CN114065625A - High-dimensional multi-target co-evolution method based on subspace search - Google Patents

High-dimensional multi-target co-evolution method based on subspace search Download PDF

Info

Publication number
CN114065625A
CN114065625A CN202111351876.7A CN202111351876A CN114065625A CN 114065625 A CN114065625 A CN 114065625A CN 202111351876 A CN202111351876 A CN 202111351876A CN 114065625 A CN114065625 A CN 114065625A
Authority
CN
China
Prior art keywords
individuals
population
individual
convergence
subspace
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202111351876.7A
Other languages
Chinese (zh)
Inventor
刘耿耿
裴镇宇
郭文忠
陈国龙
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Fuzhou University
Original Assignee
Fuzhou University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Fuzhou University filed Critical Fuzhou University
Priority to CN202111351876.7A priority Critical patent/CN114065625A/en
Publication of CN114065625A publication Critical patent/CN114065625A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/004—Artificial life, i.e. computing arrangements simulating life
    • G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/06—Multi-objective optimisation, e.g. Pareto optimisation using simulated annealing [SA], ant colony algorithms or genetic algorithms [GA]

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Evolutionary Computation (AREA)
  • General Physics & Mathematics (AREA)
  • General Engineering & Computer Science (AREA)
  • Software Systems (AREA)
  • Artificial Intelligence (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Biophysics (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Computer Hardware Design (AREA)
  • Health & Medical Sciences (AREA)
  • Medical Informatics (AREA)
  • Biomedical Technology (AREA)
  • Geometry (AREA)
  • Computational Linguistics (AREA)
  • Data Mining & Analysis (AREA)
  • General Health & Medical Sciences (AREA)
  • Molecular Biology (AREA)
  • Computing Systems (AREA)
  • Mathematical Physics (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

Abstract

The invention relates to a high-dimensional multi-target co-evolution method based on subspace search. Firstly, analyzing a problem to be optimized, dividing a decision space into a convergence subspace and a diversity subspace, respectively searching the convergence subspace and the diversity subspace in the early stage and the later stage of the method, then utilizing a filing set to reserve elite individuals with better convergence in population evolution, and mating the elite individuals of the filing set with population individuals; and finally, selecting the individuals according to the included angles among the individuals, thereby maintaining the diversity of the population. The method can improve the convergence of the population and the searching efficiency of the method.

Description

High-dimensional multi-target co-evolution method based on subspace search
Technical Field
The invention belongs to the field of evolutionary algorithms, and particularly relates to a high-dimensional multi-target co-evolutionary method based on subspace search.
Background
Multi-objective optimization problems (MOP) exist in various fields of real life, such as sewage treatment control, vehicle route planning, power distribution, and the like. Such problems require simultaneous optimization of several conflicting objectives, so the optimal solution for MOP is not a single solution, but a solution set composed of a set of solutions with better convergence and diversity. When the number of targets of the MOP is more than three, the MOP is called a high-dimensional multi-target optimization problem (MaOP). The Multi-objective evolutionary algorithm (MOEA) is based on population optimization, and a characteristic that a group of solutions can be obtained through a single operation is a research hotspot of recent scholars. With the increase of the target dimension, the optimization difficulty of the problem rises sharply, and mainly appears in the following aspects.
Firstly, in an m-dimensional target space, the probability of comparing the advantages and disadvantages of any two individuals is 1/2 through Pareto dominationm-1Thus, as the target dimension increases, the number of non-dominant individuals in the population grows exponentially, i.e., a phenomenon of "dominant resistance" occurs.
Since the primary criterion for selecting individuals (i.e., Pareto dominance) is not valid, the diversity maintenance mechanism plays a decisive role, and this mechanism is not favorable for convergence of the algorithm. In addition, diversity maintenance mechanisms may favor the selection of dominant resistant solutions. Dominant resistant solutions refer to non-dominant individuals who have poor at one or more objective function values, but good at other objective function values, a feature that makes them difficult to dominate by other individuals. On the other hand, the difficulty of eliminating dominant-resistance solutions is further increased by the presence of the phenomenon of "dominant resistance". The dominant resistant solution is often far away from the Pareto front, and the generated descendants are also far away from the Pareto front with high probability, so that the convergence of the algorithm is not facilitated. Secondly, in each iteration of the algorithm, the number of individuals capable of being reserved is limited, the dominant resistant solution exists in the population for a long time, and excellent offspring can not be reserved in time, so that the performance of the algorithm is affected.
As the number of objective functions increases, collisions between different objectives are exacerbated, making it more difficult for the algorithm to balance convergence and diversity. The existing algorithm usually optimizes convergence and diversity at the same time, and the performance of the algorithm is poor due to the conflict between the convergence and the diversity and the limited searching capability of the algorithm.
Disclosure of Invention
The invention aims to provide a high-dimensional multi-target co-evolution method based on subspace search, which can improve the convergence of a population and the efficiency of method search.
In order to achieve the purpose, the technical scheme of the invention is as follows: a high-dimensional multi-target co-evolution method based on subspace search comprises the following steps:
step S1, grouping the decision variables by using a decision variable grouping strategy, and dividing a search space into two subspaces; at different stages of the method, two subspaces are searched respectively to realize independent optimization of convergence and diversity;
step S2, providing an index-based archive set, using Iε+The method has the characteristic of good convergence, and the elite individuals with good convergence are reserved in the filing set; the population and the filing set co-evolve, and the population inherits the good convergence of elite individuals in the filing set; introducing a self-adaptive adjusting strategy of the archive collection capacity, wherein in the early stage of the method, the population realizes rapid convergence under the guidance of a few elite individuals; in the later stage of the method, the population is influenced by more elite individuals, so that the coverage of the population is ensured;
step S3, providing a boundary individual selection strategy, eliminating boundary individuals with poor convergence on the premise of ensuring the diversity of the boundary individuals, and further accelerating the convergence of the method; and a diversity maintenance strategy is provided, and the distribution uniformity and coverage of the population are ensured.
In an embodiment of the present invention, step S1 is implemented as follows:
analyzing a problem to be optimized, and dividing a decision space into a convergence subspace and a diversity subspace by using a decision variable grouping strategy; then, dividing the whole method into two stages, firstly searching in a convergence subspace to enable the population to quickly approach to the Pareto front edge; when the population is close enough to Pareto frontier, then search in diversity subspace, enable population to have good distribution.
In an embodiment of the present invention, the archive set update manner in step S2 is as follows: firstly, combining the offspring and the individual in the archive set, and calculating the capacity of the archive set according to a capacity self-adaptive adjustment strategy; then, calculating the fitness values of all individuals in the archive set, and removing the individual with the minimum fitness value; finally, updating the fitness values of the rest individuals; the removing of individuals in the archive set is repeated until the number of individuals in the archive set meets the current capacity.
In one embodiment of the present invention, step S2 utilizes Iε+The specific implementation process of retaining the elite individual with better convergence to the archive set is as follows:
by the use of Iε+As an index for selecting individuals; i isε+And an individual x1Fitness value F (x)1) The calculation method of (c) is as follows:
Figure BDA0003356062860000021
Figure BDA0003356062860000022
wherein x1And x2Two individuals in the population P.
In an embodiment of the present invention, in step S2, the capacity formula for calculating the archive set by using the capacity adaptive adjustment policy is as follows:
Figure BDA0003356062860000023
where lb and ub represent the lower and upper bounds of the capacity, respectively, and FE and MaxFE represent the current number of evaluations and the maximum number of evaluations, respectively.
In an embodiment of the present invention, the boundary individual selection policy in step S3 provides an index with a penalty factor to select the boundary individual, and defines the following formula Hj(x) The smallest individual is the boundary individual B on the jth target axisj：
Figure BDA0003356062860000031
Bj＝argminHj(x)
Wherein f isi(x) The function value of the individual x on the ith target function is taken, and alpha is a penalty factor; by using
Figure BDA0003356062860000032
Representing the closeness degree of the individual x and the jth target axis, wherein the smaller the value is, the closer the individual is to the target axis is, the higher the possibility of being at the boundary is; in addition, if a certain object has the objective function value fjToo large, i.e. dominating the resistant solution, the priority of the individual selected will be reduced by introducing a penalty term.
In one embodiment of the present invention, the diversity maintenance strategy in step S3 uses the included angle between individuals as the density of individuals, and the individual x1And x2The included angle between the two is calculated as follows
Figure BDA0003356062860000033
Calculating the unselected non-dominant individual x ∈ F1With the already reserved individual y ∈ Pt+1The minimum angle min (angle (x, y)) is taken as the density [ x ] of the individual x]And keeping the individuals with the maximum density to the next generation, and repeating the steps until the population size reaches n.
Compared with the prior art, the invention has the following beneficial effects: the method can improve the convergence of the population and the searching efficiency of the method.
Drawings
Fig. 1 is a decision variable grouping strategy: (a) disturbing the decision variables; (b) calculating the included angle between the fitting straight line and the plane; (c) grouping the decision variables according to the included angles;
FIG. 2 is a two-phase search;
FIG. 3 is density calculation versus individual retention: (a) reserving boundary individuals; (b) retention of the most dense individual s 4; (c) retention of the most dense individual s 6;
FIG. 4 is a SSCEM flow diagram.
Detailed Description
The technical scheme of the invention is specifically explained below with reference to the accompanying drawings.
The invention relates to a high-dimensional multi-target co-evolution method based on subspace search, which comprises the following steps:
step S1, grouping the decision variables by using a decision variable grouping strategy, and dividing a search space into two subspaces; at different stages of the method, two subspaces are searched respectively to realize independent optimization of convergence and diversity;
step S2, providing an index-based archive set, using Iε+The method has the characteristic of good convergence, and the elite individuals with good convergence are reserved in the filing set; the population and the filing set co-evolve, and the population inherits the good convergence of elite individuals in the filing set; introducing a self-adaptive adjusting strategy of the archive collection capacity, wherein in the early stage of the method, the population realizes rapid convergence under the guidance of a few elite individuals; in the later stage of the method, the population is influenced by more elite individuals, so that the coverage of the population is ensured;
step S3, providing a boundary individual selection strategy, eliminating boundary individuals with poor convergence on the premise of ensuring the diversity of the boundary individuals, and further accelerating the convergence of the method; and a diversity maintenance strategy is provided, and the distribution uniformity and coverage of the population are ensured.
The following are specific embodiments of the present invention.
The invention relates to a high-dimensional multi-target co-evolution method based on subspace search, which comprises the following specific implementation processes:
1. and (3) subspace searching:
the multi-objective optimization algorithm aims to obtain a set of compromise solution sets with good convergence and diversity, and most of the existing algorithms have the idea that the two performances are optimized simultaneously in the searching process, namely, the population always keeps good population distribution in the process of approaching to a Pareto frontier.
The method comprises the steps of firstly analyzing a problem to be optimized, utilizing a decision variable grouping strategy to divide a decision space into a convergence subspace and a diversity subspace, then, dividing the whole method into two stages, firstly searching the convergence subspace to enable a population to quickly approach to a Pareto front edge, and then searching in the diversity subspace after the population is close to the Pareto front edge, so that the population can have good distribution.
FIG. 1 is an example of a decision variable grouping strategy, the optimization problem having two objective functions, five decision variables x to be classified1,x2,x3,x4And x5As shown in fig. 1 a, q samples (q is 2 in the figure) are randomly extracted from the population, the decision variable of each sample is disturbed p times (p is 10 in the figure) in sequence, and the decision variable value of the solution after disturbance is normalized, and then as shown in fig. 1 b, a straight line is fitted to the solution after disturbance of each group, and the straight line and the plane f are calculated1+…+fmThe smaller the included angle is, the different values of the decision variable are shown, and the diversity is greatly influenced; on the contrary, the larger the included angle is, the larger the influence of the decision variable on the convergence is shownClass, where the smaller angle class of variables is the diversity decision variable and the larger angle class is the convergence decision variable, the result is shown in fig. 1 (c).
In terms of selection of crossover operators and mutation operators, the conventional multi-objective optimization algorithm usually uses simulated binary crossover and polynomial mutation to generate filial generations, which means that the search space of the algorithms is the whole decision space, namely, convergence and diversity of a population are optimized simultaneously, and when the number of decision variables is large, the algorithm is undoubtedly stressed by large search pressure.
After the population is close enough to the Pareto front, the method enters the second stage, only search on the diversity subspace, the purpose is to change the distribution structure of the population, make the population cover on the whole Pareto front evenly; when the diversity subspace is searched, only the value of the diversity decision variable is changed, so that the search space is reduced, and the search efficiency of the method is enhanced under the condition of limited computing resources.
2. An archive set:
the invention adopts a filing set to keep individuals with excellent convergence in the evolution process of the population, and mates the individuals in the filing set with the population individuals, so that the generated offspring can inherit good convergence, and the filing set and the population co-evolve to accelerate the convergence of the method.
The basic flow of the archive set updating is shown as algorithm 1, firstly, the filial generation is combined with the individual bodies in the archive set, the capacity of the archive set is calculated according to the capacity self-adaptive adjustment strategy mentioned later, then, the fitness values of all the individual bodies in the archive set are calculated, the individual body with the minimum fitness value is removed, finally, the fitness values of the rest individual bodies are updated, and the individual bodies in the archive set are removed repeatedly until the number of the individual bodies in the archive set meets the current capacity.
Figure BDA0003356062860000051
Figure BDA0003356062860000061
In order to screen elite individuals from a population, we need to introduce appropriate indicators or relationships between individuals to compare the convergence of the individuals and thus guide the evolution of the population. The proportion of non-dominated individuals in a population is sharply increased along with the increase of a target dimension, and the effect of enabling the population to approach a Pareto front is not good by using a Pareto domination relation, the sum of the target functions is a special case of the weighted sum, namely all weights are 1, although the index can rapidly guide the population to converge towards the Pareto front, the nonlinear Pareto front can cause the population to gather at a local position: when the Pareto front is convex, individuals in the middle of the Pareto front will have a higher selection priority than individuals at the edges; when the Pareto front is concave, individuals at the edges will have a higher selection priority than individuals in the middleε+As an indicator of the selected individualsε+And an individual x1Fitness value F (x)1) The calculation method of (c) is as follows:
Figure BDA0003356062860000062
Figure BDA0003356062860000063
wherein x1And x2Two individuals in the population P.
If the capacity of the filing set is small, only the best few elite individuals are reserved in each iteration process, and the population approaches to the Pareto frontier under the guidance of the elite individuals, so that the effect of rapid population convergence is realized; if the capacity of the archive set is large, the existence of a large number of elite individuals disperses the evolution direction of the population, and the convergence information of a few excellent elite individuals in the archive set cannot be fully utilized, so that the convergence speed of the method is reduced.
Figure BDA0003356062860000071
Where lb and ub represent the lower and upper bounds of the capacity, respectively, and FE and MaxFE represent the current number of evaluations and the maximum number of evaluations, respectively.
After the self-adaptive adjustment strategy is introduced, in the early stage of the method, a few elite individuals mate with the population and generate offspring with good convergence, so that the whole population is quickly converged.
3. Selecting an environment:
the specific process of environment selection is shown as algorithm 2, and the offspring and the parent are merged, non-dominant individuals in the population are obtained by utilizing non-dominant sorting, ideal points in the non-dominant individuals are calculated, and the function values of the non-dominant individuals are subjected to standardization processing.
Figure BDA0003356062860000072
Figure BDA0003356062860000081
In order to better balance convergence and diversity and eliminate dominant resistant solutions as much as possible, the invention does not directly select individuals with extreme values, but proposes indexes with penalty factors to select boundary individuals, and the invention defines that the following formula H can be used for leading the following formula H to be widely distributed on Pareto frontier, and preferentially selects m boundary individuals in all non-dominant solutionsj(x) The smallest individual is the boundary individual B on the jth target axisj：
Figure BDA0003356062860000082
Bj＝argminHj(x)
Wherein f isi(x) The function value of the individual x on the ith objective function is represented by alpha, which is a penalty factor.
We use
Figure BDA0003356062860000083
Representing the closeness of an individual x to the jth target axis, a smaller value indicating that the individual is closer to the target axis and more likely to be at the boundaryjToo large, i.e. dominating the resistant solution, the selected priority of the individual will be given by introducing a penalty termDecrease, thereby eliminating to some extent the dominant resistant solutions in the population.
In addition, when solving the high-dimensional multi-target optimization problem, the angle is a more effective diversity measurement mode compared with the Euclidean distance, so that the invention takes the included angle between individuals as the density of the individuals, and x is the individual1And x2The calculation formula of the included angle is as follows:
Figure BDA0003356062860000091
calculating the unselected non-dominant individual x ∈ F1With the already reserved individual y ∈ Pt+1The minimum angle min (angle (x, y)) is taken as the density [ x ] of the individual x]And keeping the individuals with the maximum density to the next generation, and repeating the steps until the population size reaches n.
FIG. 3 illustrates a specific process of environment selection, SSCEM calculates a boundary point s in a population as shown in FIG. 3(a)1And s8And remaining to the next generation, calculating the remaining unselected individuals and s1And s8The smaller of the included angles is taken as the density of the individuals, as shown in FIG. 3(b), the densities of all the remaining individuals are calculated and compared
Figure BDA0003356062860000092
Discovery s4Is the highest, so that the retention s is selected4Once new individuals remain, the density of the remaining individuals is recalculated, as shown in FIG. 3(c), recalculating unselected individuals and s1,s4And s8The included angle therebetween, get s6Is the highest, so that the retention s is selected6。
SSCEM procedure:
the algorithm based on the Pareto domination can effectively avoid the phenomenon, but the method for evaluating the individuals is simple, so that the selected individuals have preference.
First, the population is initialized, decision variables are analyzed, and a decision space is divided into a convergence subspace and a diversity subspaceε+The method comprises the steps of obtaining elite particles, guiding and accelerating the evolution direction and speed of a population, mating the elite individuals in a filing set with the individuals in the population and searching in a specific subspace, wherein the population is subjected to a Pareto governing strategy, so that the convergence and the diversity of the population are both considered, on one hand, offspring can inherit the good convergence of the elite particles, on the other hand, the searching efficiency of the method is further improved by searching the subspace in a targeted manner, and when the evaluation times reach the maximum evaluation times, the population is used as the final solution set of output, and the method is terminated.
The above are preferred embodiments of the present invention, and all changes made according to the technical scheme of the present invention that produce functional effects do not exceed the scope of the technical scheme of the present invention belong to the protection scope of the present invention.

Claims (7)

1. A high-dimensional multi-target co-evolution method based on subspace search is characterized by comprising the following steps:
step S1, grouping the decision variables by using a decision variable grouping strategy, and dividing a search space into two subspaces; at different stages of the method, two subspaces are searched respectively to realize independent optimization of convergence and diversity;
step S2, providing an index-based archive set, using Iε+The method has the characteristic of good convergence, and the elite individuals with good convergence are reserved in the filing set; the population and the filing set co-evolve, and the population inherits the good convergence of elite individuals in the filing set; introducing a self-adaptive adjusting strategy of the archive collection capacity, wherein in the early stage of the method, the population realizes rapid convergence under the guidance of a few elite individuals; method of producing a composite materialIn the later period, the population is influenced by more elite individuals, so that the coverage of the population is ensured;
step S3, providing a boundary individual selection strategy, eliminating boundary individuals with poor convergence on the premise of ensuring the diversity of the boundary individuals, and further accelerating the convergence of the method; and a diversity maintenance strategy is provided, and the distribution uniformity and coverage of the population are ensured.
2. The subspace search-based high-dimensional multi-objective co-evolution method as claimed in claim 1, wherein the step S1 is implemented as follows:
analyzing a problem to be optimized, and dividing a decision space into a convergence subspace and a diversity subspace by using a decision variable grouping strategy; then, dividing the whole method into two stages, firstly searching in a convergence subspace to enable the population to quickly approach to the Pareto front edge; when the population is close enough to Pareto frontier, then search in diversity subspace, enable population to have good distribution.
3. The subspace search based high-dimensional multi-objective co-evolution method according to claim 1, wherein the archive set update mode in step S2 is: firstly, combining the offspring and the individual in the archive set, and calculating the capacity of the archive set according to a capacity self-adaptive adjustment strategy; then, calculating the fitness values of all individuals in the archive set, and removing the individual with the minimum fitness value; finally, updating the fitness values of the rest individuals; the removing of individuals in the archive set is repeated until the number of individuals in the archive set meets the current capacity.
4. The subspace search based high-dimensional multi-objective co-evolution method of claim 1, wherein in step S2, I is usedε+The specific implementation process of retaining the elite individual with better convergence to the archive set is as follows:
by the use of Iε+As an index for selecting individuals; i isε+And an individual x1Fitness value F (x)1) The calculation method of (c) is as follows:
Figure FDA0003356062850000011
Figure FDA0003356062850000012
wherein x1And x2Two individuals in the population P.
5. The subspace search based high-dimensional multi-objective co-evolution method according to claim 1 or 3, wherein the capacity formula for calculating the archive set by using the capacity adaptive adjustment strategy in step S2 is as follows:
Figure FDA0003356062850000021
where lb and ub represent the lower and upper bounds of the capacity, respectively, and FE and MaxFE represent the current number of evaluations and the maximum number of evaluations, respectively.
6. The subspace search based high-dimensional multi-objective co-evolution method of claim 1, wherein the boundary individual selection strategy in step S3 provides an index with penalty factor to select boundary individuals, defining the following formula Hj(x) The smallest individual is the boundary individual B on the jth target axisj：
Figure FDA0003356062850000022
Bj＝argminHj(x)
Wherein f isi(x) The function value of the individual x on the ith target function is taken, and alpha is a penalty factor; by using
Figure FDA0003356062850000023
Representing the closeness degree of the individual x and the jth target axis, wherein the smaller the value is, the closer the individual is to the target axis is, the higher the possibility of being at the boundary is; in addition, if a certain object has the objective function value fjToo large, i.e. dominating the resistant solution, the priority of the individual selected will be reduced by introducing a penalty term.
7. The subspace search based high-dimensional multi-objective co-evolution method of claim 1, wherein the diversity maintenance strategy in step S3 uses the included angle between individuals as the density of individuals, and the individual x1And x2The included angle between the two is calculated as follows
Figure FDA0003356062850000024
Calculating the unselected non-dominant individual x ∈ F1With the already reserved individual y ∈ Pt+1The minimum angle min (angle (x, y)) is taken as the density [ x ] of the individual x]And keeping the individuals with the maximum density to the next generation, and repeating the steps until the population size reaches n.
CN202111351876.7A 2021-11-16 2021-11-16 High-dimensional multi-target co-evolution method based on subspace search Pending CN114065625A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202111351876.7A CN114065625A (en) 2021-11-16 2021-11-16 High-dimensional multi-target co-evolution method based on subspace search

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202111351876.7A CN114065625A (en) 2021-11-16 2021-11-16 High-dimensional multi-target co-evolution method based on subspace search

Publications (1)

Publication Number Publication Date
CN114065625A true CN114065625A (en) 2022-02-18

Family

ID=80272486

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202111351876.7A Pending CN114065625A (en) 2021-11-16 2021-11-16 High-dimensional multi-target co-evolution method based on subspace search

Country Status (1)

Country Link
CN (1) CN114065625A (en)

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115062882A (en) * 2022-08-19 2022-09-16 湖南师范大学 Evolution method for solving optimal layout of flow sensor in large-scale industrial process
CN115619030A (en) * 2022-10-28 2023-01-17 清华大学 Factory network collaborative optimization method and device for urban sewage system and electronic equipment

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115062882A (en) * 2022-08-19 2022-09-16 湖南师范大学 Evolution method for solving optimal layout of flow sensor in large-scale industrial process
CN115619030A (en) * 2022-10-28 2023-01-17 清华大学 Factory network collaborative optimization method and device for urban sewage system and electronic equipment
CN115619030B (en) * 2022-10-28 2023-05-16 清华大学 Factory network collaborative optimization method and device for urban sewage system and electronic equipment

Similar Documents

Publication Publication Date Title
CN114065625A (en) High-dimensional multi-target co-evolution method based on subspace search
Liu et al. An improved NSGA-III algorithm using genetic K-means clustering algorithm
Wang et al. A hybrid multi-swarm particle swarm optimization to solve constrained optimization problems
CN111814251A (en) Multi-target multi-modal particle swarm optimization method based on Bayesian adaptive resonance
CN105930862A (en) Density peak clustering algorithm based on density adaptive distance
CN108573274A (en) A kind of selective clustering ensemble method based on data stability
CN111275132A (en) Target clustering method based on SA-PFCM + + algorithm
CN108280236A (en) A kind of random forest visualization data analysing method based on LargeVis
Wang et al. An improved k NN text classification method
Zhang et al. Radar signal recognition based on TPOT and LIME
Dey et al. A comparative study of SMOTE, borderline-SMOTE, and ADASYN oversampling techniques using different classifiers
Wang et al. A multi-constraint handling techniquebased niching evolutionary algorithm for constrained multi-objective optimization problems
Lozano et al. Modified fuzzy C-means algorithm for cellular manufacturing
CN114861760A (en) Improved research based on density peak value clustering algorithm
Li et al. A multi-objective particle swarm optimization algorithm based on enhanced selection
CN109934344B (en) Improved multi-target distribution estimation method based on rule model
Mir et al. Improving data clustering using fuzzy logic and PSO algorithm
Lin et al. A new density-based scheme for clustering based on genetic algorithm
Zhang et al. A modified random forest based on kappa measure and binary artificial bee colony algorithm
Luo et al. A reduced mixed representation based multi-objective evolutionary algorithm for large-scale overlapping community detection
Zhang et al. A K-harmonic means clustering algorithm based on enhanced differential evolution
CN113408602A (en) Tree process neural network initialization method
Davarynejad et al. Accelerating convergence towards the optimal pareto front
CN112308160A (en) K-means clustering artificial intelligence optimization algorithm
Luo et al. An entropy driven multiobjective particle swarm optimization algorithm for feature selection

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination