High-dimensional multi-objective evolutionary computing method, device and equipment

Abstract

The invention relates to a high-dimensional multi-objective evolutionary computing method, device and equipment. The high-dimensional multi-objective problem evolutionary calculation method comprises the steps of S1, performing population initialization to obtain a primary parent population; s2, performing iterative operation on the parent population to obtain a fusion population; s3, calculating the population aggregation degree of the fusion population; s4, evaluating the diversity and convergence of the fused population according to the population aggregation degree to obtain an evaluation result; s5, balancing and updating the fused population according to the evaluation result to obtain a balanced population; s6, judging whether a termination condition is met or not, and if the termination condition is met, outputting the balanced population as an optimal solution; and if the termination condition is not met, taking the balanced population as a new parent population, and returning to the step S2 to carry out iterative operation again. The high-dimensional multi-objective evolutionary calculation method has the advantages that the population can be adaptively adjusted to avoid excessive aggregation or difficulty in convergence of the population.

Description

Technical Field

[0001] The present invention relates to multi-objective optimization problems, and in particular to a high-dimensional multi-objective evolutionary computing method, apparatus, and device. Background Art

[0002] Optimization problems are a common type of problem in real life, referring to the problem of finding the optimal solution of an objective function through given constraint conditions. When the number of objectives is greater than or equal to 4, the optimization problem is called a high-dimensional multi-objective optimization problem, and its mathematical formula generally includes multiple decision variables and objectives, where multiple objectives form an objective space. The many-objective evolutionary algorithm (MaOEA) is a method for solving high-dimensional multi-objective problems.

[0003] Currently, the existing high-dimensional multi-objective evolutionary algorithms mainly include evolutionary computing methods solved by several different ideas such as dominance-based methods, decomposition-based methods, and performance metric-based methods. Currently, the process of a metric-based high-dimensional multi-objective computing method in the prior art is as follows: randomly initialize a population as the parent population, iteratively update through the parent population to obtain a new population and update the reference point or reference vector set, select a better population to enter the next generation, determine whether the population meets the termination condition, and output the optimal solution.

[0004] When the number of objectives increases in the above-mentioned many-objective evolutionary computing method, a series of problems will occur. First, when the number of objectives increases, the number of non-dominated solutions in the solution set obtained by this many-objective evolutionary computing method will increase exponentially, making it difficult for this computing method to distinguish the superiority and inferiority of individuals, weakening the evolutionary pressure of the population, reducing the convergence of the computing method, and unable to obtain an effective solution set. Second, its high-dimensional objective space is prone to generating dominance conflict solutions. These solutions have very small values in some objectives but are far from the Pareto front and are often ignored and excluded by the computing method, having a significant impact on the convergence performance of the solution set. Among them, the non-dominated solution is a solution that performs better than other solutions in some objectives but worse in some objectives. The dominance conflict solution is not worse than other solutions under all objectives and is superior to other solutions in at least one objective. The Pareto front refers to a set of solutions that achieve the best trade-off among multiple objectives. Summary of the Invention

[0005] Based on this, the purpose of the present invention is to provide a high-dimensional multi-objective evolutionary computing method, apparatus, and device.

[0006] The present invention provides a high-dimensional multi-objective evolutionary computation method. S1: Initialize the population to obtain the initial parental population. S2: Perform iterative operations on the parental population to obtain a fused population. S3: Calculate the population aggregation degree of the fused population. S4: Evaluate the diversity and convergence of the fused population according to the population aggregation degree to obtain an evaluation result. S5: Balance and update the fused population according to the evaluation result to obtain a balanced population. S6: Determine whether the termination condition is satisfied. If the termination condition is satisfied, output the balanced population as the optimal solution. If the termination condition is not satisfied, use the balanced population as the new parental population and return to step S2 to perform iterative operations again.

[0007] Compared with the prior art, the high-dimensional multi-objective evolutionary computation method of the present invention adaptively adopts different-biased indicators to guide the population evolution at different iterative stages by analyzing the aggregation situation of the fused population, so that the population can purposefully and adaptively correct its own state during the evolution process, avoiding the situation that the population is too aggregated or difficult to converge to the Pareto front, and effectively solving the problems that there are too many dominant conflicting solutions in the population or it is difficult to achieve the balance between population diversity and convergence when the existing algorithms handle high-dimensional multi-objective problems.

[0008] Further, step S1 further includes setting a guiding element. Step S3 specifically is: Calculate the average value and standard deviation of the Euclidean distances between each individual in the fused population and the guiding element to obtain the population aggregation degree. The individuals in the fused population include Pareto front optimal solution points and non-contributing solutions.

[0009] Further, step S4 specifically includes: Comparing the standard value and the average value. When the standard deviation is less than the average value, the evaluation result is that the fused population is not aggregated. When the standard deviation is greater than the average value, the evaluation result is that the fused population is aggregated.

[0010] Further, step S5 specifically includes:

[0011] When the evaluation result is that the fused population is aggregated, use the formula:

[0012]

[0013] Perform iterative update on the fused population. In the formula, P is the approximate Pareto solution set obtained in the fused population, R is the reference point set uniformly sampled from the Pareto front of the high-dimensional multi-objective optimization problem to be solved, P* is the set composed of those non-contributing solutions in the population P, y is the Pareto front optimal solution point, x is the reference point, z is the non-contributing solution point, is the Euclidean distance between the solution point y and the reference point closest to it, The angle of the non - contributing solution to the reference vector farthest from it.

[0014] Further, step S5 specifically further includes:

[0015] When the evaluation result is that the fusion population is not aggregated, the formula:

[0016]

[0017] is used to iteratively update the fusion population. In the formula, P is the approximate Pareto solution set obtained by algorithm A, R is the reference point set uniformly sampled from the Pareto front of the high - dimensional multi - objective optimization problem to be solved, P* is the set composed of those non - contributing solutions in the population P, y is the Pareto front optimal solution point, x is the reference point, and \(d(y,x)\) is the Euclidean distance between the solution point y and the reference point x closest to it.

[0018] Further, the guiding element is a uniformly distributed reference point or reference vector.

[0019] Further, step S2 specifically includes: S21: performing crossover and mutation on the parental population to generate an offspring population; S22: merging the parental population and the offspring population to obtain a fusion population; S23: updating the guiding element according to the fusion population.

[0020] Further, the termination condition of step S6 is: the performance of the balanced population meets a preset condition, or the number of iterations of the iterative operation reaches a preset maximum number of iterations.

[0021] Based on the same inventive concept, the present invention also provides a high - dimensional multi - objective evolutionary computing device, including an initialization module for initializing a population to obtain an initial parental population; an iterative operation module for performing iterative operations on the parental population to obtain a fusion population; a population aggregation degree calculation module for calculating the population aggregation degree of the fusion population; a diversity and convergence evaluation module for evaluating the diversity and convergence of the fusion population according to the population aggregation degree to obtain an evaluation result; a balance update module for balancing and updating the fusion population according to the evaluation result to obtain a balanced population; and a termination judgment module for judging whether the balanced population meets the termination condition. If the balanced population meets the termination condition, the balanced population is output as the optimal solution; if not, the balanced population is used as the new parental population to re - perform iterative operations.

[0022] Based on the same inventive concept, the present invention also provides an electronic device, including a processor; a memory for storing a computer program executed by the processor; wherein, when the processor executes the computer program, the above - mentioned high - dimensional multi - objective evolutionary computing method is implemented.

[0023] For better understanding and implementation, the present invention will be described in detail below with reference to the accompanying drawings. Description of the Drawings

[0024] Figure 1 It is a schematic diagram of the modules of the high-dimensional multi-objective evolutionary computing device of the present invention;

[0025] Figure 2 It is a schematic flowchart of the high-dimensional multi-objective evolutionary computing method of the present invention;

[0026] Figure 3 It is a schematic flowchart of step S2 in the high-dimensional multi-objective evolutionary computing method of the present invention;

[0027] Figure 4 It is a schematic diagram of the fusion population of the high-dimensional multi-objective evolutionary computing method of the present invention in an aggregated state;

[0028] Figure 5 It is a schematic diagram of the fusion population of the high-dimensional multi-objective evolutionary computing method of the present invention in a non-aggregated state

[0029] Figure 6 It is a line graph showing the change of the mean IGD obtained by each algorithm in the DTLZ test problem with the number of evaluations in the high-dimensional multi-objective evolutionary computing method of the present invention and the comparative example. Detailed Embodiment

[0030] In view of the problems that occur when the existing index-based multi-objective evolutionary computing method has an increasing number of objectives, the inventor designed a high-dimensional multi-objective evolutionary computing method, which is based on an improved index-based fusion population adaptive balance strategy, and is used to reasonably disperse when the population in high-dimensional multi-objective evolutionary computing is too aggregated, and reasonably aggregate when the population is not aggregated, thereby assisting the population to achieve the balance of population diversity and convergence, and reducing the occurrence of too many dominated conflicting solutions, thereby solving the problems brought by the current multi-objective evolutionary computing method when the number of objectives increases.

[0031] Please refer to Figure 1-2 , Figure 1 It is a schematic diagram of the modules of the computing device of the high-dimensional multi-objective evolutionary computing method of the present invention, Figure 2 It is a schematic flowchart of the high-dimensional multi-objective evolutionary computing method of the present invention. The computing device of the high-dimensional multi-objective evolutionary computing method of the present invention is used to execute the high-dimensional multi-objective evolutionary computing method of the present invention, and it includes: an initialization module M1, an iterative operation module M2, a population aggregation degree calculation module M3, a diversity and convergence evaluation module M4, a balance operation module M5, and a termination judgment module M6.

[0032] The initialization module M1 is used to execute the step S1: initialize the population to obtain the initial parental population. In the step S1, a guiding element is also set, and the guiding element is a uniformly distributed reference point or reference vector. The guiding element is an element used to guide the search process of population individuals in the high-dimensional multi-objective evolutionary calculation method, helping the algorithm gradually converge to the optimal solution set. The reference point and the reference vector are two forms of the guiding element, which are used to decompose a multi-objective problem into a series of sub-problems.

[0033] Please refer to Figure 3 , Figure 3 which is a schematic flowchart of step S2 of the high-dimensional multi-objective evolutionary calculation method with a fusion population adaptive balance strategy according to the present invention. The iterative operation module M2 is used to execute the step S2: perform iterative operations on the parental population to obtain a fusion population. The step S2 specifically includes:

[0034] S21: Perform crossover and mutation on the parental population to generate an offspring population. When performing the initial iterative operation, use the result of step S1 as the initial parental population and perform crossover and mutation on it using the crossover and mutation operator to generate an offspring population; in subsequent iterative operations, use the balanced population obtained in step S5 of the previous cycle as the parental population and perform crossover and mutation using the crossover and mutation operator to generate the offspring population.

[0035] S22: Merge the parental population and the offspring population to obtain a fusion population.

[0036] S23: Update the guiding element according to the fusion population.

[0037] The population aggregation degree calculation module M3 is used to execute the step S3: calculate the population aggregation degree of the fusion population. In the step S3, calculate the Euclidean distance between each individual in the fusion population and the reference point or reference vector, and use the Euclidean distances of the individuals in the fusion population from the guiding element as the data points of an array, calculate the standard deviation and the average value of the array, and represent the population aggregation degree of the fusion population by the standard deviation and the average value of the Euclidean distances of the individuals in the fusion population from the guiding element.

[0038] The diversity and convergence evaluation module M4 is used to execute the step S4: evaluate the diversity and convergence of the fusion population according to the population aggregation degree to obtain an evaluation result. The step S4 is specifically:

[0039] Compare the standard deviation and the average value obtained in S3; when the standard deviation is greater than the average value, the evaluation result is: the fusion population is not aggregated; when the standard deviation is greater than the average value, the evaluation result is: the fusion population is aggregated.

[0040] Please refer to Figure 4 and Figure 5 , Figure 4 which is a schematic diagram of the fusion population in the aggregated state of the high-dimensional multi-objective evolutionary computation method of the present invention, Figure 5 and which is a schematic diagram of the fusion population in the non-aggregated state of the high-dimensional multi-objective evolutionary computation method of the present invention.

[0041] Figure 4 The dots in Figure 4 represent each individual in the fusion population, and the vector wi represents the reference vector as the guiding element. Compare Figure 4-5 It can be seen that when the fusion population is in the non-aggregated state, the Euclidean distance between each individual and the reference vector is relatively stable with small fluctuations, and the population distribution is relatively uniform. At this time, the calculated standard deviation is less than the average value; when the fusion population is in the aggregated state, most individuals are distributed near each reference vector, the change range of the Euclidean distance between each individual and the reference vector is large, and the difference between the data is large. At this time, the calculated standard deviation is greater than the average value. Therefore, in step S4, when the standard deviation is greater than the average value, it is determined that the evaluation result of the fusion population is population aggregation, and when the standard deviation is less than or equal to the average value, it is determined that the evaluation result of the fusion population is population non-aggregation.

[0042] The balance operation module M5 is used to execute step S5: balance and update the fusion population according to the evaluation result to obtain a balanced population.

[0043] When the evaluation result of step S4 is that the fusion population is aggregated, the following formula is used to perform a balance operation on the fusion population to increase its diversity, and then a fusion population with balanced diversity and convergence is obtained and output:

[0044]

[0045] In the formula, P is the approximate Pareto solution set obtained in the fusion population, R is the reference point set uniformly sampled from the Pareto front of the high-dimensional multi-objective optimization problem to be solved, P* is the set of those non-contributing solutions in the population P, y is the optimal solution point on the Pareto front, x is the reference point, z is the non-contributing solution point, is the Euclidean distance between the solution point y and the reference point x closest to it, is the angle from the non - contributing solution to the reference vector farthest from it, and this angle is expressed as the included angle between the vector of the reference point x and the non - contributing solution point z and the vector of the reference point x and the non - contributing solution point y. The non - contributing solution is a solution that makes no positive contribution to the optimization process of the entire population, that is, a solution that is not better than other solutions in all objectives or is worse in some objectives; the solution is a Pareto - front optimal solution, and there is no solution in the entire population that is better than this Pareto - front optimal solution in all objectives and is better than other solutions in at least one objective.

[0046] When the evaluation result of step S4 is that the fused population is not aggregated, the following formula is used to perform a balancing operation on the fused population to increase its convergence, and then a fused population with balanced diversity and convergence is obtained and output:

[0047]

[0048] In the formula, P is the approximate Pareto solution set obtained by algorithm A, R is the reference point set uniformly sampled from the Pareto front of the high - dimensional multi - objective optimization problem to be solved, P* is the set composed of those non - contributing solutions in the population P, y is the Pareto - front optimal solution point, x is the reference point, is the Euclidean distance between the solution point y and the reference point x closest to it.

[0049] The termination judgment module M6 executes step S6: Determine whether the termination condition is satisfied. If the termination condition is satisfied, the balanced population is output as the optimal solution; if not, the balanced population is used as the new parent population and returns to step S2 to perform iterative operations again. Step S632 is specifically:

[0050] S61: Determine whether the termination condition is satisfied. In step S61, the termination condition is that the performance of the balanced population meets the preset condition, or the number of iterations of the iterative operation reaches the preset maximum number of iterations.

[0051] S62: When the performance of the balanced population meets the preset condition, or the number of iterations of the iterative operation does not reach the preset maximum number of iterations, the balanced population is output as the optimal solution;

[0052] S63: When the performance of the balanced population does not meet the preset condition, or the number of iterations of the iterative operation does not reach the preset maximum number of iterations, the balanced population is used as the new parent population and returns to step S2 to perform iterative operations again.

[0053] The technical effects of the present invention are illustrated by experimental data below:

[0054] The high-dimensional multi-objective evolutionary algorithm (MaOEA / PABS) of the present invention is used to solve the DTLZ test problems. The DTLZ test problems are a set of standard test functions for testing the performance of multi-objective optimization algorithms, aiming to evaluate the performance of algorithms in dealing with complex, multi-modal, and deceptive multi-objective problems. In this embodiment, DTLZ1-DTLZ4 are selected as test functions, and two metrics, the Inverted Generational Distance (IGD) and the Hypervolume (HV), are selected to evaluate the convergence and diversity of the approximate solution sets obtained by the algorithm. Among them, in each test problem, the number of generations T satisfies T = EN / N, where N is the population size and EN is the number of evaluations; simulated binary crossover (SBX) and polynomial mutation (PM) are used to generate new individuals; the remaining specific parameters are set to the recommended values in the original literature. The specific experimental parameter settings for the benchmark problems are shown in the following table:

[0055]

[0056] When dealing with the DTLZ1 test problem, the preset parameters are input into the high-dimensional multi-objective evolutionary algorithm of the present invention, and the high-dimensional multi-objective evolutionary algorithm generates the corresponding initial population and the uniformly distributed reference vectors. Subsequently, taking the initial population as the parent population, the crossover and mutation operators are used to generate the offspring population, and the parent population and the offspring population are merged to obtain the merged population, and the reference vectors are updated according to the merged population. Next, the algorithm calculates the sum of the Euclidean distances between each individual in the merged population and the reference vectors, and calculates its standard deviation and average value as a one-dimensional array. When the standard deviation is greater than the average value, the merged population is iteratively updated using the metric operation formula 1; when the standard deviation is less than the average value, the merged population is iteratively updated using the metric operation formula 2; at this time, the high-dimensional multi-objective evolutionary algorithm of the present invention obtains a balanced population with a balance between diversity and convergence. Subsequently, the results of the balanced population are evaluated. According to the preset number of evaluations, when the preset number of evaluations is not reached, the balanced population is used as the parent population, and a series of steps from crossover and mutation of the parent population to evaluation of the balanced population are cycled until the preset number of evaluations is reached. When the preset number of cycles is reached, the high-dimensional multi-objective evolutionary algorithm outputs the final generation population.

[0057] When dealing with the DTLZ2-DTLZ4 test problems, the steps are the same.

[0058] The mean IGD values obtained by the present high-dimensional multi-objective evolutionary algorithm in dealing with the DTLZ series of test problems are shown in the following table:

[0059]

[0060]

[0061] The mean HV values obtained by this high-dimensional multi-objective evolutionary computation method in dealing with the DTLZ series of test problems are shown in the following table:

[0062]

[0063] It can be seen from the above two tables that in dealing with the DTLZ series of problems, the high-dimensional multi-objective evolutionary computation method with the fusion population adaptive balance strategy of the present invention has good IGD and mean HV values regardless of whether the number of objectives is 5, 10, 15 or 20. Especially in the DTLZ1 test problem, the algorithm of the present invention has good IGD and mean HV values and variances for different numbers of objectives.

[0064] In addition, when this high-dimensional multi-objective evolutionary computation method is dealing with the DTLZ3 test problem, by changing the number of evaluations EN, making the number of evaluations increase gradually from 10 4 to 10 5 , the situation of this high-dimensional multi-objective evolutionary computation method changing with the change of the number of evaluations is tested. In this process, the mean IGD of the algorithm of the present invention decreases rapidly with the increase of the number of evaluations, showing a relatively fast convergence speed and good mean IGD.

[0065] Comparative example:

[0066] Select MaOEA / IGD, MOEA / IGD-NS, AR-MOEA, d2_NSGA-II and MaOEA-IT algorithms for comparison, and deal with the DTLZ1-DTLZ4 series of problems respectively. Their number of evaluations EN and benchmark problem parameters are the same as those of the algorithm of the present invention, and the remaining specific parameters are set to the recommended values of the original literature.

[0067] The following table shows the mean IGD values of this comparative example in dealing with the DTLZ series of problems. Among them, the optimal results under each objective are marked in bold in the following table:

[0068]

[0069]

[0070] By comparing the mean IGD values obtained by each algorithm in the comparative examples and the high-dimensional multi-objective evolutionary calculation method of the present invention, it can be seen that the algorithm of the present invention obtains the best mean IGD values in 8 out of 16 test cases, namely, the DTLZ1 problem with 5 and 10 processing objectives, the DTLZ2 problem with 5, 10, and 20 objectives, the DTLZ3 problem with 5 objectives, and the DTLZ4 problem with 5 and 15 objectives. Among other algorithms, MaOEA / IGD obtains 1 best mean IGD value, AR-MOEA obtains 4 best mean IGD values, d2_NSGA-II obtains 3 best mean IGD values, while MOEA / IGD-NS and MaOEA-IT do not obtain any best mean IGD values. The results of each algorithm in the comparative examples are all worse than those of the high-dimensional multi-objective evolutionary calculation method of the present invention when dealing with the DTLZ test problems. Through this comparison, it can be seen that the algorithm of the present invention performs better in terms of the mean IGD value when dealing with high-dimensional objective problems than each of the existing algorithms in the comparative examples.

[0071] The following table shows the mean HV values of each comparative example and the algorithm of the present invention when dealing with the DTLZ series of problems:

[0072]

[0073]

[0074] By comparing the mean HV values obtained by each algorithm in the comparative examples and the high-dimensional multi-objective evolutionary calculation method of the present invention, it can be seen that the algorithm of the present invention obtains 7 best results in 16 test cases, namely, DTLZ1 with 5, 10, and 15 processing objectives, all DTLZ2 problems, DTLZ3 problems, and DTLZ4 problems with 5 objectives. Among the algorithms of each comparative example, MaOEA / IGD obtains 3 best mean HV values, AR-MOEA obtains 5 best mean HV values, d 2 _NSGA-II obtains 1 best mean HV value, while MOEA / IGD-NS and MaOEA-IT do not obtain any best mean HV values. The results of each algorithm in the comparative examples are all worse than those of the high-dimensional multi-objective evolutionary calculation method of the present invention when dealing with the DTLZ test problems. Through this comparison, it can be seen that the algorithm of the present invention can obtain a better mean HV value than each of the existing algorithms in the comparative examples when dealing with high-dimensional objective problems.

[0075] By separately processing the DTLZ series of problems with each algorithm in the comparative examples and the algorithm of the present invention, and comprehensively comparing the obtained mean IGD values and mean HV values, the results of the algorithm of the present invention are significantly better than those of the commonly used MaOEA / IGD, MOEA / IGD-NS, AR-MOEA, d 2_NSGA-II and MaOEA-IT algorithms. In summary, the high-dimensional multi-objective evolutionary computing method of the present invention is superior to each existing algorithm in the comparative example in terms of the ability to handle high-dimensional multi-objective problems.

[0076] In another embodiment, when using each algorithm in the comparative example to process the DTLZ3 test problem, the number of evaluations is changed, and the number of evaluations is made to gradually increase from 10 4 to 10 5 , and the mean IGD values of each algorithm in the comparative example at different numbers of evaluations are recorded respectively.

[0077] Please refer to Figure 6 , Figure 6 the line chart of the change of the mean IGD values obtained by the high-dimensional multi-objective evolutionary computing method of the present invention and each algorithm in the comparative example in the DTLZ test problem. When the number of evaluations increases, the mean IGD value obtained by the algorithm of the present invention decreases fastest; followed by AR-MOEA and MaOEA / IGD respectively; and after about 10 5 evaluations, the mean IGD value of MaOEA / IGD shows a large fluctuation; the mean IGD value of MOEA / IGD-NS shows an up-and-down fluctuation trend throughout the iterative process, it is difficult to remain stable, and it is finally difficult to drop to a lower level; MaOEA-IT generally shows a fluctuating and gradually increasing trend. In summary, when the number of evaluations for processing the DTLZ3 test problem increases, the algorithm of the present invention shows a faster convergence speed and better mean IGD value results, and has better performance compared with each commonly used existing algorithm in the comparative example.

[0078] Compared with the prior art, the high-dimensional multi-objective evolutionary computing method of the present invention analyzes the aggregation situation of the fusion population, and adaptively adopts different-biased indicators to guide the population evolution at different iterative stages, so that the population can purposefully and adaptively correct its own state during the evolution process, avoiding the situation that the population falls into an overly aggregated situation or is difficult to converge to the Pareto front, and effectively solves the problems that there are too many dominant conflicting solutions in the population or it is difficult to achieve the balance between population diversity and convergence when the existing algorithms handle high-dimensional multi-objective problems.

[0079] Based on the same inventive concept, the present application also provides an electronic device, which can be a server, a desktop computing device or a mobile computing device (such as a laptop computing device, a handheld computing device, a tablet computer, a netbook, etc.) and other terminal devices. The device includes one or more processors and a memory, wherein the processor is used to execute a program to implement the model training method based on diverse hard negative sample mining in the embodiments of the present invention; the memory is used to store a computer program executable by the processor.

[0080] Based on the same inventive concept, the present application also provides a computer-readable storage medium, corresponding to the embodiments of the model training method based on diverse hard negative sample mining described above. The computer-readable storage medium stores a computer program, and when the program is executed by a processor, it implements the steps of the model training method based on diverse hard negative sample mining described in any of the above embodiments.

[0081] The present application may be in the form of a computer program product implemented on one or more storage media (including but not limited to disk memories, CD-ROMs, optical memories, etc.) containing program codes. Computer-usable storage media include permanent and non-permanent, removable and non-removable media, and information storage can be implemented by any method or technology. The information may be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include but are not limited to: phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassette tapes, magnetic disk storage or other magnetic storage devices, or any other non-transmission media that can be used to store information accessible by a computing device.

[0082] The terms used in the embodiments of the present application are only for the purpose of describing specific embodiments and are not intended to limit the embodiments of the present application. The singular forms "a", "the", and "said" used in the embodiments and claims of the present application are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that unless otherwise stated, "a plurality" means two or more; the terms "first", "second", "third", etc. are only used for distinction and not for describing a specific order or sequence, nor can they be understood as indicating or implying relative importance. The term "and / or" used herein means and includes any or all possible combinations of one or more of the associated listed items. When the above description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. In the description of the present application, for those of ordinary skill in the art, the specific meanings of the above terms in the present application can be understood according to specific circumstances.

[0083] The above-described embodiments only represent several implementation manners of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention patent. It should be noted that for those of ordinary skill in the art, without departing from the inventive concept of the present invention, several modifications and improvements can be made, and the present invention is also intended to include these modifications and improvements.

Claims

1. A high-dimensional multi-objective evolutionary computation method, characterized in that: include S1: Population initialization, obtaining the parent population of the first generation; S2: performing iterative operations on the parent population to obtain a fusion population; S3: Calculate the population aggregation degree of the fusion population; S4: According to the population aggregation degree, the diversity and convergence of the fusion population are evaluated to obtain an evaluation result; S5: Balancing and updating the fusion population according to the evaluation result to obtain a balanced population; S6: Determine whether the termination condition is met. If the termination condition is met, output the balanced population as the optimal solution; if the termination condition is not met, use the balanced population as the new parent population and return to step S2 to perform iterative calculations again.

2. The high-dimensional multi-objective evolutionary computation method according to claim 1, characterized in that: Step S1 also includes setting a guide element; Step S3 specifically includes: calculating the average and standard deviation of the Euclidean distance between each individual in the fused population and the guiding element to obtain the population aggregation degree; the individuals in the fused population include the Pareto frontier optimal solution point and the non-contribution solution point.

3. The high-dimensional multi-objective evolutionary computation method according to claim 2, characterized in that: Step S4 specifically includes: comparing the standard value and the average value; When the standard deviation is less than the average value, the evaluation result is: the fusion population is not aggregated; When the standard deviation is greater than the average value, the evaluation result is: the fusion population is clustered.

4. The high-dimensional multi-objective evolutionary computation method according to claim 3, characterized in that: Step S5 specifically includes: When the evaluation result is that the fusion population is aggregated, the formula is used: The fusion population is iteratively updated, where P is the approximate Pareto solution set obtained in the fusion population, R is the reference point set uniformly sampled from the Pareto front of the high-dimensional multi-objective optimization problem to be solved, P* is the set of non-contributing solutions in the population P, y is the optimal solution point on the Pareto front, x is the reference point, and z is the non-contributing solution point. is the Euclidean distance between the solution point y and its nearest reference point, is the angle from the non-contributing solution to the reference vector that is farthest away from it.

5. The high-dimensional multi-objective evolutionary computation method according to claim 3, characterized in that: Step S5 specifically also includes: When the evaluation result is that the fusion population is not aggregated, the formula is used: The fusion population is iteratively updated, where P is the approximate Pareto solution set obtained by algorithm A, R is the reference point set uniformly sampled from the Pareto front of the high-dimensional multi-objective optimization problem to be solved, P* is the set of non-contributing solutions in the population P, y is the optimal solution point on the Pareto front, x is the reference point, is the Euclidean distance between the solution point y and the nearest reference point x.

6. The high-dimensional multi-objective evolutionary computation method according to claim 2, characterized in that: The guiding elements are uniformly distributed reference points or reference vectors.

7. The high-dimensional multi-objective evolutionary computation method according to claim 6, characterized in that: Step S2 specifically includes: S21: performing crossover mutation on the parent population to generate a progeny population; S22: merging the parent population and the offspring population to obtain a fused population; S23: Update the guiding element according to the fused population.

8. The high-dimensional multi-objective evolutionary computation method according to claim 7, characterized in that: The termination condition of step S6 is: the performance of the balanced population meets a preset condition, or the number of iterations of the iterative operation reaches a preset maximum number of iterations.

9. A high-dimensional multi-objective evolutionary computing device, characterized in that: include: Initialization module, which is used to initialize the population and obtain the initial parent population; An iterative operation module, which is used to perform iterative operations on the parent population to obtain a fusion population; A population aggregation calculation module, which is used to calculate the population aggregation of the fused population; A diversity and convergence evaluation module, which is used to evaluate the diversity and convergence of the fusion population according to the population aggregation degree to obtain an evaluation result; A balance update module, balancing and updating the fused population according to the evaluation result to obtain a balanced population; The termination judgment module is used to judge whether the balanced population meets the termination condition. If the balanced population meets the termination condition, the balanced population is output as the optimal solution; if not, the balanced population is used as the new parent population for re-iteration calculation.

10. An electronic device, characterized in that: include: processor; a memory for storing a computer program executed by the processor; Wherein, when the processor executes the computer program, the high-dimensional multi-objective evolutionary computing method described in any one of claims 1-8 is implemented.

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