Fine-Grained Ensemble of Evolutionary Operators for Objective Space Partition Based Multi-Objective Optimization

Decomposition-based multi-objective optimization algorithms have been widely accepted as a competitive technique in solving complex multi-objective optimization problems (MOPs). Motivated by the facts that evolutionary operators are sensitive to the properties of problems, and even different search stages of an evolutionary operator often pose distinct properties when solving a problem. So far, numerous ensemble approaches have been designed to adaptively choose evolutionary operators for evolving population during different optimization stages. Then, during one stage, all the subproblems/subspaces in these existing ensemble approaches use the same evolutionary operator. But, for a complex MOP, the properties of its subproblems/subspaces are different. Based on the fact that existing ensemble approaches ignore this point, this article develops a fine-grained ensemble approach, namely FGEA, to choose suitable evolutionary operators for different subspaces during one generation. To be specific, the local and global contributions for each evolutionary operator in each subproblem/subspace are first defined. Then, an adaptive strategy is designed to encourage evolutionary operators making more contributions to obtain more opportunities to generate more offspring solutions. When choosing an evolutionary operator for a subspace, the proposed adaptive strategy considers both the local and global contributions of the evolutionary operators. Finally, based on 35 complex MOPs, we evaluate the effectiveness of the proposed FGEA by comparing it with five baseline algorithms. The experimental results reveal the competitive performance of the FGEA, which achieves the lowest inverted generational distance (IGD) values and the highest hypervolume values on 20 and 19 MOPs, respectively.


I. INTRODUCTION
Real-world problems in various fields, such as hybrid electric vehicle control problem [1], optimizing wireless networks [2], [3], feature selection for classification [4], service composition in clouds [5], resource allocation in radar networks [6], [7], intelligent traffic management [8], [9], and resource investment project scheduling [10], usually involve simultaneously optimizing at least two conflicting objectives. These problems are known as multi-objective optimization problems (MOPs) [11]. Their mathematical models can be The associate editor coordinating the review of this manuscript and approving it for publication was Guangcun Shan . summarized as: where x = (x 1 , x 2 , . . . , x n ) denotes a decision vector, is the decision space, n and m refer to the number of decision variables and optimization objectives. Besides, the f j (x), 1 ≤ j ≤ m represents the j-th optimization objective. For the m optimization objectives, there are at least two objectives that conflict with each other [12], [13]. Because of the conflicting nature among different optimization objectives, when minimizing one objective of a solution on the Pareto front, the values on other objectives tend to deteriorate [14]. Thus, there exists a set of trade-off solutions, rather than one single solution optimizing all the objectives at the same time. A solution x 1 is termed to dominate another one x 2 (denoted as x 1 ≺ x 2 ) if and only if all the objectives of solution x 1 are not worse than that of solution x 2 and solution x 1 is superior to solution x 2 in at least one objective. A solution is considered as Pareto-optimal if and only if no solution can dominate it. All the Pareto-optimal solutions are called Pareto set (PS) in decision space and Pareto front (PF) in objective space, respectively.
Population-based evolutionary algorithms are capable of searching multiple solutions concurrently during each run, and they are good at getting a set of compromise solutions for MOPs. Thus, multi-objective evolutionary algorithms (MOEAs) have been widely employed to approximate the PFs of MOPs. The popularity of evolutionary algorithms in solving MOPs results in a prolific research direction, particularly, a plethora of MOEAs have been developed until now [15]- [18].
Based on the environmental selection mechanisms, most MOEAs can be roughly divided into three categories, i.e., dominance-based, indicator-based, and decompositionbased MOEAs [15]. Compared with the previous two categories, the decomposition-based MOEAs have been well accepted as a competitive technique in solving multi-objective optimization problems with complex PSs [19]- [21]. For decomposition-based MOEAs, one branch is to employ a set of weight vectors to transform an MOP into a series of single-objective sub-problems, and then solve these sub-problems in a cooperative fashion [18], [22]. The other branch is the objective space partition-based MOEAs [20], [22], [23]. The algorithms in this branch, such as MOEA/D-M2M [20], OPE-MOEA [23], and RVEA [24], partition the objective space into a series of sub-spaces using a set of reference vectors, and then search solutions for each sub-spaces.
Different evolutionary operators have distinct capabilities of exploitation and exploration, which leads to different advantages in solving different MOPs [25], [26]. For instance, differential evolution [27], [28] and simulated binary crossover [29] exhibit qiute different search characteristics for exploration, while polynomial-based mutation [30] owns strong local search capacity (exploitation). An MOEA equipped with one single evolutionary operator often has good performance on some certain MOPs, but may performs poorly in other MOPs [25]. Even for the same MOP, an evolutionary operator performs quite differently during different optimization stages. Thus, it is difficult for one single operator to solve various types of MOPs. An intuitive idea is to integrate multiple evolutionary operators to play their respective advantages [31].
So far, there exist numerous ensemble approaches adaptively choosing evolutionary operators during different optimization stages, such improving the capability of decomposition-based MOEAs in coping with MOPs. For instance, Hitomi et al. recognized the difficulty in defining a suitable credit assignment for adaptive operator selection, and experimentally compared nine credit assignment mechanisms on benchmark functions [31]. Li et al. employed the sliding window method to store the fitness improvement rates of each evolutionary operators, and designed an adaptive operator selection mechanism to select one of four differential evolution variants for decomposition-based MOEA during each generation [32]. Wang et al. designed an ensemble framework to combine multiple evolutionary operators and selection criteria on the basis of multiple populations, also employed competition and cooperation strategies to respectively adjust evolutionary operators for different populations and select offspring solutions [25]. Zhao et al. employed a learning automaton technique to select evolutionary operators for decomposition-based MOEAs based on feedback from the optimization process, also developed an adaptive strategy to adjust the reference vectors using the obtained solutions in the external archive [33]. Santiago et al. suggested fuzzy logic to dynamically choose evolutionary operators during each generation, and proposed a new density estimator with polynomial complexity to decide which solutions should be retained [34]. To enhance the performance of decomposition-based MOEAs, Lin et al. designed an adaptive mechanism for dynamically choosing evolutionary operators during the optimization process [35]. Wu et al. reported a bicriteria-based adaptive operator selection approach to improve the performance of decomposition-based MOEAs [36]. However, most ensemble approaches are limited to selecting an evolutionary operator during one stage, that is, all the sub-problems or sub-spaces apply the same evolutionary operator.
The MOPs coming from various real-world applications [5], [37], [38] have complex relationships among decision variables, e.g., linear linkage, non-linear linkage, rotation, epistasis, and alike. Then, different sub-problems or sub-spaces of an MOP have distinct properties [31], and the requirements of evolutionary operators should vary from one sub-space to another. Motivated by this, this article proposes a fine-grained ensemble approach, namely FGEA, to choose suitable evolutionary operators for different sub-spaces during different optimization stages. In the proposed FGEA, even for the same generation, different sub-spaces may employ different evolutionary operators to generate new solutions.
The key contributions of this article can be summarized as follows.
(1) We define the local and global contributions of evolutionary operators to measure their fitness to subspaces.
(2) A novel adaptive strategy is designed to choose suitable evolutionary operators for each sub-space. When choosing an evolutionary operator for a sub-space, both local and global contributions of evolutionary operators are fully considered. This article is organized as follows. Section II describes the proposed FGEA, followed by extensive comparison experiments to assess the its performance in Section III. Finally, Section IV concludes this article with two future directions.

II. ALGORITHM DESCRIPTION
In this section, the main process of the proposed FGEA is first introduced. Then, the core idea of fine-grained ensemble approach and the adaptive strategy are detailed. Besides, the time complexity of the FGEA is given.

A. MAIN PROCESS
The objective space partition-based multi-objective evolutionary optimization [20], [23], [39], [40] is one competitive branch of decomposition-based approaches [41]. The algorithms in this branch employ a set of reference vectors to partition the objective space of an MOP into a series of connected and disjoint subspaces, and a reference vector corresponds to a subspace. During environmental selection process, each solution is associated to a reference vector with the minimum acute angle, and then a solution with the best fitness in each subspace is selected to survive to the next generation. To visually detail the concepts of objective space partition strategy and solution fitness, two intuitive diagrams are given in Fig. 1.
Suppose that the population size is N and the set of reference vectors is R = {r 1 , r 2 , · · · , r N }, these N reference vectors divide a two-dimensional objective space into N subspaces, as illustrated in Fig. 1(a). The boundaries between subspaces are represented by dashed orange lines. For a combined population in Fig. 1(a), when each subspace can preserve a solution, the selected population in Fig. 1(b) of course have good diversity. But, how to strengthen the population convergence for various MOPs is still a challenging task.
In this article, the framework of objective space partition-based multi-objective evolutionary optimization [20] is extended to support a fine-grained ensemble strategy to adaptively select efficient evolutionary operators for each subspace during each generation on the basis of evolutionary operators' local and global contributions. For the main process of the FGEA, its Pseudo-code is illustrated in Algorithm 1.
As shown in Algorithm 1, before running the proposed FGEA, the user needs to input the multi-objective optimization problem (MOP) to be solved, population size N and maximum function evaluations (MFE). Once the proposed FGEA completes the optimization search, it will output a population, denoted as P, with well convergence and diversity.
Update ideal and nadir points as Z min and Z max ; 10 Fit ← Calculate the fitness of each subspace with population P; 11 P ← EnvironmentalSelection(R, P Q); 12 NewFit ← Calculate the fitness of each subspace with new population P; Before entering the main optimization search, the FGEA performs the following five initialization operations. Similar to other decomposition-based algorithms [24], [39], [42], the method in work [42] is used to generate a set of uniformly distributed reference vectors (line 1). Also, a population with N solutions is initialized in a random way (line 2), and the used function evaluations (UFE) is initialized (line 3). Then, the FGEA initializes the number of available evolutionary operators K and the memory length L (line 4). After that, one K × L memory matrix M is initialized for a subspace, and each element in each matrix is initialized as zero (line 5). The matrix M i is created for the i-th subspace. Assume l denotes the index of generation, the element M i (k, l) stores the contribution of the k-th evolutionary operator in the i-th subspace to the population in the previous (L + 1 − l)-th generation.
After the above initialization, the FGEA continues to perform the following four main operations: 1) generate a new offspring population; 2) update ideal and nadir points; 3) update the population using environmental selection; 4) update the memory matrix for each subspace. Since how to integrate multiple evolutionary operators to improve the population convergence is our main focus, the first and fourth operations are detailed in Algorithm 2 and Algorithm 3, respectively.
In FGEA, all the non-dominated solutions in the combined population P ∪ Q are employed to update the ideal and nadir points (line 9), where P and Q are the parent and offspring population, respectively. Assuming that the subpopulation D ⊆ P ∪ Q contains all the non-dominated solutions in the combined population, then the ideal point Z min and nadir point Z max are updated as For a subspace, it may contain multiple associated solutions, then the penalty-based boundary intersection method [41] is employ to sort these solutions. Then, the fitness Fit(x j ) of a solution x j , which is associated to the i-th subspace, is defined as: ; the r i denotes the reference vecotors corresponding to the i-th subspace.
In order to visually illustrate how to calculate the fitness for a solution, Fig. 2(a) gives an example. Assuming that solution x 1 is associated to the second subspace, the normalized objective vector of solution x 1 is represented as a red dot, and its projection on the reference vector r 2 is shown as a blue dot, then the fitness value of the solution is Fit( For a subspace, its fitness value corresponds to the fitness value of its associated solution. The symbol Fit in line 10 is a 1×N array recording the fitness values of all the N subspaces before environmental selection, and the Fit(i) corresponds to fitness of the i-th subspace. Similarly, the array NewFit in line 12 represents the fitness for all the subspaces after environmental selection.
For the environmeantal selection approach (line 11), it is not the main contribution of this paper, and we employ the classical objective space partition-based environmeantal selection approach [20]. All the solutions in the combined population are first associated to different subspaces, and one solution with the minimal fitness is selected from each subspace.

B. ADAPTIVE STRATEGY
Assuming that the solution x is generated by the k-th evolutionary operator in the i-th subspace, the contribution C i,k of the k-th evolutionary operator in the i-th subspace is defined as the fitness improvement of the subspace associated with solution x. Fig. 2(b) gives an example to illustrate how to calculate the contribution. Assume that the solution x 1 is previously associated with the second subspace defined by reference vector r 2 . Since the solutions associated with a subspace are not necessarily generated in this subspace, we assume that the solution x 2 is generated by the first evolutionary operator in the sixth subspace and is also associated to the second subspace. Then, the contribution C(6, 1) of the first evolutionary operator in the sixth subspace can be calculated as When selecting an evolutionary operator for a subspace, both the local and global contributions of this evolutionary operator are considered, and the aggregation of local and global conributions is called overall conribution. The local contribution of an evolutionary operator refers to the sum of its contribution values in this space during the past L generations, while its global contribution is defined as its contributions in all the subspaces during this generation. Assume that k and i are respectively indexes of evolutionary operator and subspace, and then the overall conribution OC i,k of k-th evolutionary operator in i-th subspace is defined as follows.
where LC i,k and GC k denotes the local and global contribution of the k-th evolutionary operator, respectively. They can be calculated as: where M i represents the memory matrix for storing the contributions of different evolutionary operators in the i-th subspace.
With the overall contribution of each evolutionary operator in each subspace, the selection probability p i,k of the k-th evolutionary operator for the i-th subspace is defined as: where is a very small positive number, e.g., 1 × e −6 , to avoid the case that the denominator is 0. This definition can guarantee that the sum of selection probabilities of all the K evolutionary operators is 1 for a subspace. That is, On the basis of the selection probability of each evolutionary operator for each subspace, we design an algorithm VOLUME 9, 2021 to generate an offspring population, which is described in Algorithm 2.
As shown in Algorithm 2, the inputs of function Genera-teOffspring() are the current population and the N memory matrices. Since this function is used to generate an offspring population based on the contributions of different evolutionary operators, its output is naturally this offspring population, denoted as Q. First of all, the population Q is initialized to an empty set (line 1). Then, all the subspaces are checked to generate new solutions (lines 2-10). When checking a subspace, this function makes use of roulette-wheel approach [43] to select one evolutionary operator based on the selection probabilities (lines 3-8). The symbol r represents a random number, and t denotes the index of evolutionary operators. The process from line 3 to 8 seems to be complex, an example is given to detail it. Suppose there are three evolutionary operators, their selection probabilities are respectively p i,1 = 0.1, p i,2 = 0.6, and p i,3 = 0.3. When the random number r satisfying 0.1 < r ≤ 0.7, the second evolutionary operator will be selected since r > p i,1 and r ≤ p i,1 + p i,2 . Then, the selected evolutionary operator will be applied to the solutions coming from the subspace and its neighborhoods to generate a new solution (line 9).
In each generation, according to the fitness value of each subspace before and after environment selection, the proposed FGEA updates memory matrices storing contribution of each evolutionary operator in each subspace, which is shown in Algorithm 3.
As shown in Algorithm 3, the main inputs of Function UpdateContributionMatrix() are the fitness of each subspace before and after environmental selection, and memory matrix for each subspace.
The Function UpdateContributionMatrix() consists of two steps. The first step checks each subspace to retain the contributions of each evolutionary operator from the first to the (L − 1)-th generation (lines 2-4), and initialize the con-

Algorithm 3: UpdateContributionMatrix()
Input: Fit and NewFit; memory matrix for each subspace, i.e., M 1 , M 2 , · · · , M N ; Output: Updated memory matrix for each subspace, i.e., M 1 , M 2 , · · · , M N ; 8 if NewFit(i) > 0 then 9 if Fit(i) > 0 then 10 Con ← Fit(i) − NewFit(i); tribution of each evolutionary operator in the current generationto 0 (line 5). Then, on the basis of the fitness improvement of each subspace, the second step updates the contributions of corresponding evolutionary operators in corresponding subspaces (lines 7-15). When a subspace has an associated solution, its fitness value will be larger than zero (line 8).
In this case, the contribution generated by this new associated solution is calculated (lines 9-12). Then, the indexes of the subspace and evolutionary operator are found (lines [13][14]. After that, the contribution of the corresponding evolutionary operator in the corresponding subspace is updated (line 15).

C. TIME COMPLEXITY ANALYSIS
From Algorithm 1, we can observe that the time complexity of the proposed FGEA mainly comes from three parts: 1) generate offspring population (line 7, Algorithm 1); 2) environmental selection operator (line 11, Algorithm 1); 3) update contribution matrix (line 13, Algorithm 1). Next, we analyze these three parts respectively.
The main process of the first part is shown in Algorithm 2.  For the environmental selection operator [20], the time complexity of associating a solution to a reference vector is O (N · m)
Stop condition: As is frequently done, the stop condition in comparison experiments is set as maximal function evaluations (MFE). The MFE for MOPs from test suites MOP [20] and BT [21] are set as 4 × 10 5 , and that for MOPs from test suites IF [44] and LF [19] are set as 1 × 10 5 .
Population size: Referring to existing works [39], the settings of population size N only consider the number of optimization objectives. For the 2-and 3-objective MOP, we set the population size as 200 and 300, respectively.
Comparison indicator: The indicators inverted generational distance (IGD) [45] and hypervolume (HV) [46] can simultaneously measure both convergence and diversity of the output population. They have been frequently employed to examine the performance of MOEAs. Based on this, we also employ these two indicators to compare the performance of the proposed FGEA and the five peer MOEAs. 1) IGD: For an output population P, calculation formula of indicator IGD is as follows: where P * denotes a set of uniformly distributed solutions on the true PF, D(F(q), F(p)) represents the Euclidean distance between objective vectors of the two solutions q and p. From the definition of indicator IGD in (8), it can be derived that a smaller IGD value of an output population means the corresponding MOEAs having better performance in terms of both convergence and diversity. In the experiments, the number of solutions in the set P * is set to about 8000 for each MOP.
2) HV: Suppose r = {r 1 , r 2 , . . . , r m } is a reference point. For an output population P, the indicator HV corresponds to the volume of space consisting of the objective vectors of all the solutions in P and the reference point, which is defined as follows.
where L( ) denotes the Lebesgue measure. For each MOP, the reference point is set as 1.2 times of the nadir point of its PF. From the definition of indicator HV in (9), a larger HV value of an output population means better performance of the corresponding MOEA with respect to both the convergence and diversity. Evolutionary operator pool for FGEA: The simulated binary crossover (SBC) [29] and differential evolution (DE) [47] have distinct search patterns and have been widely employed in multi-objective optimization. In the proposed FGEA, the simulated binary crossover [29] and two classical variants of differential evolution (i.e., DE/rand/1 and DE/rand/2) are choosed to construct evolutionary operator pool.
The main parameters for the evolutionary operators are set as follows. The simulated binary crossover employs a distribution index as 20. For the DE/rand/1 and DE/rand/2, the crossover constant and weighting factor are set as CR = 1.0 and F = 0.5. Similar to the work [32], after applying these evolutionary operators, each new generated solution also performs the polynomial mutation operator [30]. For the polynomial mutation (PM) operator, we set η = 20 and p m = 1/n.
The main parameters of the five comparison MOEAs are summarized in Table 1. For the DE operator, T represents the   Tables 2 and 3, respectively. To ensure statistical significance, the two-sided Wilcoxon's rank sum test with significance degree as 0.05 is conducted to compare the results of the FGEA with each peer MOEA. The marks +, −, and ≈ in Tables 2 and 3 respectively represent that the peer MOEA performs better than, worse than, and similar to the FGEA. Regarding each MOP, the best average value among the six MOEAs is emphasized using the gray background.
From the results with gray backgrounds in Tables 2 and 3, we can notice that the proposed FGEA ranks first in more than half of the MOPs. In terms of indicator IGD, as shown in Table 2 Table 3, the proposed FGEA has better performance than all the five comparison algorithms in 19 out of the 35 MOPs with respect to the indicator HV. As summarized in the last row of Table 2 Table 3, compared with the five comparation algorithms, the algorithm FGEA as before has obvious advantages in obtaining output populations with higher HV values. To sum up, the proposed FGEA has competitive overall performance with respect to both IGD and HV indicators.
The excellent performance of the proposed FGEA is twofold. Firstly, the proposed FGEA employs the objective space partition strategy to maintain population diversity. Although the comparison algorithm FRRMAB also includes an ensemble strategy to integrate multiple evolutionary operators, its performance on the functions MOP1-MOP7 is far worse than the proposed FGEA. As the analysis in the work [23] that the populations of these functions are outwardly divergent, except for the objective space partition strategy, it is difficult for other strategies to maintain good diversity. Secondly, the FGEA considers both local and global contributions of evolutionary operators when selecting evolutionary operators for each subspace. The comparison algorithms MOEA/D-M2M and MOEA/D-AM2M also employes an objective space partition strategy, but their performance is far behind the algorithm proposed in this article. The main difference between the proposed FGEA and these two comparison algorithms is that the FGEA includes a fine-grained ensemble strategy. By comparing the proposed FGEA and these two comparison algorithms, we can contribute to the advantages of the FGEA to its fine-grained ensemble strategy.
Although both IGD and HV indicators can simultaneously measure the convergence and diversity of populations, the comparison results in Tabele 2 and Tabele 3 are not always consistent according to these two indicators. Taking MOP BT5 as an example, algorithm NSGA-III ranks first based on the indicator IGD, while the algorithm ranked first by HV is our proposed FGEA. The reason lies in the way these two indicators are calculated. The IGD is computed based on the distance between output population and true PF, while the HV is calculated using a predefined reference vector and the non-dominated solutions in output populations.
It is easy to notice that in some MOPs, the HV values of some algorithms are 0, for instance, the HV value of algorithm MOEA/D-M2M in MOP BT1. This is because the convergence of corresponding algorithm is not good enough, and there is no solution in its output population dominating the reference vector.  Fig. 3(c). But, many solutions distributed in the middle region are still far away from the Pareto-front of MOP1, and the convergence of IM-MOEA can be further improved. Among the five comparison algorithms, the MOEA/D-M2M shows the best convergence and diversity, as shown in Fig. 3(b). Compared the output populations in Fig. 3(b) and Fig. 3(f), we can observe that the proposed FGEA and MOEA/D-M2M have similar diversity, but the FGEA has better convergence.   is capable of acquiring a better approximation for the PF of MOP1.
To further compare the behaviors of the six algorithms, the downtrends of their IGD values in solving MOP1-MOP6 are provided in Fig. 5. The horizontal axis represents the number of iteration generations, and the vertical axis represents the IGD values of the output populations from the six algorithms. On each MOP, each algorithm run 31 times, and the change of its average IGD values with the advance of iterations is plotted.
As can be observed from Fig. 5, as the optimization progresses, the IGD values of the algorithms FRRMAB, MOEA/D-M2M, IM-MOEA, NSGA-III, and FGEA decrease gradually. This is easy to understand. With the progress of optimization search, the populations of these algorithms keep approaching the Pareto-fronts, resulting in lower IGD values. For the comparison algorithm MOEA/D-AM2M, it has an abnormal situation, first falling and then rising. This is because the algorithm MOEA/D-AM2M adjusts the reference vector according to the obtained population. When the obtained population can not well cover the Pareto-fronts, the adjusted reference vector can not cover the Pareto-fronts, resulting in poor diversity.
Comparing with the five comparison algorithms, the proposed FGEA appears to contribute significantly to the outstanding convergence speed. Especially before 1000 generations, the convergence speed of the FGEA has an overwhelming advantage. These comparison results visually demonstrate that the fine-grained ensemble mechanism in FGEA is capable of effectively improving the convergence speed.

IV. CONCLUSION AND FUTURE WORK
This article focuses on the properties of complex multi-objective problems that vary throughout both the decision and objective spaces, and develops a fine-grained ensemble approach to choose a suitable evolutionary operator for a subspace during each generation. When choosing an evolutionary operator for a subspace, we design an adaptive strategy to consider both the local and global contributions of the evolutionary operators. To assess the effectiveness of the proposed ensemble approach, extensive experiments on 35 complex MOPs are carried out to compare the FGEA with five baseline algorithms. The numeral experiments demonstrate that the proposed FGEA performs the best overall performance in terms of both convergence and diversity.
Applying the proposed fine-grained ensemble approach to solving real-world MOPs coming from various fields, such as internet of things [48]- [50] and collaborative robots [51], worths future direction. Also, the MOPs from real-world applications often have a large number of decision variables, terms as large-scale MOPs [52]- [56]. It is interesting and challenging to research new techniques for large-scale MOPs.
XUEFENG HONG graduated in software engineering from Hunan University. He is currently a Lecturer with the School of Internet Finance and Information Engineering, Guangdong University of Finance. He has presided over or participated in five national, provincial, and ministerial projects. He has published more than ten papers in top conferences and journals. His research interests include multi-objective optimization, data mining, education, and teaching management.
MINGFANG JIANG graduated in computer technology from the School of Information Science and Engineering, Hunan University. She is currently an Associate Research Librarian with Hunan First Normal University. She has presided over one national project and five provincial and ministerial projects. She has also participated in many projects of national and provincial projects as the main researcher. She has published more than 20 academic articles. Her research interests include digital resource management, information security, multimedia intelligence, and evolutionary optimization.
JINGLIN YU graduated in software engineering from East China Normal University. She is currently a Teacher with the Internet Finance and Information Engineering College, Guangdong University of Finance. She has presided over or participated in two provincial projects. She has published several academic articles. Her research interests include computer application and multimedia technology. VOLUME 9, 2021