Nuclear energy system design parameter feasible region adaptive extension method based on genetic algorithm

Abstract

The invention provides a nuclear energy system design parameter feasible region adaptive extension method based on a genetic algorithm. According to the method, an improved genetic algorithm is adopted to implement optimization, statistical analysis is carried out on the aggregation degree and the fitness of a boundary area reactor design scheme in the algorithm operation process, and when the individual proportion of a boundary area exceeds a preset threshold value and the boundary fitness is continuously improved, a system automatically expands a search space in the direction. The method further comprises a boundary trend prediction mechanism, and the extension direction and amplitude are accurately predicted through boundary fitness gradient analysis; and a self-adaptive crossover mutation operator is adopted to accelerate exploration of the expansion area. According to the method, rapid design iteration and efficient global optimization of nuclear energy system design parameters can be remarkably improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of advanced nuclear energy system design optimization algorithm, and particularly relates to a nuclear energy system design parameter feasible region adaptive expansion method based on a genetic algorithm, which is used for improving the fast design iteration and efficient global optimization of nuclear reactor nuclear energy system design parameters. BACKGROUND

[0002] In the nuclear energy system design optimization process, the feasible region range of design variables such as the geometric size of system equipment and the structural layout of the system usually needs to be pre-set depending on expert experience. This method has the following defects: (1) If the initial feasible region is set too small, the optimization potential of the system will be limited, and it is easy to fall into local optimum; (2) The fixed feasible region range cannot adapt to the dynamic changes in the optimization process, and it is difficult to find potential optimal solutions outside the boundary.

[0003] In the prior art, there is no systematic method to solve this problem, and only by re-setting the feasible region, re-developing high-precision calculation to obtain a training database, and highly relying on expert experience, the universality and adaptability of the technology are lacking. Therefore, it is urgent to develop a method that can adaptively monitor the boundary characteristics and intelligently adjust the search space, thereby improving the extrapolation optimization search ability and global search ability. SUMMARY

[0004] The purpose of the present application is to provide a nuclear energy system design parameter feasible region adaptive expansion method based on a genetic algorithm, which core idea is to monitor the distribution characteristics of the reactor design scheme at the boundary of the feasible region in the optimization process in real time, automatically identify the potential expansion direction and dynamically adjust the search space, so as to realize the efficient search of the global optimal solution outside the initial feasible region. The technical scheme adopted by the present application is as follows:

[0005] A nuclear energy system design parameter feasible region adaptive expansion method based on a genetic algorithm, comprising:

[0006] S110, based on the knowledge and experience of experts in the field, the initial feasible region range of each design variable in the multi-dimensional design space is preliminarily determined, and the initial feasible region range of each design variable is determined Set the initial upper and lower bounds ;

[0007] S120, within the determined initial feasible region range, an initial population meeting the constraint conditions is generated by using a random sampling method, so as to ensure that the population size and diversity meet the optimization requirements;

[0008] S130, in the genetic algorithm iteration process, the distribution of individuals in each generation population in the boundary region of the feasible region is monitored and counted in real time, the boundary region individuals are identified and their clustering characteristics are analyzed;

[0009] S140, analyze the fitness of the boundary region individuals, calculate the boundary aggregation degree, the boundary fitness advantage and the boundary fitness gradient, and predict the potential of the expansion direction;

[0010] S150, when the proportion of the boundary region individuals exceeds the preset threshold and the boundary fitness continues to improve, the expansion direction is determined and the dynamic expansion range is calculated according to the boundary fitness gradient and the boundary aggregation degree, and the design domain is automatically expanded along the direction;

[0011] S160, in the new design domain after expansion, additional exploration individuals are generated by using the directional population injection technology and added to the current population, and an enhancement coefficient is applied to the design variables in the expansion direction The mutation probability and the mutation strength are improved, and the historical high-quality individuals are ensured not to be lost through the boundary elite reservation mechanism, so that the new region exploration is accelerated and the convergence of the algorithm is ensured;

[0012] S170, iterative optimization: repeat step until the termination condition is met.

[0013] A computing device comprising at least one processor and a memory storing program instructions; when the program instructions are read and executed by the processor, the computing device performs a genetic algorithm-based adaptive expansion method of a nuclear energy system design parameter feasible region.

[0014] A readable storage medium storing program instructions, when the program instructions are read and executed by a computing device, the computing device performs a genetic algorithm-based adaptive expansion method of a nuclear energy system design parameter feasible region.

[0015] A computer program product comprising a computer program, the computer program being executed by a processor to implement a genetic algorithm-based adaptive expansion method of a nuclear energy system design parameter feasible region.

[0016] From the above technical solutions, the beneficial effects of the present application are:

[0017] First, the present application realizes intelligent adaptive expansion of the feasible region by monitoring the distribution characteristics of the reactor design parameter boundary region in real time, breaks through the limitation of fixed search space in traditional nuclear reactor design optimization, and provides the possibility for further miniaturization and light weight;

[0018] Second, the present application designs a multi-dimensional boundary evaluation system based on aggregation degree, fitness advantage and gradient analysis, which accurately identifies the potential expansion direction;

[0019] Thirdly, the extended range dynamic calculation method avoids the search efficiency reduction caused by blind expansion, and realizes reasonable growth of the search space.

[0020] Fourthly, the application adopts the strategy of combining directional population injection with adaptive mutation operator, which speeds up the efficient exploration of the newly expanded area.

[0021] Fifthly, the application guarantees the convergence and stability of the algorithm in the domain expansion process through the boundary elite reservation mechanism, effectively balancing the global exploration and local development capabilities. BRIEF DESCRIPTION OF DRAWINGS

[0022] Figure 1 The overall framework program flowchart of the nuclear energy system design parameter feasible region adaptive expansion method based on the genetic algorithm of the application is shown in the figure. DETAILED DESCRIPTION

[0023] Exemplary embodiments of the present disclosure will be described in greater detail below with reference to the accompanying drawings. Although exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure can be implemented in various forms, and the present disclosure should not be limited by the embodiments described herein. Rather, these embodiments are provided so that the present disclosure can be more thoroughly understood, and the scope of the present disclosure can be accurately conveyed to those skilled in the art.

[0024] Figure 1 The overall framework program flowchart of the nuclear energy system design parameter feasible region adaptive expansion method based on the genetic algorithm of the application is shown in the figure. This method mainly combines genetic algorithm, multi-dimensional boundary evaluation system, dynamic expansion range calculation method, efficient new domain exploration strategy and boundary elite reservation mechanism to realize dynamic update of the design region. As shown in the figure, the method comprises: Figure 1

[0025] S110, based on the knowledge and experience of experts in the field, the initial feasible region range of each design variable in the multi-dimensional design space is preliminarily determined, and the initial feasible region range of each design variable is set as the initial upper and lower bounds of the design variable.

[0026] S120, within the determined initial feasible region range, an initial population meeting the constraint condition is generated by using a random sampling method, so as to ensure that the population size and diversity meet the optimization requirements. The random sampling method can be a Latin hypercube sampling technique.

[0027] S130, in the iterative process of the genetic algorithm, the distribution of individuals in each generation population in the boundary region of the feasible region is monitored and counted in real time, the boundary region individuals are identified, and their aggregation characteristics are analyzed. The aggregation characteristics refer to the concentration degree and spatial distribution characteristics of the boundary region individuals in the distribution of the boundary region of the feasible region. ​​​

[0028] S140, analyze the fitness of the boundary region individuals, calculate the boundary concentration, boundary fitness advantage and boundary fitness gradient, and predict the potential of the expansion direction;

[0029] S150, when the proportion of boundary region individuals exceeds the preset threshold and the boundary fitness continues to improve, determine the expansion direction and calculate the dynamic expansion range according to the boundary fitness gradient and boundary concentration, and automatically expand the design domain along the direction;

[0030] S160, in the new design domain after expansion, additional exploration individuals are generated by using the directional population injection technology and added to the current population, and an enhancement coefficient is applied to the design variables in the determined expansion direction Increase the mutation probability and mutation strength, and ensure that the historical high-quality individuals are not lost through the boundary elite retention mechanism, accelerate the exploration of new regions while ensuring the convergence of the algorithm; The directional population injection technology refers to generating new individuals in the new design domain after expansion and injecting them into the current population; The new region refers to the design domain mentioned in S150;

[0031] S170, iterative optimization: repeat steps S130-S160 until the termination condition is met.

[0032] Further, the step S130 specifically comprises the following steps:

[0033] S130-1, for dimensional design space, the feasible region of each design variable is , the boundary region is defined as the region satisfying the condition or , wherein is the boundary region of the dimension, is the initial lower and upper bounds of the design variable, is the boundary threshold value of the dimension, usually set to , is the boundary proportion coefficient;

[0034] S130-2, in each generation of population , identify the individual set located in the boundary region , the formula is as follows:

[0035] ,

[0036] S130-3, the boundary region is subdivided into sub-regions, respectively corresponding to the upper and lower boundaries of each variable, and the formula is as follows:​

[0037] ,

[0038] ;

[0039] in, , For the first Subregions with lower and upper boundaries of each variable, .

[0040] Furthermore, step S140 specifically includes the following steps:

[0041] S140-1, calculates the proportion of individuals in each boundary sub-region to the overall population as the boundary clustering degree, and the formula is as follows:

[0042] ,

[0043] ;

[0044] in, , For the first The percentage of individuals in the sub-regions of the lower and upper boundaries of each variable. The cardinality of a set;

[0045] S140-2, the ratio of the average fitness of individuals in the boundary sub-region to the average fitness of the overall population is used as the boundary fitness advantage, and the formula is as follows:

[0046] ,

[0047] ;

[0048] in, , For the fitness advantage of the lower and upper boundaries, Represents the fitness function. This represents the average value;

[0049] S140-3 estimates the fitness gradient at the boundary to predict the potential for expansion, using the following formula:

[0050] ,

[0051] ;

[0052] in, , The fitness gradients are the lower and upper boundaries. and respectively, are inner regions adjacent to the boundary sub-region.

[0053] Further, the step S150 specifically comprises the following steps:

[0054] S150-1, expanding trigger condition: when the following conditions are met simultaneously, trigger design domain expansion:

[0055] and and or and and wherein, and are the threshold values of the aggregation degree and the fitness advantage, respectively, denotes the boundary fitness gradient;

[0056] S150-2, for the boundary that meets the trigger condition, expand the direction and amplitude as follows:

[0057] The expansion direction is: if is the lower boundary , then expand downward; if is the upper boundary , then expand upward;

[0058] The expansion amplitude is calculated as follows:

[0059] ,

[0060] ;

[0061] wherein, is the expansion coefficient, which controls the relative amplitude of each expansion;

[0062] S150-3, expanding the design domain: update the feasible region of the design variable to .

[0063] Further, the S160 specifically comprises the following steps:

[0064] S160-1, after each design domain expansion, randomly generate a set of additional individual sets in the expanded new design domain , and add them to the current population to form the expanded population , whose formula is as follows:

[0065] ,

[0066] wherein, is the set of individuals randomly generated in the expanded new design domain;

[0067] S160-2, for the expansion direction of the design variable , the mutation probability and mutation intensity are increased to times of the original value respectively, and the formula is as follows:

[0068] ,

[0069] ;

[0070] wherein, and are the basic mutation probability and intensity, is the enhancement coefficient;

[0071] S160-3, from the boundary region before expansion , the top individuals are selected to form an elite set , is a dynamic parameter, which is determined based on the number of individuals in the boundary region, the total size of the population and the quality (fitness distribution) of the boundary region. In practical applications, , the value is usually 5-15% of the population size, so that enough elite individuals can be retained, and the exploration space of the new region is not excessively limited. These elite individuals and the individuals selected from the population after expansion through normal selection operation are combined to form the next generation population , which ensures that high-quality individuals are not lost while accelerating the exploration of the new region, and the formula is as follows:

[0072] ,

[0073] ;

[0074] wherein, indicates that the top individuals are selected, indicates the normal selection operation.

[0075] Further, the termination condition in the step S170 is to reach the maximum number of iterations, reach the preset fitness threshold or continuously improve the optimal fitness for multiple generations. The fitness threshold is used to judge whether the optimization target is reached and terminate the algorithm.

[0076] The application also provides a computing device, comprising: at least one processor and a memory storing program instructions; when the program instructions are read and executed by the processor, the computing device performs the genetic algorithm-based nuclear energy system design parameter feasible region adaptive expansion method.

[0077] The application further provides a readable storage medium storing program instructions, which, when read and executed by a computing device, enable the computing device to perform the genetic algorithm-based adaptive expansion method of a feasible region of a nuclear power system design parameter.

[0078] The application further provides a computer program product comprising a computer program, which, when executed by a processor, implements the genetic algorithm-based adaptive expansion method of a feasible region of a nuclear power system design parameter.

[0079] A genetic algorithm is a computational model inspired by the principles of natural selection and genetics, which can effectively solve complex optimization problems by simulating selection, crossover and mutation operations in the biological evolution process. It has the advantages of fast solution speed, strong global search ability, parallel computing characteristics, wide adaptability, simple implementation, and wide application in combination optimization, machine learning, neural network training, production scheduling and engineering design, etc., and has become a powerful tool for solving high-dimensional nonlinear optimization problems.

[0080] The multi-dimensional boundary evaluation system comprehensively analyzes the design space boundary based on multiple evaluation indicators, and determines the direction with the most expansion value by multi-angle evaluation of the quality, distribution and potential of the boundary point solution. The evaluation system can comprehensively measure the boundary characteristics and provide a scientific basis for domain expansion, ensuring the effectiveness of the expansion direction.

[0081] The dynamic expansion range calculation method adaptively adjusts the expansion step size based on the solution distribution characteristics and search history of the current boundary region. In the solution sparse region, a larger amplitude expansion is adopted, while in the solution dense region, a small amplitude fine expansion is implemented. Through the adaptive mechanism, the global exploration and local mining are balanced, and the search efficiency of the algorithm is improved.

[0082] The efficient new domain exploration strategy combines local search and jump exploration to quickly locate high-quality solutions in the expanded new region. Through a hybrid prediction model to guide the search direction, combined with a dynamic population allocation mechanism, efficient exploration and utilization of the new region are realized, and the convergence process is accelerated.

[0083] The boundary elite reservation mechanism preserves high-quality solutions on the historical boundary during the domain expansion process, ensuring that excellent genes are not lost. By establishing an elite solution library and selectively introducing it during the evolution process, the memory capacity of the algorithm is enhanced, the population diversity is improved, and premature convergence is effectively prevented.

[0084] In summary, the adaptive domain expansion method based on genetic algorithm proposed in the application realizes intelligent dynamic expansion of the complex design space of the nuclear reactor through the organic combination of the multi-dimensional boundary evaluation system, dynamic expansion range calculation, efficient new domain exploration strategy and boundary elite reservation mechanism; on the one hand, the method can automatically identify and expand the potential boundary region according to the initial design space set by experts, greatly improving the discovery ability of the global optimal solution; on the other hand, by adaptively adjusting the expansion direction and range, combined with the efficient new domain exploration mechanism, the convergence speed and solution accuracy of the algorithm are significantly improved, compared with the traditional fixed domain method, a wider solution space can be covered, and the complex optimization problem of unknown or difficult to determine design space can be better solved, providing a more flexible and efficient optimization method for the design optimization of advanced nuclear energy systems.

[0085] In the description provided herein, a large number of specific details are explained. However, it can be understood that the embodiments of the application can be practiced without these specific details. In some instances, well-known methods, structures and techniques have not been shown in detail in order not to obscure the understanding of this description.

[0086] Although the application has been described in accordance with the embodiments, it is to be understood that the application is not limited to these embodiments. It is to be understood that other embodiments can be utilized and modifications can be made without departing from the scope of the present application. Furthermore, it is to be noted that the language used in the specification has been principally selected for readability and instructional purposes and can not have been selected to expressly convey all necessary product, offering, and / or functional limitations of the application.

Claims

1. A method for adaptively expanding the feasible region of nuclear energy system design parameters based on genetic algorithms, characterized in that, include: S110, based on domain expert knowledge and historical experience, preliminarily determines the initial feasible region range of each design variable in the multidimensional design space, and for each design variable... Set initial upper and lower bounds ; S120. Within the determined initial feasible region, an initial population that meets the constraints is generated using a random sampling method to ensure that the population size and diversity meet the optimization requirements. S130: During the iteration of the genetic algorithm, the distribution of individuals in the feasible region boundary area of ​​each generation of the population is monitored and statistically analyzed in real time, and individuals in the boundary area are identified and their aggregation characteristics are analyzed. S140 analyzes the fitness of individuals in the boundary region, calculates the boundary clustering degree, boundary fitness advantage, and boundary fitness gradient, and predicts the potential for expansion direction. S150: When the proportion of individuals in the boundary region exceeds the preset threshold and the boundary fitness continues to improve, the expansion direction is determined and the dynamic expansion magnitude is calculated based on the boundary fitness gradient and the boundary aggregation, and the design domain is automatically expanded along that direction. S160, within the expanded new design domain, uses targeted population injection technology to generate additional exploratory individuals and add them to the current population, while applying enhancement coefficients to the design variables in the expansion direction. Increase mutation probability and mutation intensity, and ensure that historical high-quality individuals are not lost through the boundary elite retention mechanism, thereby accelerating the exploration of new areas while ensuring algorithm convergence. S170, Iterative optimization: Repeat steps S130-S160 until the termination condition is met.

2. The method for adaptively expanding the feasible region of nuclear energy system design parameters based on genetic algorithm according to claim 1, characterized in that, In S120, the random sampling method is the Latin hypercube sampling technique.

3. The method for adaptively expanding the feasible region of nuclear energy system design parameters based on genetic algorithm according to claim 1, characterized in that, Step S130 specifically includes the following steps: S130-1, for a d-dimensional design space, each design variable The feasible domain is Define the boundary region as satisfying the condition or area ,in, For the first A boundary region in each dimension. Let be the initial lower and upper bounds of the i-th design variable. For the first The boundary thresholds for each dimension are typically set to... , This is the boundary scaling factor; S130-2, in each generation of the population In the process, identify the set of individuals located in the boundary region. The formula is as follows: ； S130-3 subdivides the boundary region into Each subregion corresponds to the upper and lower boundaries of each variable, and its formula is as follows: ； in, , For the first Subregions with lower and upper boundaries of each variable, .

4. The method for adaptively expanding the feasible region of nuclear energy system design parameters based on genetic algorithm according to claim 3, characterized in that, Step S140 specifically includes the following steps: S140-1, calculates the proportion of individuals in each boundary sub-region to the overall population as the boundary clustering degree, and the formula is as follows: ； in, , For the first The percentage of individuals in the sub-regions of the lower and upper boundaries of each variable; S140-2, the ratio of the average fitness of individuals in the boundary sub-region to the average fitness of the overall population is used as the boundary fitness advantage, and the formula is as follows: ； ； in, , For the fitness advantage of the lower and upper boundaries, Represents the fitness function. This represents the average value; S140-3 estimates the fitness gradient at the boundary to predict the potential for expansion, using the following formula: ； in, , The fitness gradients are the lower and upper boundaries. and These are the internal regions adjacent to the boundary sub-regions.

5. The method for adaptively expanding the feasible region of nuclear energy system design parameters based on genetic algorithm according to claim 4, characterized in that, Step S150 specifically includes the following steps: S150-1, when conditions are met simultaneously and and or meet the conditions and and When this occurs, the design domain expansion mechanism is triggered, in which... and These are the thresholds for clustering degree and fitness advantage, respectively. Represents the boundary fitness gradient; S150-2, for boundaries that satisfy the triggering conditions The direction of expansion is determined as follows: if lower boundary If, then expand downwards; if upper boundary If so, then it expands upwards; the formula for calculating the expansion range is as follows: ； in, This is the expansion coefficient, which controls the relative magnitude of each expansion. The cardinality of a set; S150-3 updates the feasible domain of the design variables to .

6. The method for adaptively expanding the feasible region of nuclear energy system design parameters based on genetic algorithm according to claim 5, characterized in that, Step S160 specifically includes the following steps: S160-1, after each design domain expansion, randomly generate an additional set of individuals within the expanded new design domain. And add it to the current population to form an expanded population. The formula is as follows: ； in, A set of individuals randomly generated within the expanded new design domain; S160-2, for the direction of expansion Design variables Increase its mutation probability and mutation intensity to their original values. The formula for multiplying by 1 is as follows: ； in, and Based on the probability and intensity of mutation, For enhancement coefficient; S160-3, from the boundary region before expansion Select the one with the highest fitness Individuals constitute an elite group , These are dynamic parameters, and these elite individuals, along with those selected from the expanded population through ordinary selection, form the next generation of the population. To ensure that valuable historical individuals are not lost while accelerating the exploration of new areas, the formula is as follows: ； in, This indicates selecting the one with the highest fitness. Individual, This indicates a normal selection operation.

7. The method for adaptively expanding the feasible region of nuclear energy system design parameters based on genetic algorithm according to claim 1, characterized in that, The termination conditions in step S170 are reaching the maximum number of iterations, reaching the preset fitness threshold, or no significant improvement in the optimal fitness over multiple consecutive generations.

8. A computing device, characterized in that, include: At least one processor and a memory storing program instructions; When the program instructions are read and executed by the processor, the computing device performs the adaptive expansion method for the feasible domain of nuclear energy system design parameters based on genetic algorithms as described in any one of claims 1-7.

9. A readable storage medium storing program instructions, characterized in that, When the program instructions are read and executed by the computing device, the computing device performs the adaptive expansion method for the feasible domain of nuclear energy system design parameters based on genetic algorithms as described in any one of claims 1-7.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the method for adaptive expansion of the feasible domain of nuclear energy system design parameters based on genetic algorithms as described in any one of claims 1-7.

Images