Dynamic multi-objective evolutionary method, device and equipment for aluminum electrolysis process and storage medium

Abstract

The application provides a dynamic multi-objective evolutionary method, device and equipment in an aluminum electrolysis process and a storage medium, and relates to the technical field of aluminum electrolysis. The method takes multiple candidate operation parameter combinations of an aluminum electrolysis cell as a population, takes current efficiency and single-cell aluminum direct current power consumption per ton as optimization targets, and includes the following steps: adopting non-dominated sorting and crowded distance for regular evolution during an environment stable period; when a working condition change is detected, constructing an elite set and calculating center drift and direction vector, then adopting a confidence phase response strategy to adaptively adjust the response intensity of directional translation and random restart to generate a response population; at the same time, applying a perturbation to historical good operation parameters through a lightweight memory playback mechanism to generate immigrant individuals; fusing multiple source candidate solutions for environment selection, and online updating a confidence coefficient according to performance feedback to obtain a Pareto optimal solution set under a set condition. The method provided by the application has significant advantages in the balance between environment tracking stability, convergence and diversity.

Description

Technical Field

[0001] This application relates to the field of aluminum electrolysis technology, and in particular to a dynamic multi-objective evolution method, apparatus, equipment and storage medium in aluminum electrolysis process. Background Technology

[0002] Multi-objective optimization problems are widely found in process control, engineering design, and resource allocation. However, in practical applications, the drift of system operating conditions, disturbances in the external environment, and changes in constraints make optimization problems exhibit significant dynamic characteristics. The core challenge of dynamic multi-objective optimization problems (DMOPs) lies in the migration of their Pareto optimal front (PF) and Pareto optimal solution set (PS) over time. If the algorithm relies solely on steady-state evolution mechanisms, it is easily trapped in local searches of the old environment, making it difficult for the population to keep up with the new environment. This leads to performance degradation phenomena such as increased inverted generational distance (IGD), decreased hypervolume (HV), and uneven distribution of the solution set. For example, in the electrolytic aluminum production process, operating condition disturbances cause the trade-off between current efficiency and energy consumption targets to change over time, which is a typical engineering-type dynamic multi-objective optimization problem scenario.

[0003] To address the challenge of rapid adaptation in DMOPs, existing research mainly employs the following strategies, but limitations remain. First, migration and restart-based strategies enhance population diversity by introducing random individuals or performing local restarts. While these methods are generally applicable, they often sacrifice convergence stability in high-frequency changing environments, easily leading to drastic fluctuations in the solution set. Second, prediction-driven methods aim to estimate the moving manifold of PF / PS using historical data. The papers "XF Liu, XX Xu, ZH Zhan, et al. Interaction-based prediction for dynamic multiobjective optimization. IEEE Transactions on Evolutionary Computation, 2023, 27(6): 1881-1895" and "Y. Ye, S. Liu, J. Zhou, et al. Learning-Based Directional Improvement Prediction for Dynamic Multiobjective Optimization. IEEE Transactions on Evolutionary Computation, 2025, 29(4): 948-962" shorten the tracking path through interactive prediction and directional learning, respectively. However, when environmental changes exhibit nonlinear coupling, phase lag, or abrupt changes, the cumulative error generated by the prediction model often pushes the population into invalid regions. Furthermore, knowledge reuse and memory-assisted methods utilize transfer learning or external memory to reuse historical information to accelerate recovery.The papers "Y. Guo, G. Chen, M. Jiang, et al. A Knowledge Guided Transfer Strategy for Evolutionary Dynamic Multiobjective Optimization. IEEE Transactions on Evolutionary Computation, 2023, 27(6): 1750–1764" and "Y. Xie, Q. Zhao, W. Zhou, et al. Evolutionary Dynamic Multiobjective Optimization With Learning AcrossProblems. IEEE Transactions on Evolutionary Computation, 2025, 29(5): 1561–1574" respectively proposed knowledge-guided transfer and cross-problem learning frameworks. However, these methods not only face high computational costs but also need to address the risk of negative transfer caused by differences in cross-environmental distribution; direct memory replay without perturbation mechanisms may reduce population diversity. Finally, some studies have attempted to fuse multiple strategies using adaptive weights, but in high-frequency changing scenarios, competition among multiple strategies may induce population oscillations.

[0004] From an engineering perspective, the most challenging aspect of dynamic environments lies in the contradiction between the uncertainty of environmental change intensity and the limited resources available for algorithm evaluation. Existing fixed response patterns are prone to two failure dilemmas: over-response during minor environmental changes, leading to convergence regression; and tracking lag during dramatic environmental changes, resulting in continuous performance degradation. In continuous industrial processes like aluminum electrolysis, excessive response can cause strategy oscillations, while insufficient response can lead to lag in tracking energy-saving targets. Therefore, this balance problem has direct engineering significance. Thus, achieving an effective balance between rapid response and stable convergence is a pressing technical problem that needs to be solved. Summary of the Invention

[0005] This application provides a dynamic multi-objective evolution method, apparatus, equipment, and storage medium for aluminum electrolysis processes. It aims to address the dynamic drift and operating parameter coupling characteristics of aluminum electrolysis cell operating conditions by replacing completely random parameter restarts with directional responses of controllable intensity, and by using a lightweight memory playback mechanism to enhance the migration of high-quality operating parameter information across operating conditions, thereby achieving rapid adaptive optimization between conflicting objectives of current efficiency and DC power consumption.

[0006] In a first aspect, this application provides a dynamic multi-objective evolutionary method for aluminum electrolysis processes. The method uses multiple sets of candidate operating parameter combinations for the aluminum electrolysis cell as a population, with current efficiency and DC power consumption per ton of aluminum per cell as optimization objectives, and performs the following process: In each iteration, the environmental conditions of the aluminum electrolysis process are checked for changes. When no environmental changes are detected, conventional evolution is performed on the population using selection and genetic operators based on non-dominated sorting and crowding distance to generate the next generation population. When an environmental change is detected, a response and recovery process is executed to generate a new population. The new population is then used as the current population, and regular evolution is performed to generate the next generation of population. The next generation of the population is evaluated and the cumulative number of evaluations is recorded. If the cumulative number of evaluations does not reach the preset maximum number of evaluations, environmental changes are continuously monitored until the cumulative number of evaluations reaches the preset maximum number of evaluations. The population with the best evaluation is output as the Pareto optimal solution set. The Pareto optimal solution set includes the working voltage, series current, number of feedings, feeding amount, molecular ratio, cell temperature, aluminum level, fluoride salt addition amount, actual aluminum output and electrolyte level of the aluminum electrolysis cell. The response and recovery process includes: The current population is re-evaluated and non-dominated sorting is performed. The first non-dominated layer is selected as the elite set, which represents the combination of operating parameters with the best performance under the current environment. The center vector, drift intensity and direction vector of the elite set are calculated. Based on the drift intensity and direction vector, and by introducing phase weights and confidence coefficients to adaptively adjust the response intensity, a directional translation is performed on some combinations of operating parameters in the population, and a random restart is performed on another combination of operating parameters to generate a response population, which represents the candidate combinations of operating parameters after adapting to environmental changes. Maintain a limited-capacity elite memory bank, which stores historically excellent combinations of operating parameters; when the environment changes, extract memory individuals from the elite memory bank, which are historically excellent combinations of operating parameters, and apply perturbation to the memory individuals to generate immigrant individuals, which are combinations of operating parameters after the perturbation. The response population, immigrant individuals, and current candidate solutions are merged, and environmental selection is performed using non-dominated sorting and crowding distance to obtain a new population. Based on the performance feedback before and after the environmental change, the confidence coefficient is updated online to adjust the response strength for the next environmental change. The first non-dominated layer in the new population is used as the updated elite set and written into the elite memory, with entries retained according to a preset capacity.

[0007] In one possible design, the current center vector c of the elite set is...t Calculated using the following formula: Where A is the elite set, x is the individual decision-making variable in the elite set, and |A| is the size of the elite set; The drift intensity S t Through the center vector c at the previous time of change ( t -1) and the current center vector c( t Calculation of Euclidean distance; The direction vector passes through the current center vector. c ( t ) and the center of the entire population Calculation of vector difference.

[0008] In one possible design, when performing a directional translation on a partial combination of operational parameters in the population, the directional translation vector... Calculated using the following formula: in, Scaling factor S t For drift strength, The preset maximum translation coefficient, and These are the upper and lower bounds of the decision variable, respectively. It is the direction vector.

[0009] The scaling factor Calculated using the following formula: in, c Here is the confidence coefficient. w p is the phase weight, and clip is the clipping function.

[0010] In one possible design, the data is sourced from an elite memory bank. Individual memories extracted from Applying perturbations to generate immigrant individuals The method is expressed by the following formula: in, To revisit the disturbance intensity, and These represent the upper and lower bounds of the decision variable, respectively, and ⊙ indicates element-wise multiplication. It follows a normal distribution with a mean of 0 and a covariance of the identity matrix I. A random vector.

[0011] In one possible design, the confidence coefficient is updated online based on performance feedback before and after environmental changes, including: The confidence coefficient is updated based on the improvement magnitude imp of the reverse generation distance index before and after environmental change, wherein the improvement magnitude imp is calculated by the following formula: in, The reverse generational distance of the elite group before the change. This represents the reverse generation distance after the change. Here, `max` is a preset constant, and `maximum` is the function for the maximum value. Map imp to the target confidence level and update the confidence coefficients using exponential smoothing.

[0012] In one possible design, the metrics used to evaluate the next generation population include the reverse generation distance or hypervolume, the reverse generation distance being calculated as follows: in, For reverse generation distance, i The true Pareto frontier is represented by the first... The Euclidean distance between each solution and the individual closest to the obtained solution. SP Representing reality The number of upsampling points, | SP | represents the number of sampling points; The supervolume is calculated using the following formula: in, HV ( P,r (This is a supervolume) For an approximate solution set, As a reference point, For the first Solution in each target direction The interval to the reference point The volume of a multidimensional spatial region.

[0013] In one possible design, the method further includes a dynamic scene construction process, which specifically includes: A time-varying environment mechanism is introduced during the optimization process, and an environment index is defined. t : in, FE This is the current number of reviews. N For population size, The length of the evaluation window corresponding to each environmental test. The number of discrete slices within each window; Based on the environmental index, dynamic perturbations are applied to the decision variables to simulate the drift of aluminum electrolysis operating conditions. The method of applying dynamic perturbations to the decision variables based on the environmental index is expressed as follows: in, dηnAmp The disturbance amplitude coefficient, and Here, represents the upper and lower bounds of the decision variable, and x represents the individual decision variable in elite concentration. To use the environment index t Decision variables after perturbation.

[0014] Secondly, this application provides a dynamic multi-objective evolution device for aluminum electrolysis processes. The device includes an evolution module configured to use multiple sets of candidate operating parameters of the aluminum electrolysis cell as a population, and to obtain a Pareto optimal solution set by optimizing current efficiency and DC power consumption per ton of aluminum per cell. The evolution module includes: The environmental change detection unit is configured to detect whether environmental changes occur during each iteration of the aluminum electrolysis process; The conventional evolutionary unit is configured to perform conventional evolution on the population to generate the next generation population when no environmental change is detected, using selection and genetic operators based on non-dominated sorting and crowding distance. The response and recovery unit is configured to perform a response and recovery process to generate a new population when an environmental change is detected, and to use the new population as the current population to perform regular evolution to generate the next generation population; The iterative judgment unit is configured to evaluate the next generation of population and record the cumulative number of evaluations. When the cumulative number of evaluations has not reached the preset maximum number of evaluations, it continues to detect environmental changes until the cumulative number of evaluations reaches the preset maximum number of evaluations. The optimal population is then output as the Pareto optimal solution set. The Pareto optimal solution set includes parameters for adjusting the working voltage, series current, number of feedings, feeding amount, molecular ratio, cell temperature, aluminum level, fluoride salt addition amount, actual aluminum output, and electrolyte level of the aluminum electrolysis cell. The response and recovery process includes: The current population is re-evaluated and non-dominated sorting is performed. The first non-dominated layer is selected as the elite set, which represents the combination of operating parameters with the best performance under the current environment. The center vector, drift intensity and direction vector of the elite set are calculated. Based on the drift intensity and direction vector, and by introducing phase weights and confidence coefficients to adaptively adjust the response intensity, a directional translation is performed on some combinations of operating parameters in the population, and a random restart is performed on another combination of operating parameters to generate a response population, which represents the candidate combinations of operating parameters after adapting to environmental changes. Maintain a limited-capacity elite memory bank, which stores historically excellent combinations of operating parameters; when the environment changes, extract memory individuals from the elite memory bank, which are historically excellent combinations of operating parameters, and apply perturbation to the memory individuals to generate immigrant individuals, which are combinations of operating parameters after the perturbation. The response population, immigrant individuals, and current candidate solutions are merged, and environmental selection is performed using non-dominated sorting and crowding distance to obtain a new population. Based on the performance feedback before and after the environmental change, the confidence coefficient is updated online to adjust the response strength for the next environmental change. The first non-dominated layer in the new population is used as the updated elite set and written into the elite memory, with entries retained according to a preset capacity.

[0015] Thirdly, embodiments of this application provide an electronic device, including: at least one processor and a memory; the memory stores computer execution instructions; the at least one processor executes the computer execution instructions stored in the memory, causing the at least one processor to perform the dynamic multi-objective evolution method in the aluminum electrolysis process as described in the first aspect and various possible designs of the first aspect.

[0016] Fourthly, embodiments of this application provide a computer-readable storage medium storing computer-executable instructions. When a processor executes the computer-executable instructions, it implements the dynamic multi-objective evolution method in the aluminum electrolysis process described in the first aspect and various possible designs of the first aspect.

[0017] Fifthly, embodiments of this application provide a computer program product, including a computer program that, when executed by a processor, implements the dynamic multi-objective evolution method in the aluminum electrolysis process as described in the first aspect and various possible designs of the first aspect.

[0018] The dynamic multi-objective evolution method, apparatus, equipment, and storage medium for aluminum electrolysis provided in this application have at least the following beneficial effects: (1) This application proposes a confidence phase response mechanism, which accurately estimates the environmental change vectors of parameters such as working voltage, series current, and feed rate by utilizing the center displacement of the elite solution set in the decision space (i.e., the operating parameter combination space) before and after changes in the operating conditions of the aluminum electrolysis cell. It also introduces phase weights and confidence coefficients to adaptively adjust the response intensity of the directional translation, while combining a small amount of random reinitialization. This confidence phase response mechanism can achieve a fast and robust parameter response to the time-varying drift of the target relationship between current efficiency and DC power consumption during aluminum electrolysis, avoiding over-adjustment caused by small changes in operating conditions or response lag during drastic changes.

[0019] (2) This application designs a lightweight memory replay mechanism, which generates immigrant individuals by maintaining a limited-capacity elite archive (i.e., historical optimal operating parameter combinations) and applying controllable perturbations to historical elite individuals when the environment changes. This lightweight memory replay mechanism significantly enhances the population's resilience and operating parameter diversity under different operating conditions with extremely low additional computational overhead, effectively solving the problem of aluminum electrolysis production falling into local optima due to long-term solidification of operating parameters.

[0020] (3) This application establishes a feedback-driven confidence update strategy. Under a unified evolutionary framework, the response confidence is dynamically updated online based on the performance feedback before and after changes in aluminum electrolysis operating conditions (such as the increase in current efficiency or the decrease in DC power consumption), thereby effectively reducing the risk of erroneous responses caused by misjudging the intensity of environmental changes. Multiple standard dynamic multi-objective test problems and actual aluminum electrolysis data-driven optimization scenarios have demonstrated that this confidence update strategy achieves excellent tracking stability and can continuously provide the electrolyzer with optimal operating parameter configurations to adapt to operating condition drift. Attached Figure Description

[0021] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0022] Figure 1 A flowchart of a dynamic multi-objective evolution method in an aluminum electrolysis process provided in this application embodiment; Figure 2 A flowchart of a dynamic multi-objective evolution method in an aluminum electrolysis process provided in this application embodiment; Figure 3 This is another flowchart of a dynamic multi-objective evolution method in an aluminum electrolysis process provided in an embodiment of this application; Figure 4 A comparison of the Pareto front distribution of the method provided in this application and the comparative method on the DF1 dynamic multi-objective test problem; wherein, (a) CPRLMR (the method of this application); (b) AENSGAII; (c) CGLP; (d) KLNSGAII; Figure 5 A three-dimensional Pareto front distribution comparison diagram of the method and comparison algorithm provided in the embodiments of this application on the FDA5 dynamic multi-objective testing problem; wherein, (a) CPRLMR (the method of this application); (b) AENSGAII; (c) CGLP; (d) KLNSGAII; Figure 6 The performance index fitting curves of the No. 301 electrolytic cell model provided in the embodiments of this application are shown; where (a) is the current efficiency fitting curve and (b) is the DC power consumption fitting curve per ton of aluminum in a single cell. Figure 7 This is a structural diagram of the dynamic multi-objective evolution device in the aluminum electrolysis process provided in the embodiments of this application.

[0023] The accompanying drawings illustrate specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concepts of this application to those skilled in the art through reference to specific embodiments. Detailed Implementation

[0024] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0025] The collection, storage, use, processing, transmission, provision, and disclosure of relevant data and information in the technical solution of this application all comply with the provisions of relevant laws and regulations and do not violate public order and good morals.

[0026] It should be noted that in the embodiments of this application, certain software, components, models and other existing solutions in the industry may be mentioned. These should be regarded as exemplary and are only intended to illustrate the feasibility of implementing the technical solution of this application. However, it does not mean that the applicant has used or necessarily used the solution.

[0027] The technical solution of this application and how the technical solution of this application solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will now be described with reference to the accompanying drawings.

[0028] To address the challenges of Pareto front and solution set drift caused by time-varying environments in dynamic multi-objective optimization, leading to algorithm response lag, loss of diversity, and insufficient tracking accuracy, this embodiment proposes a dynamic multi-objective evolutionary method (Confidence-phase response with light memory replay, CPRLMR) for aluminum electrolysis. This method establishes a two-layer response mechanism: First, a confidence-phase response strategy is proposed, using the displacement of the elite solution set center within the decision space to estimate the environmental change vector. Phase weights and confidence coefficients are introduced to adaptively adjust the response intensity, and directional translation and random reinitialization are combined to achieve rapid environmental response. Second, a lightweight memory replay mechanism is designed, maintaining a limited-capacity elite database and introducing perturbations to generate immigrant individuals during environmental changes, enhancing the population's cross-environmental resilience and diversity. Furthermore, the main body of this dynamic multi-objective evolutionary method employs a selection framework based on non-dominated sorting and updates the response confidence online based on performance feedback before and after environmental changes, thereby reducing the risk of misjudgment. Simulation experiments and IGD and HV index analyses on multiple benchmark dynamic problems demonstrate that CPRLMR exhibits significant advantages in balancing environmental tracking stability, convergence, and diversity. Further application results in an aluminum electrolysis process optimization scenario validate the effectiveness and generalizability of this algorithm in practical industrial dynamic decision-making.

[0029] The dynamic multi-objective evolutionary method in this aluminum electrolysis process follows a framework of steady-state evolution and change response: during stable environmental periods, conventional evolution is performed using selection based on non-dominated sorting and crowding distance, along with genetic operators; once an environmental change is detected, a collaborative recovery mechanism consisting of confidence phase response (CPR) and lightweight memory replay (LMR) is immediately triggered, and the response confidence is dynamically updated based on performance feedback before and after the environmental change, thus achieving a balance between rapid tracking of the dynamic environment and stable convergence of the algorithm. Specifically, this method uses multiple sets of candidate operating parameter combinations for the aluminum electrolysis cell as a population, with current efficiency and DC power consumption per ton of aluminum per cell as optimization objectives, and performs a combination of... Figure 1 Steps S10-S40 are shown.

[0030] S10: In each iteration, detect whether the aluminum electrolysis operating conditions have changed.

[0031] In practical implementation, at the beginning of each iteration cycle (i.e., each generation of evolution), a preset environmental change detection function in the dynamic multi-objective optimization problem interface can be invoked to re-evaluate the current population and determine whether the aluminum electrolysis operating conditions have drifted. Specifically, the objective function values ​​(i.e., current efficiency and DC power consumption per ton of aluminum per cell) of individuals in the current iteration are compared with the objective function values ​​of the same individuals in the previous iteration. If the difference between the re-evaluated objective function value and its historical value for any individual exceeds a preset threshold, for example, if the absolute value of the change in current efficiency exceeds 0.1%, or the absolute value of the change in DC power consumption per ton of aluminum exceeds 5 kWh / t-AL, then it is determined that the aluminum electrolysis operating conditions have changed environmentally. If the change in the objective function values ​​of all individuals does not exceed the threshold, then it is determined that the environment has not changed. If no environmental change is detected, step S20 is executed. If an environmental change is detected, step S30 is executed.

[0032] S20: When no environmental changes are detected, the population is subjected to conventional evolution using selection and genetic operators based on non-dominated sorting and crowding distance to generate the next generation of population.

[0033] In step S20, when it is determined that the aluminum electrolysis operating conditions have not changed, a steady-state evolution mode is entered. First, based on the non-dominated ordination results and crowding distance in the current population, a tournament selection mechanism is used to select parent individuals from the population to form a mating pool. Subsequently, genetic operators such as simulated binary crossover and polynomial mutation are applied to the parent individuals in the mating pool to generate offspring populations. After merging the parent and offspring populations, environmental selection is performed again using non-dominated ordination and crowding distance to select the next generation population with a population size of N. This process maintains population convergence (approaching the true Pareto front of current efficiency and DC power consumption) while ensuring the uniform distribution of operating parameter combinations in the decision space, and can also reserve diverse candidate solutions for possible subsequent operating condition drift.

[0034] S30: When an environmental change is detected, a response and recovery process is executed to generate a new population. The new population is used as the current population, and regular evolution is performed to generate the next generation of population.

[0035] The purpose of step S30 is to update the population by performing a response and recovery process in response to environmental changes, and to generate the next generation of population by performing regular evolution on the updated population. The method of regular evolution is the same as that of step S20, so it will not be described in detail here.

[0036] like Figure 2 As shown, the response and recovery process in step S30 includes the following steps S301-S305.

[0037] S301: Re-evaluate the current population and perform non-dominated sorting. Select the first non-dominated layer as the elite set, which represents the best combination of operating parameters under the current environment. Calculate the center vector, drift intensity, and direction vector of the elite set.

[0038] The purpose of step S301 is to construct elite information. In dynamic multi-objective optimization problems, environmental changes over time can cause PF / PS to drift, resulting in tracking lag and ineffective search in the population after environmental switching. In some embodiments, in order to characterize environmental changes without significantly increasing computational overhead, an elite information construction module is introduced after detecting environmental changes: the first non-dominated elite set in the current environment is used as the most stable and representative sample. The main trend of environmental changes is approximated by the center drift of the elite set in the decision space, and reference information at the population level (such as the overall center) is constructed simultaneously to help characterize the offset structure of the superior region relative to the population. In each iteration, change detection is first performed through the problem interface. When environmental changes are detected, the current population is updated or re-evaluated and non-dominated sorting is performed, and the first non-dominated layer is selected as the elite set A. Let the set of decision variables corresponding to the elite set be X, and its center vector is defined as shown in equation (1): (1) Where A is the elite set, x is the individual decision-making variable in the elite set, and |A| is the size of the elite set.

[0039] This embodiment maintains the center vector at the previous time of change. And the drift amount, i.e., the drift intensity As an approximate measure of the intensity of change. Furthermore, let the center of the entire population be... Then define the direction vector. This is used to characterize the offset trend of the superior region relative to the overall population. The drift intensity, drift direction, and relative offset parameters output by this elite information construction module will serve as important bases for the adaptive CPR response intensity and directional translation in subsequent steps.

[0040] S302: Based on the drift intensity and direction vector, and introducing phase weight and confidence coefficient to adaptively adjust the response intensity, a directional translation is performed on some combinations of operating parameters in the population, and a random restart is performed on another combination of operating parameters to generate a response population. The response population represents the candidate combinations of operating parameters after adapting to environmental changes.

[0041] Step S302 specifically involves the confidence phase response step. In dynamic multi-objective optimization, the intensity and direction of environmental changes often exhibit irregular fluctuations, encompassing various modes ranging from slight drift to significant migration. This uncertainty poses a dilemma for fixed-amplitude response strategies: excessively large amplitudes can lead to over-perturbation and performance degradation; excessively small amplitudes result in response lag, causing tracking failure. To accurately match the intensity of dynamic changes, this embodiment proposes an adaptive response strategy.

[0042] The core of this adaptive response strategy lies in introducing an amplitude scaling mechanism that combines phase weights and response confidence. First, based on the number of evaluations or generations, the current environment within the time window is estimated. The evolution phase within the time frame is determined, and the phase weights are calculated. First, it adaptively adjusts the sensitivity to environmental changes at different stages; second, it maintains a response confidence level and confidence coefficient. This is used to characterize the effectiveness of the current response strategy in the near term.

[0043] When environmental changes are detected, the proportion of the population is... Individuals perform directional translation, with a ratio of Individuals undergo random restarts. The directional translation vector is defined as shown in equation (2): (2) Among them, among them, Scaling factor S t For drift strength, The preset maximum translation coefficient, and These are the upper and lower bounds of the decision variable, respectively. For direction vector, scaling factor The definition is shown in equation (3): (3) Where clip is the clipping function. In addition, to maintain population diversity, noise terms can be superimposed during the translation process. Randomly restarted individuals are then uniformly sampled directly within the search space boundary. After these two types of operations are completed, the newly generated decision variables are boundary-corrected and re-evaluated to obtain a population that has adapted to environmental changes. Through this adaptive scaling and hybrid response mechanism, the convergence structure of the population can be effectively reconstructed, enabling fast and robust tracking of dynamic targets.

[0044] S303: Maintain a limited-capacity elite memory bank to store historically excellent combinations of operating parameters; when the environment changes, extract memory individuals from the elite memory bank, which are historically excellent combinations of operating parameters, and apply perturbation to the memory individuals to generate immigrant individuals, which are combinations of operating parameters after the perturbation.

[0045] Step S303 is the Lightweight Memory Replay (LMR) step. To compensate for the insufficient robustness of a single predictive response and overcome the high cost of full memory storage, this embodiment introduces a Lightweight Memory Replay (LMR) strategy. This strategy constructs a miniature dynamic elite library. When the environment drifts, the algorithm selects a small number of elite individuals from the pool and applies random perturbations to them to generate "immigrants" that are injected into the current population. The core mechanism of LMR lies in "constrained capacity" and "perturbation injection," which enables the proposed method to effectively utilize historical experience to accelerate convergence with extremely low additional computational overhead, while avoiding the risk of diversity depletion caused by direct replay.

[0046] Relying solely on the current prediction response may lead to delayed population recovery due to the complexity of environmental changes. Therefore, this embodiment maintains a limited-capacity elite memory bank. It continuously accumulates recent non-dominant frontier individuals. When a change is detected and LMR is triggered, it is retrieved from the elite memory bank. Individual memories extracted from And apply a small perturbation to its decision vector, as shown in equation (4): (4) in, To revisit the disturbance intensity, and These represent the upper and lower bounds of the decision variable, respectively, and ⊙ indicates element-wise multiplication. It follows a normal distribution with a mean of 0 and a covariance of the identity matrix I. A random vector.

[0047] Subsequently, the generated individuals are subjected to boundary constraints and re-evaluated to form a migration set. This lightweight memory replay strategy can quickly replenish a batch of "historically feasible and high-quality" candidate solutions after environmental changes, while avoiding population aggregation and premature convergence caused by static replay through perturbation strategies.

[0048] S304: Merge the responding population, immigrant individuals, and current candidate solutions, and use non-dominated ranking and crowding distance to select the environment and obtain a new population; based on the performance feedback before and after the environmental change, update the confidence coefficient online to adjust the response strength for the next environmental change.

[0049] Step S304 involves response fusion and confidence update. In dynamic environments, candidate solutions often originate from multiple sources, such as elite retention, prediction generation, and memory replay. Faced with such multi-source information, directly replacing the population without an effective screening and evaluation mechanism can easily lead to over-response or misjudgment of evolutionary direction, resulting in algorithm performance degradation due to uncertainty. Therefore, this embodiment proposes a response fusion and confidence update strategy to specifically implement steps S60 and S70. First, a response fusion mechanism is constructed: the population after response, LMR migrants, and other candidate solution sets are merged into a mixing pool, and environmental selection criteria such as non-dominated sorting and crowding distance are used to selectively retain the best solutions, achieving robust fusion and smooth transition of multi-source information. Second, an online confidence update mechanism is introduced: an evaluation system based on performance feedback is established, which determines the effectiveness of the response online by quantifying the differences in indicators before and after environmental changes, and dynamically corrects the subsequent response intensity accordingly, thereby effectively avoiding the risk of misleading information while utilizing historical information.

[0050] After the change response, the original elite set, LMR migrants, and the current candidate solution pool are merged, and a selection is made using non-dominated ranking and crowding distance (or reference point association strategy) to obtain a new population of size 𝑁. To mitigate the risk of erroneous responses, feedback is constructed using the improvement magnitude of IGD before and after the change: Let the IGD of the elite set before the change be denoted as . After the change, the elite group IGD became The relative improvement is shown in equation (5): (5) in, The reverse generational distance of the elite group before the change. This represents the reverse generation distance after the change. is a preset constant, and max is the maximum value function.

[0051] The imp is mapped to the target confidence level, and the confidence level parameter, i.e., the confidence coefficient c, is updated using exponential smoothing. When the response leads to significant degradation, a selection mechanism is used to backtrack or merge the populations before and after the change to avoid further performance decline. Finally, the process returns to the normal evolutionary stage and continues the selection-crossover-mutation iterative process until the maximum number of evaluations is reached. Through the above response fusion and confidence update mechanism, the reliability of the environmental response and the diversity of the population are effectively balanced. While suppressing performance fluctuations caused by erroneous responses, the long-term tracking stability in dynamic scenarios is significantly improved.

[0052] S305: The first non-dominated layer in the new population is used as the updated elite set, written into the elite memory, and the entries are retained according to the preset capacity.

[0053] In step S305, a non-dominated sort is performed on the new population obtained in step S304, and the first non-dominated layer is extracted as the updated elite set. This elite set represents the optimal combination of operating parameters under the current environment. All individuals in this elite set are written into an elite memory bank with a preset capacity. If the number of individuals in the memory bank exceeds the preset capacity after writing, for example, 100 individuals, they are eliminated according to the strategy of retaining the latest entry or retaining the best entry. Retaining the latest entry means deleting the earliest stored individual, and retaining the best entry means deleting the worst-quality individual based on the non-dominated sort and crowding distance, thereby ensuring that the memory bank always stores the most valuable historical optimal combination of operating parameters within a limited capacity. This elite memory bank is used to extract memory individuals and apply perturbation to generate immigrant individuals when environmental changes are detected again, so as to enhance the population recovery capacity and diversity under different working conditions.

[0054] S40: Evaluate the next generation population and record the cumulative number of evaluations. If the cumulative number of evaluations does not reach the preset maximum number of evaluations, continue to monitor environmental changes until the cumulative number of evaluations reaches the preset maximum number of evaluations. Output the population with the best evaluation as the Pareto optimal solution set. The Pareto optimal solution set includes the working voltage, series current, number of feedings, feeding amount, molecular ratio, cell temperature, aluminum level, fluoride salt addition amount, actual aluminum output, and electrolyte level of the aluminum electrolysis cell.

[0055] In step S40, the objective function value (current efficiency and DC power consumption per ton of aluminum per cell) is calculated for each individual in each generation of the population (i.e., each combination of candidate operating parameters). Each calculation is counted as one evaluation, and the results are accumulated to the cumulative evaluation count. When the cumulative evaluation count is less than the preset maximum evaluation count (e.g., 60,000 times), the process returns to step S10 to continue iterating; otherwise, the optimization process is terminated, and the non-dominated individuals in the current population (i.e., all individuals in the first non-dominated layer) are output as the final Pareto optimal solution set. This maximum evaluation count control mechanism ensures that the algorithm has sufficient search resources to fully approximate the Pareto front in a dynamic environment, while avoiding computational redundancy caused by infinite iteration. Thus, within a limited computational budget, the optimal solution set suitable for adjusting the operating parameters of the aluminum electrolysis cell is obtained.

[0056] In one specific embodiment, the dynamic multi-objective evolution method for aluminum electrolysis proposed in this application follows a unified operational framework of normal evolution and change-triggered recovery, aiming to balance convergence and diversity in dynamic environments. Figure 3As shown, in the initialization phase, based on the given population size N, target dimension M, decision variable dimension D, and their upper and lower bounds, the algorithm first generates an initial solution set using an oversampling strategy and then truncates it to a preset size through environmental selection. Subsequently, it performs several hot-start iterations involving selection, crossover, and mutation to quickly form a stable first non-dominated front, laying the foundation for subsequent evolution.

[0057] After entering the main loop, the operational logic of this application's method is divided into two branches based on the environmental state. During the stable period when the environment remains unchanged, a normal evolutionary mode is maintained: parent generations are selected through an environmental selection mechanism based on non-dominated sorting and crowding distance, a mating pool is constructed using tournament selection, and genetic operators are applied to generate the offspring population. After merging parent and offspring generations, environmental selection is performed again to maintain the population size N, and the first frontier and elite memory are updated simultaneously, thereby ensuring the convergence accuracy and distribution breadth of the population in a static environment.

[0058] Once environmental changes are detected through the detection mechanism, the system immediately switches to the collaborative recovery branch. First, an elite set is constructed based on the current first frontier, and its center drift and relative direction are calculated to approximate the trend and intensity of environmental changes. Then, a confidence phase response (CPR) strategy is implemented: on the one hand, a directional translation is applied to some individuals using phase weights and confidence coefficients, with a small amount of noise superimposed; on the other hand, a small number of individuals are randomly restarted to enhance global exploration capabilities. Next, a lightweight memory replay (LMR) mechanism is activated, extracting historically superior individuals from a limited-capacity elite memory bank, applying perturbations to generate migration solutions, supplementing sampling of potential advantageous regions and improving population diversity.

[0059] After the response operation is completed, the candidate set is merged. Specifically, the predicted population, replay migrants, and the current candidate solution set are merged, and robust selection is performed again using non-dominated ranking and crowding distance to restore the population size to N. Simultaneously, the response confidence is updated online based on performance feedback before and after environmental changes. If significant performance degradation is detected, a rollback or fusion strategy is adopted to mitigate the risks of erroneous responses. After completing the above recovery process, the process returns to the normal evolutionary phase and continues iterating until the maximum number of evaluations or the termination condition is met.

[0060] To verify the tracking ability and stability of the proposed method (CPRLMR) in dynamic environments, this embodiment conducts comparative experiments on typical dynamic multi-objective testing problems within the PlatEMO framework. All methods are run under the same evaluation budget and population size, and are repeatedly run independently multiple times to reduce the impact of randomness. The performance index changes over time at each environmental moment to measure the method's ability to continuously approximate and preserve the distribution of dynamic PF.

[0061] The proposed method was compared with three representative dynamic multi-objective methods—AENSGA-II, CGLP, and KLNSGA-II—on the DF and FDA classic dynamic multi-objective test sets. Specific parameter configurations are shown in Table 1. Among them, AENSGA-II refers to the existing literature "L. Feng, W. Zhou, W. Liu, et al. Solving Dynamic Multiobjective Problemvia Autoencoding Evolutionary Search. IEEE Transactions on Cybernetics, 2022,52(5): 2649-2662", and CGLP refers to the existing literature "K. Yu, D. Zhang, J. Liang, et al. ACorrelation-Guided Layered Prediction Approach for Evolutionary DynamicMultiobjective Optimization. IEEE Transactions on Evolutionary Computation, 2023, 27(5): 1398-1412", KLNSGA-II refers to the existing literature "Q. Zhao, B. Yan, Y. Shi, M.Middendorf. 6119-6130》.

[0062] To ensure fairness, all methods are uniformly set to a population size of N, and the maximum number of evaluations is [value missing]. And the same crossover and mutation operators are used. The frequency of environmental changes is determined by a time window. With time slices To ensure the effectiveness of the method, multiple environmental changes were implemented throughout the evaluation process, allowing for the assessment of its resilience. Each experiment was run independently 10 times, and the mean and standard deviation were used as the final results.

[0063] Table 1 Parameter Settings

[0064] This embodiment uses two types of indicators, IGD and HV, to evaluate the algorithm performance, and continuously records its change curves over several generations after each environmental change. IGD The average nearest distance from the sampling point of the real PF to the non-dominated solution set obtained by the method can simultaneously reflect the approximation and distribution. The smaller the value, the more accurate the tracking of the current PF. The calculation process is shown in Equation (6): (6) in, i Represents the first true Pareto front (PF) on the true Pareto front. The Euclidean distance between each solution and the individual closest to the obtained solution. SP Representing reality The number of upsampling points, | SP | Number of sampling points HV measures the hypervolume covered by the solution set relative to the reference point, comprehensively reflecting convergence and diversity. A larger value indicates that the solution set covers more fully. The calculation process is shown in formula (7): (7) in, HV ( P,r (This is a supervolume) For an approximate solution set, As a reference point, For the first Solution in each target direction The interval to the reference point The volume of a multidimensional spatial region.

[0065] As can be seen from the statistical data in Tables 2 and 3, CPRLMR exhibits a significant performance advantage on the vast majority of test problems. In terms of the IGD metric (Table 2) for convergence and the HV metric (Table 3) for overall performance, CPRLMR achieves superior statistical results compared to baseline algorithms such as AENSAGAII, CGLP, and KLNSGAII (see the "+ / - / =" statistical rows at the bottom of Tables 2 and 3). Specifically, in the DF series and most FDA series problems, CPRLMR consistently achieves lower mean IGD and higher mean HV. This indicates that the proposed method not only more accurately approximates the true Pareto front (PF) but also performs well in terms of the breadth and uniformity of solution distribution. In contrast, baseline algorithms often experience a sharp increase in IGD and drastic fluctuations in HV when the environment changes drastically, and require a long number of generations to recover to a steady state. This usually means that the population fails to respond promptly to environmental migration and remains trapped in an ineffective search for outdated PFs.

[0066] To delve deeper into the source of CPRLMR's performance advantages, this embodiment analyzes the algorithm mechanism in conjunction with the dynamic characteristics of the environment. From the IGD data fluctuations in Table 2, it can be inferred that CPRLMR, by introducing the directional translation mechanism of the CPR strategy, can rapidly push the population to the high-potential zone of the new environment during environmental transitions, thus significantly suppressing the occurrence of IGD peaks and shortening the time for the population to reconverge to a steady state. Simultaneously, the LMR mechanism promptly supplements a batch of candidate solutions with historical transferability after environmental changes and applies small perturbations through the lmrJitter strategy, effectively avoiding the problem of solution set homogenization caused by over-clustering. This improvement in mechanism is intuitively confirmed in the HV data in Table 3: even in environments with large changes or periodic variations, CPRLMR can still maintain a relatively smooth HV curve, successfully achieving a balance between rapid response and convergence stability, avoiding the convergence regression phenomenon that may be caused by conventional restart strategies.

[0067] Table 2 Comparison of IGD values

[0068] Table 3 Comparison of HV values

[0069] Figure 4 and Figure 5 The comparison plot of the Pareto front distribution further visually corroborates the conclusions of the above numerical analysis. Figure 4 Taking the DF1 problem in the example, Figure 4 (a) shows that the solution set generated by CPRLMR is closely distributed near the real Pareto front in the target space formed by the target values ​​f1 and f2, and has good convergence and uniform distribution. Figure 4 In (b), although the solution set generated by AENSAGAII is generally distributed along the true Pareto front, its dispersion is relatively large, and there is still some deviation in some regions; in contrast, Figure 4 In (c), the solution set distribution of CGLP is relatively scattered and deviates significantly from the true Pareto front. Figure 4 In (d), KLNSGAII also exhibits some convergence bias. Similarly, in Figure 5 In the FDA Question 5 three-objective frontier distribution shown, Figure 5 (a) shows that the solution set obtained by CPRLMR can cover the real Pareto front surface relatively comprehensively and uniformly; Figure 5 While AENSAGAII in (b) can cover part of the real frontier region, its overall distribution is not uniform, and there is insufficient coverage in some areas; Figure 5 The solution set of CGLP in (c) is relatively sparse. Figure 5 In the middle (d) region, KLNSGAII exhibits a clear local aggregation phenomenon. (Comprehensive) Figure 4 and Figure 5 It can be seen that CPRLMR exhibits good convergence and distribution across different dimensions and types of dynamic problems, indicating that the proposed method can recover quickly after environmental changes and maintain good solution set stability and coverage in subsequent evolution.

[0070] This embodiment further compares the above-mentioned existing methods with the method of this application in a practical application case of optimizing aluminum electrolysis operating parameters to illustrate the progress of the method of this application.

[0071] The aluminum electrolysis process is based on the Hall-Héroult mechanism, reducing alumina (Al₂O₃) to metallic aluminum in a high-temperature molten electrolyte. The electrolytic cell, as the core reaction unit, consists of an anode, a cathode, an electrolyte (primarily cryolite-based), and a liquid aluminum layer. In industrial production, a high-current direct current passes through the cell, causing liquid aluminum to deposit at the cathode and gas to be generated at the anode. This process operates under high-temperature conditions for extended periods, making the system's energy efficiency highly sensitive to process parameters.

[0072] From an operational perspective, current efficiency and DC power consumption per ton of aluminum are key indicators affecting economic efficiency and energy consumption levels. These two factors exhibit typical coupling and conflict: improving current efficiency often requires adjusting voltage, current, and electrolyte state, which can lead to changes in power consumption; conversely, reverse voltage drop can sacrifice some efficiency. Therefore, achieving a better compromise solution under conflicting objectives is of practical value for on-site optimization.

[0073] This embodiment divides the modeling and optimization process of the electrolytic aluminum case into six steps: Step 1: Define the objective and decision variables.

[0074] The objective function is set as current efficiency. C e DC power consumption per ton of aluminum in a single cell C DC Under the unified minimization framework, the objective function is expressed as: f 1=- C e , f 2= C DC Decision variables include operating voltage. Series current Number of feedings Material feed amount Molecular ratio bath temperature Aluminum level A. Fluoride addition amount Actual aluminum output and electrolyte levels .

[0075] Step 2, data collection and sample screening.

[0076] The data comes from daily stable operating data of tank No. 301 of an aluminum company in Chongqing, totaling 1365 sets. The original data was validated, missing, abnormal codes, and illegal samples were removed, and variable boundary consistency was checked to form a modelable sample set.

[0077] Step 3: Data partitioning and preprocessing.

[0078] A fixed-random partitioning method was used: first, the training pool and test set were divided in an 8:2 ratio; then, within the training pool, the training set and validation set were divided in an 8:2 ratio, resulting in 874 training sets, 218 validation sets, and 273 test sets. Input variables were standardized to reduce the impact of differences in units on the stability of network training.

[0079] Step 4, Model Building.

[0080] A dynamic multi-objective optimization model for aluminum electrolytic cells is established using a backpropagation neural network (BPNN). ]

[2222] Establish decision variables to objectives C e and C DC The mapping relationship is as follows. The network structure is 10-16-8-2, the training function is trainbr (Bayesian Regularization), the hidden layer transfer function is tansig, the output layer transfer function is purelin, and the maximum number of training epochs is 1000. Model parameters and variable constraints are shown in Tables 4 and 5, and the comparison between predicted and true values ​​on the test set is shown in Table 5. Figure 6 .

[0081] Table 4 Parameter settings for BPNN

[0082] Table 5 Boundary conditions for decision variables

[0083] Step 5, Dynamic Scene Construction.

[0084] To reflect the dynamic multi-objective characteristics, a time-varying environment mechanism is introduced. The environment index is defined as: Where N is the population size. This indicates the length of the evaluation window corresponding to each environmental test. This represents the number of discrete slices within each window.

[0085] And adjust the dynamic disturbance of the decision variable: in, dηnAmp The disturbance amplitude coefficient, Let x be the individual decision-making variable for elite concentration. To use the environment index t Decision variables after perturbation.

[0086] The data is then projected back to the variable boundary interval. This process is used to simulate the dynamic changes in the target relationship under operating condition drift and load fluctuation.

[0087] Step 6: Dynamic optimization and performance evaluation.

[0088] Experiments were conducted on the proposed algorithm and comparative algorithms under a consistent computational budget, with Hreto value (HV) used as the evaluation metric. Table 6 shows the HV comparison results for each algorithm in the electrolytic aluminum application problem, and Table 7 shows the comparison of target values ​​before and after optimization. Experimental results show that the proposed method is superior in terms of overall HV, indicating that it can obtain a higher quality Pareto solution set in the trade-off between improving current efficiency and reducing DC power consumption.

[0089] Table 6. Comparison of HV results of various methods in electrolytic aluminum application problems.

[0090] Table 7 Comparison of target values ​​before and after optimization

[0091] In summary, to address the challenges of inconsistent environmental change intensity, unstable response strategies, and the difficulty in balancing tracking accuracy and population diversity in dynamic multi-objective optimization, a dynamic multi-objective evolutionary method, CPRLMR, is proposed for aluminum electrolysis. During the normal evolution phase, this method employs a steady-state selection mechanism based on non-dominated ranking and crowding distance to maintain population convergence and distribution. At environmental change moments, the method utilizes the elite center drift vector to estimate the direction and intensity of change and constructs a confidence phase response (CPR) mechanism. This mechanism adaptively adjusts the directional translation amplitude through phase weights and confidence coefficients, while incorporating a small number of random restarts to restore exploration capabilities. Furthermore, lightweight memory replay (LMR) provides transferable candidate solutions and supplements diversity for new environments through a finite-capacity elite memory and perturbation replay. Experiments show that online confidence updates based on performance feedback before and after changes effectively suppress over-response and false responses, achieving more stable PF tracking and smoother performance evolution under multiple environment switches. Compared with baseline and typical comparative methods, CPRLMR achieves superior IGD / HV indices on most dynamic benchmark problems, especially exhibiting smaller performance drops and faster recovery speeds during periods of rapid change. Further results in the dynamic multi-objective optimization application of electrolytic aluminum demonstrate that the proposed algorithm achieves better HV performance in the trade-off between current efficiency and DC power consumption per ton of aluminum, validating the effectiveness and applicability of the method in real-world industrial data-driven scenarios.

[0092] This application also provides a dynamic multi-objective evolution device for aluminum electrolysis processes, used to implement the methods described in any of the above embodiments, such as... Figure 7 As shown, the dynamic multi-objective evolution device in this aluminum electrolysis process includes an evolution module 700. The evolution module 700 is configured to use multiple sets of candidate operating parameter combinations of the aluminum electrolysis cell as a population, and to obtain a Pareto optimal solution set by optimizing current efficiency and DC power consumption per ton of aluminum per cell. The evolution module 700 includes: The environmental change detection unit 701 is configured to detect whether environmental changes occur during each iteration of the aluminum electrolysis process; The conventional evolutionary unit 702 is configured to perform conventional evolution on the population using selection and genetic operators based on non-dominated sorting and crowding distance when no environmental change is detected, to generate the next generation population. The response and recovery unit 703 is configured to perform a response and recovery process to generate a new population when an environmental change is detected, and to use the new population as the current population to perform regular evolution to generate the next generation population; The iterative judgment unit 704 is configured to evaluate the next generation of population and record the cumulative number of evaluations. When the cumulative number of evaluations has not reached the preset maximum number of evaluations, it continues to detect environmental changes until the cumulative number of evaluations reaches the preset maximum number of evaluations. The population with the best evaluation is then output as the Pareto optimal solution set. The Pareto optimal solution set includes parameters for adjusting the working voltage, series current, number of feedings, feeding amount, molecular ratio, cell temperature, aluminum level, fluoride salt addition amount, actual aluminum output, and electrolyte level of the aluminum electrolysis cell. The response and recovery process includes: The current population is re-evaluated and non-dominated sorting is performed. The first non-dominated layer is selected as the elite set, which represents the combination of operating parameters with the best performance under the current environment. The center vector, drift intensity and direction vector of the elite set are calculated. Based on the drift intensity and direction vector, and by introducing phase weights and confidence coefficients to adaptively adjust the response intensity, a directional translation is performed on some combinations of operating parameters in the population, and a random restart is performed on another combination of operating parameters to generate a response population, which represents the candidate combinations of operating parameters after adapting to environmental changes. Maintain a limited-capacity elite memory bank, which stores historically excellent combinations of operating parameters; when the environment changes, extract memory individuals from the elite memory bank, which are historically excellent combinations of operating parameters, and apply perturbation to the memory individuals to generate immigrant individuals, which are combinations of operating parameters after the perturbation. The response population, immigrant individuals, and current candidate solutions are merged, and environmental selection is performed using non-dominated sorting and crowding distance to obtain a new population. Based on the performance feedback before and after the environmental change, the confidence coefficient is updated online to adjust the response strength for the next environmental change. The first non-dominated layer in the new population is used as the updated elite set and written into the elite memory, with entries retained according to a preset capacity.

[0093] This application provides an electronic device. The electronic device may include a processor and a memory, wherein the processor and the memory can communicate; exemplarily, the processor and the memory communicate via a communication bus.

[0094] The processor executes computer execution instructions stored in memory, causing the processor to perform the scheme in the above embodiments. The processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0095] The communication bus can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. The system bus can be divided into address bus, data bus, control bus, etc. Transceivers are used to enable communication between database access devices and other computers (e.g., clients, read-write libraries, and read-only libraries). Memory may include random access memory (RAM) and may also include non-volatile memory.

[0096] The electronic device provided in this application embodiment can be the terminal device described in the above embodiments.

[0097] This application also provides a computer-readable storage medium storing computer instructions. When the computer instructions are executed on a computer, the computer performs the technical solution of the dynamic multi-objective evolution method in the aluminum electrolysis process described above.

[0098] This application also provides a computer program product, which includes a computer program stored in a computer-readable storage medium. At least one processor can read the computer program from the computer-readable storage medium. When the at least one processor executes the computer program, it can implement the technical solution of the dynamic multi-objective evolution method in the aluminum electrolysis process described in the above embodiments.

[0099] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, devices, or modules, and may be electrical, mechanical, or other forms.

[0100] The modules described as separate components may or may not be physically separate. The components shown as modules may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to implement the solution of this embodiment according to actual needs.

[0101] Furthermore, the functional modules in the various embodiments of this application can be integrated into one processing unit, or each module can exist physically separately, or two or more modules can be integrated into one unit. The unit composed of the above modules can be implemented in hardware or in the form of hardware plus software functional units.

[0102] The integrated modules described above, implemented as software functional modules, can be stored in a computer-readable storage medium. These software functional modules, stored in a storage medium, include several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute some steps of the methods of the various embodiments of this application.

[0103] It should be understood that the aforementioned processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. A general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this invention can be directly manifested as execution by a hardware processor, or execution by a combination of hardware and software modules within the processor.

[0104] The memory may include high-speed RAM, and may also include non-volatile storage (NVM), such as at least one disk storage device, and may also be a USB flash drive, external hard drive, read-only memory, disk or optical disc, etc.

[0105] Buses can be Industry Standard Architecture (ISA) buses, Peripheral Component Interconnect (PCI) buses, or Extended Industry Standard Architecture (EISA) buses, etc. Buses can be categorized into address buses, data buses, control buses, etc.

[0106] The aforementioned storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The storage medium can be any available medium that can be accessed by a general-purpose or special-purpose computer.

[0107] An exemplary storage medium is coupled to a processor, enabling the processor to read information from and write information to the storage medium. Alternatively, the storage medium can be an integral part of the processor. The processor and storage medium can reside in an Application Specific Integrated Circuit (ASIC). Alternatively, the processor and storage medium can exist as discrete components in an electronic control unit or main control device.

[0108] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0109] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A dynamic multi-objective evolution method for aluminum electrolysis, characterized in that, The method uses multiple sets of candidate operating parameter combinations for the aluminum electrolysis cell as a population, with current efficiency and DC power consumption per ton of aluminum per cell as optimization objectives, and performs the following process: In each iteration, the environmental conditions of the aluminum electrolysis process are checked for changes. When no environmental changes are detected, conventional evolution is performed on the population using selection and genetic operators based on non-dominated sorting and crowding distance to generate the next generation population. When an environmental change is detected, a response and recovery process is executed to generate a new population. The new population is then used as the current population, and regular evolution is performed to generate the next generation of population. The next generation of the population is evaluated and the cumulative number of evaluations is recorded. If the cumulative number of evaluations does not reach the preset maximum number of evaluations, environmental changes are continuously monitored until the cumulative number of evaluations reaches the preset maximum number of evaluations. The population with the best evaluation is output as the Pareto optimal solution set. The Pareto optimal solution set includes the working voltage, series current, number of feedings, feeding amount, molecular ratio, cell temperature, aluminum level, fluoride salt addition amount, actual aluminum output and electrolyte level of the aluminum electrolysis cell. The response and recovery process includes: The current population is re-evaluated and non-dominated sorting is performed. The first non-dominated layer is selected as the elite set, which represents the combination of operating parameters with the best performance under the current environment. The center vector, drift intensity and direction vector of the elite set are calculated. Based on the drift intensity and direction vector, and by introducing phase weights and confidence coefficients to adaptively adjust the response intensity, a directional translation is performed on some combinations of operating parameters in the population, and a random restart is performed on another combination of operating parameters to generate a response population, which represents the candidate combinations of operating parameters after adapting to environmental changes. Maintain a limited-capacity elite memory bank, which stores historically excellent combinations of operating parameters; when the environment changes, extract memory individuals from the elite memory bank, which are historically excellent combinations of operating parameters, and apply perturbation to the memory individuals to generate immigrant individuals, which are combinations of operating parameters after the perturbation. The response population, immigrant individuals, and current candidate solutions are merged, and environmental selection is performed using non-dominated sorting and crowding distance to obtain a new population. Based on the performance feedback before and after the environmental change, the confidence coefficient is updated online to adjust the response strength for the next environmental change. The first non-dominated layer in the new population is used as the updated elite set and written into the elite memory, with entries retained according to a preset capacity.

2. The method according to claim 1, characterized in that, The current center vector c of the elite set ( t Calculated using the following formula: Where A is the elite set, x is the individual decision-making variable in the elite set, and |A| is the size of the elite set; The drift intensity S t Through the center vector c at the previous time of change ( t -1) and the current center vector c( t Calculation of Euclidean distance; The direction vector passes through the current center vector. c ( t ) and the center of the entire population Calculation of vector difference.

3. The method according to claim 1, characterized in that, When performing a directional translation on a partial combination of operation parameters in the population, the directional translation vector... Calculated using the following formula: in, Scaling factor S t For drift strength, The preset maximum translation coefficient, and These are the upper and lower bounds of the decision variable, respectively. It is the direction vector; The scaling factor Calculated using the following formula: in, c , is the confidence coefficient w p is the phase weight, and clip is the clipping function.

4. The method according to claim 1, characterized in that, From the elite memory bank Individual memories extracted from Applying perturbations to generate immigrant individuals The method is expressed by the following formula: in, To revisit the disturbance intensity, and These represent the upper and lower bounds of the decision variables, respectively, and ⊙ indicates element-wise multiplication. It follows a normal distribution with a mean of 0 and a covariance of the identity matrix I. A random vector.

5. The method according to claim 1, characterized in that, Based on performance feedback before and after environmental changes, the confidence coefficient is updated online, including: The confidence coefficient is updated based on the improvement magnitude imp of the reverse generation distance index before and after environmental change, wherein the improvement magnitude imp is calculated by the following formula: in, The reverse generational distance of the elite group before the change. This represents the reverse generation distance after the change. Here, `max` is a preset constant, and `maximum` is the function for the maximum value. Map imp to the target confidence level and update the confidence coefficients using exponential smoothing.

6. The method according to claim 5, characterized in that, The indicators used to evaluate the next generation population include the reverse generation distance or hypervolume, and the formula for calculating the reverse generation distance is as follows: in, For reverse generation distance, i The true Pareto frontier is represented by the first... The Euclidean distance between each solution and the individual closest to the obtained solution. SP Representing reality The number of upsampling points, | SP | represents the number of sampling points; The supervolume is calculated using the following formula: in, HV ( P,r (This is a supervolume) For an approximate solution set, As a reference point, For the first Solution in each target direction The interval to the reference point The volume of a multidimensional spatial region.

7. The method according to claim 1, characterized in that, The method also includes a dynamic scene construction process, which specifically includes: A time-varying environment mechanism is introduced during the optimization process, and an environment index is defined. t : in, FE This is the current number of reviews. N For population size, The length of the evaluation window corresponding to each environmental test. The number of discrete slices within each window; Based on the environmental index, dynamic perturbations are applied to the decision variables to simulate the drift of aluminum electrolysis operating conditions. The method of applying dynamic perturbations to the decision variables based on the environmental index is expressed as follows: in, dηnAmp The disturbance amplitude coefficient, and Here, represents the upper and lower bounds of the decision variable, and x represents the individual decision variable in elite concentration. To use the environment index t Decision variables after perturbation.

8. A dynamic multi-objective evolution device for aluminum electrolysis process, characterized in that, The device includes an evolution module configured to use multiple sets of candidate operating parameter combinations of the aluminum electrolysis cell as a population, and to obtain a Pareto optimal solution set with current efficiency and DC power consumption per ton of aluminum per cell as optimization objectives. The evolution module includes: The environmental change detection unit is configured to detect whether environmental changes occur during each iteration of the aluminum electrolysis process; The conventional evolutionary unit is configured to perform conventional evolution on the population to generate the next generation population when no environmental change is detected, using selection and genetic operators based on non-dominated sorting and crowding distance. The response and recovery unit is configured to perform a response and recovery process to generate a new population when an environmental change is detected, and to use the new population as the current population to perform regular evolution to generate the next generation population; The iterative judgment unit is configured to evaluate the next generation of population and record the cumulative number of evaluations. When the cumulative number of evaluations has not reached the preset maximum number of evaluations, it continues to detect environmental changes until the cumulative number of evaluations reaches the preset maximum number of evaluations. The optimal population is then output as the Pareto optimal solution set. The Pareto optimal solution set includes parameters for adjusting the working voltage, series current, number of feedings, feeding amount, molecular ratio, cell temperature, aluminum level, fluoride salt addition amount, actual aluminum output, and electrolyte level of the aluminum electrolysis cell. The response and recovery process includes: The current population is re-evaluated and non-dominated sorting is performed. The first non-dominated layer is selected as the elite set, which represents the combination of operating parameters with the best performance under the current environment. The center vector, drift intensity and direction vector of the elite set are calculated. Based on the drift intensity and direction vector, and by introducing phase weights and confidence coefficients to adaptively adjust the response intensity, a directional translation is performed on some combinations of operating parameters in the population, and a random restart is performed on another combination of operating parameters to generate a response population, which represents the candidate combinations of operating parameters after adapting to environmental changes. Maintain a limited-capacity elite memory bank, which stores historically excellent combinations of operating parameters; when the environment changes, extract memory individuals from the elite memory bank, which are historically excellent combinations of operating parameters, and apply perturbation to the memory individuals to generate immigrant individuals, which are combinations of operating parameters after the perturbation. The response population, immigrant individuals, and current candidate solutions are merged, and environmental selection is performed using non-dominated sorting and crowding distance to obtain a new population. Based on the performance feedback before and after the environmental change, the confidence coefficient is updated online to adjust the response strength for the next environmental change. The first non-dominated layer in the new population is used as the updated elite set and written into the elite memory, with entries retained according to a preset capacity.

9. An electronic device, characterized in that, include: A processor, and a memory communicatively connected to the processor; The memory stores computer-executed instructions; The processor executes computer execution instructions stored in the memory to implement the dynamic multi-objective evolution method in the aluminum electrolysis process as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions, which, when executed by a processor, are used to implement the dynamic multi-objective evolution method in the aluminum electrolysis process as described in any one of claims 1-7.

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