Method and device for optimizing coupling coordination degree of complex system

Abstract

The application discloses a complex system coupling coordination degree optimization method and device, and the method comprises the following steps: acquiring a multilevel coupling parameter set in a complex system; screening a to-be-optimized parameter variable from the multilevel coupling parameter set to obtain a to-be-optimized parameter variable set; constructing a Bayesian statistical model; taking the Bayesian statistical model as a proxy model for describing a probability mapping relationship between a target function and a parameter variable; determining a sampling function; and iteratively optimizing the to-be-optimized parameter variable by using the Bayesian statistical model and the sampling function to obtain an optimized parameter. The application can improve the coupling coordination degree of the complex system and meet the requirements of stable operation and intelligent control of the complex system.

Description

Technical Field

[0001] This invention relates to the field of multi-objective optimization of complex systems, and specifically to a method and apparatus for optimizing the coupling coordination degree of complex systems. Background Technology

[0002] With the acceleration of urbanization and the deep integration of urban development and information technology, complex systems such as urban organisms exhibit heterogeneous characteristics of multi-subsystem collaboration and multi-element linkage. The optimal functioning and stable, sustainable evolution of these systems depend on the efficient exchange and coordinated operation of matter, energy, and information among the subsystems. Coupling coordination degree, as a core indicator for quantitatively describing the level of coordinated development of various elements and subsystems within a complex system, directly determines the stability, adaptability, and overall efficiency of the complex system through parameter optimization, and has significant application value in fields such as urban governance. Focusing on the coupling of urban transportation and energy systems, and addressing typical scenarios such as urban traffic congestion, there is an urgent need to optimize coupling coordination degree to improve the overall efficiency of complex urban systems.

[0003] Existing research often employs a full-chain approach of "sensing-transmission-knowledge-control" for modeling complex urban systems. This involves the perception stage, which collects physical data from traffic sensors and power grid loads; the transmission stage, which transforms the impact of perceived data on other subsystems; the knowledge stage, which characterizes the coupling logic between subsystems; and the control stage, which focuses on intervention strategy design and simulation evaluation. Among these, the coupling coordination degree of complex systems involves optimizing the coupling coordination parameters between subsystems. However, in practical implementation, it faces core challenges such as inefficient high-dimensional parameter optimization, imbalance in multi-objective coordination, and high evaluation costs. The parameters exhibit strong coupling and nonlinear correlations, making traditional optimization methods such as brute-force search and grid search inadequate for handling parameter combination explosion problems, easily leading to local optima and failing to achieve globally optimal parameter configuration. Summary of the Invention

[0004] This invention provides a method and apparatus for optimizing the coupling coordination of complex systems, which overcomes the limitations of traditional single-objective optimization, inefficient high-dimensional parameter optimization, and insufficient multi-objective coordination, and achieves efficient and adaptive optimization of the coupling coordination of complex systems.

[0005] Therefore, the present invention provides the following technical solution: A method for optimizing the coupling coordination degree of a complex system, the method comprising: Obtain a multi-level coupling parameter set in a complex system; the multi-level coupling parameter set includes parameter variables at multiple different granularity levels, including: element layer, subsystem layer, and macroscopic layer; The set of parameter variables to be optimized is obtained by filtering the multi-level coupling parameter set; A Bayesian statistical model is constructed for the parameter variables to be optimized, and the Bayesian statistical model is used as a surrogate model to describe the probability mapping relationship between the objective function and the parameter variables; Determine the sampling function; the sampling function is used to describe the sampling criteria for multi-objective optimization; The optimized parameters are obtained by iteratively optimizing the parameter variables to be optimized using the Bayesian statistical model and the sampling function.

[0006] Optionally, the step of filtering the parameter variables to be optimized from the multi-level coupling parameter set includes: Determine the contribution of each parameter variable in the multi-level coupling parameter set to the index of interest; The parameter variables to be optimized are obtained by filtering based on the contribution level.

[0007] Optionally, the objective function includes an element-level objective function, a subsystem-level objective function, and a macro-level objective function; constructing the Bayesian statistical model includes constructing a Bayesian statistical model for each level of objective function.

[0008] Optionally, the determination of the sampling function includes: constructing an improved EHVI sampling function based on hypervolume expectation; the EHVI sampling function is used to evaluate the merits of candidate parameter points and guide the sampling direction.

[0009] Optionally, the iterative optimization of the parameter variable to be optimized using the Bayesian statistical model and the sampling function to obtain the optimized parameters includes: Initialization, determining the initial dataset; Based on the current dataset, construct or update the proxy model for the objective function of each layer; Determine the Pareto set of the current estimate and its corresponding Pareto front in the target space; New sampling points are obtained based on the Pareto front and the sampling function; Based on the new sampling points, a multi-objective function evaluation is performed to obtain the objective function value; Determine whether the iteration termination condition has been met; If so, stop the iteration; select the parameter combination that meets the index from the currently estimated Pareto set to obtain the optimized parameters; Otherwise, add the new sampling point to the current dataset and continue the iteration process.

[0010] Optionally, the initialization, determining the initial dataset, includes: Based on the set of parameters to be optimized, a set of initial parameter samples is generated in the parameter space; Using a simulation model based on the complex system dynamics equations coupled with each subsystem, the index values ​​of each layer corresponding to each initial parameter sample are calculated to obtain the initial dataset.

[0011] A device for optimizing the coupling coordination of a complex system, the device comprising: The parameter set acquisition module is used to acquire a multi-level coupling parameter set in a complex system; the multi-level coupling parameter set includes parameter variables at multiple different granularity levels, including: element layer, subsystem layer, and macroscopic layer; The filtering module is used to filter the parameter variables to be optimized from the multi-level coupling parameter set to obtain the set of parameter variables to be optimized; The model building module is used to construct a Bayesian statistical model for the parameter variables to be optimized, and to use the Bayesian statistical model as a proxy model to describe the probability mapping relationship between the objective function and the parameter variables. A sampling function determination module is used to determine a sampling function; the sampling function is used to describe the sampling criteria for multi-objective optimization. The parameter optimization module is used to iteratively optimize the parameter variable to be optimized using the Bayesian statistical model and the sampling function to obtain the optimized parameters.

[0012] Optionally, the filtering module includes: The contribution calculation unit is used to determine the contribution of each parameter variable in the multi-level coupling parameter set to the index of interest. The selection unit is used to filter and obtain the parameter variables to be optimized based on the contribution.

[0013] Optionally, the objective function includes an element-level objective function, a subsystem-level objective function, and a macro-level objective function; The model building module is specifically used to construct Bayesian statistical models for the objective functions of each layer.

[0014] Optionally, the parameter optimization module includes: Initialization unit, used to determine the initial dataset; The proxy model update unit is used to construct or update the proxy model for the objective function of each layer based on the current dataset. The sampling function calculation unit is used to determine the currently estimated Pareto set and its corresponding Pareto front in the target space; A sampling update unit is used to obtain new sampling points based on the Pareto front and the sampling function; The objective function calculation unit is used to perform multi-objective function evaluation based on the new sampling points to obtain the objective function value; The decision unit is used to determine whether the iteration termination condition has been met. The output unit is used to select parameter combinations that meet the index from the currently estimated Pareto set to obtain optimized parameters when the judgment unit determines that the iteration termination condition has been met. The dataset update unit is used to add the new sampling point to the current dataset for the next iteration optimization if the judgment unit determines that the iteration termination condition has not been met.

[0015] On the other hand, the present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when run by a processor, executes the steps of the complex system coupling coordination optimization method.

[0016] The method and apparatus for optimizing the coupling coordination of complex systems provided by this invention are based on the dynamic characteristics of the entire chain of "sensing-transmission-knowledge-control" in urban complex systems. They combine multi-objective Bayesian optimization to achieve adaptive parameter iterative optimization, improve the coupling coordination of complex systems, ensure the coordinated improvement of three-level indicators at the element level, subsystem level, and macro level, meet the needs of stable operation and intelligent regulation of complex systems, and provide a feasible optimization and regulation framework.

[0017] Furthermore, by using a sampling function improved based on hypervolume expectation and combining it with a Gaussian process surrogate model, the exploration and utilization of multi-objective optimization can be balanced. This allows for efficient approximation of the Pareto optimal solution within a finite number of evaluations, significantly reducing the computational overhead and time cost of evaluating the coupling coordination degree parameters of complex systems. This solves the pain points of high evaluation cost and low efficiency in traditional optimization methods and adapts to the optimization needs of complex systems with high evaluation costs.

[0018] Furthermore, by constructing a multi-objective collaborative optimization framework, we break through the limitations of traditional single-objective optimization or simple weighted summation. We fully consider the conflict and correlation of multiple objectives in the coupling coordination of complex systems. Through Pareto optimal solution screening, we achieve the optimal trade-off between multiple objectives. At the same time, we take into account the dynamic evolution characteristics of complex systems, improve the adaptability and timeliness of optimization results, and make up for the lack of dynamism in existing models. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly described below. Obviously, the drawings described below are merely some embodiments of the present invention, and those skilled in the art can obtain other drawings based on these drawings without creative effort.

[0020] Figure 1 This is a flowchart of a method for optimizing the coupling coordination degree of complex systems provided in an embodiment of the present invention; Figure 2This is a flowchart illustrating an iterative optimization of the parameter variable to be optimized according to an embodiment of the present invention. Figure 3 This is a schematic diagram of a complex system coupling coordination optimization device provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of a parameter optimization module in an embodiment of the present invention. Detailed Implementation

[0021] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0022] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0023] Existing methods for optimizing coupling coordination largely rely on single-objective optimization frameworks, neglecting the conflict and correlation of multiple objectives in optimizing coupling coordination of complex systems. For example, improving the synchronicity of the element level may lead to increased coordination costs at the subsystem level, while emergent optimization at the macro level may sacrifice the stability of local elements. Such methods struggle to find the optimal balance among multiple conflicting objectives, failing to meet the coordinated optimization requirements of the "element-subsystem-macro" three-level evaluation system for complex systems. Furthermore, they suffer from unclear definition of coupling coordination metrics and ambiguous operational mechanisms. Some studies have attempted to introduce Bayesian optimization methods for parameter optimization in complex systems, but most are limited to single-objective scenarios and do not fully adapt to the needs of multi-objective coordinated optimization. Simultaneously, existing methods are not specifically designed for the dynamic nature and high evaluation costs of complex systems. In addition, existing coupling coordination models suffer from strong data dependence and insufficient dynamism; many studies focus on static analysis, making dynamic optimization adjustments difficult.

[0024] To address this, embodiments of the present invention provide a method and apparatus for optimizing the coupling coordination degree of complex systems. Addressing the inherent conflicts and correlations among multiple objectives at the element level, subsystem level, and macroscopic level of the coupling coordination degree of complex urban systems, this invention constructs a Bayesian statistical model to fit the objective function, designs an appropriate data collection function to guide the next sampling, balances the exploration and utilization of multi-objective optimization, and achieves efficient approximation of the Pareto optimal solution. This allows for approximation of the Pareto optimal solution within a limited number of evaluations, thereby optimizing the coupling coordination degree parameters of complex systems.

[0025] The following is a brief explanation of the existing iterative optimization process based on Bayesian statistical models.

[0026] Iterative optimization based on Bayesian statistical models (often called Bayesian optimization) is a global optimization method for expensive black-box functions. Its core idea is to approximate the unknown objective function with a probabilistic surrogate model (usually a Gaussian process) and intelligently determine the location of the next sampling step using the uncertainty information of this model, thereby finding the optimal solution with as few evaluations as possible.

[0027] In existing technologies, Bayesian optimization follows the standard steps below: (1) Initialization: When the objective function is unknown, an initial set of candidate solutions is first generated. Common methods include: Random sampling: uniformly and randomly selecting within the parameter space; Latin hypercube sampling: more uniformly covers the parameter space; Sobol sequences: low-difference sequence sampling.

[0028] These initial points were used for the first evaluation of the true objective function, forming the initial observation dataset. .

[0029] (2) Gaussian process modeling: based on existing observation data A Gaussian process surrogate model is established. Representing the The input vector for each observation point Representing the The target output value corresponding to each observation point, where t represents the total amount of existing observation data. The Gaussian process model can use one or more of the following kernel functions: squared exponential kernel, ... Nucleus, rational quadratic nucleus.

[0030] (3) Acquisition function calculation and optimization: Based on the posterior distribution of the Gaussian process, the acquisition function is constructed and maximized to determine the next sampling point.

[0031] (4) Evaluation of the true objective function: The recommended sampling points Substitute the values ​​into the true (expensive) objective function to obtain the true observed values. .

[0032] (5) Dataset update: Add the newly evaluated points to the historical dataset, i.e.: ; Repeat steps (2) to (5) until the preset termination condition is met.

[0033] Multi-objective Bayesian optimization is a method for optimizing multiple objective functions, primarily consisting of two parts: a Bayesian statistical model for modeling the objective functions, and a sampling function for determining the next sampling location. It fits the objective functions by establishing a surrogate model, quantifies the uncertainty in the surrogate model using Gaussian process regression, and then uses the sampling function defined from this surrogate model to determine the sampling location. Its goal is to find a set of optimal solutions that balance different objectives, known as Pareto optimal solutions. The entire set of Pareto optimal solutions in the decision space is called the Pareto set, and the mapping in the objective space is called the Pareto front. The aim of multi-objective optimization is to find a representative subset of the Pareto front.

[0034] To address the optimization problem of coupling coordination parameters in complex urban systems, this invention provides a method and apparatus for optimizing the coupling coordination of complex systems. Based on a three-level dynamic evaluation system of element layer, subsystem layer, and macroscopic layer, a Bayesian statistical model and sampling function are constructed for the parameter variables to be optimized. The Bayesian statistical model is used as a surrogate model to describe the probability mapping relationship between the objective function and the parameter variables. The Bayesian statistical model and sampling function are used to iteratively optimize the parameter variables to obtain the optimized parameters.

[0035] like Figure 1 The diagram shown is a flowchart of a method for optimizing the coupling coordination of complex systems provided in an embodiment of the present invention, which includes the following steps: Step 101: Obtain a multi-level coupling parameter set in a complex system; the multi-level coupling parameter set includes parameter variables at multiple different granularity levels, including: element layer, subsystem layer, and macroscopic layer.

[0036] Assuming features in the feature layer and elements The coupling parameters are ,in i , j This indicates the coupling parameter They come from the element layer respectively i and element layer j Subsystems in the subsystem layer and subsystem The coupling parameters are ,in p , q This indicates the coupling parameter They come from the subsystems respectively p and subsystem q Multi-level coupling parameter set in complex systems for: ; in, This represents the number of elements in the element layer. This represents the number of subsystems in the subsystem layer.

[0037] The following example uses a complex system composed of an urban transportation subsystem and a power grid subsystem to illustrate the elements and indicators of interest in these two subsystems at the element layer.

[0038] (1) The elements of the transportation subsystem are shown in Table 1 below: Table 1

[0039] (2) The indicators of interest in the traffic subsystem are shown in Table 2: Table 2

[0040] (3) The elements in the power grid subsystem are shown in Table 3 below: Table 3

[0041] (4) The indicators of interest in the power grid subsystem are shown in Table 4: Table 4

[0042] It should be noted that the elements and indicators of interest in the above subsystems are merely illustrative examples and are not intended to limit the specific implementation of the present invention. In practice, the elements and indicators of interest in each subsystem can be determined based on their characteristics and requirements; however, this embodiment of the present invention does not impose any limitations on this.

[0043] Step 102: Select the parameter variables to be optimized from the multi-level coupling parameter set to obtain the parameter variable set to be optimized.

[0044] To mitigate the problem of high-dimensional parameters, it is first necessary to identify the input variables that are of significant importance to the metrics of interest. This involves considering all parameter sets in the complex system. Based on the initial collected data, sensitivity analysis was used to assess the relative importance of each variable relative to the indicator of interest, and the parameter variables with greater contributions were selected as the parameter variables to be optimized.

[0045] Assume the parameter sets from the element layer, subsystem layer, and macro layer are as follows: For all parameter sets of coupling coordination degree Based on the initial collected data, sensitivity analysis can be used to assess the relative importance of each parameter variable relative to the indicator of interest, and the parameter variables with greater contributions can be selected to obtain the set of parameter variables to be optimized. The set of parameter variables to be optimized It includes several parameter variables that need to be optimized.

[0046] The following examples illustrate the parameter variables to be optimized at each layer.

[0047] 1. Element layer At the element level, the focus can be on evaluating the degree of synchronization of various elements in the transportation subsystem and power grid subsystem over time, that is, using the synchronization index as the optimization target of the element level.

[0048] By applying Dynamic Time Warping (DTW), two different time-series data are non-linearly aligned to measure the total distance of their optimal matching path. A smaller DTW indicates that the two elements are more synchronized in their change patterns, exhibiting strong temporal coupling characteristics. This can be used to determine the optimization parameters for the element layer. .

[0049] 2. Subsystem Layer At the subsystem level, the consistency of the linkage mechanism and overall behavioral trends between the urban transportation subsystem and the power grid subsystem can be evaluated. By assessing their dynamic synergy, the temporal change trends of the state variables of each subsystem, such as sudden increases, sudden decreases, and inflection points, can be extracted, and the frequency of their simultaneous occurrence at key nodes can be measured. If multiple subsystems frequently exhibit significant changes within the same time window, it indicates the existence of a potential behavioral linkage mechanism, which can be considered strong synergy. Based on this, the parameters to be optimized at the subsystem level can be determined. .

[0050] 3. Macro level The macro-level represents the overall presentation of the urban organism, characterizing the collaborative network of different subsystems in structural nesting and dynamic evolution, and revealing the overall macro-regulation pattern of complex systems. The macro-level focuses on whether the overall coupling structure at the macro scale exhibits stable and clear emergent organizational characteristics. Based on causal emergence theory, Effective Information (EI) can be used as a quantitative indicator to calculate the effective information of the system at different levels. If the effective information at the macro-level is significantly higher than that at the micro-level and subsystem levels, it indicates that causal emergence has occurred in the urban system at the macro-scale, and the parameters to be optimized at the macro-level can be determined accordingly. .

[0051] Step 103: Construct a Bayesian statistical model for the parameter variables to be optimized; the Bayesian statistical model is a surrogate model used to describe the probability mapping relationship between the objective function and the parameter variables.

[0052] For the parameter variables to be optimized (For example, adjustable parameters at the element level, subsystem level, and macro level), construct a Bayesian statistical model as a surrogate model to describe the objective function. The probability mapping relationship between the parameter variables and the parameter variables.

[0053] The surrogate model employs Gaussian process regression. Gaussian process regression is a Bayesian method for function modeling, and its logic is as follows: First, for any finite number of parameter points... Assuming its corresponding objective function The value of follows a multidimensional normal distribution (prior), which is given by the mean function. Sum of covariance functions (kernel functions) Decision. Wherein, at any finite number of input points... At these points, the mean vector is evaluated by the mean function at each of these points. To obtain, that is At each pair of points At this point, by evaluating the kernel function Obtain the first of the matrix The kernel function should be designed to satisfy the following condition: points that are closer together in the input space have a larger covariance, meaning that the function values ​​at these points have a stronger positive correlation (implying that the function values ​​are more similar). Furthermore, the kernel function must guarantee that the generated covariance matrix is ​​positive semi-definite.

[0054] Then, observational data are obtained by evaluating the true objective function at a small number of parameter points.

[0055] By updating the prior distribution using Bayes' theorem, a posterior Gaussian process is obtained, which operates at any unobserved parameter point. The complete probability distribution (including mean and covariance) of the objective function values ​​is given here. Thus, a surrogate model is obtained, which realizes the transformation from parameter variables... This surrogate model provides probability mapping data to the distribution of objective function values. It can then be further used for Bayesian optimization to efficiently search for optimal parameter configurations.

[0056] It should be noted that a Bayesian statistical model needs to be constructed for each objective function at each level.

[0057] Step 104: Determine the sampling function; the sampling function is used to describe the sampling criteria for multi-objective optimization.

[0058] The sampling function is the core decision model of multi-objective Bayesian optimization. Its function is to recommend the next most valuable parameter combination based on the currently constructed Gaussian process surrogate model, so as to guide the optimization process to efficiently approach the real Pareto Front (PF).

[0059] In this embodiment, for the costly high-dimensional optimization problem of optimizing the coupling coordination parameters of complex systems, a multi-objective extension of the Expected Improvement (EI) criterion is adopted as the basis for the sampling function. For multi-objective optimization problems, the sampling function is further generalized to Expected Hypervolume Improvement (EHVI) based on hypervolume.

[0060] Hypervolume is an important performance indicator for measuring the quality of Power Factor (PF). Its calculation method is as follows: determine the current non-dominated solution set, and then calculate the volume of the region enclosed by this solution set and a predefined reference point in the target space. In this embodiment, since it includes three optimization objectives ( The hypervolume is a three-dimensional hypervolume. Generally speaking, the larger the hypervolume, the closer the current solution set is to the true Power Factor (PF), and the higher the quality of the solution set.

[0061] For any combination of parameters that has not yet been evaluated The corresponding objective function value is: ; The target value is a random vector composed of the posterior distributions of multiple Gaussian processes. By calculating the EHVI, a balance between exploration and exploitation can be achieved, enabling a reference point sampling strategy.

[0062] For a new point, determine whether it should become the next sampling point by evaluating how much improvement the expected results of all its possible target values ​​would bring to the current hypervolume.

[0063] Step 105: Iteratively optimize the parameter variable to be optimized using the Bayesian statistical model and the sampling function to obtain the optimized parameters.

[0064] The specific process of iteratively optimizing the parameter variable to be optimized is as follows: Figure 2 As shown, it includes the following steps: Step 201, Initialization, determine the initial dataset.

[0065] Specifically, based on the set of parameter variables to be optimized A set of initial parameter samples is generated in the parameter space using methods such as Latin hypercube sampling, Sobol sequence, or random sampling. Then, using a simulation model of complex system dynamics equations based on the coupling of subsystems such as transportation and energy, the corresponding element-level, subsystem-level, and macroscopic-level index values ​​for each initial parameter sample are calculated to form the initial dataset. .

[0066] Dataset Each sample is in the following format: ,Right now .

[0067] Step 202: Construct or update the proxy model for each objective function based on the current dataset.

[0068] Based on the current dataset , which is the objective function for each layer, such as the synchronicity index function for the feature layer. Synergy index function of subsystem layer Emergent index function at the macro level They can independently construct or update their Gaussian process models.

[0069] Step 203: Determine the currently estimated Pareto set and its corresponding Pareto front in the target space.

[0070] Specifically, in the current dataset In this process, a non-dominated sorting algorithm is applied to identify the current non-dominated solution set, which is the currently estimated Pareto set. and its corresponding Pareto front in the target space .

[0071] Step 204: Obtain new sampling points based on the Pareto front and the sampling function.

[0072] Specifically, based on the Gaussian process posterior distribution of all objective functions and the current Pareto front. Calculate the value of the sampling function over the entire parameter space; maximize the EHVI sampling function using an optimization algorithm, i.e., find the point that maximizes the sampling function, and obtain the new sampling point. .

[0073] Given the current Pareto approximation set P Reference points used to define hypervolume New target vector Super volume improvement As shown below: ; in, For the solution set Regarding reference points The super-volume.

[0074] The sampling function for the desired improvement of hypervolume is defined by the following formula: ; in, The predicted probability density given by the Gaussian process, i.e., the solution set Dominant and in With reference point The target space Lebesgue measure between them.

[0075] Step 205: Perform multi-objective function evaluation based on the new sampling points to obtain the evaluation results.

[0076] Specifically, utilizing new sampling points Perform a dynamic simulation and deduction of the coupling coordination degree of a complex system to obtain the index function values ​​at the element level, subsystem level, and macroscopic level, and obtain the objective function value. ,Right now: .

[0077] Step 206: Determine whether the iteration termination condition has been met; if yes, proceed to step 207; otherwise, proceed to step 208. The iteration termination condition can be that the number of iterations reaches a set number, or the objective function value is... The set threshold has been reached.

[0078] Step 207: Select parameter combinations that meet the criteria from the currently estimated Pareto set to obtain the optimized parameters.

[0079] Step 208: Add the new sampling points to the current dataset. Then execute step 202 to continue the iterative process.

[0080] The current dataset after adding the new sampling points is: .

[0081] The Pareto set obtained based on the multi-objective Bayesian optimization method Based on the optimal parameters from the Pareto front Obtain the corresponding indicator values, combine the synchronicity improvement ratio requirements at the element level, the synergistic effect and overall consistency improvement ratio requirements at the subsystem level, and the emergence improvement ratio requirements at the macro-law level, from the Pareto set The final parameter combination that meets the criteria is selected to ultimately improve the system's coupling and coordination.

[0082] The method for optimizing the coupling coordination of complex systems provided in this invention targets a multi-level set of coupling parameters in a complex system, determines the parameter variables to be optimized, and achieves adaptive parameter iterative optimization by combining multi-objective Bayesian optimization. This method can effectively improve the coupling coordination of complex systems, ensure the coordinated improvement of indicators at the element level, subsystem level, and macro level, and better meet the needs of stable operation and intelligent control of complex systems.

[0083] Accordingly, embodiments of the present invention also provide a device for optimizing the coupling coordination of complex systems, such as... Figure 3 The diagram shown is a structural schematic of the device.

[0084] The complex system coupling coordination optimization device 300 includes the following modules: The parameter set acquisition module 301 is used to acquire a multi-level coupling parameter set in a complex system; the multi-level coupling parameter set includes parameter variables at multiple different granularity levels, including: element layer, subsystem layer, and macro layer; The filtering module 302 is used to filter the parameter variables to be optimized from the multi-level coupling parameter set to obtain the parameter variable set to be optimized; The model building module 303 is used to build a Bayesian statistical model for the parameter variables to be optimized, and to use the Bayesian statistical model as a proxy model to describe the probability mapping relationship between the objective function and the parameter variables. The sampling function determination module 304 is used to determine the sampling function; the sampling function is used to describe the sampling criteria for multi-objective optimization. The parameter optimization module 305 is used to iteratively optimize the parameter variable to be optimized using the Bayesian statistical model and the sampling function to obtain the optimized parameters.

[0085] One specific structure of the filtering module 302 may include a contribution calculation unit and a selection unit. The contribution calculation unit is used to determine the contribution of each parameter variable in the multi-level coupling parameter set to the index of interest; the selection unit is used to filter and obtain the parameter variables to be optimized based on the contribution.

[0086] In one non-limiting embodiment, the objective function may include an element-level objective function, a subsystem-level objective function, and a macro-level objective function.

[0087] In this embodiment of the invention, the model building module 303 can construct Bayesian statistical models for each layer of objective functions.

[0088] like Figure 4 The diagram shown is a structural schematic of the parameter optimization module in an embodiment of the present invention.

[0089] The parameter optimization module 305 includes the following units: Initialization unit 351 is used to determine the initial dataset; The proxy model update unit 352 is used to construct or update the proxy model for the objective function of each layer based on the current dataset. The sampling function calculation unit 353 is used to determine the currently estimated Pareto set and its corresponding Pareto front in the target space; Sampling update unit 354 is used to obtain new sampling points based on the Pareto front and the sampling function; The objective function calculation unit 355 is used to perform multi-objective function evaluation based on the new sampling points to obtain the objective function value; Judgment unit 356 is used to determine whether the iteration termination condition has been met; The iteration termination condition can be that the number of iterations reaches a set number, or the objective function value is... The set threshold has been reached.

[0090] Output unit 307 is used to select parameter combinations that meet the index from the currently estimated Pareto set to obtain optimized parameters when the judgment unit 306 determines that the iteration termination condition has been met. The dataset update unit 308 is used to add the new sampling point to the current dataset for the next iteration optimization when the judgment unit 306 determines that the iteration termination condition has not been met.

[0091] The specific implementation methods of the above modules and units can be referred to the description in the previous embodiments of the present invention, and will not be repeated here.

[0092] The method and apparatus for optimizing the coupling coordination of complex systems provided in this invention can improve the coupling coordination of complex systems, meeting the requirements for stable operation and intelligent control of complex systems. For example, for complex urban systems composed of subsystems such as transportation and energy, a multi-objective Bayesian optimization method can be used to find a combination of coupling coordination parameter variables to maximize a set of three-level index values, thereby improving the coupling coordination of complex systems.

[0093] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that the present invention is not limited to the described order of actions, because according to the present invention, some steps can be performed in other orders or simultaneously. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to the present invention.

[0094] The present invention also provides a storage medium, which is a computer-readable storage medium storing a computer program thereon, the computer program being executable when it runs. Figure 1 or Figure 2 The method shown may include some or all of the steps. The storage medium may include read-only memory (ROM), random access memory (RAM), magnetic disk, or optical disk, etc. The storage medium may also include non-volatile memory or non-transitory memory, etc.

[0095] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer program are loaded or executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data provider to another website, computer, server, or data provider via wired or wireless means.

[0096] The embodiments of the present invention have been described in detail above. Specific implementation methods have been used to illustrate the present invention. The descriptions of the embodiments above are merely for the purpose of helping to understand the method and apparatus of the present invention, and are only a part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention, and the content of this specification should not be construed as a limitation of the present invention. Therefore, any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for optimizing the coupling coordination degree of a complex system, characterized in that, The method includes: Obtain a multi-level coupling parameter set in a complex system; the multi-level coupling parameter set includes parameter variables at multiple different granularity levels, including: element layer, subsystem layer, and macroscopic layer; The set of parameter variables to be optimized is obtained by filtering the multi-level coupling parameter set; A Bayesian statistical model is constructed for the parameter variables to be optimized, and the Bayesian statistical model is used as a surrogate model to describe the probability mapping relationship between the objective function and the parameter variables; Determine the sampling function; the sampling function is used to describe the sampling criteria for multi-objective optimization; The optimized parameters are obtained by iteratively optimizing the parameter variables to be optimized using the Bayesian statistical model and the sampling function.

2. The method for optimizing the coupling coordination degree of complex systems according to claim 1, characterized in that, The step of selecting the parameter variables to be optimized from the multi-level coupling parameter set includes: Determine the contribution of each parameter variable in the multi-level coupling parameter set to the index of interest; The parameter variables to be optimized are obtained by filtering based on the contribution level.

3. The method for optimizing the coupling coordination degree of complex systems according to claim 1, characterized in that, The objective function includes an element-level objective function, a subsystem-level objective function, and a macro-level objective function; The construction of the Bayesian statistical model includes: Construct Bayesian statistical models for the objective functions of each layer.

4. The method for optimizing the coupling coordination degree of complex systems according to claim 3, characterized in that, The determined sampling function includes: An improved EHVI sampling function based on hypervolume expectation is constructed; the EHVI sampling function is used to evaluate the merits of candidate parameter points and guide the sampling direction.

5. The method for optimizing the coupling coordination degree of complex systems according to claim 3, characterized in that, The iterative optimization of the parameter variable to be optimized using the Bayesian statistical model and the sampling function yields the following optimized parameters: Initialization, determining the initial dataset; Based on the current dataset, construct or update the proxy model for the objective function of each layer; Determine the Pareto set of the current estimate and its corresponding Pareto front in the target space; New sampling points are obtained based on the Pareto front and the sampling function; Based on the new sampling points, a multi-objective function evaluation is performed to obtain the objective function value; Determine whether the iteration termination condition has been met; If so, stop the iteration; select the parameter combination that meets the index from the currently estimated Pareto set to obtain the optimized parameters; Otherwise, add the new sampling point to the current dataset and continue the iteration process.

6. The method for optimizing the coupling coordination degree of complex systems according to claim 5, characterized in that, The initialization, which determines the initial dataset, includes: Based on the set of parameters to be optimized, a set of initial parameter samples is generated in the parameter space; Using a simulation model based on the complex system dynamics equations coupled with each subsystem, the index values ​​of each layer corresponding to each initial parameter sample are calculated to obtain the initial dataset.

7. A device for optimizing the coupling coordination degree of a complex system, characterized in that, The device includes: The parameter set acquisition module is used to acquire a multi-level coupling parameter set in a complex system; the multi-level coupling parameter set includes parameter variables at multiple different granularity levels, including: element layer, subsystem layer, and macroscopic layer; The filtering module is used to filter the parameter variables to be optimized from the multi-level coupling parameter set to obtain the set of parameter variables to be optimized; The model building module is used to construct a Bayesian statistical model for the parameter variables to be optimized, and to use the Bayesian statistical model as a proxy model to describe the probability mapping relationship between the objective function and the parameter variables. A sampling function determination module is used to determine a sampling function; the sampling function is used to describe the sampling criteria for multi-objective optimization. The parameter optimization module is used to iteratively optimize the parameter variable to be optimized using the Bayesian statistical model and the sampling function to obtain the optimized parameters.

8. The complex system coupling coordination optimization device according to claim 7, characterized in that, The filtering module includes: The contribution calculation unit is used to determine the contribution of each parameter variable in the multi-level coupling parameter set to the index of interest. The selection unit is used to filter and obtain the parameter variables to be optimized based on the contribution.

9. The complex system coupling coordination optimization device according to claim 7, characterized in that, The objective function includes an element-level objective function, a subsystem-level objective function, and a macro-level objective function; The model building module is specifically used to construct Bayesian statistical models for the objective functions of each layer.

10. The complex system coupling coordination optimization device according to claim 9, characterized in that, The parameter optimization module includes: Initialization unit, used to determine the initial dataset; The proxy model update unit is used to construct or update the proxy model for the objective function of each layer based on the current dataset. The sampling function calculation unit is used to determine the currently estimated Pareto set and its corresponding Pareto front in the target space; A sampling update unit is used to obtain new sampling points based on the Pareto front and the sampling function; The objective function calculation unit is used to perform multi-objective function evaluation based on the new sampling points to obtain the objective function value; The decision unit is used to determine whether the iteration termination condition has been met. The output unit is used to select parameter combinations that meet the index from the currently estimated Pareto set to obtain optimized parameters when the judgment unit determines that the iteration termination condition has been met. The dataset update unit is used to add the new sampling point to the current dataset for the next iteration optimization if the judgment unit determines that the iteration termination condition has not been met.

11. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is run by the processor, it performs the steps of the method for optimizing the coupling coordination of complex systems according to any one of claims 1 to 6.

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