A solid rocket core stage energy management method
By using a mixed optimization algorithm of snowball algorithm and bee algorithm in the sub-level energy management of solid rocket cores, combined with the real-time monitoring module to dynamically adjust the algorithm parameters, the problem of poor flexibility of energy management methods in the existing technology is solved, intelligent adjustment and optimization of energy management strategies are realized, and the performance stability and fuel utilization of the system are improved.
Patent Information
- Application Number
- CN202410492432.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-04-23
- Publication Date
- 2025-04-01
- Estimated Expiration
- 2044-04-23
AI Technical Summary
The existing solid rocket core energy management methods have limitations in adapting to variable flight environments and achieving global optimization, and lack flexibility and adaptability, resulting in the inability to effectively adjust energy management strategies to deal with changes in flight.
A hybrid optimization algorithm based on snowball algorithm and bee algorithm is adopted, and the algorithm parameters are dynamically adjusted by global search and local adjustment, combined with real-time monitoring modules, intelligent adjustment and optimization of energy management strategies are achieved.
It improves the flexibility and adaptability of energy management strategies, enhances the performance stability and fuel utilization of the system, and can achieve efficient energy management in complex dynamic environments.
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Figure CN118395855B_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of solid rocket launching, and in particular to a solid rocket core-level energy management method. Background Art
[0002] Energy management of solid rocket core stages has always been a key issue that needs to be urgently addressed in the field of aerospace engineering. Traditional energy management methods usually rely on empirical methods, PID control or traditional optimization algorithms. However, these methods have certain limitations in adapting to changing flight environments and achieving global optimization. Traditional methods are mainly adjusted through prior knowledge and rules. They bind preset energy management parameters into the onboard computer before flight, which is not adaptable enough to the dynamically changing conditions of solid rocket core stages during flight. Solid rockets may face highly variable wind fields, load changes and other factors during flight. Lack of sufficient adaptability may make it impossible to flexibly adjust energy management strategies to cope with these changes. Although it works well under specific conditions, it lacks flexibility and global search capabilities in the face of complex changes.
[0003] Some energy management systems use PID control methods to maintain system output by adjusting proportional, integral and differential parameters, but performance may degrade when dealing with nonlinear and time-varying systems. Optimization algorithms, such as genetic algorithms and particle swarm algorithms, have been tried to optimize energy management, however, these methods are still limited by global search and convergence speed. Model predictive control (MPC) builds a system model for prediction to adjust the control input. Although it has certain advantages, it requires complex models and a lot of computing resources and is not suitable for real-time control needs.
[0004] Therefore, it is necessary to invent a completely new solid rocket core stage energy management method to address the defects in the existing methods. Summary of the invention
[0005] In order to solve the technical problems in the prior art that the energy management methods have poor flexibility, require large computing resources, and cannot meet the needs of implementing control, the present invention proposes a solid rocket core-level energy management method to improve energy utilization efficiency and improve the adaptability and performance stability of the system.
[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is: a solid rocket core sub-level energy management method, comprising the following steps:
[0007] Step 1: Initialize a set of initial solutions in the search space, each solution represents a potential energy management strategy; at the same time, set the parameters and weight parameters of the snowball algorithm and the bee algorithm, and set the termination conditions;
[0008] Step 2: Use the snowball algorithm to perform a global search and update the position and size of each solution; use the bee algorithm to make local adjustments to the solution obtained from the global search; use the aggregation algorithm to simulate the interactive behavior of the snowball, attract, collide or merge the solutions in the search space to obtain the aggregated solution; then use the hybrid collaborative update algorithm to exchange information between the snowball algorithm and the bee algorithm to achieve global-local collaborative cooperation and obtain the solution after hybrid collaborative update;
[0009] Step 3: Obtain the flight status data of the solid rocket core stage in real time through the real-time monitoring module. According to the real-time flight status data, adjust the radius and rolling speed of the snowball algorithm and the local search range parameters of the bee algorithm, and repeat step 2;
[0010] Step 4: Determine whether the termination condition is met. If so, output the final energy management strategy as the optimal energy management strategy.
[0011] In step 1, setting the termination condition specifically refers to setting the maximum number of iterations and setting a predetermined performance target.
[0012] In step 4, if the number of iterations reaches a maximum number of iterations, or the performance reaches a predetermined performance target, it is determined that the termination condition is met.
[0013] In the step 1, the parameters of the snowball algorithm and the bee algorithm are set, including the radius and rolling speed of the snowball algorithm, and the number of bees and the local search range of the bee algorithm.
[0014] In step 1, the weight parameters include the weight of the snowball algorithm, the weight of the honey bee algorithm, the weight of the aggregation process, and the weight of the collaborative update.
[0015] The specific formula of the aggregation algorithm is:
[0016] S[i]'=S[i]+W_aggregate*force*(S[j]-S[i]);
[0017] Among them, S[i]' represents the updated solution, S[i] represents the initial solution, W_aggregate represents the weight of the aggregation process, force = G / distance**2, where G represents the gravitational constant of the aggregation process, and distance represents the distance between solution S[i] and solution S[j].
[0018] In step S2, the specific formula of the hybrid collaborative update algorithm is:
[0019] S[i]”=S[i]’+W_cooperation*(W_snowball*R*np.random.rand(solution_dimensions)*np.sign(np.random.rand(solution_dimensions)-0.5)+W_bees*D_bees*np.random.r and(solution_dimensions)*np.sign(np.random.rand(solution_dimensions)-0.5)+P_random*np.random.rand(solution_dimensions)+W_aggregate*force*(S[j]-S[i]));
[0020] Where S[i]” represents the solution after hybrid cooperative update, W_cooperation represents the weight of information transmission in hybrid cooperative update, W_snowball represents the weight of the snowball algorithm, R represents the radius of the snowball algorithm, np.random.rand(solution_dimensions) represents a random solution, np.sign(np.random.rand(solution_dimensions) represents the sign function, W_bees represents the weight of the bee algorithm when updating the solution position, D_bees represents the local search range of the bee algorithm, P_random represents the randomness parameter of the local search of the bee algorithm, W_aggregate represents the weight of the aggregation process, force = G / distance**2, where G represents the gravitational constant of the aggregation process, and distance represents the distance between solution S[i] and solution S[j].
[0021] In step 3, the update formula of the radius of the snowball algorithm is:
[0022] R'=R*(1-W_monitor)+W_monitor*np.random.rand();
[0023] Among them, R' represents the radius of the updated snowball algorithm, R represents the radius of the snowball algorithm, W_monitor represents the weight of the real-time monitoring module, and np.random.rand() represents a random number;
[0024] The update formula of the local search range parameter of the bee algorithm is:
[0025] D_bees'=D_bees*(1-W_monitor)+W_monitor*np.random.rand();
[0026] Where D_bees' represents the local search range parameter of the updated honey bee algorithm.
[0027] The step 4 also includes the following steps: calculating the performance value of the current solution and outputting the performance value.
[0028] Compared with the prior art, the present invention has the following beneficial effects:
[0029] 1. The present invention provides a solid rocket core stage energy management method. Based on a hybrid optimization algorithm of the snowball algorithm and the honey bee algorithm, the energy management strategy of the solid rocket core stage is optimized so that the energy management strategy can be intelligently adjusted both globally and locally to obtain the best performance. This optimization method that comprehensively considers global and local information can more effectively find the optimal solution. Therefore, the present invention can maximize fuel utilization, stability and performance during flight.
[0030] 2. Moreover, the present invention detects flight status data in real time and uses real-time monitoring results and feedback information to adjust the search strategy in real time, so that the algorithm can dynamically adjust the search space and parameters to adapt to the changing conditions during the flight of the solid rocket, improve the flexibility of practical application, and enhance the robustness and adaptability of the algorithm.
[0031] 3. In addition, the present invention introduces performance evaluation and termination conditions to ensure that the algorithm can automatically terminate after reaching a predetermined performance target or a set number of iterations, thereby improving the practicality of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS
[0032] Figure 1 A schematic flow chart of a solid rocket core sub-stage energy management method provided in an embodiment of the present invention. DETAILED DESCRIPTION
[0033] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments; based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.
[0034] Embodiment 1
[0035] like Figure 1 As shown, the first embodiment of the present invention provides a solid rocket core stage energy management method, which is implemented based on a hybrid optimization algorithm of a snowball algorithm and a sealing algorithm, and includes the following steps:
[0036] Step 1: Initialize a set of initial solutions in the search space, each solution represents a potential energy management strategy; at the same time, set the parameters and weight parameters of the snowball algorithm and the bee algorithm, and set the termination conditions.
[0037] Specifically, in step 1, setting the termination condition specifically refers to setting the maximum number of iterations and setting a predetermined performance target.
[0038] Specifically, in step 1, the parameters of the snowball algorithm and the bee algorithm are set to include the radius and rolling speed of the snowball algorithm, and the number of bees and local search range of the bee algorithm.
[0039] Furthermore, the initialization parameters include:
[0040] The set of initial solutions: S = {x1, x2, ..., xn}, where xi represents the i-th initial solution and the number of initial solutions is n;
[0041] The radius of the snowball algorithm: R, which represents the influence range of the snowball in the search space;
[0042] The rolling speed of the snowball algorithm: V_snowball, which indicates the speed at which the snowball rolls in the search space;
[0043] The number of bees in the bee algorithm: N_bees, which indicates the number of individual bees;
[0044] The local search range of the bee algorithm: D_bees, which represents the movement range of the bee in the local search;
[0045] The number of iterations of the hybrid optimization algorithm: T_max, which indicates the maximum number of iterations of the algorithm;
[0046] Update frequency of the real-time monitoring module: F_monitor, indicating the update frequency of the real-time monitoring flight status;
[0047] The weight parameter of the real-time monitoring module: W_monitor, which indicates the weight of real-time monitoring in the dynamic adjustment algorithm parameters;
[0048] The gravitational constant of the aggregation process: G, which represents the strength of attraction and merging during the aggregation process;
[0049] The target performance threshold in the termination condition: P_target, which indicates the target performance threshold reached;
[0050] The weight of the snowball algorithm when updating the solution position: W_snowball, which indicates the weight of the snowball algorithm when updating the solution position;
[0051] The weight of the honey bee algorithm when updating the solution position: W_bees, which indicates the weight of the honey bee algorithm when updating the solution position;
[0052] Weight of the aggregation process: W_aggregate, which represents the influence weight of the initial solution in the aggregation process;
[0053] The randomness parameter of the local search of the bee algorithm: P_random, which indicates the degree of randomness of the local search of the bee algorithm.
[0054] The weight of information transfer in hybrid cooperative updating: W_cooperation.
[0055] Step 2: Optimization process.
[0056] aUse the snowball algorithm to perform global search and update the position and size of each solution; when the snowball algorithm performs global search, it simulates the process of snowball rolling in the search space. Among them, the snowball algorithm can update the position and size of each solution, and the size of the solution reflects its performance level.
[0057] Specifically, the global search formula of the snowball algorithm is:
[0058] S[i]'=S[i]+W_snowball*R*np.random.rand(solution_dimensions)*np.sign(np.random.rand(solution_dimensions)-0.5); (1)
[0059] Among them, S[i]' represents the updated solution, S[i] represents the initial solution, np.random.rand(solution_dimensions) represents the random solution, and np.sign() represents the sign function.
[0060] b. Use the bee algorithm to make local adjustments to the solution obtained from the global search; individual bees search around the solution based on local information to fine-tune the strategy to adapt to the energy management needs of the current flight phase.
[0061] Specifically, the specific formula of the bee algorithm is:
[0062] S[i]'=S[i]+W_bees*D_bees*np.random.rand(solution_dimensions)*np.sign(np.random.rand(solution_dimensions)-0.5)+P_random*np.random.rand(solution_dimensions); (2)
[0063] Among them, S[i]' represents the updated solution and S[i] represents the initial solution.
[0064] c Aggregation process: The aggregation algorithm simulates the interactive behavior of snowballs, attracts, collides or merges the solutions in the search space to obtain the aggregated solution;
[0065] Specifically, the calculation formula of the aggregated solution is:
[0066] S[i]'=S[i]+W_aggregate*force*(S[j]-S[i]); (3)
[0067] Among them, S[i]' represents the updated solution, S[i] represents the initial solution, W_aggregate represents the weight of the aggregation process, G represents the gravitational constant of the aggregation process, and distance represents the distance between solution S[i] and solution S[j].
[0068] force=G / distance**2; (4)
[0069] distance=np.linalg.norm(S[i]-S[j]); (5)
[0070] Among them, np.linalg.norm() represents the norm function, and S[j] represents a solution different from S[i].
[0071] dThen, the snowball algorithm and the bee algorithm are exchanged with each other through the hybrid collaborative update algorithm to achieve global-local collaborative cooperation and obtain the solution after hybrid collaborative update.
[0072] The specific formula of the hybrid collaborative update algorithm is:
[0073] S[i]”=S[i]’+W_cooperation*(W_snowball*R*np.random.rand(solution_dimensions)*np.sign(np.random.rand(solution_dimensions)-0.5)+W_bees*D_bees*np.random.r and(solution_dimensions)*np.sign(np.random.rand(solution_dimensions)-0.5)+P_random*np.random.rand(solution_dimensions)+W_aggregate*force*(S[j]-S[i])); (6)
[0074] Where S[i]” represents the solution after hybrid cooperative update, W_cooperation represents the weight of information transmission in hybrid cooperative update, W_snowball represents the weight of the snowball algorithm, R represents the radius of the snowball algorithm, np.random.rand(solution_dimensions) represents a random solution, np.sign() represents the sign function, W_bees represents the weight of the bee algorithm when updating the position, D_bees represents the local search range of the bee algorithm, P_random represents the randomness parameter of the local search of the bee algorithm, W_aggregate represents the weight of the aggregation process, force = G / distance**2, where G represents the gravitational constant of the aggregation process, and distance represents the distance between the solution S[i] and the solution S[j].
[0075] In this embodiment, in each iteration, the snowball algorithm and the bee algorithm are exchanged with each other through the hybrid collaborative update algorithm to achieve global-local collaborative cooperation. Through the hybrid collaborative update algorithm, the better solution can be transferred to the bee algorithm through information transmission, guiding the local search to be more accurate.
[0076] Step 3: Obtain the flight status data of the solid rocket core stage in real time through the real-time monitoring module. According to the real-time flight status data, adjust the radius and rolling speed of the snowball algorithm and the local search range parameters of the bee algorithm, and repeat step 2.
[0077] In this embodiment, by introducing a real-time monitoring module, the real-time flight status data of the solid rocket core stage is obtained, and the real-time flight status data is used to dynamically adjust the parameters of the snowball algorithm and the bee algorithm, so as to ensure that the algorithm adapts to different flight stages. Specifically, in this embodiment, the radius and rolling speed of the snowball algorithm and the local search range of the bee algorithm can be adjusted according to the real-time flight status data, so as to ensure that the hybrid optimization algorithm of the present invention can perform well under different flight environments and load conditions.
[0078] Specifically, in this embodiment, the update formula of the radius of the snowball algorithm is:
[0079] R'=R*(1-W_monitor)+W_monitor*np.random.rand(); (7)
[0080] Among them, R' represents the radius of the updated snowball algorithm, R represents the radius of the snowball algorithm, W_monitor represents the weight of the real-time monitoring module, and np.random.rand() represents a random number;
[0081] The update formula of the local search range parameter of the bee algorithm is:
[0082] D_bees'=D_bees*(1-W_monitor)+W_monitor*np.random.rand(); (8)
[0083] Where D_bees' represents the local search range parameter of the updated honey bee algorithm.
[0084] Step 4: Determine whether the termination condition is met. If so, output the final energy management strategy as the optimal energy management strategy.
[0085] In step 4, if the number of iterations reaches a maximum number of iterations, or the performance reaches a predetermined performance target, it is determined that the termination condition is met.
[0086] Specifically, the step 4 further includes the following steps: calculating the performance value of the current solution and outputting the performance value.
[0087] The technical problems solved by the present invention are:
[0088] 1. Global-local optimization balance problem: Solid rocket core stages face the balance problem between global and local optimization during flight. Global search requires extensive exploration of possible solutions for energy management, while local adjustments require precise optimization at the detail level. This invention achieves global-local collaboration by introducing a hybrid optimization strategy based on the snowball algorithm and the honey bee algorithm, balancing the needs of both and improving the efficiency of global search and local adjustment.
[0089] 2. Real-time and adaptability challenges: Solid rocket core stages face dynamically changing conditions during flight, and energy management strategies need to be adjusted in real time to meet the needs of different flight phases. This invention uses a hybrid optimization algorithm, especially the dynamic global search capability of the snowball algorithm, to enhance the system's adaptability to dynamic environments, improve real-time performance, and ensure efficient response of energy management strategies in different flight phases.
[0090] 3. Optimization problems in complex dynamic environments: Solid rocket core stages operate in complex atmospheric and dynamic environments, which makes energy management problems complicated. Traditional algorithms may not be able to fully consider these factors, resulting in inaccurate optimization results. Through the global search of the snowball algorithm and the local adjustment of the bee algorithm, the present invention can more comprehensively consider and optimize the energy management strategy in complex environments.
[0091] 4. Efficient utilization of computing resources: Solid rocket core-stage energy management involves a large amount of data and calculations, requiring efficient algorithms to ensure the effective utilization of computing resources. The present invention improves the utilization efficiency of computing resources by hybrid optimization algorithms, especially combining the randomness of the snowball algorithm and the synergy of the bee algorithm, so that complex energy management optimization tasks can be completed under limited computing resources.
[0092] In summary, the present invention aims to solve the challenges of global-local balance, real-time and adaptability in the energy management of solid rocket core sub-stage, consider the optimization problems in complex dynamic environments, and efficiently utilize computing resources to improve the performance and adaptability of energy management strategies.
[0093] The following is the code for implementing the hybrid optimization algorithm in the present invention based on Python language:
[0094]
[0095]
[0096]
[0097]
[0098] The feasibility of the present invention has been demonstrated through a series of experiments, simulations and practical applications.
[0099] 1. Experimental verification: Through a large number of tests and experiments in a laboratory environment, the performance of the hybrid optimization algorithm in the solid rocket core-level energy management system was verified. During the experiment, a variety of test scenarios and simulation environments were used to simulate the complex conditions of different flight phases. Through real-time monitoring and feedback, the present invention can dynamically adjust the energy management strategy, effectively improving fuel utilization, stability and overall performance.
[0100] 2. Simulation verification: Through computational simulation and simulation experiments, using real environment data and system parameters, running the hybrid optimization algorithm and analyzing the results. These simulation verification results show that the hybrid optimization algorithm of the present invention can produce a control strategy with high stability for solid rocket core stage energy management.
[0101] In summary, the present invention provides a solid rocket core-level energy management method based on a hybrid optimization algorithm. Based on the hybrid optimization algorithm of the snowball algorithm and the bee algorithm, the energy management strategy of the solid rocket core-level is optimized, so that the energy management strategy can be intelligently adjusted both globally and locally to obtain the best performance, and can maximize fuel utilization, stability and performance during flight. Moreover, the present invention detects flight status data in real time, and uses real-time monitoring results and feedback information to adjust the search strategy in real time, so that the algorithm can dynamically adjust the search space and parameters to adapt to the changing conditions during the flight of the solid rocket, improve the flexibility of practical application, and enhance the robustness and adaptability of the algorithm. In addition, the present invention introduces performance evaluation and termination conditions to ensure that the algorithm can automatically terminate after reaching a predetermined performance target or a set number of iterations, thereby improving the practicality of the algorithm.
[0102] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.
Claims
1. A solid rocket core stage energy management method, characterized in that: The following steps are involved: Step 1: Initialize a set of initial solutions in the search space, each solution represents a potential energy management strategy; at the same time, set the parameters and weight parameters of the snowball algorithm and the bee algorithm, and set the termination conditions; Step 2: Use the snowball algorithm to perform a global search and update the position and size of each solution; use the bee algorithm to make local adjustments to the solution obtained from the global search; use the aggregation algorithm to simulate the interactive behavior of the snowball, attract, collide or merge the solutions in the search space to obtain the aggregated solution; then use the hybrid collaborative update algorithm to exchange information between the snowball algorithm and the bee algorithm to achieve global-local collaborative cooperation and obtain the solution after hybrid collaborative update; The global search formula of the snowball algorithm is as follows: S[i]'=S[i]+W_snowball*R*np.random.rand(solution_dimensions)* np.sign(np.random.rand(solution_dimensions)-0.5); Among them, S[i]' represents the updated solution, S[i] represents the initial solution, W_snowball represents the weight of the snowball algorithm, np.random.rand(solution_dimensions) represents the random solution, np.sign() represents the sign function; R represents the radius of the snowball algorithm; The specific formula of the bee algorithm is: S[i]'=S[i]+W_bees*D_bees*np.random.rand(solution_dimensions)* np.sign(np.random.rand(solution_dimensions)-0.5)+P_random* np.random.rand(solution_dimensions); Among them, W_bees represents the weight of the bee algorithm when updating the solution position, P_random represents the randomness parameter of the local search of the bee algorithm; D_bees represents the local search range of the bee algorithm; The specific formula of the aggregation algorithm is: S[i]'=S[i]+W_aggregate*force*(S[j]-S[i]); Where W_aggregate represents the weight of the aggregation process, force = G / distance**2, where G represents the gravitational constant of the aggregation process, and distance represents the distance between solution S[i] and solution S[j]; The specific formula of the hybrid collaborative update algorithm is: S[i]”=S[i]’+W_cooperation*(W_snowball*R* np.random.rand(solution_dimensions)* np.sign(np.random.rand(solution_dimensions)-0.5)+W_bees*D_bees* np.random.rand(solution_dimensions)* np.sign(np.random.rand(solution_dimensions)-0.5)+ P_random*np.random.rand(solution_dimensions)+W_aggregate*force*(S[j]-S[i])); Among them, S[i]” represents the solution after hybrid cooperative updating, and W_cooperation represents the weight of information transmission in hybrid cooperative updating; Step 3: Obtain the flight status data of the solid rocket core stage in real time through the real-time monitoring module. According to the real-time flight status data, adjust the radius and rolling speed of the snowball algorithm and the local search range parameters of the bee algorithm, and repeat step 2; Step 4: Determine whether the termination condition is met. If so, output the final energy management strategy as the optimal energy management strategy.
2. A solid rocket core stage energy management method according to claim 1, characterized in that: In step 1, setting the termination condition specifically refers to setting the maximum number of iterations and setting a predetermined performance target.
3. A solid rocket core stage energy management method according to claim 2, characterized in that: In step 4, if the number of iterations reaches a maximum number of iterations, or the performance reaches a predetermined performance target, it is determined that the termination condition is met.
4. A solid rocket core sub-stage energy management method according to claim 1, characterized in that: In the step 1, the parameters of the snowball algorithm and the bee algorithm are set, including the radius and rolling speed of the snowball algorithm, and the number of bees and the local search range of the bee algorithm.
5. A solid rocket core sub-stage energy management method according to claim 1, characterized in that: In step 1, the weight parameters include the weight of the snowball algorithm, the weight of the honey bee algorithm, the weight of the aggregation process, and the weight of the collaborative update.
6. A solid rocket core stage energy management method according to claim 1, characterized in that: In step 3, the update formula of the radius of the snowball algorithm is: R'=R*(1-W_monitor)+W_monitor*np.random.rand(); Among them, R' represents the radius of the updated snowball algorithm, W_monitor represents the weight of the real-time monitoring module, and np.random.rand() represents a random number; The update formula of the local search range parameter of the bee algorithm is: D_bees'=D_bees*(1-W_monitor)+W_monitor*np.random.rand(); Where D_bees' represents the local search range parameter of the updated honey bee algorithm.
7. A solid rocket core sub-stage energy management method according to claim 1, characterized in that: The step 4 also includes the following steps: calculating the performance value of the current solution and outputting the performance value.
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