A multi-modal multi-objective evolution method and device based on dual-population co-evolution

Abstract

The present invention relates to a multi-modal multi-objective evolution method and device based on dual-population co-evolution, which is used to optimize a user feature set; the method maintains two weakly cooperative populations, namely: an assisting population P that gives priority to fitness value and secondly considers decision space diversity and target space diversity. 1 and the output population P that prioritizes decision space diversity and secondarily considers fitness value 2 ; Assisting population P 1 and the output population P 2 are all subsets of the total user feature set; among them: the assisting population P 1 The principle of convergence priority is adopted, and the diversity of the two spaces is considered at the same time to ensure the convergence of the final solution; the output population P 2 The principle of exploring sparse solutions is adopted, mainly considering the diversity in the decision space, retaining solutions with poor convergence but good diversity, and improving the algorithm's search ability in the decision space; assisting the population P 1 and the output population P 2 Information complementation in evolution is achieved through three special mechanisms: preferential fitness calculation, independent offspring generation and information sharing. Compared with the prior art, the present invention has the advantages of high accuracy.

Description

Technical Field

[0001] The present invention relates to the field of user preference mining, and in particular to a multi-modal multi-objective evolution method and device based on dual-population co-evolution. Background Art

[0002] In the field of e-commerce, user portraits are often created. Creating user portraits requires accurate capture of user preferences. To this end, feature selection of appropriate user features to create user portraits is one of the keys.

[0003] Some existing technologies use principal component analysis to select multiple key features from a large number of features for support vector machine screening, but this method has poor flexibility. In response to this, some improved existing technologies use traditional multi-objective optimization algorithms such as NSGA-II, MOEA / D and IBEA, which usually show good performance when solving multi-objective optimization problems that only consider the target space. However, real problems are very complex, and the feasible solutions obtained are very likely to no longer be feasible under the constraints of real problems. With the change of requirements for problem solutions: on the one hand, traditional multi-objective optimization algorithms only consider the distribution of the obtained solutions in the target space, and cannot obtain the equivalent Pareto optimal solution in the decision space; on the other hand, many evolutionary algorithms for multi-modal problems are too inclined to the decision space, resulting in poor diversity of the final solution in the target space, which cannot meet the needs of decision makers. How to ensure the convergence and diversity of the final solution for multi-modal multi-objective optimization problems (MMOP) while being able to find all Pareto optimal solution sets is a research difficulty in the field of multi-modal multi-objective evolution. In recent years, the academic community has proposed a variety of multi-modal and multi-objective evolutionary algorithms, which can be divided into three categories based on selection strategies: Pareto dominance-based, decomposition-based, and indicator-based. However, current research still has problems that need to be solved, which are mainly manifested as follows:

[0004] (1) Insufficient search capabilities

[0005] Existing algorithms mainly prioritize convergence, which will cause the population to converge to a certain area too early, making it impossible to find an equivalent Pareto optimal solution. In order to solve MMOP, the algorithm needs to adopt a specific mechanism to improve its search ability in the decision space.

[0006] (2) Difficulty in balancing the conflicts between the target space and the decision space

[0007] Among the existing algorithms, traditional multi-objective evolutionary algorithms focus too much on the target space, while most multi-modal multi-objective evolutionary algorithms focus too much on the decision space. MMOP needs to consider both the decision space and the target space, but the diversity of the decision space and the convergence of the target space are a pair of interacting goals. In order to find a high-quality solution, the algorithm needs to balance the weights in the decision space and the target space.

[0008] In summary, when the sample size is small, it is difficult for existing multi-objective optimization to select appropriate features to mine accurate user preferences. Summary of the invention

[0009] The purpose of the present invention is to provide a multi-modal and multi-objective evolution method and device based on dual-population co-evolution.

[0010] The purpose of the present invention can be achieved by the following technical solutions:

[0011] A multi-modal multi-objective evolutionary method based on dual-population co-evolution, which is used to optimize the user feature set;

[0012] The method maintains two weakly cooperative populations, namely: the assisting population P that prioritizes fitness value and secondarily considers decision space diversity and target space diversity 1 and the output population P that prioritizes decision space diversity and secondarily considers fitness value 2 ; Assisting population P 1 and the output population P 2 They are all subsets of the total feature set of the user;

[0013] Among them: assisting population P 1 The principle of convergence priority is adopted, and the diversity of the two spaces is considered at the same time to ensure the convergence of the final solution; the output population P 2 The principle of exploring sparse solutions is adopted, mainly considering the diversity in the decision space, retaining solutions with poor convergence but good diversity, and improving the algorithm's search ability in the decision space;

[0014] Assisting population P 1 and the output population P 2 Information complementarity in evolution is achieved through three special mechanisms: preferential fitness calculation, independent offspring generation and information sharing.

[0015] The method specifically comprises the following steps:

[0016] Step 1) Initialize the adaptive adjustment factor ∈;

[0017] Step 2) Randomly initialize the assisting population P 1 and the output population P 2 ;

[0018] Step 3) Calculate the assisting population P respectively 1 and the output population P 2 The individual fitness value of 1 The fitness calculation of is based on the Pareto dominance relationship, which is obtained by adding the evaluation of convergence and the evaluation of diversity in the two spaces, and the output population P 2 The fitness calculation is based on the neighborhood Pareto dominance relationship, which is obtained by adding the evaluation of local convergence and the evaluation of the diversity of the decision space;

[0019] Step 4) In the assisting population P 1 In parent selection, convergence is prioritized as the principle, total fitness is the primary criterion, and the diversity of the decision space is evaluated Evaluation of diversity in target space Selection was made for the secondary criteria, thus considering diversity in both spaces simultaneously;

[0020] Step 5) Output population P 2 Evaluation of Diversity in Decision Space in Parent Selection As the primary criterion, the total fitness is selected as the secondary criterion, so as to mainly consider the diversity of the decision space;

[0021] Step 6) Based on the individuals selected in step 4) and step 5), the two populations reproduce independently to generate offspring O 1 With O 2 ;

[0022] Step 7) Assisting population P 1 The following steps are performed during the environment selection process:

[0023] S1, the original population P 1 and the offspring O 1 , O 2 Merge so that the newly generated population can inherit the advantages of the two parent populations;

[0024] S2, based on P 1 The fitness calculation method is used to calculate the fitness of the merged population, and based on the calculation results, individuals with better quality are selected to form a new population, guiding the population to evolve in the direction of convergence of the target space;

[0025] Step 8) Output population P 2 The following steps are performed during the environment selection process:

[0026] S1, the original population P 2 and the offspring O 1 , O 2Merge so that the newly generated population can inherit the advantages of the two parent populations;

[0027] S2, select the corresponding global and local Pareto optimal solutions based on fast non-dominated sorting and ∈-dominance non-dominated sorting;

[0028] S3, based on P 2 The fitness calculation method is used to calculate the fitness of the remaining population, and based on the calculation results, individuals with better quality are selected to form a new population, guiding the population to evolve towards the direction of decision space diversity;

[0029] Step 9) Repeat steps 3) to 8) until a preset number of iterations is reached to generate an optimal solution set.

[0030] The individual fitness calculation is used as the criterion for parent selection of the two populations.

[0031] The individual fitness calculation is used as the standard for selecting the parent generation of the two populations:

[0032] fit(x) = R x +D x

[0033] Where: R x represents the evaluation of convergence, D x It represents a diversity evaluation.

[0034] The evaluation of convergence in the individual fitness calculation is characterized by:

[0035] For P 1 , the convergence evaluation is expressed by the number of individuals dominated by Pareto, which is specifically:

[0036]

[0037] Where: x will be 1 The dominance relationship is judged by other individuals y in the group. When y dominates x, r(x,y) is 1, otherwise it is 0. x represents the number of solutions dominated by x;

[0038] For P 2 , the evaluation of its convergence only needs to consider the dominance relationship of neighbor solutions, which is specifically:

[0039]

[0040] Where: N x represents the neighbors of x, and the assisting population P 1 The convergence of is similar to that of 2Evaluation of the convergence of individual x in When it is 0, x is a non-dominated solution in the current neighborhood. Otherwise, x is dominated by multiple neighbor individuals and has poor quality.

[0041] Output population P 2 The middle neighborhood relationship is characterized by:

[0042] If the Euclidean distance between a solution x and another solution y in the decision space is less than the first threshold V, then x and y are called neighbors of each other, and x and y are in the same neighborhood, specifically:

[0043]

[0044] Where: M is the number of decision variables, and are the maximum and minimum values ​​of the mth decision variable in the current evolution stage, respectively, and θ is used to control the average length of the neighborhood.

[0045] The evaluation of diversity in the individual fitness calculation is characterized by:

[0046] For the assisting population P 1 , its diversity needs to consider both the decision space and the target space diversity, specifically:

[0047]

[0048] Among them: dist obj (x,x′) represents the Euclidean distance between solution x and its nearest kth solution x′ in the target space. dist dec (x, x′) represents the Euclidean distance between solution x and its nearest kth solution x′ in the decision space. If the diversity of solutions is good, D x The value of is close to 0, otherwise it is close to 0.5. The parameter k is That is, the integer part of the population size under the square root;

[0049] For the output population P 2 , which mainly considers the diversity of decision space, specifically:

[0050]

[0051] Where: i is the number of generations of evolution, ∈ is the preset local Pareto optimal solution quality. In the entire evolution process, in order to ensure that the output population P 2 In the early stage, as many promising solutions as possible can be found. At this time, the value of ∈ should be large, so that the output population P 2These solutions can be retained, and in the later stage, the value of ∈ should be made smaller so that the output population P 2 It can retain the solution that has converged to the corresponding local Pareto frontier while enhancing the convergence of the solution in the target space.

[0052] Assisting population P 1 With the output population P 2 Weak cooperation is used to exchange information. 1 Prioritize convergence, and individuals approach the Pareto frontier in the target space; the output population P 2 In the process, exploration is the main focus, and individuals are far away from PF in the target space. Individuals in the two populations are far apart in the target space. If the parents in the two populations are directly mated, the offspring produced will often be between PF and the external area, which is not conducive to evolution.

[0053] A multi-modal multi-objective evolution device based on dual-population co-evolution comprises a memory, a processor, and a program stored in the memory, wherein the processor implements the above method when executing the program.

[0054] Compared with the prior art, the present invention has the following beneficial effects:

[0055] 1) Different from most existing multimodal multi-objective evolutionary algorithms that use a single population or a single population plus external archiving, the present invention is based on a dual-population collaborative algorithm, using two populations with different biases to evolve independently and share information at specific stages, thereby achieving collaborative evolution and mutual complementation, allowing the algorithm to avoid falling into local optimal solutions while finding more high-quality solutions.

[0056] 2) Different from most existing multimodal multi-objective evolutionary algorithms that adopt the principle of convergence priority, the individual fitness value calculation of the present invention considers both convergence and diversity, retains solutions with poor convergence but good diversity, enhances the search capability in the decision space, and increases the probability of finding all Pareto optimal solution sets.

[0057] 3) Based on the ∈-dominance relationship, an environmental selection strategy that retains the local Pareto optimal solution is designed, and an adaptive adjustment factor that changes with the evolutionary stage is designed, which can achieve different goals in different stages and ensure the quality of the final solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is a multi-modal and multi-objective evolution method framework based on dual-population co-evolution of the present invention;

[0059] Figure 2 is the output population P of the present invention2 Demonstration diagram of neighbor relationship in convergence evaluation;

[0060] Figure 3 It is a parallel coordinate diagram of the multi-modal multi-objective evolutionary method based on dual-population co-evolution on the test function IDMPM2T1_e in an embodiment of the present invention. DETAILED DESCRIPTION

[0061] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0062] The present invention provides a multi-modal multi-objective evolution method based on dual-population co-evolution, which maintains two weakly cooperative populations: an assisting population P and a 1 and the output population P 2 .P 1 and P 2 Have different preferences;

[0063] (1) Assisting population P 1 Prioritize fitness value, taking into account the diversity of decision space and target space;

[0064] (2) Output population P 2 Prioritize decision space diversity while taking fitness value into consideration;

[0065] Weak cooperation mechanism: Due to the population P 1 Prioritize convergence, individuals approach PF in the target space; population P 2 The exploration is the main focus, and the individuals are far away from PF in the target space. The individuals in the two populations are far apart in the target space, and directly mating the parents in the two populations is not conducive to evolution. 1 and P 2 During the environmental selection stage, the offspring are shared to ensure that the new populations generated by each can inherit the advantages of the two parent populations.

[0066] Adaptive adjustment factor: population P 2 The environmental selection strategy needs to retain the local Pareto optimal solution of the corresponding quality. The ∈-dominance based on the adaptive adjustment factor can adjust the granularity of the dominance relationship at different evolutionary stages. Specifically: In the early stage, in order to ensure that the population P 2 In the early stage, we can find as many promising solutions as possible, and ∈ takes a larger value, so that the population P 2 These solutions can be retained. In the later stage, ∈ takes a smaller value, making the population P 2It can retain the solution that has converged to the corresponding local Pareto frontier while enhancing the convergence of the solution in the target space. Specific embodiments

[0068] Multimodal and multi-objective evolutionary methods based on dual population co-evolution are Figure 1 As shown in Figure 2, this method supports two weakly cooperative populations, namely, the assisting population P that prioritizes fitness value and secondarily considers decision space diversity and target space diversity. 1 and the output population P that prioritizes decision space diversity and secondarily considers fitness value 2 . Among them: population P 1 The principle of convergence priority is adopted, taking into account the diversity of the two spaces, and ensuring the convergence of the final solution; the population P 2 The principle of exploring sparse solutions is adopted, taking into account the diversity and convergence in the decision space, retaining solutions with poor convergence but good diversity, and improving the algorithm's search ability in the decision space. 1 and P 2 Information complementation in evolution is achieved through three special mechanisms: preferential fitness calculation, independent offspring generation, and information sharing. The specific evolution steps of the method are as follows:

[0069] Step 1) Initialize the adaptive adjustment factor ∈, specifically:

[0070]

[0071] Where: i is the number of evolution generations, ∈ is the preset local Pareto optimal solution quality.

[0072] Step 2) Randomly initialize the population P 1 and P 2 ;

[0073] Step 3) Calculate P 1 and P 2 The individual fitness value of , in this embodiment, the individual fitness value is calculated as follows:

[0074] fit(x) = R x +D x

[0075] Where: R x represents the evaluation of convergence, D x It represents a diversity evaluation.

[0076] For P 1 , the convergence evaluation is expressed by the number of individuals dominated by Pareto, which is specifically:

[0077]

[0078] Where: x will be 1 The dominance relationship is determined by other individuals y in S. When y dominates x, r(x,y) is 1, otherwise it is 0. x represents the number of solutions dominated by x.

[0079] For P 2 , the evaluation of its convergence only needs to consider the dominance relationship of neighbor solutions, which is specifically:

[0080]

[0081] Where: N x represents the neighbors of x. 1 The convergence of is similar to that of When is 0, x is a non-dominated solution in the current neighborhood. Otherwise, x is dominated by multiple neighbor individuals and the quality is not good. Figure 2 is the output population P 2 Demonstration diagram of neighbor relationship in convergence evaluation. If the Euclidean distance between a solution x and another solution y in the decision space is less than a specific threshold V, then x and y are called neighbors of each other, and x and y are in the same neighborhood, specifically:

[0082]

[0083] Where: M is the number of decision variables, and are the maximum and minimum values ​​of the mth decision variable in the current evolution stage. θ is used to control the average length of the neighborhood. By limiting the scope of the Pareto dominance relationship, the direct comparison between the local optimal solution and the global optimal solution can be avoided, ensuring that the local optimal solution can be retained in the subsequent environmental selection environment.

[0084] For P 1 , its diversity needs to consider both the decision space and the target space diversity, specifically:

[0085]

[0086]

[0087] Among them: for dist obj (x,x′) represents the Euclidean distance between solution x and its nearest kth solution x′ in the target space. dist dec (x,x′) represents the Euclidean distance between solution x and its nearest kth solution x′ in the decision space. Obviously, if the diversity of the solution is good, then D xThe value of is close to 0.

[0088] For P 2 , which mainly considers the diversity of decision space, specifically:

[0089]

[0090] Step 4) In P 1 In parent selection, convergence is prioritized as the principle, overall fitness is the primary criterion, and Selection was made for the secondary criteria, thus considering diversity in both spaces simultaneously;

[0091] Step 5) In P 2 In parent selection, As the primary criterion, fitness is selected as the secondary criterion, so as to mainly consider the diversity of the decision space;

[0092] Step 6) Based on the individuals selected in step 4) and step 5), the two populations reproduce independently to generate offspring O 1 With O 2 ;

[0093] Step 7) Assisting population P 1 The following steps are performed during the environment selection process:

[0094] S1, the original population P 1 and the offspring O 1 , O 2 Merge so that the newly generated population can inherit the advantages of the two parent populations;

[0095] S2, based on P 1 The fitness calculation method is used to calculate the fitness of the merged population, and based on the calculation results, individuals with better quality are selected to form a new population, guiding the population to evolve in the direction of convergence of the target space;

[0096] Step 8) Output population P 2 The following steps are performed during the environment selection process:

[0097] S1, the original population P 2 and the offspring O 1 , O 2 Merge so that the newly generated population can inherit the advantages of the two parent populations;

[0098] S2, select the corresponding global and local Pareto optimal solutions based on fast non-dominated sorting and ∈-dominance non-dominated sorting;

[0099] S3, based on P 2The fitness calculation method is used to calculate the fitness of the remaining population, and based on the calculation results, individuals with better quality are selected to form a new population, guiding the population to evolve towards the direction of decision space diversity;

[0100] Step 9) Repeat steps 3) to 8) until a preset number of iterations is reached to generate an optimal solution set.

[0101] This embodiment simulates and verifies the above-mentioned multimodal multi-objective evolutionary method based on dual-population collaborative evolution on the PlatEMO platform on the Windows 11 system. The simulation experiment adopted the mainstream CEC2019, IDMP and IDMP_e test sets. Each test problem was run independently 20 times, and each experiment was iterated 50 times. Compared with several most advanced multimodal multi-objective evolutionary algorithms, this embodiment achieved the best performance in 22 of the 40 test problems. The experimental results prove the advancement of this embodiment. Among them, taking the comparison between DN-NSGA-II and MMOEA / DC algorithm on CEC2019 as an example, the results shown in Table 1 are obtained; taking the distribution of solutions obtained by the method of IDMPM2T1_e as an example, it is obtained Figure 3 result.

[0102] Table 1 Comparison of IGDX results of three algorithms on the CEC2019 test set

[0103] Test Questions DN-NSGA-II MMOEA / DC Method of the present invention MMF1 5.4218e-2(1.03e-2)- 4.5360e-2(1.76e-3)- 3.8729e-2(1.32e-3) MMF2 8.0156e-2(6.00e-2)- 2.2936e-2(1.92e-2)+ 2.6262e-2(4.38e-3) MMF3 5.1983e-2(1.67e-2)- 1.8589e-2(8.22e-3)+ 2.0995e-2(4.54e-3) MMF4 3.0001e-2(5.43e-3)- 2.6122e-2(2.74e-3)- 1.9132e-2(5.96e-4) MMF5 9.2921e-2(8.69e-3)- 7.7938e-2(2.51e-3)- 6.7391e-2(2.73e-3) MMF6 7.8032e-2(7.56e-3)- 6.7718e-2(2.72e-3)- 5.8134e-2(1.64e-3) MMF7 2.6403e-2(5.08e-3)- 2.8216e-2(2.19e-3)- 1.8493e-2(9.52e-4) MMF8 1.3471e-1(4.18e-2)- 7.0981e-2(2.04e-2)- 5.0128e-2(1.01e-2) MMF9 6.0872e-3(8.03e-4)- 6.6228e-3(2.62e-4)- 4.7971e-3(1.54e-4) MMF10 1.9609e-1(8.37e-3)- 1.8284e-2(3.87e-2)- 8.2405e-3(3.47e-4) MMF11 2.4907e-1(3.29e-4)- 7.6751e-3(2.79e-4)- 6.3827e-3(2.24e-4) MMF12 2.4488e-1(3.13e-4)- 3.2085e-3(1.82e-4)- 2.7939e-3(1.09e-4) MMF13 2.5913e-1(2.35e-3)- 1.0520e-1(5.57e-3)- 5.8366e-2(1.54e-3) MMF14 4.9159e-2(1.17e-3)- 5.2159e-2(1.53e-3)- 4.1218e-2(3.85e-4) MMF14_a 6.0607e-2(1.66e-3)- 7.8290e-2(3.44e-3)- 5.1042e-2(5.74e-4) MMF15 2.5993e-1(4.92e-3)- 6.6428e-2(3.21e-3)- 4.5833e-2(6.84e-4) MMF15_a 2.1544e-1(5.03e-3)- 1.1624e-1(2.32e-2)- 5.4910e-2(9.43e-4) Omni_test 2.8478e-1(1.97e-1)- 1.6585e-1(2.45e-2)- 7.4117e-2(4.64e-3) SYM_PART_rotated 7.3166e-1(6.66e-1)- 8.1140e-2(4.02e-3)- 7.4549e-2(8.81e-3) SYM_PART_simple 2.3158e-1(7.33e-1)- 4.9977e-2(3.40e-3)- 4.4383e-2(2.90e-3) + / - / ＝ 0 / 20 / 0 2 / 18 / 0

[0104] The technical problem to be solved by the present invention is how to alleviate the problem of inaccurate feature selection caused by the difficulty in balancing the diversity of decision space and target space faced by multimodal multi-objective optimization problems during user feature selection. The technical solution adopted is: a multimodal multi-objective evolution method based on dual-population co-evolution. This method maintains two weakly cooperative populations and adopts three special mechanisms of preferential fitness calculation, independent offspring generation and information exchange to achieve information complementarity in evolution. In addition, this method has the advantages of strong search capability, good robustness and strong adaptability.

[0105] In this application, the specific application process is as follows: taking the proportion and error rate of selected features as the problem optimization objectives, and taking computational complexity, feature relevance, privacy protection, and real-time requirements as constraints, a multi-objective constrained optimization model for feature selection is established; secondly, the total number of user features is used as the chromosome length, and the population individuals are encoded with 0-1 variables; then, the population P is initialized based on a specific encoding method. 1 and P 2 , and follow Figure 1The dual-population co-evolution process shown performs parent selection, offspring production, environment selection and information exchange until the corresponding number of iterations is reached or the optimal solution that meets the problem requirements is found; and finally outputs a Pareto optimal solution set with two conflicting indicators, the proportion of selected features and the error rate, as optimization targets.

[0106] User characteristics can be click-through rate, browsing time, average order value, etc.

[0107] If the above functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc., which can store program code.

Claims

1. A multi-modal multi-objective evolution method based on dual-population co-evolution, characterized in that: This method is used to optimize the user feature set; The method maintains two weakly cooperative populations, namely: an assisting population P1 that prioritizes fitness value and secondarily considers decision space diversity and target space diversity, and an output population P2 that prioritizes decision space diversity and secondarily considers fitness value; both the assisting population P1 and the output population P2 are subsets of the total feature set of users; Among them: the assisting population P1 adopts the principle of convergence priority, while considering the diversity of the two spaces to ensure the convergence of the final solution; the output population P2 adopts the principle of exploring sparse solutions, mainly considering the diversity in the decision space, retaining solutions with poor convergence but good diversity, and improving the algorithm's search ability in the decision space; The assisting population P1 and the output population P2 achieve information complementarity in evolution through three special mechanisms: preferential fitness calculation, independent offspring generation and information sharing.

2. A multi-modal multi-objective evolution method based on dual-population co-evolution according to claim 1, characterized in that: The method specifically comprises the following steps: Step 1) Initialize the adaptive adjustment factor ∈ ; Step 2) Randomly initialize the auxiliary population P1 and the output population P2; Step 3) Calculate the individual fitness values ​​of the assisting population P1 and the output population P2 respectively, wherein the fitness calculation of the assisting population P1 is based on the Pareto dominance relationship, which is obtained by adding the evaluation of convergence to the evaluation of the diversity of the two spaces, while the fitness calculation of the output population P2 is based on the neighborhood Pareto dominance relationship, which is obtained by adding the evaluation of local convergence to the evaluation of the diversity of the decision space; Step 4) In assisting the selection of the parent generation of population P1, the principle of convergence priority is adopted, the total fitness is taken as the primary criterion, and the evaluation of the diversity in the decision space is taken as the evaluation criteria. Evaluation of diversity in target space Selection was made for the secondary criteria, thus considering diversity in both spaces simultaneously; Step 5) In the output population P2 parent selection, the diversity evaluation in the decision space is used As the primary criterion, the total fitness is selected as the secondary criterion, so as to mainly consider the diversity of the decision space; Step 6) Based on the individuals selected in step 4) and step 5), the two populations reproduce independently to generate offspring O1 and O2; Step 7) Assisting population P1 to perform the following steps in the environmental selection process: S1, merge the original population P1 with the generated offspring O1 and O2, so that the newly generated population can inherit the advantages of the two parent populations; S2, based on the fitness calculation method of P1, the fitness of the merged population is calculated, and based on the calculation results, individuals with better quality are selected to form a new population, guiding the population to evolve in the direction of convergence of the target space; Step 8) The output population P2 performs the following steps in the environmental selection process: S1, merge the original population P2 with the generated offspring O1 and O2, so that the newly generated population can inherit the advantages of the two parent populations; S2, select the corresponding global and local Pareto optimal solutions based on fast non-dominated sorting and ∈-dominance non-dominated sorting; S3, based on the fitness calculation method of P2, the fitness of the remaining population is calculated, and based on the calculation results, individuals with better quality are selected to form a new population, guiding the population to evolve in the direction of decision space diversity; Step 9) Repeat steps 3) to 8) until a preset number of iterations is reached to generate an optimal solution set.

3. A multi-modal multi-objective evolution method based on dual-population co-evolution according to claim 2, characterized in that: The individual fitness calculation is used as the criterion for parent selection of the two populations.

4. According to the multi-modal multi-objective evolution method based on dual-population co-evolution in claim 3, the individual fitness calculation is used as the standard for selecting the parent generation of the two populations: fit(x)=R x +D x in: R x represents the evaluation of convergence, D x It represents a diversity evaluation.

5. According to the multi-modal multi-objective evolution method based on dual-population co-evolution in claim 4, the evaluation of convergence in the individual fitness calculation is characterized by: For P1, the convergence is evaluated by the number of individuals dominated by Pareto, which is: Among them: x will judge the dominance relationship with other individuals y in P1. When y dominates x, r(x, y) is 1, otherwise it is 0. S x represents the number of solutions dominated by x; For P2, the evaluation of its convergence only needs to consider the dominance relationship of neighbor solutions, which is specifically: Where: N x Represents the neighbors of x, which is similar to the evaluation of the convergence of the assisting population P1. When the evaluation of the convergence of the individual x in the output population P2 is When it is 0, x is a non-dominated solution in the current neighborhood. Otherwise, x is dominated by multiple neighbor individuals and has poor quality.

6. According to claim 5, a multi-modal multi-objective evolution method based on dual-population co-evolution outputs the neighborhood relationship in population P2, characterized in that: If the Euclidean distance between a solution x and another solution y in the decision space is less than the first threshold V, then x and y are called neighbors of each other, and x and y are in the same neighborhood, specifically: Where: M is the number of decision variables, and are the maximum and minimum values ​​of the mth decision variable in the current evolution stage, respectively, and θ is used to control the average length of the neighborhood.

7. According to the multi-modal multi-objective evolution method based on dual-population co-evolution according to claim 4, the evaluation of diversity in the individual fitness calculation is characterized by: For the assisting population P1, its diversity needs to consider both the decision space and the target space diversity, specifically: Among them: dist obj (x, x′) represents the Euclidean distance between solution x and its nearest kth solution x′ in the target space. dist dec (x, x′) represents the Euclidean distance between solution x and its nearest kth solution x′ in the decision space. If the diversity of solutions is good, D x The value of is close to 0, otherwise it is close to 0.

5. The parameter k is That is, the integer part of the population size under the square root; For the output population P2, it mainly considers the diversity of the decision space, specifically:

8. According to the multi-modal multi-objective evolution method based on dual-population co-evolution according to claim 1 or 2, the adaptive adjustment factor is characterized by: Where: i is the number of evolutionary generations, ∈ is the preset local Pareto optimal solution quality. During the entire evolutionary process, in order to ensure that the output population P2 can find as many promising solutions as possible in the early stage, the ∈ value should be large so that the output population P2 can retain these solutions. In the later stage, the ∈ value should be small so that the output population P2 can retain the solutions that have converged to the corresponding local Pareto frontier while enhancing the convergence of the solution in the target space.

9. A multi-modal multi-objective evolution method based on dual-population co-evolution according to claim 1 or 2, characterized in that: The assisting population P1 and the output population P2 adopt a weak cooperation method to exchange information. Since the assisting population P1 prioritizes convergence, the individuals are close to the Pareto frontier in the target space; the output population P2 is mainly exploration, and the individuals are far away from the PF in the target space. The individuals in the two populations are far apart in the target space. If the parents in the two populations are directly mated, the offspring produced will often be between the PF and the external area, which is not conducive to evolution.

10. A multi-modal multi-objective evolution device based on dual-population co-evolution, comprising a memory, a processor, and a program stored in the memory, characterized in that: When the processor executes the program, the method according to any one of claims 1 to 9 is implemented.

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