Key region identification method and device based on multi-objective optimization, equipment and medium

Abstract

The invention relates to a key area identification method and device based on multi-objective optimization, equipment and a medium, and the method comprises the steps: obtaining an agent model corresponding to target equipment to be designed, and randomly generating the initial position and speed of an initial particle according to the agent model, design parameters and preset related parameters of a particle swarm optimization algorithm; wherein each particle corresponds to a to-be-optimized parameter design area, performing iterative optimization on the initial particle swarm for multiple times, and storing the updated individual optimal position and global optimal position of each particle in an external file; and solving a Pareto optimization solution according to all individual optimal positions after each historical iteration optimization and the global optimal position until the number of iteration optimization times meets the preset number of iteration times, and obtaining a preset number of optimal particles according to the Pareto optimization solution in the external archive, namely, taking the parameter design region as the key region. By adopting the method, the accuracy and efficiency of key region identification can be effectively improved.

Description

Technical Field

[0001] The present application relates to the cross-technical field of engineering and computers, and in particular to a key area identification method, device, equipment and medium based on multi-objective optimization. Background Art

[0002] In large-scale projects, it is necessary to conduct scheme design in advance through experimental design methods. In order to reduce the cost of the project, etc., digital models will be constructed in advance for large-scale engineering projects (such as aircraft manufacturing). In the experimental sample space of the digital model, each indicator that affects the performance of the entity is called a key indicator, and the factors that affect the key indicators are called factors. The key indicators can be regarded as sub-models constructed by multiple factors, and the range of factor combinations that affect the performance of the entity is called the key area. Then, a response model between the key indicators and each factor can be constructed, and experimental design can be carried out in the key area through optimization algorithms to guide more accurate experiments. The original digital model obtained through mechanism analysis, mathematical derivation, etc. will have a certain error with the entity, and the entity needs to be tested to correct the original digital model.

[0003] Although the digital model is accurate, it still takes a long time to conduct experiments on the digital model, which is not conducive to the subsequent large-scale search of key areas. In order to improve efficiency, a proxy model can be constructed by sampling on the digital model. The proxy model is usually a black box function, which has no specific mathematical expression. The key area usually refers to the area in the function space that changes dramatically and has the most obvious impact on the response. Identifying the key area of ​​the proxy model is to search in the space of black box functions. A black box function refers to a function whose internal structure is unknown and whose analytical expression is unavailable. The study of such functions usually relies on limited input and output observation data.

[0004] However, black box functions are not analytic, and traditional analytical methods are difficult to apply. They need to rely on numerical approximation or random sampling techniques to determine the key areas. At the same time, the non-smoothness and nonlinear behavior of black box functions increase the difficulty of characterizing key areas. Conventional optimization or search methods are difficult to converge, and more complex algorithms need to be introduced. The search efficiency is affected by the objective function evaluation and the region division strategy. It is necessary to find a balance between global exploration and local development. In addition, the key areas are dynamic, requiring the algorithm to be sufficiently adaptable. Summary of the invention

[0005] Based on this, it is necessary to provide a key area identification method, device, equipment and medium based on multi-objective optimization that can quickly and accurately search for key areas in response to the above technical problems.

[0006] A key area identification method based on multi-objective optimization, the method comprising: Obtaining a digital model corresponding to the target device to be designed, and obtaining a corresponding proxy model based on the digital model; Acquire design parameters related to the target device, wherein the design parameters include parameters of multiple dimensions and a value range of each parameter; According to the proxy model, the design parameters and the preset particle swarm optimization algorithm related parameters, the initial position and speed of the particles are randomly generated to construct an initial particle swarm, wherein each particle corresponds to a parameter design region to be optimized; The initial particle swarm is iteratively optimized for multiple times. In each iteration, the position and speed of each particle are updated according to the current state, individual optimal position and global optimal position of each particle. The fitness of each updated particle is evaluated by a multi-dimensional fitness evaluation mechanism, and the updated particles are mutated at a preset mutation probability, and the individual optimal position and global optimal position of each particle are updated. The updated individual optimal position and the global optimal position of each particle are saved in an external archive, in which a Pareto optimal solution is solved according to all individual optimal positions and the global optimal position after each historical iteration optimization, and the solution result is saved in the external archive; Until the number of iterative optimizations meets the preset number of iterations, a Pareto optimization solution is obtained from the external archive, and a preset number of optimal particles are obtained according to the Pareto optimization solution. The parameter design region corresponding to the optimal particle is the key region, so as to realize the identification of the key region.

[0007] In one embodiment, when constructing the initial particle group: Define the sampling space of particles according to the numerical range of design parameters in each dimension; The Latin hypercube sampling method is used to generate multi-dimensional uniformly distributed initial positions in the particle sampling space; According to the preset particle swarm optimization algorithm related parameters, a preset number of initial particles are randomly generated in the particle sampling space; The velocity of each initial particle is randomly initialized to obtain the initial particle group.

[0008] In one embodiment, after the initial particle group is generated, it is determined whether the initial position of each initial particle satisfies the quantitative constraint, and a repair strategy is adopted to adjust the position of the initial particle that does not satisfy the quantitative constraint to a position that satisfies the quantitative constraint.

[0009] In one embodiment, during each iteration, an algorithm improvement strategy is used to adaptively adjust the inertia weight and learning factor when updating the position and velocity of each particle.

[0010] In one embodiment, the multi-dimensional fitness evaluation mechanism includes an information surface measurement index and a gradient index; When evaluating the fitness of each particle, a Latin hypercube sampling method is used to perform sampling in the area represented by the particle to obtain a plurality of sampling points, and a function value of each sampling point is calculated; According to the sampling points and function values, the information surface measurement index and the gradient index are calculated, and the calculated results are used as the fitness of the corresponding particles.

[0011] In one embodiment, during the iterative optimization of the particle swarm, according to the periodic restart strategy, some particles are selected in the current particle swarm at a preset period with a preset probability to reinitialize the position and speed.

[0012] In one embodiment, when solving the Pareto optimization solution according to all individual optimal positions and the global optimal position after historical iterative optimization: According to the fitness, all particles corresponding to the individual optimal positions and the global optimal position are non-dominated and sorted, and the particles are divided into different frontier levels; Calculate the crowding distance of each solution in the objective function, and sort the solutions in the first frontier in descending order according to the crowding distance; Through the elite selection strategy, the elite solution is selected from the sorted solution set, and the solution with the largest congestion distance is selected from the elite solution as the optimal Pareto front solution.

[0013] The present application also provides a key area identification device based on multi-objective optimization, the device comprising: The proxy model obtaining module is used to obtain the digital model corresponding to the target device to be designed, and obtain the corresponding proxy model according to the digital model; A design parameter acquisition module, used to acquire design parameters related to the target device, wherein the design parameters include parameters of multiple dimensions and a value range of each parameter; An initial particle swarm construction module is used to randomly generate initial positions and velocities of particles according to the proxy model, design parameters and preset particle swarm optimization algorithm related parameters, and construct an initial particle swarm, wherein each particle corresponds to a parameter design region to be optimized; An iterative optimization module, used for performing multiple iterative optimizations on the initial particle swarm. In each iterative process, the position and speed of each particle are updated according to the current state, individual optimal position and global optimal position of each particle, a multi-dimensional fitness evaluation mechanism is used to evaluate the fitness of each updated particle, and the updated particles are mutated under a preset mutation probability, and the individual optimal position and global optimal position of each particle are updated; A Pareto optimization solution solving module is used to save the individual optimal position and the global optimal position of each particle after update to an external archive, in which the Pareto optimization solution is solved according to all the individual optimal positions and the global optimal positions after each historical iteration optimization, and the solution result is saved to the external archive; The key area identification completion module is used to obtain a Pareto optimization solution from the external archive until the number of iterative optimizations meets a preset number of iterations, and obtain a preset number of optimal particles according to the Pareto optimization solution. The parameter design area corresponding to the optimal particle is the key area, so as to realize the identification of the key area.

[0014] A computer device comprises a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the following steps are implemented: Obtaining a digital model corresponding to the target device to be designed, and obtaining a corresponding proxy model based on the digital model; Acquire design parameters related to the target device, wherein the design parameters include parameters of multiple dimensions and a value range of each parameter; According to the proxy model, the design parameters and the preset particle swarm optimization algorithm related parameters, the initial position and speed of the particles are randomly generated to construct an initial particle swarm, wherein each particle corresponds to a parameter design region to be optimized; The initial particle swarm is iteratively optimized for multiple times. In each iteration, the position and speed of each particle are updated according to the current state, individual optimal position and global optimal position of each particle. The fitness of each updated particle is evaluated by a multi-dimensional fitness evaluation mechanism, and the updated particles are mutated at a preset mutation probability, and the individual optimal position and global optimal position of each particle are updated. The updated individual optimal position and the global optimal position of each particle are saved in an external archive, in which a Pareto optimal solution is solved according to all individual optimal positions and the global optimal position after each historical iteration optimization, and the solution result is saved in the external archive; Until the number of iterative optimizations meets the preset number of iterations, a Pareto optimization solution is obtained from the external archive, and a preset number of optimal particles are obtained according to the Pareto optimization solution. The parameter design region corresponding to the optimal particle is the key region, so as to realize the identification of the key region.

[0015] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the following steps: Obtaining a digital model corresponding to the target device to be designed, and obtaining a corresponding proxy model based on the digital model; Acquire design parameters related to the target device, wherein the design parameters include parameters of multiple dimensions and a value range of each parameter; According to the proxy model, the design parameters and the preset particle swarm optimization algorithm related parameters, the initial position and speed of the particles are randomly generated to construct an initial particle swarm, wherein each particle corresponds to a parameter design region to be optimized; The initial particle swarm is iteratively optimized for multiple times. In each iteration, the position and speed of each particle are updated according to the current state, individual optimal position and global optimal position of each particle. The fitness of each updated particle is evaluated by a multi-dimensional fitness evaluation mechanism, and the updated particles are mutated at a preset mutation probability, and the individual optimal position and global optimal position of each particle are updated. The updated individual optimal position and the global optimal position of each particle are saved in an external archive, in which a Pareto optimal solution is solved according to all individual optimal positions and the global optimal position after each historical iteration optimization, and the solution result is saved in the external archive; Until the number of iterative optimizations meets the preset number of iterations, a Pareto optimization solution is obtained from the external archive, and a preset number of optimal particles are obtained according to the Pareto optimization solution. The parameter design region corresponding to the optimal particle is the key region, so as to realize the identification of the key region.

[0016] The above-mentioned critical area identification method, device, equipment and medium based on multi-objective optimization obtains the proxy model corresponding to the target device to be designed, and randomly generates the initial position and speed of the particles according to the proxy model, design parameters and preset particle swarm optimization algorithm related parameters, constructs an initial particle swarm, wherein each particle corresponds to a parameter design area to be optimized, performs multiple iterative optimizations on the initial particle swarm, and saves the individual optimal position and the global optimal position of each particle after the update to an external archive, and solves the Pareto optimization solution according to all the individual optimal positions and the global optimal positions after each historical iterative optimization, until the number of iterative optimizations meets the preset number of iterations, then obtains a preset number of optimal particles according to the Pareto optimization solution from the external archive, and the parameter design area corresponding to the optimal particle is the critical area, thereby realizing the identification of the critical area. The adoption of this method can effectively improve the accuracy and efficiency of critical area identification. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 A schematic diagram of a process flow of a key area identification method based on multi-objective optimization in one embodiment; Figure 2 A schematic diagram of the particle swarm optimization process steps in one embodiment; Figure 3It is a structural block diagram of a key area identification device based on multi-objective optimization in one embodiment; Figure 4 FIG. 4 is a diagram showing the internal structure of a computer device in one embodiment. DETAILED DESCRIPTION

[0018] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0019] In view of the many problems existing in the existing technology when using proxy models to search for key areas, such as Figure 1 As shown, a key area identification method based on multi-objective optimization is provided, which specifically includes the following steps: Step S100, obtaining a digital model corresponding to a target device to be designed, and obtaining a corresponding proxy model according to the digital model.

[0020] Step S110, obtaining design parameters related to the target device, the design parameters including parameters of multiple dimensions and a value range of each parameter.

[0021] Step S120, randomly generating initial positions and velocities of particles according to the proxy model, design parameters and preset particle swarm optimization algorithm related parameters, and constructing an initial particle swarm, wherein each particle corresponds to a parameter design region to be optimized.

[0022] Step S130, the initial particle swarm is iteratively optimized for multiple times. In each iteration, the position and speed of each particle are updated according to the current state, individual optimal position and global optimal position of each particle. The fitness of each updated particle is evaluated using a multi-dimensional fitness evaluation mechanism, and the updated particles are mutated at a preset mutation probability, and the individual optimal position and global optimal position of each particle are updated.

[0023] Step S140, saving the updated individual optimal position of each particle and the global optimal position to an external archive, solving the Pareto optimization solution in the external archive according to all individual optimal positions and the global optimal position after each historical iteration optimization, and saving the solution result to the external archive.

[0024] Step S150, until the number of iterative optimizations meets the preset number of iterations, a Pareto optimization solution is obtained from the external archive, and a preset number of optimal particles are obtained according to the Pareto optimization solution. The parameter design area corresponding to the optimal particle is the key area, so as to realize the identification of the key area.

[0025] In this application, the digital model corresponding to the target device to be designed is first obtained, and the corresponding proxy model is obtained according to the simulation data of the digital model to achieve accurate fitting of the digital model, and the key area is characterized by a multi-objective function, and then an improved adaptive particle swarm optimization algorithm is used to solve the key area in the proxy model, so that multiple key areas that meet the requirements of subsequent test design can be obtained through one solution, and then the specific values ​​of each design parameter are selected from the key area for subsequent tests. While ensuring the accuracy of the test, time, economic and other costs are greatly saved.

[0026] In step S100, the target equipment to be designed may include large mechanical equipment such as aircraft, radar, etc. The digital model may be an existing one, that is, the corresponding digital model may be obtained according to the type of the target equipment to be designed.

[0027] Furthermore, when obtaining the corresponding proxy model based on the digital model, a variety of existing algorithms can be used, and the algorithm type can be selected according to the current design requirements. When modeling small sample data and uncertainty quantification is required, the general sampling Gaussian process regression is used to build the proxy model, such as when building the dynamic model of an engine or robot. For problems with high-dimensional data, moderate data volume, and obvious nonlinear characteristics, support vector machines can be used to build proxy models, for example: simulating the relationship between complex material properties (such as thermal conductivity, elastic modulus) and process parameters.

[0028] In step S110, the design parameters of the target device to be designed are obtained, that is, the design requirements of the target device, which include multiple types of parameters, that is, parameters of multiple dimensions, and a value range of each parameter. Take the target device to be designed as an aircraft or a radar as an example for explanation.

[0029] The radar system consists of multiple sub-models, each of which can be converted into a digital model. Taking the radar anti-interference sub-model as an example, it is necessary to focus on the influence of parameters such as interference-to-signal ratio, intermittent period, duty cycle, and interference bandwidth on the angular tracking accuracy of the radar. According to domain knowledge, the reasonable value range of parameters such as interference-to-signal ratio, intermittent period, duty cycle, and interference bandwidth can be obtained. For example, for meteorological radar, the interference-to-signal ratio is 15dB~40dB, the intermittent period is 100 μs~5 ms, the duty cycle is 0.1%~10%, and the interference bandwidth is 1MHz~10 MHz.

[0030] In step S120, an optimized particle swarm optimization algorithm is used to solve the key area based on the proxy model and the design parameters of the target device to be designed. The preset particle swarm optimization algorithm related parameters include conventional parameters that need to be set in the particle swarm optimization algorithm, such as the number of iterations, the number of particles in the particle swarm, etc.

[0031] In this embodiment, some problems existing in the existing particle swarm optimization algorithm and the drawbacks of directly applying it to the key area search are addressed. For example, in fitness evaluation, a single or limited index is used, which is difficult to reflect the complexity of the multidimensional optimization target. In terms of parameter setting, the inertia weight in the particle swarm optimization algorithm is fixed and cannot be dynamically adjusted according to different stages, which limits the search and balance performance. When dealing with complex constraints, a simple penalty function or position adjustment method is used, which cannot effectively meet the constraint requirements. The archive management and elite strategy are simple, and there is a lack of non-dominated sorting and crowding calculation, which affects the quality and diversity of the non-dominated solution set. At the same time, the population diversity is not maintained enough, which makes it easy for the population to converge to the local optimal solution too early, and there is a lack of search methods for super rectangular areas. This means that the existing particle swarm optimization algorithm cannot be directly applied to the key area search.

[0032] Here we further explain that the key area actually corresponds to multiple feasible design solutions. It is understandable that the design solution for the equipment is actually the specific values ​​of countless related parameters, and a good design solution can meet various needs while also meeting good performance. In the early design, only the selectable range of relevant parameters can be given, which means that there are countless design solutions. The key area refers to further determining a smaller range within the selectable range given by each parameter, and this range actually includes multiple values. Then, different values ​​are selected for each parameter in the key area according to the space filling design method, so as to obtain multiple design solutions with better performance and satisfying constraints.

[0033] It is further explained here that the critical area actually corresponds to multiple feasible design schemes. The design scheme of the equipment can be regarded as a combination of specific values ​​of countless related parameters. An excellent design scheme not only meets multiple needs, but also needs to have good performance. In the early stages of design, usually only the optional range of each parameter can be given, which means that there may be countless design schemes. The so-called critical area refers to further determining a smaller range within the optional range of the parameter. This range still contains multiple possible parameter combinations. In the critical area, by selecting different parameter values ​​through the space filling design method, multiple design schemes with excellent performance and meeting the constraints can be obtained.

[0034] Furthermore, in the optimized particle swarm optimization algorithm, a particle encoding method is proposed to characterize the region in the numerical range of each design parameter so that it can be adjusted adaptively.

[0035] In this embodiment, when constructing the initial particle swarm: the sampling space of the particles is defined according to the numerical range of the design parameters of each dimension, a Latin hypercube sampling method is used to generate a multi-dimensional uniformly distributed initial position in the sampling space of the particles, and a preset number of initial particles are randomly generated in the sampling space of the particles according to the preset particle swarm optimization algorithm related parameters, and the speed of each initial particle is randomly initialized to obtain the initial particle swarm.

[0036] Specifically, suppose there is a d dimensional black box function ,in is the decision variable vector. Since the analytical expression of the function cannot be obtained, the corresponding function value can only be obtained by sampling the input. Based on the black box function, the particles are designed and initialized. In high-dimensional space, each particle is represented as a hyper-rectangular region, and its position vector is defined as: (1) In formula (1), For particles i In the d The starting coordinates of the dimension, is the window size (region length) of this dimension, d is the dimension of the problem. The velocity vector of the particle is defined as: (2) In formula (2), For particles i In the d The velocity of the starting coordinate, For the d The speed of the dimension window size.

[0037] In this embodiment, in order to ensure the uniformity of the initial distribution of particles and cover the entire search space, Latin Hypercube Sampling (LHS) is used to uniformly generate the starting position and window size of particles within the range of each dimension. j The dimensions, starting position and window size are initialized as: (3) (4) In formula (3) and formula (4), and Respectively j The lower and upper bounds of the dimension (i.e. the range of the parameter), and are the minimum and maximum window sizes, U ( a ,b ) means that in the interval [ a , b ] is uniformly distributed on .

[0038] In this embodiment, after the initial particle group is generated, it is determined whether the initial position of each initial particle satisfies the quantitative constraint, and a repair strategy is adopted to adjust the position of the initial particle that does not satisfy the quantitative constraint to a position that satisfies the quantitative constraint.

[0039] Specifically, assuming that the constraints are known, the quantitative constraints are the mathematical relationships between the factors of each dimension (i.e., the design parameters mentioned above), that is, the particles need to satisfy the constraints during initialization and also during subsequent iterations and mutations.

[0040] Specifically, the repair strategy is to reinitialize particles that do not meet the constraints and force them to meet the constraints.

[0041] Furthermore, the constraints are divided into simple linear constraints and complex nonlinear constraints. When generating the initial particle swarm, the simple linear constraints are solved to obtain the reduced search space, and the particles obtained after initialization are checked to verify whether they satisfy all the simple linear constraints. t At generation +1, if the particle i No. j Dimensional Position or window size If the boundary is exceeded, the boundary correction is performed in the following ways: (5) (6) In formula (5), and Indicates j The minimum and maximum values ​​of the range of values ​​for each dimension.

[0042] For particles with complex constraints and those that do not meet the simple constraints above, a penalty term is imposed in the fitness calculation to reduce the priority of the solution in the optimization process. For particles that do not meet the constraints, the position parameters of the particles are randomly regenerated so that they are within the allowed area; according to the current state of the particle, its position parameters are dynamically adjusted. and , to avoid falling into regions that do not meet the constraints: (7) In formula (7), is the penalty coefficient, which usually takes a large positive value. Indicates that in the inequality constraint Increase the penalty when it is violated. pis the number of inequality constraints, Refer to formula (1) for the definition of represents the objective function without considering constraints, represents the objective function taking into account the constraints.

[0043] In other embodiments, in addition to using Latin hypercube sampling (LHS), other methods such as Sobol sequence sampling or random uniform sampling can also be used to generate the position of the initial particle swarm. These methods further enhance the diversity of the particle swarm and the global search capability of the optimization algorithm by providing different particle distribution characteristics, and provide better initial conditions for complex optimization problems.

[0044] In step S130, the iterative optimization process generally includes updating the particle position and velocity, calculating the fitness of the updated particle, obtaining the individual optimal position of the updated particle and the global optimal particle in the particle swarm, so as to assist the particle in updating in the next iterative optimization.

[0045] In this embodiment, in order to improve the performance of the algorithm, an algorithm improvement strategy is also used to update the inertia weight of each particle in each iteration. and learning factor , Make adaptive adjustments.

[0046] Specifically, inertia weight By number of iterations t To gradually adjust to balance global exploration and local development capabilities. The adjustment formula is: (8) In formula (8), and are the maximum and minimum values ​​of the inertia weight, respectively. is the maximum number of iterations, t is the current iteration number, To avoid small amount of function divergence.

[0047] Specifically, the learning factor , Similarly, by the number of iterations t Perform dynamic adjustments and set initial values and , and adjust according to the learning factor adjustment strategy. Learning factor and learning factor The dynamic adjustment of enhances the dependence of particles on individual optimal and global optimal, and improves the optimization effect.

[0048] Furthermore, the following formula is used to calculate the learning factor Make adjustments: (9) The learning factor is calculated using the following formula: Make adjustments: (10) In formula (9) and formula (10), and To adjust the amplitude, In this embodiment, in each iteration process, after the weights are adaptively adjusted, the position and velocity of each particle are updated.

[0049] Specifically, the particle velocity and position updates follow the basic principles of particle swarm optimization, but are adjusted for high-dimensional and regional representations. i , which is in j The velocity and position update formulas of the dimension are: (11) (12) In formula (11) and formula (12), is the inertia weight, and is the learning factor, and is a random number uniformly distributed between [0,1]. For particles i In Dimension j The best historical position on For the dimension j The global optimal position on .

[0050] In this embodiment, the fitness of each particle is calculated after the particles in the particle group are evaluated. In order to comprehensively evaluate the area where the particles are located, the fitness surface related features are introduced: information surface measure and gradient measure. These two indicators measure the distribution diversity and degree of change of the objective function value in the area respectively. When evaluating the fitness of each particle, the Latin hypercube sampling method is used to sample the position to obtain multiple sampling points, and the function value of each sampling point is calculated. The information surface measure index and the gradient index are calculated according to each sampling point and the function value, and the calculated result is used as the fitness of the corresponding particle.

[0051] Specifically, for each particle, Latin hypercube sampling is performed according to the specified number of sampling points in the hyperrectangular region defined by it to evaluate the quality of the region. The sampling method still uses Latin hypercube sampling, and the range in each dimension is: (13) In formula (13), Represents particles i In the j The window size in each dimension.

[0052] generate N Sampling points , and calculate the corresponding function value According to these sampling points and function values, the information surface measure and gradient are calculated as the multi-objective fitness of the particle.

[0053] Furthermore, when calculating the information surface measure in space, the information surface is defined as a triple , X represents the set of all possible solutions in the solution space, N Defined as X The neighborhood relationship on , describing the proximity, distance or reachability between solutions, t : X × X →[0,1] represents the random information function, which is used to give the relative probabilities of superiority and inferiority between any pair of solutions in the solution space. and , Representation solution Better than solution The probability of using the information function t An information matrix can be constructed ,function t It can usually be assumed that: (14) The information surface measure is calculated by calculating the problem information surface vector and reference information surface vector The distance between them is obtained. It is defined as follows: (15) In formula (15), The information surface vector representing the problem p extracts the information matrix from the solution space structure of the problem M It is composed of related terms and is used to describe the relative solution structure of the problem; is the information surface vector of the reference surface, which represents the structural information of the ideal solution space; n is the number of elements in the information vector, usually ,in is the number of solutions in the solution space. The position of the global optimal point of the reference surface needs to coincide with the estimated optimal point of the problem surface. D dimensional spherical function The spherical function can be translated so that the optimal solution is located at any position in the search space, thus coinciding with the estimated optimal solution of the problem surface. Therefore, the reference function is taken as D dimensional spherical function.

[0054] when When the value is large, it means that there is a large difference between the solution space of the problem and the ideal reference surface, which means that the search path is more rugged and complex, and the optimization difficulty increases; on the contrary, when the distance is small, the solution space is smoother and the search difficulty is lower.

[0055] Furthermore, when calculating the gradient index in the space, in the multidimensional search space, the gradient is used as a key indicator for evaluating the local change rate and is used to evaluate the steepness and fitness change of the region to determine whether the region is a key region. In the multidimensional search space with fitness function 𝑓, from the initial point x ( t ) starts with T Walk with equal steps to get the sequence points x ( t ), x ( t +1),…, x ( t + T ). In this process, the gradient norm between adjacent points can be estimated by the following formula: (16) In formula (16), Yes and The Euclidean distance between T By walking for a few steps, you can get T A gradient estimate.

[0056] Based on these gradient values, we can define several metrics to describe the local gradient characteristics in the search space. First, the average estimated gradient within the walk Represents the average gradient between adjacent points, which is defined as: (17) In the calculation of formula (14), each The absolute value of is used to quantify the steepness and avoid the mutual cancellation of positive and negative slopes, which can better evaluate the overall slope in the region. If the walk sample covers enough search space, then It can be regarded as an estimate of the gradient of neighboring points in the entire search space. Secondly, the standard deviation of the gradient relative to the mean It is used to measure the degree of gradient change during walking, and its definition is as follows: (18) Maximum gradient within a walk Represents the maximum fitness mutation between adjacent points: (19) when Significantly greater than When , it may indicate the presence of a sharp change in surface structure such as a cliff, a steep valley, or a peak, while when and When both are high, it indicates that the landscape is more rugged and the fitness changes dramatically.

[0057] In order to ensure that the calculation of the gradient is not affected by the fitness value range or function definition domain, the fitness difference and the distance between points can be normalized. The normalized gradient estimation formula is: (20) In formula (20), and are the maximum and minimum fitness values ​​during the walk, and For the i This normalization process can eliminate the interference of fitness value range and spatial scale on gradient calculation, making the gradient values ​​of different regions comparable.

[0058] In other embodiments, in addition to the above-mentioned information surface measurement and gradient index, other indicators such as the number of extreme points can be introduced. These newly added indicators can enrich the fitness evaluation function by measuring the distribution characteristics of extreme points in the function space, thereby more comprehensively reflecting the optimization effect of the particles and improving the reliability and applicability of the optimization results.

[0059] Furthermore, according to a preset mutation probability, the positions of some of the updated particles are mutated, while the positions of the other particles remain unchanged.

[0060] In this embodiment, particles update their individual optimal positions according to the fitness function, the global optimal position is selected from a set of non-dominated solutions maintained in an external archive, and the solutions in the external archive are updated to store the current set of non-dominated solutions.

[0061] In step S140, an external archive mechanism is introduced to save the set of non-dominated solutions. In each iteration, new non-dominated solutions are added to the archive and solutions dominated by the new solutions are removed. To prevent the archive from being too large, a maximum archive capacity is set. When the archive capacity exceeds this value, the solutions in the archive are sorted according to the crowding distance and the solutions with smaller crowding are removed to maintain the diversity of solutions.

[0062] In this embodiment, when solving the Pareto optimization solution based on all individual optimal positions and the global optimal position after historical iterative optimization: according to the fitness, the particles corresponding to all individual optimal positions and the global optimal position are non-dominated sorted, the particles are divided into different frontier levels, the crowding distance of each solution in the objective function is calculated, the solutions in the first front are sorted in descending order according to the crowding distance, and the elite solution is selected from the sorted solution set through the elite selection strategy, and the solution with the largest crowding distance is selected from the elite solution as the optimal Pareto frontier solution.

[0063] Specifically, in the external archive, in order to solve the Pareto optimal solution, firstly, according to all the individual optimal positions optimized in the historical iteration and the global optimal position, the corresponding particles are non-dominated sorted, and the particles are divided into different frontier levels. Then, the crowding distance of each solution in the target space is calculated, and the selection is made according to the non-dominated sorting level and crowding distance, and finally the Pareto optimal solution is obtained. Among them, the non-dominated sorting is used to stratify the particles and identify their optimization priority. The crowding distance calculation is used to evaluate the sparsity of the solution and maintain diversity. The particles are finally sorted according to the level priority and crowding priority, and the external archive is updated and the redundant solutions are removed.

[0064] Furthermore, in order to deal with multi-objective optimization problems (maximization objectives), a non-dominated sorting method based on Pareto optimality is adopted. p and particles q If the following conditions are met, the particle is called p Dominate Particles q : For all objective functions m ,have ; There is at least one objective function m , so that In fact, the multi-objective optimization problem is to solve the two proposed indicators in a multi-objective way, namely, objective 1: maximizing the information surface measure, and objective 2: maximizing the gradient.

[0065] Based on the above definition, all particles are sorted non-dominatedly and divided into different frontier levels. Then, the crowding distance of particles in each frontier layer is calculated to evaluate the sparseness of particles in the target space and to maintain the diversity of solutions. For particles in a certain frontier, the crowding distance is calculated. Includes: For each objective function m , sort the particles in ascending order according to the fitness value. For the sorted particles, the crowding distance of the first and last particles is set to infinity, that is: (twenty one) For the particle in the middle, the crowding distance is calculated as: (twenty two) In formula (22), and Respectively, in the objective function m Located on the i The objective function of the nearest particles on both sides of a particle is and Respectively represent all particles in the objective function m The maximum and minimum values ​​on .

[0066] The total crowding distance of each particle is the sum of its distances on all objective functions: (twenty three) Then, elite selection is performed. Specifically, the particles are first sorted according to the level of non-dominated sorting. If the number of Pareto-optimal solutions in the external archive exceeds the preset capacity limit, further screening is required. For particles at the same level, they are sorted from large to small according to the crowding distance. Particles with large crowding distances are distributed in sparse areas and are retained first; particles with small crowding distances are distributed in dense areas and are removed first. According to the sorting of non-dominated levels and crowding distances, particles with the lowest priority are removed starting from the particles with the lowest priority until the capacity of the Pareto-optimal solutions in the external archive meets the requirements.

[0067] In this embodiment, in each iteration, when the particle velocity is updated, the global optimal position The choice of is crucial to the performance of the algorithm. In this algorithm, an elite strategy is adopted to select solutions with larger crowding distance from the first frontier (non-dominated solution set) in the external archive as the global optimal position, which helps to maintain the diversity of solutions and avoid premature convergence.

[0068] In this embodiment, in order to prevent the particle swarm from falling into the local optimum and increase the diversity of the population, a periodic restart strategy is introduced. During the iterative optimization of the particle swarm, according to the periodic restart strategy, some particles are selected in the current particle swarm with a preset probability to reinitialize the position and speed in a preset period.

[0069] In step S150, particles that are pre-positioned before sorting can be selected from the external archive as the final key area output according to the needs, and in each key area, specific values ​​of each dimensional parameter are selected to generate a device design solution.

[0070] like Figure 2 The figure shows the schematic diagram of the particle swarm optimization process steps.

[0071] In the above-mentioned critical area identification method based on multi-objective optimization, an improved particle swarm optimization algorithm is used to effectively search for critical areas in the proxy model. After obtaining the design parameters and their ranges of the target device and the proxy model obtained by the target device, the initial population is generated by randomly initializing the initial position and velocity of each particle. During the initialization process, if the initial position of the particle does not meet the quantitative constraints, a repair strategy is applied to adjust it to the feasible area. Subsequently, the algorithm updates the weight of the particle through an adaptation strategy, and in each round of iteration, adjusts its position and velocity according to the fitness calculation including the penalty function to ensure that the generated solution satisfies all constraints while optimizing the target.

[0072] During the optimization process, the algorithm determines whether to mutate the particle's position based on the mutation probability. If the mutation condition is not met, the current position remains unchanged. After each iteration, the individual optimal solution and the global optimal solution of the particle are updated, and the trusteeship information of these solutions is saved in an external archive to ensure the stability and accuracy of the results. In addition, in order to further improve the algorithm's exploration ability, the flow chart introduces the strategies of non-dominated solution sorting and elite selection, and updates the Pareto solution set through the feasibility priority method, so that the algorithm can show better solution set quality in multi-objective optimization problems.

[0073] As the number of iterations increases, the algorithm adopts a periodic restart strategy to prevent the algorithm from falling into the local optimum and ensure the diversity of the solution set. After reaching the set number of iterations, the Pareto optimal solution is extracted from the external archive and the global optimization result is finally output.

[0074] This method characterizes the region by proposing a new encoding method for particles and enables adaptive adjustment. At the same time, by introducing a multi-dimensional fitness evaluation mechanism, the two dimensions of information surface measurement and gradient are comprehensively used for multi-objective fitness evaluation, which fully reflects the optimization effect and improves the diversity and comprehensiveness of the optimization results. In this method, a dynamic parameter adjustment strategy is designed to dynamically adjust the values ​​of inertia weight, cognitive factor and social factor according to the iterative process, balance the ability of global search and local search, and improve the convergence speed and search range of the algorithm. Combined with the archive management and elite strategy of non-dominated sorting and crowding calculation, high-quality and diverse non-dominated solution sets are maintained to improve the overall performance of the optimization algorithm. Diversity and exploratory evaluation indicators are introduced to dynamically evaluate and maintain population diversity by calculating the variance, coverage radius and uniform distribution indicators of the population, prevent the particle swarm from converging to the local optimal solution too early, and ensure the comprehensive coverage of the search space and the continuous exploration ability of the optimization process. Finally, the in-depth analysis in the fitness evaluation is increased, and the number of extreme points in the optimization area is statistically analyzed using the local minimum search algorithm to further evaluate the diversity and complexity of the optimization objectives, providing a deeper analysis basis for fitness evaluation. Through these improvements, this method can effectively solve the shortcomings of the existing technology and improve the application effect of multi-objective optimization algorithms in complex problems.

[0075] It should be understood that although Figure 1 The steps in the flowchart are shown in sequence as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. Moreover, Figure 1 At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0076] In one embodiment, Figure 3 As shown, a key area identification device based on multi-objective optimization is provided, including: an agent model acquisition module 200, a design parameter acquisition module 210, an initial particle swarm construction module 220, an iterative optimization module 230, a Pareto optimization solution solution module 240 and a key area identification completion module 250, wherein: The proxy model obtaining module 200 is used to obtain a digital model corresponding to the target device to be designed, and obtain a corresponding proxy model according to the digital model; A design parameter acquisition module 210, used to acquire design parameters related to the target device, wherein the design parameters include parameters of multiple dimensions and a value range of each parameter; An initial particle swarm construction module 220 is used to randomly generate initial positions and velocities of particles according to the proxy model, design parameters and preset particle swarm optimization algorithm related parameters, and to construct an initial particle swarm, wherein each particle corresponds to a parameter design region to be optimized; Iterative optimization module 230, used for performing multiple iterative optimizations on the initial particle swarm. In each iterative process, the position and speed of each particle are updated according to the current state, individual optimal position and global optimal position of each particle, the fitness of each updated particle is evaluated by using a multi-dimensional fitness evaluation mechanism, and the updated particles are mutated under a preset mutation probability, and the individual optimal position and global optimal position of each particle are updated; A Pareto optimization solution solving module 240 is used to save the updated individual optimal position of each particle and the global optimal position to an external archive, in which the Pareto optimization solution is solved according to all individual optimal positions and the global optimal position after each historical iteration optimization, and the solution result is saved to the external archive; The key area identification completion module 250 is used to obtain a Pareto optimization solution from the external archive until the number of iterative optimizations meets a preset number of iterations, and obtain a preset number of optimal particles according to the Pareto optimization solution. The parameter design area corresponding to the optimal particle is the key area, thereby realizing the identification of the key area.

[0077] For the specific definition of the key area identification device based on multi-objective optimization, please refer to the definition of the key area identification method based on multi-objective optimization above, which will not be repeated here. Each module in the above-mentioned key area identification device based on multi-objective optimization can be implemented in whole or in part by software, hardware and a combination thereof. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.

[0078] In one embodiment, a computer device is provided. The computer device may be a terminal, and its internal structure diagram may be as follows: Figure 4As shown. The computer device includes a processor, a memory, a network interface, a display screen and an input device connected through a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The network interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a key area identification method based on multi-objective optimization is implemented. The display screen of the computer device can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device can be a touch layer covered on the display screen, or a key, trackball or touchpad set on the computer device housing, or an external keyboard, touchpad or mouse, etc.

[0079] Those skilled in the art will understand that Figure 4 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0080] In one embodiment, a computer device is provided, including a memory and a processor, wherein a computer program is stored in the memory, and when the processor executes the computer program, the following steps are implemented: Obtaining a digital model corresponding to the target device to be designed, and obtaining a corresponding proxy model based on the digital model; Acquire design parameters related to the target device, wherein the design parameters include parameters of multiple dimensions and a value range of each parameter; According to the proxy model, the design parameters and the preset particle swarm optimization algorithm related parameters, the initial position and speed of the particles are randomly generated to construct an initial particle swarm, wherein each particle corresponds to a parameter design region to be optimized; The initial particle swarm is iteratively optimized for multiple times. In each iteration, the position and speed of each particle are updated according to the current state, individual optimal position and global optimal position of each particle. The fitness of each updated particle is evaluated by a multi-dimensional fitness evaluation mechanism, and the updated particles are mutated at a preset mutation probability, and the individual optimal position and global optimal position of each particle are updated. The updated individual optimal position and the global optimal position of each particle are saved in an external archive, in which a Pareto optimal solution is solved according to all individual optimal positions and the global optimal position after each historical iteration optimization, and the solution result is saved in the external archive; Until the number of iterative optimizations meets the preset number of iterations, a Pareto optimization solution is obtained from the external archive, and a preset number of optimal particles are obtained according to the Pareto optimization solution. The parameter design region corresponding to the optimal particle is the key region, so as to realize the identification of the key region.

[0081] In one embodiment, a computer readable storage medium is provided, on which a computer program is stored, and when the computer program is executed by a processor, the following steps are implemented: Obtaining a digital model corresponding to the target device to be designed, and obtaining a corresponding proxy model based on the digital model; Acquire design parameters related to the target device, wherein the design parameters include parameters of multiple dimensions and a value range of each parameter; According to the proxy model, the design parameters and the preset particle swarm optimization algorithm related parameters, the initial position and speed of the particles are randomly generated to construct an initial particle swarm, wherein each particle corresponds to a parameter design region to be optimized; The initial particle swarm is iteratively optimized for multiple times. In each iteration, the position and speed of each particle are updated according to the current state, individual optimal position and global optimal position of each particle. The fitness of each updated particle is evaluated by a multi-dimensional fitness evaluation mechanism, and the updated particles are mutated at a preset mutation probability, and the individual optimal position and global optimal position of each particle are updated. The updated individual optimal position and the global optimal position of each particle are saved in an external archive, in which a Pareto optimal solution is solved according to all individual optimal positions and the global optimal position after each historical iteration optimization, and the solution result is saved in the external archive; Until the number of iterative optimizations meets the preset number of iterations, a Pareto optimization solution is obtained from the external archive, and a preset number of optimal particles are obtained according to the Pareto optimization solution. The parameter design region corresponding to the optimal particle is the key region, so as to realize the identification of the key region.

[0082] Those of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application may include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0083] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0084] The above-described embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the method of the present application shall be subject to the attached claims.

Claims

1. A key area identification method based on multi-objective optimization, characterized in that: The method comprises: Obtaining a digital model corresponding to the target device to be designed, and obtaining a corresponding proxy model based on the digital model; Acquire design parameters related to the target device, wherein the design parameters include parameters of multiple dimensions and a value range of each parameter; According to the proxy model, the design parameters and the preset particle swarm optimization algorithm related parameters, the initial position and speed of the particles are randomly generated to construct an initial particle swarm, wherein each particle corresponds to a parameter design region to be optimized; The initial particle swarm is iteratively optimized for multiple times. In each iteration, the position and speed of each particle are updated according to the current state, individual optimal position and global optimal position of each particle. The fitness of each updated particle is evaluated by a multi-dimensional fitness evaluation mechanism, and the updated particles are mutated at a preset mutation probability, and the individual optimal position and global optimal position of each particle are updated. The updated individual optimal position and the global optimal position of each particle are saved in an external archive, in which a Pareto optimal solution is solved according to all individual optimal positions and the global optimal position after each historical iteration optimization, and the solution result is saved in the external archive; Until the number of iterative optimizations meets the preset number of iterations, a Pareto optimization solution is obtained from the external archive, and a preset number of optimal particles are obtained according to the Pareto optimization solution. The parameter design region corresponding to the optimal particle is the key region, so as to realize the identification of the key region.

2. The key area identification method based on multi-objective optimization according to claim 1 is characterized in that: When constructing the initial particle swarm: Define the sampling space of particles according to the numerical range of design parameters in each dimension; The Latin hypercube sampling method is used to generate multi-dimensional uniformly distributed initial positions in the particle sampling space; According to the preset particle swarm optimization algorithm related parameters, a preset number of initial particles are randomly generated in the particle sampling space; The velocity of each initial particle is randomly initialized to obtain the initial particle group.

3. The key area identification method based on multi-objective optimization according to claim 2 is characterized in that: After the initial particle group is generated, it is determined whether the initial position of each initial particle satisfies the quantitative constraint, and a repair strategy is adopted to adjust the position of the initial particle that does not satisfy the quantitative constraint to a position that satisfies the quantitative constraint.

4. The key area identification method based on multi-objective optimization according to claim 3 is characterized in that: In each iteration, an algorithm improvement strategy is used to adaptively adjust the inertia weight and learning factor when updating the position and velocity of each particle.

5. The key area identification method based on multi-objective optimization according to claim 4 is characterized in that: The multi-dimensional fitness evaluation mechanism includes information surface measurement indicators and gradient indicators; When evaluating the fitness of each particle, a Latin hypercube sampling method is used to perform sampling in the area represented by the particle to obtain a plurality of sampling points, and a function value of each sampling point is calculated; According to the sampling points and function values, the information surface measurement index and the gradient index are calculated, and the calculated results are used as the fitness of the corresponding particles.

6. The key area identification method based on multi-objective optimization according to any one of claims 1 to 5, characterized in that: In the process of iterative optimization of the particle swarm, according to the periodic restart strategy, some particles are selected from the current particle swarm with a preset probability to reinitialize the position and speed at a preset period.

7. The key area identification method based on multi-objective optimization according to claim 6 is characterized in that: When solving the Pareto optimization solution based on all individual optimal positions and the global optimal position after historical iterative optimization: According to the fitness, all particles corresponding to the individual optimal positions and the global optimal position are non-dominated and sorted, and the particles are divided into different frontier levels; Calculate the crowding distance of each solution in the objective function, and sort the solutions in the first frontier in descending order according to the crowding distance; Through the elite selection strategy, the elite solution is selected from the sorted solution set, and the solution with the largest congestion distance is selected from the elite solution as the optimal Pareto front solution.

8. A key area identification device based on multi-objective optimization, characterized in that: The device comprises: The proxy model obtaining module is used to obtain the digital model corresponding to the target device to be designed, and obtain the corresponding proxy model according to the digital model; A design parameter acquisition module, used to acquire design parameters related to the target device, wherein the design parameters include parameters of multiple dimensions and a value range of each parameter; An initial particle swarm construction module is used to randomly generate initial positions and velocities of particles according to the proxy model, design parameters and preset particle swarm optimization algorithm related parameters, and construct an initial particle swarm, wherein each particle corresponds to a parameter design region to be optimized; An iterative optimization module, used for performing multiple iterative optimizations on the initial particle swarm. In each iterative process, the position and speed of each particle are updated according to the current state, individual optimal position and global optimal position of each particle, a multi-dimensional fitness evaluation mechanism is used to evaluate the fitness of each updated particle, and the updated particles are mutated under a preset mutation probability, and the individual optimal position and global optimal position of each particle are updated; A Pareto optimization solution solving module is used to save the individual optimal position and the global optimal position of each particle after update to an external archive, in which the Pareto optimization solution is solved according to all the individual optimal positions and the global optimal positions after each historical iteration optimization, and the solution result is saved to the external archive; The key area identification completion module is used to obtain a Pareto optimization solution from the external archive until the number of iterative optimizations meets a preset number of iterations, and obtain a preset number of optimal particles according to the Pareto optimization solution. The parameter design area corresponding to the optimal particle is the key area, so as to realize the identification of the key area.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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