

[0155] Control system design: Optimize control system parameters to improve system stability and response speed. Trust region methods are used to handle complex nonlinear system models and constraints, ensuring that the designed controller performs well in real-world applications.

[0156] 2. Financial and Economic Modeling

[0157] Portfolio Optimization: In finance, portfolio optimization is the process of optimizing an investment portfolio to maximize returns and minimize risk. Trust region methods 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, formulating effective economic policies or market strategies through precise modeling and optimization.

[0159] 3. Machine Learning and Data Mining

[0160] Model parameter optimization: When training a machine learning model, optimize the algorithm's hyperparameters (such as the learning rate and regularization parameters) to improve the model's predictive performance. Trust region methods can handle complex loss functions and constraints, ensuring that the model performs well on a variety of 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. The trust region method can handle feature selection problems in high-dimensional data and ensure 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 maximize energy utilization and minimize environmental impact. Trust region methods can be used to handle complex energy demand forecasting and resource allocation models.

[0164] Environmental Monitoring and Management: In environmental science, optimizing environmental monitoring network layouts and pollution control strategies to achieve environmental protection goals is crucial. Trust region methods 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 their efficacy and safety. Trust region methods are used to process complex molecular models and optimization targets, 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] Robotic path planning: In robotic control and automation systems, optimizing the robot's path for efficient task execution. Trust region methods are used to handle complex motion models and environmental constraints, ensuring the robot can successfully navigate the real-world environment.

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

[0171] The global optimization solver of this invention not only has unique advantages in algorithm design and system construction, but also demonstrates excellent performance in practical applications. The global optimization solver can play an important role in many industrial fields, especially 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, rationally allocate resources, reduce logistics costs, and improve the overall efficiency of the supply chain.

[0174] 3. Energy management: optimize energy distribution and use, reduce energy consumption, and improve energy utilization.

[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] Establish a nonlinear optimization model based on actual needs.

[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] Use the _canonical_constraint module to normalize the input constraints and convert them into a standard form for easy subsequent processing.

[0182] Numerical differential calculations are performed through the _numdiff module to provide high-precision derivative information and ensure the accuracy of the optimization solution.

[0183] 3. Model relaxation and solution:

[0184] The piecewise relaxation method is used to relax the inequality optimization problem into an equality optimization problem.

[0185] The trust region interior point method (tr_interior_point module) is used to solve the convex relaxation problem on each segment to quickly find the local optimal solution.

[0186] Combined with the multi-starting point global optimization strategy, multiple initial points are generated and evaluated through the Sobol' sequence, and the best seed point is selected for local search to finally obtain the global optimal solution.

[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 and provide necessary subproblem solving support.

[0190] 5. Testing and Verification:

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

[0192] Apply the solver to real industrial optimization problems and evaluate its actual performance in production.

[0193] The global optimization solver of the present invention has the ability to handle complex nonlinear and non-convex optimization problems, provides high-precision derivative information and relaxation technology, and improves solution efficiency and accuracy. It supports multiple programming interfaces and platforms, which is convenient for application in different environments. The solver does not rely on initial values, avoids the initial value dependence problem of local optimal algorithms, theoretically guarantees global convergence, improves the reliability of solution results, can handle large-scale optimization problems, is suitable for practical industrial applications, and exhibits excellent performance in complex fields. These functions and advantages enable it to effectively solve complex nonlinear optimization problems, improve production efficiency and optimization effects, and provide strong technical support for various industrial production and management.

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

[0195] 1. Data structure and algorithm module

[0196] Function: Responsible for establishing the mathematical model of the optimization problem and providing the solution algorithm.

[0197] Components:

[0198] equality_constrained_sqp: Implements an equality-constrained sequential quadratic programming algorithm.

[0199] qp_subproblem: Solve a quadratic programming subproblem.

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

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

[0202] 2. Architecture design module

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

[0204] Component_minimize_constraint: Design and implement the overall optimization solution architecture.

[0205] 3. Pre-processing module

[0206] Function: Process system input to ensure that the solver can accurately reflect the actual situation.

[0207] Component_canonical_constraint: normalizes the input constraints.

[0208] 4. Test cases and application modules

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

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

[0211] 5. Third-party library call module

[0212] Function: Call external libraries to provide additional functional support.

[0213] Components:

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

[0215] _constraints: Handles complex constraints and enhances the versatility and flexibility of the solver.

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

[0217] Function: Introducing 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, which includes a processor and a memory, wherein the memory is used to store a computer program, the computer program includes program instructions, and the processor is used to execute the program instructions stored in the computer storage medium. The processor may be a central processing unit (CPU), or may be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc., which is the computing core and control core of the terminal, which is suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions to implement corresponding method processes or corresponding functions; the processor described in the embodiment of the present invention can be used to optimize the operation of the solver.

[0219] In another embodiment of the present invention, the present invention further provides a storage medium, specifically a computer-readable storage medium (Memory), which is a memory device in a terminal device for storing programs and data. It can be understood that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and, of course, the extended storage medium supported by the terminal device. The computer-readable storage medium provides a storage space, which stores the operating system of the terminal. In addition, one or more instructions suitable for being loaded and executed by the processor are also stored in the storage space. These instructions can be one or more computer programs (including program codes). It should be noted that the computer-readable storage medium here can be a high-speed RAM memory or a non-volatile memory, such as at least one disk memory.

[0220] One or more instructions stored in a computer-readable storage medium may be loaded and executed by a processor to implement the operations of the optimization solver in the above-mentioned embodiment; one or more instructions in a computer-readable storage medium may be loaded and executed by a processor.

[0221] It will be understood by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0222] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts 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, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0223] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0224] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0225] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the implementation methods of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific descriptions and embodiments. Those skilled in the art can make various other specific variations and combinations based on the technical teachings disclosed in the present invention without departing from the essence of the present invention, and such variations 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: The following steps are involved: S1. Data structure and algorithm module construction: Constructing a mathematical model for optimization problems: Use equality_constrained_sqp to implement the equality-constrained sequential quadratic programming algorithm for the core calculation of the optimization problem; Design the qp_subproblem module to solve the quadratic programming subproblem and provide the necessary subproblem solving support in the optimization algorithm; Implement the projections module to perform various projection operations to ensure that the solution is within the constraints; Combined with the tr_interior_point module, the trust region interior point method is used to quickly find the optimal solution; 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 properly under various constraints; S3. Construction of pre-processing module: Input processing: Implement the _canonical_constraint module to normalize the input constraints and convert them into a standard form for subsequent processing; S4. Test case and application module construction: Test case writing and execution: Write various test cases to cover functions and boundary conditions; Apply the solver to real problems and evaluate its applicability and stability; S5. Third-party library call module construction: Calling external libraries: Implement the _numdiff module, call the _numdiff library to perform numerical differential calculations, and provide high-precision derivative information; Implement the _constraints module and call the _constraints library to handle complex constraints, enhancing the versatility and flexibility of the solver.

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

3. The application method of the global optimization solver according to claim 1 or 2, characterized in that: include: Establish mathematical model: Establish nonlinear optimization model, including objective function and constraints; Data preprocessing: Use the _canonical_constraint module to normalize the constraints; use the numdiff module for numerical differentiation calculations; Model relaxation and solution: Use piecewise relaxation method to deal with inequality optimization problems; use trust region interior point method to solve piecewise convex relaxation problems; combine multi-starting point global optimization strategy to find the global optimal solution; Architecture design and solution: Use the _minimize_constraint module to design the overall optimization solution architecture; Use the qp_subproblem module to solve the quadratic programming subproblem; Testing and verification: Write test cases to verify the functionality and stability of the solver; The global optimization solver is applied to a real industrial optimization problem for evaluation.

4. A global optimization solver system, characterized in that: The system can be used to implement the global optimization solver described in claim 1 or 2, specifically including: Data structure and algorithm module: responsible for establishing mathematical models of optimization problems and providing solution algorithms; Components include: equality_constrained_sqp, qp_subproblem, projections, and tr_interior_point; Architecture design module: Design the overall optimization solver architecture to ensure efficient collaboration among various algorithms and modules; Components include: _minimize_constraint; Pre-processing module: processes system input to ensure that the solver can accurately reflect the actual situation; Components include: _canonical_constraint; Test Cases and Application Modules: Write and execute test cases to verify solver performance and accuracy; Components include: tests; Third-party library call module: calls external libraries to provide additional functional support; Components include: _numdiff and _constraints.

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 for introducing a multi-starting point global optimization strategy.

6. A computer device, characterized in that: The invention comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor implements the global optimization solver according to claim 1 or 2 when executing the program.

7. A computer-readable storage medium, characterized in that: A computer program is stored thereon, and when the program is executed by a processor, the global optimization solver according to claim 1 or 2 is implemented.

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