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CAAI Transactions on Intelligence Technology xx (2016) 1e21 http://www.journals.elsevier.com/caai-transactions-on-intelligence-technology/ Review Article Evolutionary computation in China: A literature survey

Maoguo Gong*, Shanfeng Wang, Wenfeng Liu, Jianan Yan, Licheng Jiao

Key Lab of Intelligent Perception and Image Understanding of Ministry of Education of China, Institute of Intelligent Information Processing, Xidian University, P.O. Box 224, Xi'an 710071, China

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Abstract

Evolutionary computation (EC) has received significant attention in China during the last two decades. In this paper, we present an overview of the current state of this rapidly growing field in China. Chinese research in theoretical foundations of EC, EC-based optimization, EC-based data mining, and EC-based real-world applications are summarized. Copyright © 2016, Chongqing University of Technology. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords: Evolutionary computation; Evolutionary algorithms; Optimization; Data mining

1. Introduction Chinese are difficult to be recognized by non-Chinese speakers. According to our statistic, a large number of books Evolutionary computation (EC) uses computational models on EC have been published in Chinese. For example, Guoliang of evolutionary processes as key elements in the design and Chen and his collaborator published a book focused on genetic implementation of computer-based problem solving systems algorithm in 1996 [2]; Haibin Duan published a book focused [1]. It has become an important part of computational intel- on ant colony Algorithms [3]; Licheng Jiao et al. published a ligence. EC has received significant attention in China during book focus on immunological computation [4]; Jinhua Zheng the last two decades. Professor Guoliang Chen of the Uni- published a book focus on evolutionary multi-objective opti- versity of Science and Technology of China published the first mization [5]; Yuping Wang published a book focus on Chinese book on EC in 1996 [2]. This book played an evolutionary algorithm [6]; Yaonan Wang et al. published a important role in introducing EC to Chinese researchers. book focus on dynamical dynamic differential evolution al- Professor Lishan Kang, Zongben Xu, Xin Yao, Licheng Jiao, gorithm [7]; Ying Tan published a book on the fireworks al- Zixing Cai, Jun Zhang, Zhi-Hua Zhou, Ling Wang, Jinhua gorithm [8]. The EC papers published in Chinese Journals and Zheng, Dunwei Gong, Yongsheng Ding, Yuhui Shi, Ying Tan, conferences are also massive. Most of them focus on modi- Yuping Wang, Haibin Duan and their collaborators and suc- fying existing EC algorithms or combining different algo- cessors paid attention to EC field one after the other. They rithms to solve specifically problems. In recent years, more have published a lot of papers and books related to EC. and more Chinese researchers prefer to publish their approving Among them, the papers published in international journals works in international Journals, such as IEEE Transactions on and conferences can be obtained all over the world. Chinese Evolutionary Computation, Evolutionary Computation Jour- can read papers in English easily for English is the most nal, IEEE Transaction on System, Man and Cybernetics series, popular language in the world, but the papers written in and some main-stream international journals on various application fields. In the last two decades, more and more papers written by Chinese researchers have been published in * Corresponding author. these journals, which will be summarized in detail in the E-mail address: [email protected] (M. Gong). following sections. Furthermore, some international events URL: http://web.xidian.edu.cn/mggong/ Peer review under responsibility of Chongqing University of Technology. related to EC, such as the International Workshop series on http://dx.doi.org/10.1016/j.trit.2016.11.002 2468-2322/Copyright © 2016, Chongqing University of Technology. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC- ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: M. Gong, et al., Evolutionary computation in China: A literature survey, CAAI Transactions on Intelligence Technology (2016), http://dx.doi.org/10.1016/j.trit.2016.11.002 + MODEL 2 M. Gong et al. / CAAI Transactions on Intelligence Technology xx (2016) 1e21

Nature Inspired Computation and Applications since 2004, the original Markov chain to analyze the one dimension random annual International Conference on Natural Computation since walk. However, this approach requires a distance function 2005, the annual International Conference on Computational which does not naturally exist in EAs. Intelligence and Security since 2005, the 2008 and 2014 IEEE He and Yao described a general analytic framework for world congress on computational intelligence (WCCI), and the analyzing first hitting times (FHTs) of EAs [10]. The FHT of Annual Workshop on Evolutionary Computation and Learning EAs is the time that EAs find the optimal solution for the first (ECOLE) since 2014, to list only a few, were held in China. time, while the expected first hitting time (expected FHT) is All of these show that Chinese researchers are more and more the average time that EAs require to find the optimal solution, active in EC field. which implies the average computational time complexity of In this paper, we will summarize the main contributions of EAs. The general framework they gave was based on a linear Chinese researchers in EC field. From 1995, lots of Chinese equation and its bounds of the FHT of an EA's Markov chain researchers have focused on evolutionary algorithms and have model. Under this framework, conditions under which an EA published a great number of papers about evolutionary algo- will need polynomial (or exponential) mean computational rithms. In this paper, we select classic works that are well time to solve a problem were studied. A number of case known or published in top journals or conferences, such as studies were given to illustrate how different results can be IEEE Transactions on Evolutionary Computation, Evolu- established by verifying these conditions. They proved that tionary Computation, IEEE Computational Intelligence hard problems to a simple (1 þ 1) EA can be classified into Magazine and IEEE Congress on Evolutionary Computation two classes: “wide gap” problems and “long path” problems. and so on. All selected papers are written in English. In addition to (1 þ 1) EAs, EAs with population size greater The remainder of this paper is organized as follows: Sec- than 2 and EAs with and without crossover were also studied tion 2 summarizes the theoretical foundation research, in their paper. However, since the analytical form was derived including time complexity analysis, convergence and diversity from homogeneous Markov chain models, only EAs with analysis. Section 3 summarizes the research results in evolu- stationary reproduction operators could be analyzed, although tionary optimization, including global optimization, multi- EAs with time-variant operators or adaptive operators are very objective optimization, many-objective optimization, con- popular and powerful. strained optimization and dynamic optimization. Section 4 He and Yao also compared (1 þ 1) EAs and (N þ N) EAs describes the EC-based real-world applications. Finally, theoretically by deriving their FHT on some problems [11].In concluding remarks are presented. their paper, by rigorous theoretical analysis, they concluded that a population may bring benefits to an EA in terms of 2. Theoretical foundation research lower time complexity, higher first hitting probabilities, and shorter FHT. It was also shown that a population-based EA 2.1. Time complexity analysis may take only average polynomial time to solve a problem that would take a (1 þ 1)EA average exponential time to In EC, time complexity analysis and convergence analysis solve, given the same mutation operator in both algorithms. are considered to be two important issues in the basic theo- He and Yao [12] analyzed the time complexity of EAs retical analysis. However, convergence describes the behaviors based on the maximum cardinality matching in a graph, which at limit points of evolutionary algorithms (EAs). If an EA with is a famous combinatorial optimization problem. They proved convergence property has tremendous time complexity, it is that the EA can find a matching with the early maximum useless for application. Therefore, it is important to develop a cardinality in polynomial time. This was noteworthy as it was systematic theoretical tool investigating into the computational the first time complexity results on classical combinational time or time complexity of EAs. optimization problems. He and Yao introduced drift analysis in estimating average Zhou and He presented a time complexity analysis of EAs computational time of EAs [9]. In their paper, one-step mean for solving constrained optimization [13]. The mean runtimes drift at the t-th generation was defined and it could be clas- of the penalty function (1 þ 1)EAs with local mutation and sified into positive and negative drift, where the positive drift global mutation for two simple knapsack problems were is the rate of the gain of a population towards the optimum and analyzed respectively. In their paper, they concluded that EAs the negative drift is that away from the optimum. The authors have benefited greatly from higher penalty coefficients in analyzed a (1 þ 1)EA on a linear function and a (N þ N)EA some examples, while in other examples, EAs benefit from on One-Max function. The upper bound of the mean first lower penalty coefficients. The systematical analysis of the hitting times of EAs were presented. Besides, by drift analysis, role of penalty coefficients in constrained optimization is they divided optimization problems into two classes (easy and original and beneficial for designing constraint optimization hard) based on the mean number of generations needed to algorithms. However, we still can not predict how to choose solve the problems. By their analysis, we could obtain that penalty coefficients for various problems. drift analysis is a useful tool in estimating the computational Yu and Zhou also established a bridge between the time of EAs. Drift analysis reduces the behavior of EAs in a convergence rate and the expected FHT of EAs [14]. In their higher-dimensional population space into one-dimensional paper, non-homogeneous Markov chain model was employed space. Therefore, it is much easier than analysis of the and the expected FHT was derived from the convergence rate

Please cite this article in press as: M. Gong, et al., Evolutionary computation in China: A literature survey, CAAI Transactions on Intelligence Technology (2016), http://dx.doi.org/10.1016/j.trit.2016.11.002 + MODEL M. Gong et al. / CAAI Transactions on Intelligence Technology xx (2016) 1e21 3 of EAs. A pair of general upper and lower bounds of the ex- to measure the time complexity of EDAs. Based on the FHT pected FHT were deduced. measure, they proved a theorem related to problem hardness For constrained optimization, Yu and Zhou [15] analyzed and the probability conditions of EDAs. After that, they pro- whether infeasible solutions are helpful or not in the evolu- posed a novel approach to analyzing the FHT of UMDA using tionary search and theoretically deduced that under what discrete dynamic systems and Chernoff bounds. In their paper, conditions infeasible solutions were beneficial. More impor- UMDAs were analyzed in depth on two problems: LEA- tantly, a sufficient condition and a necessary condition of an DINGONES and BVLEADINGONES. The experiment anal- EA will reach the optimal solution faster and infeasible in- ysis showed that LEADINGONES is easy for the UMDA, and dividuals being included were derived and discussed. Finally, they proved theoretically that the UMDA with margins can two problems were employed to judge whether exploiting solve the BVLEADINGONES efficiently. infeasible solutions is helpful or not. The up and low bound- The publications above represented a systematic compara- aries of expected FHT of the two problems were deduced. By tive study of time complexity analysis among different EAs on this paper, we can find that infeasible solutions play an different problems by their FHTs model. These contributions important role for some problem in constrained optimization, were significant to advancement of basic theory of EC. and by exploiting infeasible solutions in the search process, an EA-Hard problem can be transformed to be EA-Easy and the 2.2. Convergence and diversity analysis reverse. Yu et al. [16] developed a switch analysis approach for In the EC community, premature convergence is an running time analysis of evolutionary algorithms. The pro- important issue and open problem. Roughly speaking, pre- posed switch analysis made use of another well analyzed al- mature convergence occurs when the population in an EA gorithm and can lead to better results by contrasting them. In reaches such a suboptimal state that most of the evolutionary their paper, they defined the reducibility relationship to operators can no longer produce offspring that outperform investigate the relationship between general analysis ap- their parents. Several methods have been proposed to prevent proaches for EAs. The results showed the superior of switch premature convergence. Leung et al. [21] proposed a concept analysis for running time analysis of EAs. of a degree of population diversity and quantitatively charac- Yuet al. [17] further proved that another running time analysis terize and theoretically analyze the problem of premature approach, convergence-based analysis, is reducible to switch convergence in GA using the theory of Markov chains. In their analysis. They also showed in a case study that switch analysis paper, the degree of population diversity converged to zero leads to a tighter result than convergence-based analysis. with probability one with zero mutation probability. The re- Qian et al. [18] presented a running time analysis on ge- lationships between premature convergence and the GA pa- netic programming (GPs). The theoretical results on two rameters such as population size, mutation probability, and classical combinatorial problems theoretically supported the relevant population statistics were also studied. usefulness of rich representations in evolutionary optimiza- Leung et al. proposed a new simulated evolutionary compu- tion. From the analysis, the authors also found the variable tation model called the abstract evolutionary algorithm (AEA) solution structure might be helpful for evolutionary optimi- [22]. In their minds, the simulated evolutionary algorithms zation when the solution complexity can be well controlled. include genetic algorithms (GAs), evolutionary programming Chen et al. [19] analyzed the mean FHTs of two early (EP), and evolution strategies (ESs). These algorithms simulate versions of Estimation of distribution algorithm (EDA), Uni- the principle of evolution, and maintain a population of potential variate Marginal Distribution Algorithm (UMDA) and the solutions through repeated application of some evolutionary Incremental UMDA (IUMDA). They generalized the concept operators. The proposed AEA unified most of the currently of convergence to convergence time, and managed to estimate known EAs and described the evolution as an abstract stochastic the upper bound of the mean FHTs of UMDA and IUMDA on process composed of two fundamental operators: selection and LEADINGONES function. An EA on a problem converging to evolutionary operators. Besides, the selection pressure, selection the global optimum only implies that the EA can find the intensity, evolution aggregating rate, evolution scattering rate, global optimum. It does not mean that the EA always con- and evolution stability rate were defined, which were used to verges to the global optimum. Convergence could not measure quantitatively measure their functions and properties. By the the time complexity of almost all the EAs, while FHT could model, we can get a novel convergence analysis and convergence denote the time complexity of EAs. In principle, the conver- rate estimation method, which is not based on the usual ergodicity gence time is almost larger than FHT (for (1 þ 1) EAs, they analysis, and could be regarded as a nonergodicity approach, are equivalent). In their paper, they have obtained the upper which is important both from the viewpoint of theoretical sig- bounds of the mean convergence times of UMDA and IUMDA nificance and from the perspective of parallel computation. on LEADINGONES function. The upper bounds are all linear However, the AEA model requires essentially a certain kind of functions of the problem size if the relation between popula- full connectivity, which is an implicit limitation of their model. tion sizes and problem size is omitted. Duan and Shi et al. developed a theoretical framework Chen et al. [20] studied the FHT of a simple Estimation of based on Markov chains to model the brain storm optimiza- distribution algorithm (EDA), called the univariate marginal tion algorithm [23]. The creation of discrete Markov chain distribution algorithm (UMDA). The authors utilized the FHT models approximated the behavior of a BSO. The theoretical

Please cite this article in press as: M. Gong, et al., Evolutionary computation in China: A literature survey, CAAI Transactions on Intelligence Technology (2016), http://dx.doi.org/10.1016/j.trit.2016.11.002 + MODEL 4 M. Gong et al. / CAAI Transactions on Intelligence Technology xx (2016) 1e21 probability of the occurrence of each possible population was MAGA, an agent, a, represents a candidate solution to the opti- given as the number of generation count goes to infinity. The mization problem in hand, and the value of its energy is equal to convergence of the BSO was proved by Markov models. the negative value of the objective function, i.e., a2S, Zheng et al. presented a theory analysis for fireworks al- Energy(a) ¼f ðaÞ. The purpose is to increase its energy as much gorithm [24]. Fireworks algorithm was proved as an absorbing as possible. Each agent carries all variables of the objective Markov stochastic process. The defined Markov stochastic function to be optimized. In order to realize the local perceptivity process was used to discuss the global convergence and time of agents, the environment is organized as a lattice like structure. complexity of fireworks algorithm. The authors thought that the real natural selection only occurs in a local environment, and each individual can only interact with 3. Evolutionary optimization research those around it. That is, in some phase, the natural evolution is just a kind of local phenomenon. Therefore, each agent devised by In this section, we summarize the main contributions of them can only sense its local environment, its behaviors of Chinese researchers in evolutionary optimization, including competition and cooperation can only take place between the global optimization, multi-objective optimization, many- agent and its neighbors. There is no global selection at all, so the objective optimization, constrained optimization, and dy- global fitness distribution is not required. An agent interacts with namic optimization. its neighbors so that information is transferred to them. In addition to the aforementioned behaviors of competition and cooperation, 3.1. Global optimization each agent can also increase its energy by using its knowledge. On the basis of such behaviors, four evolutionary operators are Global optimization, arising in many fields of science, en- designed for the agents. The neighborhood competition operator gineering, and business, is widely used in EC field for testing and the neighborhood orthogonal crossover operator realize the the performance of EAs. In China, several EC researchers behaviors of competition and cooperation, respectively. The proposed their EC-based global optimization methods mutation operator and the self-learning operator realize the be- [25e44]. haviors of making use of knowledge. In [18], MAGAwas applied Jiao and Wang proposed an improved genetic algorithm to solve ten benchmark functions and the scalability with respect based on immunity (IGA) [25]. In their paper, the idea of to dimension was also investigated. It is noteworthy that, when the immunity was mainly realized through two steps based on dimensions are increased to as high as 10,000, MAGA still can reasonably selecting vaccines (i.e., a vaccination and an im- find high quality solutions at a low computational cost. mune selection), of which the former was used for raising Liu et al. proposed a novel organizational evolutionary al- fitness and the latter was for preventing the deterioration. For gorithm (OEA) and applied it into global numerical optimization vaccination, it meant modifying the genes on some bits in [28]. In the real-world situation, to achieve their purposes, or- accordance with priori knowledge so as to gain higher fitness ganizations will compete or cooperate with others so that they with greater probability. For immune selection, it was based on can gain more resources. As a result, the resources will be an immune test and annealing selection. IGA was validated by reasonably distributed among all organizations little by little. Traveling Salesman Problem (TSP) and function optimization. This process plays an important role in human societies, and can The results showed that IGA was not only feasible but also be viewed as a kind of optimization. In OEA, organizations are effective and was conducive to alleviating the premature composed of members, and a population is composed of orga- convergence in the original GA. nizations, so that a structured population results. On the basis of Leung and Wang proposed an orthogonal genetic algorithm such a structured population, all evolutionary operations are with quantization for global numerical optimization with performed on organizations, and three evolutionary operators are continuous variables [26]. In this paper, the orthogonal array developed for organizations, which are Splitting operator, specified a number of a small number of combinations that were Annexing operator, and Cooperating operator. An organization scattered uniformly over the space of all possible combinations, interacts with others so that the information can be diffused. and then, the orthogonal array was sampled evenly to generate an Obviously, such a kind of population is more similar to the real evenly distributed population. The former orthogonal design was evolutionary mechanism in nature than the traditional popula- applicable to discrete factors only. To overcome this issue, each tion. Experimental results illustrate that the OEA has an effective variable of solutions were quantized into a finite number of searching mechanism for global numerical optimization. values. With respect to orthogonal crossover, it acted on two Wang and Dang proposed level-set evolution (LEA) and parents. It quantized the solutions space defined these parents Latin square design for global optimization [29]. LEA was into a finite number of points, and applied orthogonal design to based on the mean-value-level-set method (M-L method). select a small and representative sample of solutions as the po- Besides, since Latin-square design is one of the uniform tential offspring. Finally, the proposed algorithm was validated design methods, which can generate points uniformly scat- based on 15 benchmark problems with 30 or 100 dimensions. tered in a domain, Latin-square was introduced to generate the The results showed that the proposed algorithm could find initial population. Numerical experiments were performed for optimal or close-to-optimal solutions on all the test problems. 20 standard test functions. The highest dimension of these test Zhong et al. [27] proposed a novel multiagent genetic algo- problems is 100 and some of them have many local minima. rithm (MAGA) to solve global numerical optimization. In The performance of the proposed algorithm was compared

Please cite this article in press as: M. Gong, et al., Evolutionary computation in China: A literature survey, CAAI Transactions on Intelligence Technology (2016), http://dx.doi.org/10.1016/j.trit.2016.11.002 + MODEL M. Gong et al. / CAAI Transactions on Intelligence Technology xx (2016) 1e21 5 with that of eight EAs and the Monte Carlo implementation of Zhang et al. proposed a cloud model based evolutionary al- M-L methods. The results indicate that LEA could find gorithm [34]. The excellent traits of the cloud model in expressing optimal or close-to-optimal solutions, and it was more and transforming noncanonical knowledge were integrated into competitive than almost all of the compared algorithms for genetic algorithm. The inheritance and mutation of the population these test problems. were modeled naturally and uniformly by the cloud model. The Yang et al. proposed a cooperative coevolution framework scale of them and the scope of search space were easily controlled [30] for large scale optimization problems. A random by the algorithm. Eight global classical functions were used to grouping scheme and adaptive weighting were introduced in validate its performance in the experiment. problem decomposition and coevolution. The authors adopted An intelligent evolutionary algorithm IEA was proposed by a variant of DE, SaNSDE, which combine a neighbor search using a novel intelligent gene collector (IGC) [35]. IGC was mechanism and self-adaptability of crossover rate and scaling the main phase in an intelligent recombination operator of factor. Combined with SaNSDE, they presented a novel IEA. Based on orthogonal experimental design, IGC used a cooperative coevolution optimization algorithm, called divide-and-conquer approach, which consists of adaptively DECC-G. Theoretical analysis showed that the new frame- dividing two individuals of parents into pairs of gene seg- work can be effective for optimizing large nonseparable ments, economically identifying the potentially better one of problems. Extensive computational studies were carried out to two gene segments of each pair, and systematically obtaining a evaluate the performance of DECC-G on a large number of potentially good approximation to the best one of all combi- benchmark functions with up to 1000 dimensions. The results nations using at most 2 fitness evaluations. Empirical studies showed that the new framework and algorithm were effective showed that IEA had high performance in solving benchmark and efficient for large scale optimization problems. functions comprising many parameters, as compared with Jiao et al. proposed a novel immune clonal algorithm, some existing EAs. The authors also proposed the multi- called a quantum-inspired immune clonal algorithm (QICA) objective optimization version in the same paper. [31], which was based on merging quantum computing and Ding et al. introduced a histogram-based estimation of clonal selection theory. There were three innovation points distribution algorithm for continuous optimization [36].His- listed as follows. Firstly, antibody was proliferated and divided togram probabilistic model was employed to represent multi- into a set of subpopulation groups. Antibodies in a subpopu- ple local optima by different bins with different heights. lation group were represented by multi-state gene quantum Besides, a surrounding effect and shrinking strategy were bits. The quantum bit representation had the advantage that it proposed and incorporated with histogram probabilistic can represent a linear superposition of states (classical solu- model. The hybrid estimation of distribution algorithm was tions) in search space probabilistically. Thus, the quantum bit validated by Schwefel, Griewank and two-peak functions. representation had a better characteristic of population di- Gong et al. proposed the ranking-based mutation operators versity than other representations. Secondly, in the antibody's for the differential evolution algorithm [37]. Individuals were updating, the general quantum rotation gate strategy and dy- assigned the probabilities according to their rankings, which namic adjusting angle mechanism were applied to accelerate are measured by the fitness of the individual. Some of the convergence. Quantum NOT gate was used to realize quantum parents in the mutation operators were proportionally selected mutation to avoid premature convergence. Each subpopulation according to their rankings. Experiments on the benchmark group evolved independently and enlarged the search space. functions and five real-world problems demonstrated the per- Thirdly, the proposed quantum recombination operator real- formance of the proposed algorithm. ized the information communication between the subpopula- Gong et al. introduced a multioperator search strategy for tion groups so as to improve the search efficiency. The evolutionary optimization [38]. A cheap surrogate model- algorithm was validated by ten unconstrained optimization based multioperator search strategy was proposed. In this al- problems with the dimension of 100, 200, and 1000. gorithm, multiple offspring reproduction operators are used to Tsai et al. proposed a hybrid Taguchi-genetic algorithm to generate a set of candidate offspring solutions, and the best solve global numerical optimization with continuous variables one is chosen according to the surrogate model. 30 benchmark [32]. Taguchi method is an important tool for robust design. The functions and 28 functions presented in the CEC 2013 were fundamental principal of it is to improve the quality of a product used to test the performance of the proposed algorithm. by minimizing the effect the causes of variation without elim- Hu et al. first presented a new way of extending ant colony inating them. The Taguchi method was inserted between optimization (ACO) to solving continuous optimization crossover and mutation operations of traditional GA. The pro- problems [39]. An effective sampling method was used to posed algorithm was effectively applied to solve 15 benchmark discretize the continuous space and then ACO could be used problems of global optimization with 30 or 100 dimensions. for continuous optimization. The proposed algorithm con- Zhang et al. proposed a fuzzy logic controlled scheme to sisted of three major steps, i.e., the generation of candidate adaptively adjust the probabilities of crossover and mutation variable values for selection, the ants' solution construction, [33]. K-means algorithm was employ at each iteration to and the pheromone update process. Experiments demonstrated cluster the distribution of the population in the search space. that the proposed algorithm performed better than some state- The method was tested on eight global mathematical functions of-the-art algorithms, including traditional ant-based and a buck regular design.

Please cite this article in press as: M. Gong, et al., Evolutionary computation in China: A literature survey, CAAI Transactions on Intelligence Technology (2016), http://dx.doi.org/10.1016/j.trit.2016.11.002 + MODEL 6 M. Gong et al. / CAAI Transactions on Intelligence Technology xx (2016) 1e21 algorithms and representative computational intelligence al- Yang et al. [46] proposed a novel multiple sub-models gorithms for continuous optimization. maintenance technique (MAPS) to improve the performance Chen et al. presented a novel set-based PSO (S-PSO) on multimodal problems. The proposed MAPS can explicitly method for discrete optimization problems [40]. The proposed detect the promising areas, which can accelerate the optimi- S-PSO is based on a set-based representation scheme and the zation speed. Besides that, MAPS can be combined with any scheme enabled S-PSO to characterize the discrete search EDA that adopts a single Gaussian model. The experiments space of combinatorial optimization problems. The candidate results showed that MAPS based EADs outperformed the solution and velocity were defined as a crisp set, and a set with compared algorithms with a faster optimization speed and possibilities, respectively. All related arithmetic operators in more stable solutions on most tested problems. the velocity and position updating rules were replaced by the Tang et al. [47] proposed a new EA, namely negatively operators and procedures defined on crisp sets and sets with correlated search (NCS), to solve multimodal optimization possibilities. Experiments showed that the discrete version of problems. The proposed NCS is featured by its information the PSO variants algorithm based on S-PSO was promising. sharing and cooperation schemes to explore more effectively Zhan et al. proposed an orthogonal learning (OL) strategy in the search space. The experiment results indicated the ad- for particle swarm optimization [41]. The OL strategy con- vantages of NCS in comparison to other existing EAs on structed a much promising and efficient exemplar, and different problems. discovered useful information from a particle's personal best position and its neighborhood's best position. OL could guide 3.2. Multi-objective optimization particles fly in better directions. Moreover, the OL strategy can be applied to the global and local versions of PSO, respec- In real-world optimization applications, it is often neces- tively. 16 benchmarks including unimodal, multimodal, coor- sary to optimize multiple objectives in a problem at the same dinaterotated, and shifted functions were used to test the time. The simultaneous optimization of multiple objectives is performance of the proposed algorithm. different from single-objective optimization in that there is no Chen et al. proposed a novel particle swarm optimization unique solution to multi-objective optimization problems [42]. A growing age and a lifespan are assigned to the leader of (MOPs). Multi-objective optimization involves many con- the swarm. In this way, the leader had a long lifespan to lead flicting, incomparable and non-commensurable objectives. the swarm. The lifespan of the leader was adaptively tuned Therefore, a set of optimal tradeoff solutions known as the based on the leader's leading power. Once the leader obtained a Pareto-optimal solutions should be obtained. During the past local optimum, the other individuals will challenge the lead- two decades, EAs have been obtaining an increasing attention ership which can bring in diversity. 17 benchmark functions among the multi-objective optimization community mainly were used to test the performance of the proposed algorithm. because of the fact that they can be suitably applied to deal Li et al. proposed an information sharing mechanism (ISM) simultaneously with a set of possible solutions. Chinese re- for particle swarm optimization [43]. In the proposed ISM, each searchers have made a very positive contribution to the particle could share its best search information, so that all the development of the domain. A number of evolutionary algo- other particles could use the shared information by communi- rithms have been developed by them for multi-objective cating with each other. A competitive and cooperative (CC) problems [38,48e59]. operator was designed in the proposed algorithm for a particle to Zeng et al. proposed an orthogonal multi-objective evolu- utilize the shared information properly and efficiently. The pro- tionary algorithm (OMOEA) for MOPs with constraints [48]. posed algorithm could prevent the premature convergence when Firstly, with respect to constraints in MOPs, a strict partial- solving global optimization problems. 16 benchmark functions ordered relation was defined to simplify the Pareto domi- were chosen to test the performance of the proposed algorithm. nance. Then, the orthogonal design and the statistical optimal Peng et al. [44] presented a population-based algorithm port- method were generalized to MOPs. In OMOEA, an original folio (PAP) for solving numerical optimization problems. PAP is niche evolves first, and splits into a group of sub-niches ac- easy to implement and can accommodate any existing population- cording to the output niche-population of the evolution. Then based search algorithms. After that, they proposed a pairwise every sub-niche iterates the above operations so as to enhance metric to compare the risks associated with two algorithms. The the precision of the solutions. It is noteworthy that, a niche is a experiment results showed that PAP outperformed its constituent hyper-rectangle in the decision space. The main component of algorithms. Further analysis indicated that PAP was capable of the new technique is the niche evolution procedure which increasing the probability of finding the global optimum and was consists of quantizing niches into discrete niches and pro- insensitive to control parameters of the migration scheme. ducing an initial niche-population. OMOEA was validated on Li and Tang [45] proposed a history-based topological ZDT1, ZDT2, ZDT3, ZDT4, three problems with linkages speciation (HTS) method. In their paper, the proposed HTS is among the variables: FON, modified DTLZ3, and W. parameter-free and can be integrated into a variety of niching Compared with SPEA, it performed better results in terms of techniques for solving multimodal problems. The experiment convergence and diversity. However, as the authors indicated, results demonstrated that HTS clearly outperforms existing if the model is additive and quadratic, it is valid to compute an topology-based methods when the fitness evaluations budget is optimum in the crossover operator. For a general model, fewer limited. nondominated levels may be eliminated from the

Please cite this article in press as: M. Gong, et al., Evolutionary computation in China: A literature survey, CAAI Transactions on Intelligence Technology (2016), http://dx.doi.org/10.1016/j.trit.2016.11.002 + MODEL M. Gong et al. / CAAI Transactions on Intelligence Technology xx (2016) 1e21 7 nondominated level set, and some dominated levels near a to 7, NNIA still could obtain the approximate minimum values of nondominated level may exist in the nondominated level set. convergence and spacing metrics. Evolutionary multi-objective optimization usually deals with Zhang proposed an immune optimization algorithm for the problems with low number of objectives. Multi-objective constrained nonlinear multi-objective optimization problems problems with four or more objectives are often viewed as [52]. A novel constraint-handling scheme designed in uniform many-objective optimization problems. Zou et al. [49] proposed form, specialized antibody affinity design, adaptive antibody a new evolutionary algorithm for solving the problems of this evolution mechanism, immune selection, memory pool, anti- type. In order to improve the convergence of the traditional gen pool and dynamically variable sizes of evolving pop- multi-objective optimization, thermodynamic based dynamical ulations are the main techniques in the paper. multi-objective evolutionary algorithm was studied in this paper. Li et al. proposed a running metric that could evaluate uni- Besides, L-optimality was proposed to provide reasonable so- formity of obtained solutions at every generation [53]. Besides, lutions for decision making. The algorithm was tested by the metric could compare the population with different size and DTLZ1, DTLZ2 and DTLZ6 with 3e9 objectives. different number of objectives. They presented a new multi- Jiao et al. proposed an immune dominance clonal multi- objective evolutionary algorithm based on minimum spanning objective algorithm (IDCMA) [50] which maintained three tree [54], which was employed to update the solutions in the different populations of solutions. The first population denoted external population. It was observed intuitively that good per- as the immune dominance population which is used to store formance in convergence and uniformity were obtained. the set of non-dominated solutions with the best immune Yang et al. presented an adaptive hybrid model (AHM) differential degree. In every generation, the set of recombined based on nondominated solutions for solving MOPs [55].In antibodies form the second population which is denoted as the this model, three search phases were devised according to the generic antibodies population. The rest of the antibodies will number of nondominated solutions in the current population. constitute the third population known as the immune energy In order to exploit local information efficiently, a local in- antibodies population. Besides, the authors introduced a new cremental search algorithm was merged into the model. The similarity measure between antibodies, based on distances in algorithm obtained comparatively good performance in solv- the objective space: the immune differential degree. Again, ing MOPs with 2e9 objectives. this similarity measure was used to reduce the size of the Ke et al. proposed a novel multiobjective evolutionary al- offline population in the update step. The algorithm also pre- gorithm based on decomposition and ant colony [56]. Multi- sented a different selection mechanism for cloning. In this objective optimization problem is decomposed into a number mechanism, one antibody was randomly selected from the first of single-objective optimization subproblems. Each ant is population in the beginning at each generation. The quality responsible for one subproblem. All the ants are divided into value of each individual in the second population was several groups and each group maintains a pheromone matrix. computed based on the antibodyeantibody affinity, that was, New solution is constructed for an ant by information from its similarity in the representation of the solutions. group's pheromone matrix, its own heuristic information ma- Gong et al. proposed a multi-objective immune algorithm trix, and its current solution. with nondominated neighbor-based selection [51]. The new al- Ke et al. proposed a multiobjective evolutionary algorithm gorithm, Nondominated Neighbor Immune Algorithm (NNIA), by combining evolutionary algorithm, decomposition and consisted of a novel nondominated neighbor-based selection local search [57]. In the decomposition based multiobjective technique, an immune inspired operator, two heuristic search evolutionary algorithm, Pareto local search and a single operators, and elitism. The main contribution of this algorithm to objective local search were adopted to update populations. The MO field was its unique selection technique. The selection proposed algorithm performed better than some other state-of- technique only selected minority isolated nondominated in- the art algorithms on the multiobjective traveling salesman dividuals based on their crowding-distance values. The selected problem and the multiobjective knapsack problem. individuals were then cloned proportionally to their crowding- Zhan et al. proposes a novel coevolutionary technique distance values before heuristic search. By using the non- named multiple populations for multiple objectives (MPMO) dominated neighbor-based selection and proportional cloning, [58]. In MPMO, each population corresponded with only one the new algorithm realized the enhanced local search in the less- objective, so that the fitness assignment problem could be crowded regions of the current trade-off front. Depending on the dealt with. Based on MPMO, a coevolutionary multiswarm enhanced local search realized by clonal proliferation, hyperm- PSO (CMPSO) is develop, which used many swarms as the uation and recombination, NNIA can solve MOPs with a simple objectives number and each swarm focused on optimizing one procedure. The experimental study on NNIA, SPEA2, NSGA-II, objective. These swarms worked cooperatively and commu- PESA-II and MSIA in solving three low-dimensional problems, nicated with each other by an external shared archive. An five ZDT problems and five DTLZ problems has shown that external shared archive for different populations was to ex- NNIA was able to converge to the true Pareto-optimal fronts in change search information by using two novel designs, solving most of the test problems. More importantly, for the including the modified velocity update equation and an elitist complicated problems DTLZ1 and DTLZ3, NNIA performed learning strategy. Experimental results demonstrated that the much better than the other four algorithms. Besides, with respect proposed algorithm had superior performance in solving to DTLZ1 and DTLZ3, when the number of objective increases different sets of MOPs.

Please cite this article in press as: M. Gong, et al., Evolutionary computation in China: A literature survey, CAAI Transactions on Intelligence Technology (2016), http://dx.doi.org/10.1016/j.trit.2016.11.002 + MODEL 8 M. Gong et al. / CAAI Transactions on Intelligence Technology xx (2016) 1e21

Gong et al. proposed a surrogate model-based multi-oper- ranking restriction scheme, each solution involves in the ator search strategy for evolutionary optimization [38]. The ranking on a part of aggregation functions could be better than model was used to implement multi-operator ensemble which on all. Experiments demonstrated that these two algorithms can improve the algorithm performance. Each operator performed well in balancing the convergence and diversity in generated its own candidate point, so no operator will be lost many-objective optimization. when generating the new candidate points in the subsequent running stages. An ensemble of different operators can also be 3.3. Constrained optimization implemented into different EAs. Experimental results have indicated that this approach could improve the performance Constrained optimization is another important topic in EC. for the single operator-based methods, and it could also be Many science and engineering disciplines encounter a larger applied to multi-objective optimization. number of constrained optimization problems (COPs). Re- Zhou et al. proposed a generalized resource allocation searchers have done much work in this domain. strategy for decomposition-based MOEAs [59]. In this algo- Cai and Wang proposed a multi-objective optimization rithm, each subproblem was chosen to invest by using a based evolutionary algorithm for constrained optimization probability of improvement vector. An offline measurement [63]. As multi-objective EAs have two goals (convergence to and an online measurement of the subproblem hardness were the true Pareto optimal set, and maintenance of a uniform used to maintain and update this vector. Utility functions were distribution of the Pareto front), constrained optimization proposed and studied for implementing a reasonable and sta- evolutionary algorithms (COEAs) also have two definite ob- ble online resource allocation strategy. Thirty benchmark jectives (landing in or approaching the feasible domain functions and the functions presented in the CEC 2013 were promptly, and reaching the global optimal solution in the end). chosen to test the performance of the proposed algorithm. COPs are therefore recast as biobjective optimization prob- Many objective optimization problems are the problems lems. The authors introduced a nondominated individual have more than three objectives. In China, several researchers replacement scheme for transforming COPs to MOPs. On the proposed several many-objective evolutionary algorithms for basis of the nondominated individual replacement scheme, many optimization problems [49,60e62]. two models were devised for the generation of individuals in a Zou et al. proposed a novel algorithm (MDMOEA) for population. The difference between these two models was that many-objective optimization problem [49]. In this algorithm, model 1 used all information provided by nondominated in- an L-optimality was defined and in this definition, all objectives dividuals, while model 2 only used partial information pro- were assumed equally important. L-optimal solutions were vided by nondominated individuals. Furthermore, they subsets of Pareto-optimal solutions. Experiments demonstrated realized the effects of infeasible solutions on finding the global that MDMOEA could converge to the true L-optimal front and optimum in feasible regions. Therefore an infeasible solution maintained a widely distributed set of solutions. archiving and replacement mechanism was devised. Finally, Wang et al. proposed an improved two-archive algorithm they evaluated the performance of their algorithm on thirteen for many-objective optimization [60]. In the proposed algo- well-known benchmark functions. Experimental results rithm, two main innovations, including assigning different showed that the proposed approach outperformed six selection principles to the two archives, designing a new Lp- compared algorithms in terms of the best, mean, and worst norm-based (p < 1) diversity maintenance scheme were objective function values and the standard deviations. introduced. Experiments showed that the proposed algorithm Wang et al. proposed a hybrid constrained optimization could deal with many-objective optimization (up to 20 ob- evolutionary algorithm (HCOEA) [64]. In HCOEA, a given jectives) with good convergence, diversity, and complexity. COP is converted into a biobjective optimization problem. Xu et al. [61] proposed a novel evolutionary algorithm to Two models were devised and merged into the algorithm. The deal with many-objective optimization. The fitness evaluation first model was a niching GA based on tournament selection scheme in MOEA/D was used to improve the convergence of for global search, which could reduce selection pressure and the algorithm and at the same time the diversity was preserved. maintain the diversity of the population. While the second In this algorithm, a new dominance relation was introduced. In model used local search through clustering and multiparent the designed dominance, solutions were represented by well- crossover. The population was split into disjoint sub- distributed reference points and allocated into different clus- populations according the location of individuals in the solu- ters. The solutions have the competitive relationship if they are tion space. Offspring were generated by in each within the same cluster. 80 instances of 16 test problems were subpopulation. In order to utilize infeasible individuals for used to show the performance of the proposed algorithm. They COPs, a simple best infeasible individual replacement scheme also introduced two enhanced algorithms (MOEA/D-DU and was devised. Wang et al. [65] also proposed an adaptive EFR-RR) for many objective optimization problems [62]. The tradeoff model (ATM) for COP. In this model, in order to perpendicular distance from a solution to the weight vector in obtain an appropriate tradeoff between objective function and the objective space was used to improve MOEA/D and constraint violations, three main issues were considered ac- ensemble fitness ranking algorithm (FR). In MOEA/D-DU, a cording to how many individuals in the population were distance-based updating strategy was used to update solutions. feasible versus infeasible. In [66], the authors introduced an In EFR-RR, a ranking restriction scheme was adopted. In the experimental design method, orthogonal design, to their

Please cite this article in press as: M. Gong, et al., Evolutionary computation in China: A literature survey, CAAI Transactions on Intelligence Technology (2016), http://dx.doi.org/10.1016/j.trit.2016.11.002 + MODEL M. Gong et al. / CAAI Transactions on Intelligence Technology xx (2016) 1e21 9 constrained optimization evolutionary algorithm. An experi- evolution as the search engine and a novel infeasible solution mental design is orthogonal if each factor can be evaluated replacement mechanism based on multiobjective optimization. independently of all the other factors. In the evolutionary 24 benchmark test functions were used to demonstrate the process, several individuals were chosen from the population performance of CMODE. as parents and orthogonal design was applied to pairs of par- Wang et al. presented a dynamic hybrid framework (DyHF) ents to produce a set of representative offspring. for constrained optimization problems [75]. Two models are Zeng et al. presented a lower dimensional search evolu- designed in this framework: global search model and local tionary algorithm and applied it to constrained optimization search model. In these two models, differential evolution [67]. The main characteristic of the algorithm was their served as the search engine, and Pareto dominance used in crossover operator, which searched a space with dimensions multiobjective optimization was used to compare the in- lower than 3 no matter how many dimensions the decision dividuals in the population. Global and local search models space of the optimization problem is. They concluded that their were executed dynamically according to the feasibility pro- algorithm converged fast especially for the higher-dimensional portion of the current population. The performance of DyHF problems studied. However, for some complicated problems, it was tested on 22 benchmark test functions. was trapped in local optima. Zou et al. described a dynamic Wang et al. proposed an evolutionary optimization for evolutionary algorithm (DEA) for constrained optimization constrained optimization problems [76]. The proposed algo- [68]. In the dynamic evolutionary algorithm, each solution, rithm consisted of a (m þ l)-differential evolution and an called particle, was assigned a momentum and an activity. A improved adaptive trade-off model. In (m þ l)-differential selection operator was based on the above two quantities. Zhou evolution, the offspring population was generated by three et al. presented a new approach to simple convert the con- mutation strategies and binomial crossover. The improved strained optimization to minimization of two objective func- adaptive trade-off model included three main situations: the tions [69]. By their method, one objective was the original infeasible situation, the semi-feasible situation, and the objective function and the other was the degree function feasible situation. Different constraint-handling mechanisms violating constraints. A concept of measuring the Pareto were designed for each situation. 24 well-known benchmark strength of each individual was introduced. Finally, a new real- test functions demonstrated that the proposed algorithm was coded genetic algorithm based on Pareto strength and Minimal competitive compared with other algorithms. In [77], Jia et al. Generation Gap (MGG) model was devised to solve COPs. improved the algorithm in [76]. The improved algorithm Zhang et al. proposed a novel search biases selection consisted of an improved (m þ l)-differential evolution and a strategy for constrained optimization [70]. The shortcomings novel archiving-based adaptive tradeoff model. Offspring was of stochastic ranking [71] were analyzed and the explicit generated by several mutation strategies and the binomial search biases ability in the feasible regions was enhanced. The crossover of differential evolution in the improved (m þ l)- current best feasible solutions in the population were selected differential evolution. The proposed algorithm could maintain with a high probability in order to accelerate convergence a good balance between the diversity and the convergence of speed and enhance numerical accuracy. the population during the evolution. In [78], Wang et al. pro- Yu et al. proposed a new constrained evolutionary algo- posed an algorithm to balance constraints and objective rithm to solve maintenance-cost view-selection problem in on- function in constrained evolutionary optimization. The pro- line analytical processing queries [72]. Uniform crossover, posed algorithm incorporated the objective function informa- gene bit based mutation and stochastic ranking were used in tion into the feasibility rule by the DE operators, the this paper. The experiment results showed this algorithm can replacement mechanism and the mutation strategy. provide significantly better solutions in terms of minimization Wang et al. imposed some constraints on the subproblems of query processing cost and feasibility. of decomposition-based multi-objective evolutionary algo- Liu et al. proposed a novel hybrid algorithm (PSO-DE) for rithms [79]. In this algorithm, a further strategy which uses constrained numerical and engineering optimization [73].The information collected from the search was also proposed to proposed algorithm integrated particle swarm optimization adaptively adjust constraints. Experimental results demon- (PSO) with differential evolution (DE). Only half of particles strated the good performance of the proposed algorithm in are updated by PSO, in which Deb's feasibility-based rule was balancing the population diversity and convergence. used to judge whether the pbest is updated or not. After the PSO evolution, DE is used to update pBest. Each pbest in 3.4. Dynamic optimization pBest could produce three offspring by using DE's three mu- tation strategies. The offspring that has a better fitness value Many real world optimization problems are actually dy- and lower degree of constraint violation was selected as the namic. Optimization methods capable of continuously adapt- new pbest. Experiments on 11 well-known benchmark test ing the solution to a changing environment are needed. EC is functions and five engineering optimization functions showed suitable for problems with dynamically changing environment. the performance of PSO-DE. When a problem's environment is constantly changing, the Wang et al. proposed an improved CW algorithm current best solution becomes unacceptable and another so- (CMODE) [74]. CMODE combined multiobjective optimiza- lution, which fits the current environment better, may exist. In tion with differential evolution. CMODE used differential China, Researchers have done some work on this topic.

Please cite this article in press as: M. Gong, et al., Evolutionary computation in China: A literature survey, CAAI Transactions on Intelligence Technology (2016), http://dx.doi.org/10.1016/j.trit.2016.11.002 + MODEL 10 M. Gong et al. / CAAI Transactions on Intelligence Technology xx (2016) 1e21

Zeng et al. proposed an orthogonal evolutionary algorithm solutions linkage and memory strategy based on the optimal (ODEA) for dynamic optimization problems [80]. Its popu- solution set. By adopting these operators, PMS is with better lation consisted of niches, and a niche is defined to be a small performance than other algorithms. hyper-rectangle. To evaluate the fitness of a niche, each niche selects its best solution found so far as its representative. The 4. Real-world applications fitness value of the representative was defined to be the fitness of the niche. ODEA algorithm divided its population into two EC techniques have been successfully applied to many real- groups. One group of niches, called observer niches, was for world problems since the early 1960s. In this section, we local search. The other group, called explorer niches, explored summarize the contributions of EC-based applications ob- new peaks for global search. Zeng et al. also proposed another tained by Chinese researchers. orthogonal evolutionary algorithm (ODHC) [81] for dynamic optimization problems, which incorporated hill-climbing al- 4.1. EC based methods applied in data mining gorithm. The niche and orthogonal technique are same to [45]. An archive was used to store the latest found higher peaks for Data mining is an important step in knowledge discovery in the ODHC algorithm learning from the past search. The database (KDD) as the volume of data grows rapidly in operator of climbing to a peak for a niche in the ODHC al- modern times. To the best of our knowledge, EC-based gorithm consisted of two stages: At the first stage, the niche methods are suitable for solving complex or ill-defined prob- does not cover a peak. It repeated a moving operator to lems and have been applied into data mining and knowledge approach a potential peak. At the second stage, a shrinking discovery by some researchers. operator was repeated to obtain a “close-to-peak” with a Jiao et al. proposed an organized coevolutionary algorithm higher precision until the niche size less than threshold. The for classification (OCEC) [88]. OCEC causes the evolution of experiments in [80,81] showed that ODEA and ODHC per- sets of examples, and at the end of the evolutionary process, formed better than self organizing scouts algorithm (SOS) on extracts rules from these sets. These sets of examples form one moving peaks benchmark function. The authors also organizations. Three evolutionary operators and a selection extended their algorithm to solving dynamical MOPs [82]. For mechanism are devised to simulate the interaction among or- Dynamic TSP, Kang et al. proposed some benchmarks and ganizations. OCEC dose not put emphasis on forming the provided an example of the use of the benchmark [83]. Zhou appropriately sized organizations, but on simulating the et al. [84] devised three dynamic operators, insert operator, interacting process among organizations. Besides, OCEC delete operator, and change operator, to modify a static TSP adopts a bottom-up search mechanism to avoid generating algorithm to Dynamic TSP algorithm. Besides, the inver-over meaningless rules. In [88], OCEC was compared with several algorithm combined the three operators was used to solve the well-known classification algorithms on 12 benchmarks from Dynamic TSP with size of 100. A Dynamic TSP is harder than the UCI repository datasets and multiplexer problems. The 20- a general TSP, which is a NP-hard problem, because the city and 37-multiplexer problems are used. OCEC was also applied number and the cost matrix are time varying. to radar target recognition problems. All results showed that Tang et al. [85] proposed a self-adaptive mechanism for OCEC achieved a higher predictive accuracy with a lower EAs with immigrant schemes to address dynamic optimization computational cost and obtains a good scalability. problems. In their paper, they examined the impact of Gong et al. performed unsupervised image classification by replacement rate on the performance of EAs with immigrant using a novel evolutionary clustering method, named manifold schemes in dynamic environments. The experiment results on evolutionary clustering (MEC) [89]. In MEC, the clustering a series of dynamic problems showed that the proposed problem was considered from a combinatorial optimization approach could avoid fine-tuning the parameter and out- viewpoint. Each individual was a sequence of real integers performed other immigrant schemes using a fixed replacement representing the cluster representatives. Each datum was rate. assigned to a cluster representative according to a novel Li et al. proposed a dynamic neighborhood multi-objective manifold-distance-based dissimilarity measure, which evolutionary algorithm (DNMOEA/HI) to balance conver- measured the geodesic distance along the manifold. In [89], gence and diversity of solutions [86]. The fitness of each in- the authors applied MEC to solve seven benchmark clustering dividual is evaluated by tree neighborhood density and the problems on artificial data sets, three artificial texture image Pareto strength value. A novel algorithm was proposed to classification problems, and two synthetic aperture radar optimize the hypervolume contribution of a single individual. image classification problems. The experimental results Compared with six other multi-objective evolutionary algo- showed that in terms of cluster quality and robustness, MEC rithms, the efficiency of our proposed algorithm is outperformed the K-means algorithm, a modified K-means demonstrated. algorithm using the manifold-distance-based dissimilarity Peng and Zheng et al. proposed a novel prediction and measure, and a GA-based clustering technique in partitioning memory strategies for dynamic evolutionary algorithm (PMS) most of the test problems. [87]. The proposed algorithm contained three parts: explora- Au et al. presented a novel evolutionary data mining al- tion operator based on population evolutionary direction, gorithm for churn prediction [90]. For churn prediction, it did exploitation operator based on the direction of nondominated not only need to predict whether a subscriber would switch

Please cite this article in press as: M. Gong, et al., Evolutionary computation in China: A literature survey, CAAI Transactions on Intelligence Technology (2016), http://dx.doi.org/10.1016/j.trit.2016.11.002 + MODEL M. Gong et al. / CAAI Transactions on Intelligence Technology xx (2016) 1e21 11 from one carrier to anther, also require that the likelihood of as the typical genetic algorithm operations. The experimental the subscriber's doing so be predicted. In [90], the proposed results on both the simulated datasets and the real datasets algorithm had the following characteristics. First, the initial showed that KMQGA could obtain promising results. population consisted of a set of first-order rules. Higher-order Gong et al. [96] proposed a multiobjective model for sparse rules were obtained by the iterating the initial population. feature learning in deep neural networks. A multiobjective Besides, an objective interestingness measure was employ for induced learning procedure which consisted of fast updating identifying interesting rules. Probability based function was step and multiobjective inducing step was designed to opti- used to evaluating the fitness of chromosomes. Finally, seven mize the model. In the multiobjective inducing step, MOEA/D databases were used for validating the techniques in the was improved by incorporating with self-adaptive differential algorithm. evolution. The individuals in the population are updated by Ma et al. proposed a novel evolutionary algorithm called differential operators in order to adapt to the properties of evolutionary clustering (EvoCluster) [91] to uncover inherent network parameters. clusters in gene expression microarray data. EvoCluster Gong et al. introduced a multiobjective learning process for encoded the entire cluster grouping in a chromosome so that self-paced learning [97]. The objective function of the self- each gene encodes one cluster. And it had a set of crossover paced learning was decomposed into two terms, i.e., loss and mutation operators that facilitated the exchange of term and the self-paced regularizer. In the learning process, grouping information between two chromosomes. Besides, the MOEA/D was used to learn from easy region to complex re- interestingness of a particular grouping of data records was gion of the objective space. Differential evolution operators measured by the fitness. In this algorithm, there was no were utilized to generate the offspring. requirement for the number of clusters to be decided in Though many works of evolutionary algorithms on data advance. The experiment results showed that patterns hidden mining have been done, this application has not been drew in each cluster can be explicitly revealed and the algorithm is widespread attention. Nowadays, machine learning and deep very robust in noise environment. learning are very hot study direction. Combing EAs and ma- Wong and Leung introduced a novel data mining approach chine learning and deep learning are very interesting. that employed an evolutionary algorithm to discover knowl- edge represented in Bayesian networks [92]. The algorithm 4.2. EC based methods applied in VLSI floorplanning embodied two phases: the first phase was the conditional in- dependence test for reducing the size of search space, and the Floorplanning is a critical phase in physical design of VLSI second one was the search phase, in which good Bayesian circuits and it consequence has an important relation with network models were generated by a GA. Finally, the hybrid performance of the final chip. The goal of VLSI floorplanning algorithm was applied to two data sets of direct marketing and is to find a floorplan for the modules such that no module comparative better prediction accuracy was obtained. overlaps with another and the area of the floorplan and the Query reweighting is a very important research topic of interconnections between the modules are minimized. The document retrieval. Chang and Chen presented a new method methods of floorplanning could be classified into two cate- for query reweighting to solve document retrieval [93].GAis gories: slicing structure and nonslicing structure. Because of employed to reweight user's query vector. The query vectors the generality of nonslicing floorplanning, it was obtained were encoded into chromosomes and the optimal weights of more attention and popularity. EAs employ methods of per- query terms are searched by genetic algorithm. Finally, the turbing the floorplan and searching for better solutions, and National Science Council document database, Taiwan, was have become an efficient method in solving floorplanning. In used in the experiment. The average recall rate and average China, Tang and Yao [98], Liu et al. [99] have done research in precision rate of the top ten retrieved documents and the top this domain. twenty retrieved documents were improved. Tang and Yao proposed a memetic algorithm for VLSI Time series are an important class of temporal data objects floorplanning [98]. The novel memetic algorithm combined an and can be easily obtained from financial and scientific ap- effective genetic search method to explore the search space, an plications. Chung et al. proposed an evolutionary time series efficient local search method to exploit information in the segmentation algorithm [94]. It allowed a sizeable set of search region, and a novel bias search strategy to maintain pattern templates to be generated for mining or query. With tradeoff between them. The most efficient nonslicing repre- respect to application in times series of selected Hong Kong sentation, the ordered tree (O-tree) was adopted. A subtree of stocks, a perceptually important point-based subsequence- the O-tree represents a compact placement of a cluster of matching were introduced. modules. Hence, subtrees were used as memes in their Xiao et al. proposes a quantum-inspired genetic algorithm memetic algorithm. The memes were transmitted and evolved for k-means clustering (KMQGA) [95]. Without knowing the through one crossover operator and two mutation operators. In exact number of clusters beforehand, KMQGA could obtain [98], two hard rectangle models, ami33 and ami49, were used the optimal number of clusters as well as providing the to test the performance of the algorithm. optimal cluster centroids. A Q-bit based representation was Liu et al. proposed a new nonslicing floorplan representa- applied for exploration and exploitation in discrete 0e1 hy- tion, moving block sequence (MBS) [99]. With respect to perspace by using rotation operation of quantum gate as well MBS, four moving rules were described corresponding to four

Please cite this article in press as: M. Gong, et al., Evolutionary computation in China: A literature survey, CAAI Transactions on Intelligence Technology (2016), http://dx.doi.org/10.1016/j.trit.2016.11.002 + MODEL 12 M. Gong et al. / CAAI Transactions on Intelligence Technology xx (2016) 1e21 initial positions. In MBS representation, all blocks can only be and improves the quality of solutions. Experimental study moved in the first quadrant to form a left-bottom compact showed that their method performed well for small number of floorplan sheet, that is, any block in the chip can not be moved users, while for larger number of users, it performed a little left or down any more. The MBS is suitable for evolutionary worse. algorithms since no extra constraints are exerted on the solu- In [102], particle swarm optimization was developed to find tion space. Besides, an organizational evolutionary algorithm sub-optimal multi-user detection. A de-correlating detector or incorporated the intrinsic properties of MBS was designed linear minimum mean square error detector was used as the (MBS-OEA). With the intrinsic properties of the MBS in first stage to initialize the detector. Then, the PSO algorithm mind, three new evolutionary operators were designed in the was applied to detect the received data bit by optimizing MBS-OEA. The results showed that the MBS-OEA was not objective function. Simulation showed that the performance of only suitable for solving a wide range of problems, but also the proposed method was promising. competent for solving large-scale problems. Though few works have been done on this problem, EAs VLSI floorplanning is an NP-hard problem. EAs are with were good methods to deal with this problem. With the good performance of solving NP-hard problem. Designing development of wide-band wireless systems, DS-CDMA may effective global and local search strategies are needed in be out of date nowadays. Future works will focus on other dealing with this problem. problems in the communication research community, for example, multiple-inputemultiple-output (MIMO) systems. 4.3. EC based methods applied in DS-CDMA multiuser detection 4.4. EC based methods applied in hardware-software partitioning In recent years, Direct-Sequence Code-division Multiple- access (DS-CDMA) systems have emerged as one of prime Hardware-software partitioning is one of the most impor- multiple-access solutions for 3G and future wide-band wire- tant issues of Codesign of embedded systems because it is less systems. In the DS-CDMA framework, multiple-access made at the beginning of the cycle of design. In terms of costs interference (MAI) existing at the received signal creates and delays, final results will strongly depend on partitioning. A “near-far” effects and constitutes the main limitation of DS- good partitioning scheme is a tradeoff under some constraints, CDMA systems. Multiuser detection (MUD) techniques can such as power, size, performance, and so on. efficiently suppress MAI and substantially increase the ca- In China, Zhang et al. applied artificial immune principals pacity of CDMA systems, so it has gained significant research based on negative selection algorithm towards solving this interest since the Optimal MUD (OMD) was proposed. But the problem [103]. In contrast to prior work with negative selec- computational complexity of OMD increases exponentially tion in artificial immune systems (AIS), in their paper, it did with the growth of user number. From a combinatorial opti- not have a precise self-definition, and the worst candidate mization viewpoint, OMD is an NP-complete problem and EC solutions in every generation are added into the self-set step by based methods have been introducing in solving the problems. step, while the oldest individuals in the self-set are removed In China, Gong et al. [100], Wang et al. [101], Soo et al. [102] when the self-set is full. Therefore, it is a dynamic scheme, have done some work in this domain. namely first-in-first-out updating strategy. According to their Gong et al. presented a novel clonal selection algorithm for experimental results, they concluded that their algorithm was multiuser detection (CAMUD) [100]. In their paper, an anti- more efficient than traditional evolutionary algorithm. gen was defined by the problem and its constraints, antibodies Hardware-Software partitioning is difficult problem for were represented by the limited-length character strings. engineering. This direction is popular with embedded system Except the normal clonal mutation operator and clonal selec- in recent years. However, the methods proposed and standard tion operator, it is noteworthy that, a novel clonal death benchmark test functions are fewer, and metrics used for operator was devised by the authors. Theoretical analysis and optimized are partial. Therefore, there should be much work in Monte Carlo simulations showed that the algorithm could this domain. significantly reduce the computational complexity and achieve good performance in MAI suppression and “near-far” 4.5. EC based methods applied in solving equations resistance. Wan et al. presented a (1þl) evolution strategy method to Many problems come down to linear equations or nonlinear solve asynchronous DS-CDMA multiuser detection [101]. The equations. Solving equations are of great importance in many main contribution of this paper is the analysis of the offspring systems. Traditional methods for equations solving are with size l and the mutation probability Pm. As their suggestion, the many constraints, for example, differentiable, unisolution and value of l is approximately equal to n lnn in all instances, so on. where n is equal to the product of the number of active users He et al. presented a novel application of evolutionary and the packet size. Besides, they have validated that Pm is 0.2, computation techniques in solving linear and partial differ- which makes the proposed ES escape local optima effectively ential equations [104]. Several combinations of evolutionary

Please cite this article in press as: M. Gong, et al., Evolutionary computation in China: A literature survey, CAAI Transactions on Intelligence Technology (2016), http://dx.doi.org/10.1016/j.trit.2016.11.002 + MODEL M. Gong et al. / CAAI Transactions on Intelligence Technology xx (2016) 1e21 13 computation techniques and classical numerical methods were 4.7. EC based methods applied in path planning in proposed. The experimental results showed that the proposed mobile robot system hybrid algorithms outperformed the classical numerical methods significantly in terms of effectiveness and efficiency. Path planning is one of the most important problems in Wu and Kang presented a parallel elite-subspace evolu- mobile robot control system. Environmental model of path tionary algorithm (PESEA) for solving system of non-linear planning is difficult in its physical and dynamic properties. equations [105]. The PESEA ran on the parallel computer There are already some methods that solve path planning with 2 processors and share memory. Elite-preserve strategy is problems, such as artificial potential method and grid method. adopted in their paper to conduct multi-processor crossover. It Cai and Peng [108], Duan and his collaborators [109e114] is a simple parallel algorithm applied into solving non-linear have done much work in this domain. equations. By dividing a complicated problem into several relatively Song et al. proposed a simple and generic transformation simple sub-problems and assigning them to each single- technique based on multiobjective optimization for nonlinear agent, multi-agent systems can effectively solve compli- equation systems [106]. The proposed algorithm transformed a cated problems with modularity, maintainability, extendi- nonlinear equation system into a bi-objective optimization bility, fault tolerance and robustness. In order to maintain the problem and then the transformed problem could be solved by relation of the agents, Cai and Peng proposed a cooperative MOEAs. The experimental results have demonstrated the multi-mobile robot system based on genetic algorithm performance of the proposed algorithm compared with another (CCAGA) for path planning [108]. In a multi-mobile robot state-of-the art multiobjective optimization based trans- system, the performance of it is improved by the cooperation formation technique and four single-objective optimization and coordination relation among those mobile robots. A main based approaches. characteristic of CCAGA is that potential solutions of each Compared with classic methods, EAs are more efficient and sub-problem form their own sub-population, and evolve only robust in solving equations. In reality, many systems are in their own sub-population. Besides, a novel fixed-length nonlinear equation systems and they are with many solutions, decimal encoding mechanism for paths of each mobile such that powerful MOEAs are suitable for nonlinear equation robot is also proposed in their paper. The algorithm was systems solving. Designing effective MOEAs for nonlinear validated on a cooperation two-mobile robot system and it equation systems will be an interesting research. obtained robust convergence. Duan et al. have done some investigations on ant colony 4.6. EC based methods applied in solving multiple algorithms and apply it into global trajectory planning of un- destination routing problems manned aerial vehicle [109e114].In[109], several hybrid improvement strategies were introduced and combined with Multiple destination routing (MDR) problems well up with basic ant colony algorithm for alleviating its limitation of the advance and development of network and information stagnation and prematurity. In [110], satisficing decision al- technology in modern society. Multiple destination routing gorithm was hybridized with ant colony optimization for enables widespread usage of multipoint services at a lower cost solving the uninhabited combat air vehicle path planning in than networks using point-to-point routing. An MDR problem complicated combat field environments. An acceptance func- can be stated as the determination of the best routing in a given tion and rejection function are used for selecting the next node communication network for the delivery of a message from the from the current candidate path nodes. In [111], a new hybrid source (one or more) to multiple destination nodes with meta-heuristic ant colony optimization (ACO) and differential reference to certain criteria, such as time delay and network evolution (DE) algorithm was proposed for UCAV three- bandwidth. However, the MDR problem itself is very complex. dimension path planning problem. A к-trajectory was adop- Furthermore, its optimal solution, the Steiner tree problem, is ted to make the optimized UCAV path more feasible. In [112], NP-complete and thus not suitable for real-time applications. an improved artificial bee colony (ABC) optimization algo- Leung et al. proposed a new genetic algorithm for MDR rithm was introduced for UCAV path planning. In the pro- problems without constraints [107]. The method made use of posed improved ABC algorithm, chaotic variable was the genetic operators to search the intermediate nodes for an introduced preventing the ABC algorithm falling into the local MDR problem. Besides, with respect to the algorithm, four optimum. Duan et al. proposed an improved constrained dif- basic components: representation of individuals, determination ferential evolution algorithm for path planning [113]. A novel of the fitness function, design of the genetic operators, and satisfactory level update strategy was introduced to improve determination of the probabilities controlling the genetic op- the searching ability of the proposed algorithm. Duan et al. erators were devised accordingly. The algorithm was applied applied artificial bee colony algorithm to deal with reentry to solve the B problem set of the Steiner tree problem on trajectory optimization [114]. The algorithm consisted of two graphs in the OR-library and problems with randomly gener- processes. First, the control variables of the hypersonic reentry ated dense networks. By their experiment, we can obtain that vehicle were discretized at a set of LegendreeGauss collo- this method is robust and can find the optimal solutions with cation points. Second, artificial bee colony algorithm was used high probability. However, the computational time is not to solve this problem. The feasibility and the superiority of the suitable for application. proposed method were proved by simulations.

Please cite this article in press as: M. Gong, et al., Evolutionary computation in China: A literature survey, CAAI Transactions on Intelligence Technology (2016), http://dx.doi.org/10.1016/j.trit.2016.11.002 + MODEL 14 M. Gong et al. / CAAI Transactions on Intelligence Technology xx (2016) 1e21

Yang et al. [115] presented an EA-based UAV path planner losses, ensuring voltage quality, service reliability assurance, based on a novel separate evolution strategy for solving the and minimizing switching operations. UAV path planning problems. In their paper, eight commonly It still receives a great deal of attention of EAs on power used constraints and objective functions were decomposed, system. There should be much works on applying EAs to deal and the waypoints of candidate paths were separately evalu- with more problems or solving economic dispatch problems ated and evolved. The performance of the proposed approach with different constraint by EAs. was validated by comparison with the other state-of-the-art EA-based planners. 4.9. EC based methods for image processing Path planning problem is always a hot topic. Recent re- searches have shown that EAs were very useful in path plan- Image processing includes several important issues, for ning problem under different constraint conditions, while these example image segmentation, image classification, and sparse researches are offline planning. The online planning and reconstruction et al. It is difficult for traditional algorithms to cooperative planning may be research topics because they are deal with image processing in the adjustment of parameters more practical than offline planning. and get the best solution. Some image processing problems can be modeled as single optimization problems or multi- 4.8. EC based methods applied in power system objective optimization problems. EAs perform well in these optimization problems. Many optimization problems in power systems are Liu and Tang presented an autonomous agent-based image combinatorial optimization problem. They are difficult to deal segmentation approach [121]. From the paper, we can obtain with by traditional mathematical programming algorithms. EC that a digital image is regarded as the environment in which based methods could provide near optimal or optimal solutions the agent inhabit and act. By some effective reactive behaviors for these problems under reasonable time. Several scholars such as breeding and diffusion, the agent could succeed in from Taiwan, Hongkong, and Chinese Mainland have done labeling homogeneous segments. Once the agents find the work in this domain. pixels of a specific homogeneous segment, they will breed Lin et al. proposed a hybrid algorithm by integrating offspring agents inside their neighboring regions. Finally, the evolutionary programming, tabu search and quadratic pro- distributed behavior-based agents in searching and labeling gramming methods to solve the non-convex economic dispatch various homogeneous regions in a brain-scan image are problem [116]. The problem is solved in two phase, the cost- studied. Besides, Liu et al. introduced a new evolutionary curve-selection sub-problem was solved with a hybrid evolu- autonomous agent based approach to image feature extraction tionary programming and tabu search. The typical economic [122]. The agent environment is also a digital image. The dispatch sub-problem was settled by quadratic programming. agent behaviors include self-reproduction, diffusion and cease Lin developed an improved tabu search algorithm for to exist in this paper. And the most distinct traits of this economic dispatch with non-continuous and non-smooth cost method is its bottom-up, decentralization and distributing in functions [117]. The method adaptively regulates the tabu list nature and relying on local agent behavior. size, the number of mutated and recombined individuals. The Zhong et al. introduced a novel multiple-valued immune performance was validated by its obtained accurate solutions network based supervised classification algorithm for remote- and great potential application in the power system. sensing imagery [123]. By their literature, samples in inter- Short-term load forecasting of electric power plays an esting regions were employed to train the immune network. important role in operation scheduling and secure operation of The trained immune network was used for classifying the power systems. Liao and Tsao proposed a fuzzy network imagery. The performance of this method was validated by combined with a chaos-search genetic algorithm and simu- comparison with maximum likelihood, back-propagation lated annealing to the issue [118]. A fuzzy hyperrectangular neural network, and minimum distance. composite neural network was adopted for initial load fore- Li et al. [124] proposed a new soft-thresholding evolu- casting, afterward, the genetic algorithm and simulated tionary multiobjective algorithm for sparse reconstruction in annealing are used to find the optimal parameter setting of the image processing. This algorithm optimized two competing network. In [119], particle swarm optimization was employed cost function measurement error and a sparsity-inducing term. to identify the autoregressive moving average with exogenous Besides a soft-thresholding technique, the algorithm incorpo- variable model for short-term load forecasting. The global and rated two additional heuristics. Optimal solutions were found parallel search abilities are emphasized in this article. The in knee regions on the Pareto front. Compared with five performance of the method is validated by Taiwan Power load commonly used sparse reconstruction algorithms, the algo- data. rithm was demonstrated effective for practical applications. Network reconfiguration problem is important in power A multiobjective model was built for band selection in system for enhancing service reliability and reducing power hyperspectral image processing [125]. In this model, the band losses. It is a complex nonlinear combinatorial problem. Hsiao selection problem was modeled as a multiobjective optimi- proposed a multi-objective evolution programming method for zation problem (MOP), and two objective functions with a distribution feeder reconfiguration [120]. Four objectives were conflicting relationship were designed to describe the infor- introduced in this algorithm, which were minimizing power mation contained in the selected band subsets and the number

Please cite this article in press as: M. Gong, et al., Evolutionary computation in China: A literature survey, CAAI Transactions on Intelligence Technology (2016), http://dx.doi.org/10.1016/j.trit.2016.11.002 + MODEL M. Gong et al. / CAAI Transactions on Intelligence Technology xx (2016) 1e21 15 of selected bands. A multi-objective evolutionary algorithm method was inserted between crossover and mutation opera- based on decomposition was proposed to find a balance be- tions of a traditional genetic algorithm in [130]. The system- tween these two objectives and generate a set of band subsets atic reasoning ability of the Taguchi method was incorporated with different numbers of bands in a single run. in the crossover operation for better gene selection. In [131], Gong et al. introduced a multi-objective sparse unmixing the clonal proliferation performed by hypermutation and (MOSU) model for hyperspectral sparse unmixing [126].A recombination were integrated to improve the search ability of novel multi-objective cooperative coevolutionary algorithm was the algorithm. The two algorithms were tested on seven global proposed to optimize conflicting objectives: the reconstruction numerical optimization problems and designing the digital term, the sparsity term and the total variation regularization term. low-pass, high-pass, band-pass, and band-stop filters. A random group strategy based on sparsity and the non-uniform Lin et al. modeled the electronic circuit design with uni- mutation operator were designed to obtain more sparse solutions. form search range, and proposed an efficient orthogonal Experiments on simulated and real hyperspectral data sets learning particle swarm optimization [132]. It used a novel demonstrated the effectiveness of the proposed algorithm. orthogonal learning strategy which can find useful information Duan et al. proposed an elitist chemical reaction optimi- in each particle's best position and its neighborhoods' best zation for contour-based target recognition in aerial images position. The predictive solution strategy was also used to save [127]. In this algorithm, Contours were described by edge computational burden. The effectiveness in a practical circuit potential function and contour-based target recognition was of their algorithm has been validated. formulated as an optimization problem. To optimizing this Previous works all formulated power electronic circuit problem, an improved chemical reaction optimization algo- optimization as single optimization problem. In the future, rithm was adopted. The elitist selection procedure was used to power electronic circuit optimization will be extended to improve the efficiency. Experimental results demonstrated that multi-objective optimization model and solved by MOEAs. the algorithm performed well in enhancing the accuracy and robustness of target recognition for aerial images. 4.11. EC based methods for signal processing Lots of works of EAs for image processing have been done in recent years in China. Ill posed problems or inverse problem There are many applications in signal processing, such as are frequently encountered problems. MOEAs are with good time-delay estimation, blindly separating unobservable inde- performance in solving these problems. It will be an inter- pendent source signals. In these applications, a set of param- esting and effective topic by applying EAs to solve ill posed eters should be optimized under a restrictive bounded area. problems in image processing in the future. Objective functions of these applications are usually linear or nonlinear, equality or inequality, smooth or nonsmooth. EAs 4.10. EC based methods for electronic circuits have been used for signal processing in China. Evolutionary algorithms also have been introduced to deal with Electronic circuit design and optimization are hard problem signal processing. Tang et al. [133] presented a brief summariza- in circuit system. Several EC based methods have been pro- tion of EC based methods in signal processing. Firstly, they dis- posed for power electronic circuit optimization, combinational cussed two traditional optimization techniques including calculus- logic circuits, and digital filter design by Chinese scholars. based optimization techniques and dynamic programming and Zhang et al. studied an asynchronous migration scheme by presented their shortcomings. Afterward, the basic framework of pseudo coevolutionary genetic algorithm for power electronic genetic algorithm was described in detail, including encoding circuit optimization [128]. Component values of power con- scheme, fitness techniques, genetic operation, and scheme theory. version stage and feedback network were optimized by two Then, applications in signal processing were presented, such as coadapted evolutionary training processes. An illustrative IIR adaptive filtering, nonlinear model selection, time-delay example showed that the optimized values gave a higher estimation, active noise control, and speech processing. fitness value because of the interaction between the parallel Tan and Wang proposed a novel EC and neural network conversion stage and feedback network. based method for blindly separating unobservable independent Cheang et al. developed a combinational logic circuit source signals from their nonlinear mixtures [134]. A param- learning system, named genetic parallel programming logic eterized neural network was employed to model the demixing circuit synthesizer [129]. A variable length parallel program system and the statistical dependence of the output signals structure was employed to represent combinational circuit. were measured by higher order statistic based cost functions. Two stages were divided in the program. The first stage aimed Importantly, genetic algorithm was employed to minimize the at finding 100% functional program, while in the second stage, highly complicated cost function. the method used another set of genetic operators guiding by a Tang et al. utilized a parallel on-line genetic structure to fitness function to improve the qualities of correct programs. solve time-variant delay problem [135]. Time delay estimation The method was performed on two- and four-input lookup- is present in signal processing applications, including sonar, table-based combinational logic circuits. radar, electronic circuit design and so on. In this paper, on-line In [130,131], a hybrid Taguchi genetic algorithm and time-delay estimation problem was viewed as a finite impulse Taguchi immune algorithm were introduced to solve optimal response (FIR) filter and a new genetic algorithm was digital infinite-impulse response filters design. The Taguchi employed to optimize the coefficients of the filters.

Please cite this article in press as: M. Gong, et al., Evolutionary computation in China: A literature survey, CAAI Transactions on Intelligence Technology (2016), http://dx.doi.org/10.1016/j.trit.2016.11.002 + MODEL 16 M. Gong et al. / CAAI Transactions on Intelligence Technology xx (2016) 1e21

There are lots of applications in signal processing, while CARP and a novel algorithm D-MAENS were integrated few works have focused on signal processing. In the future, it into the proposed framework. The superiority of D-MAENS is foreseen that more EAs will be launched for signal pro- was validated by comparison with LMOGA and NSGA-II. cessing applications. Mei et al. [141] proposed a new MA for solving PCARP. A new solution representation scheme and a novel crossover 4.12. EC based methods for control system design operator were used in their paper, and a Route-Merging (RM) procedure was devised and embedded in the algorithm. The Control system design has been widely viewed as con- experiment results showed that the proposed MARM could strained optimization problems, therefore, EC could be obtain better solutions than the existing meta-heuristic ap- employed for design and optimize the control system. Several proaches in much less time. EC based methods have introduced for this problem. Wang et al. [142] proposed an estimation of distribution Tang et al. proposed a structured genetic algorithm for algorithm (EDA) with stochastic local search (SLS) to tackle robust H∞ control system design [136]. H∞ optimization is a this problem. The proposed method integrated an EDA with a type of effective method for control system design and several two phase SLS procedure to minimize the maximal total cost. development has been the use of method to design robust Experiment results showed that the proposed method out- control system. One such method was the loop-shaping design performed existing state-of-art algorithms. procedure (LSDP). In [132], the proposed algorithm is Previous works dealt with capacitated arc routing problems developed to optimize simultaneously over the structures and of different scenes. In reality, uncertainties will occur. It is coefficients of the weighting functions in LSDP. Besides, a more important and interesting to take uncertainties into ac- multiple objective ranking approach was introduced for count and solve these problems by EC-based methods. achieving the design criteria of extreme plants. Ho and Chou proposed a direct computational algorithm for 4.14. EC based methods for social networks analysis solving the Takagi-Sugeno (TS) fuzzy-model-based feedback and mining dynamic equations [137]. Orthogonal functions were used for expressing the state variables by use of its elegant operational Social networks analysis problems are formulated as opti- properties. A novel algebraic computational algorithm with mization problem. These problems are always NP-hard prob- two terms of expansion coefficients for solving the TS fuzzy lem. Lots of EC based algorithms are adopted for networks control system was proposed in this study. Then, the intro- analysis and mining, such as network community detection duced computational algorithm was integrated with the hybrid [143e149], network structure balance [150,151], network in- Taguchi-genetic algorithm for quadratic optimal PDC and fluence maximum [152,153] and gene regulatory network non-PDC controller design. reconstruction [154]. Lau and Wong introduced an immunity based distributed In [143e145], single objective evolutionary algorithms or multi-agent control framework [138,139]. The framework tried swarm optimization algorithms were introduced to discover to supply an integrated solution to control and coordinate com- network community. Gong et al. proposed a novel memetic al- plex distributed systems with large number of autonomous gorithm to discover communities in networks [143]. The pro- agents. The actions of different agents in a dynamic environment posed algorithm, which is a synergy of a genetic algorithm with a were defined and allowed them to cooperate strategically by hill-climbing strategy as the local search procedure, is used to simulating the ability of immune system to fight against antigens optimize modularity density. Two-way crossover and neighbors- with different immune responses. Memory scheme of agents based mutation operations based on network structure are used to consisted of long-term and short-term memories. Long-term explore the search space. Experiments on computer-generated memory stored information for completing all the tasks in the and real-world networks show the effectiveness and the multi- workplace, and the short-term one stored data for temporary use. resolution ability of the proposed method. In [144], a multi- level learning based memetic algorithm was proposed for com- 4.13. EC based methods for capacitated arc routing munity detection. The proposed algorithm combines genetic problems algorithm and multi-level learning strategies to optimize modularity. The multi-level learning strategies are designed The capacitated arc routing problem (CARP) is a chal- based on the knowledge of the node, community and partition lenging combinatorial optimization problem. CARP is with structures of networks, respectively. Extensive experiments many real-world applications, e.g., salting route optimization demonstrated that the proposed algorithm could detect com- and fleet management. Several evolutionary algorithms have munity in large scale networks. A greedy discrete particle swarm been proposed to solve CARP in China. optimization was proposed in [145] for community detection in Mei et al. [140] proposed a decomposition-based MA with large-scale networks. In the proposed algorithm, the particle extended neighborhood search (D-MAENS) for solving MO- statuses are redefined in discrete form. The status updating rules CARP. In their paper, a MO-CARP that considers mini- are reconsidered and consider a greedy strategy. mizing the total cost and the makespan as two objectives was In [146e149], community detection was formulated as investigated. Then they proposed a decomposition-based multi-objective optimization problem and solved by multi- framework. After that, a competitive algorithm for SO- objective evolutionary algorithms. In [146], multiobjective

Please cite this article in press as: M. Gong, et al., Evolutionary computation in China: A literature survey, CAAI Transactions on Intelligence Technology (2016), http://dx.doi.org/10.1016/j.trit.2016.11.002 + MODEL M. Gong et al. / CAAI Transactions on Intelligence Technology xx (2016) 1e21 17 evolutionary algorithm based on decomposition was employed. the algorithm, four genetic operators, namely the neighborhood Two-point crossover and neighbor-based mutation are designed competition operator, the neighborhood orthogonal crossover based on the network structure. The proposed algorithm can operator, the mutation operator, and the self-learning operator are divide the network into communities at different hierarchical used to explore the evolutionary process. Experimental results levels. Shi et al. introduced a multi-objective evolutionary al- demonstrated that the proposed algorithm can proficiently handle gorithm for community detection [147]. This algorithm is the large search space of reconstructing gene regulatory networks. designed based on PESA-II. The uniform two-point crossover Lots of EC-based methods for network analysis and mining and neighbor-based mutation are also adopted. Shi et al. also have been proposed in the past decades. Previous works proposed two model selection methods to select solutions on focused on theory analysis and may not be suitable for prac- pareto front. Gong et al. [148] introduced a multiobjective tical applications, for networks in real worlds are in large scale discrete particle swarm optimization algorithm for community and dynamic. It is more useful if EC-based methods are used detection. The proposed algorithm first decomposes our mul- for large scale networks or dynamic networks. tiobjective network community detection into a number of scalar problems, and then it optimizes them simultaneously 4.15. EC based methods for evolutionary arts using a newly proposed discrete PSO framework. The proposed algorithm also was extended to detect communities in signed The goal of evolutionary arts is to investigate computational networks. Liu et al. adopted multiobjective evolutionary algo- methods which can make applicable aesthetic decisions as rithm to detect communities in signed networks [149].Two humans can. Judging beauty is a highly subjective task, but contradictory objective functions were designed for community certain features are considered important in aesthetic judgment. detection in signed networks. A direct and indirect combined Chinese researchers have done many works on evolutionary arts. representation was used, and this algorithm can detect both Li et al. introduced an adaptive learning evaluation model to separated and overlapping communities from signed social guide the evolutionary process [155]. The model selected the networks based on the proposed representation. certain aesthetic features from internal evolutionary images and Ma et al. proposed a novel memetic algorithm to compute real world paintings. Compared with multi-layer perceptron and and transform structural balance in signed networks [150].A C4.5 decision tree, the results showed that the adaptive model general energy function is designed to compute the structural was efficient at predicting user's preference. balance of signed networks both in strong and weak definitions. Li et al. introduced an adaptive model to learn aesthetic This energy function can evaluate the transformation cost in the judgments in the task of interactive evolutionary art [156]. They transformation of positive and negative edges. To solve this then reduced features to a relevant subset using feature selection, problem, a multilevel learning based memetic algorithm, which and extracted the features from previous interactions by building incorporates network-specific knowledge such as the neigh- the model. An evolutionary art system was built by adopting this borhoods of node, cluster and partition, was proposed. Exper- model to test the efficacy of the approach. The results showed imental results showed that this method can resolve the that the use of the learning model in evolutionary art systems was potential conflicts of signed networks with the minimum cost. sound and promising for predicting users' preferences. Cai et al. [151] introduced a two-step algorithm to compute In the future, more external images are needed to explore structural balance in signed networks. In the first step, the stylistic changing. Different features are needed to help us to network is divided into several communities by multiobjective understand the aesthetic criteria. evolutionary algorithm. In the second step, energy function is adopted to select the best results on the pareto front. 4.16. EC based methods for other real applications Wang et al. devised a set-based coding genetic algorithm for influence maximum problem in network analysis [152].In Except for applications above, EC-based methods were the set-based coding genetic algorithm, the chromosome is used for other real-world applications by researchers in China. coded as a set and genetic operators are redesigned based on Gong et al. proposed a novel particle swarm optimization the set operators. The convergence of this algorithm is studied (PSO) for resource allocation problems [157]. To solve resource through schema analysis and Markov chain analysis. Gong allocation problems (RAPs) effectively, a novel representation et al. proposed a novel memetic algorithm for influence of each particle in the population and a comprehensive learning maximization in social networks [153]. The algorithm consists strategy for the PSO search process were designed. of three steps. Firstly, the network is divided into several Hu et al. proposed a hybrid approach by combining a ge- communities by community detection algorithm. Secondly, netic algorithm and schedule transition operations (STHGA) candidate seeds are selected based on the community struc- [158]. The proposed algorithm aimed to find the maximum ture. Finally, the ultimate seeds are selected by memetic al- number of disjoint complete cover sets of sensors, in order to gorithm. Experimental results showed that the proposed maximize the lifetime of wireless sensor networks. A forward memetic algorithm could speed up the convergence and find encoding scheme for chromosomes in the population and some the promising solutions in a low running time. effective genetic and sensor schedule transition operations Liu et al. [154] proposed a dynamic multiagent genetic algo- were designed in STHGA. rithm to reconstruct large-scale gene regulatory networks from Wang et al. introduced a new convex hull-based multi- time-series expression profiles based on fuzzy cognitive maps. In objective genetic programming (CH-MOGP) to maximize

Please cite this article in press as: M. Gong, et al., Evolutionary computation in China: A literature survey, CAAI Transactions on Intelligence Technology (2016), http://dx.doi.org/10.1016/j.trit.2016.11.002 + MODEL 18 M. Gong et al. / CAAI Transactions on Intelligence Technology xx (2016) 1e21 receiver operating characteristic problem [159]. In CH-MOGP, objective optimization, many-objective optimization, con- two novel convex hull-based strategies, namely CWR-sorting strained optimization, and dynamic optimization. However, and area-based contribution indicator were introduced. Popu- the research results in EC-based data mining obtained by lation was parted into several rank levels by CWR-sorting and Chinese research were less. The real-world applications of EC the area-based contribution indicator was used to select the were also widely studied in China. In a word, Chinese re- survivors in the same level. searchers are more and more active in EC field. Duan et al. proposed a hybrid particle swarm optimization and genetic algorithm (HPSOGA) for the multi-UAV forma- Acknowledgements tion reconfiguration problem [160]. The multi-UAV formation reconfiguration problem was formulated as an optimal control This work was supported by the National Natural Science problem with dynamical and algebraic constraints. HPSOGA Foundation of China (Grant nos. 61273317, 61422209, could find time-optimal solutions simultaneously. 61473215), the National Program for Support of Top-notch Zuo and Gong et al. proposed a novel multiobjective Young Professionals of China, and the Specialized Research evolutionary algorithm for recommendation [161]. The pro- Fund for the Doctoral Program of Higher Education (Grant no. posed multiobjective evolutionary algorithm was used to 20130203110011). optimize two objectives of recommendation: accuracy and diversity. The proposed algorithm could return a set of References different recommendations for users. 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[17] Yang Yu, Chao Qian, Running time analysis: convergence-based anal- We have attempted to summarize the main contributions of ysis reduces to switch analysis, in: 2015 IEEE Congress on Evolu- EC performed by Chinese researchers. However, due to the tionary Computation (CEC), IEEE, 2015, pp. 2603e2610. limitation of our knowledge, some important work in EC in [18] Chao Qian, Yang Yu, Zhi-Hua Zhou, Sci. China Inf. Sci. 58 (11) (2015) China may be not covered in this review. Therefore, this is 1e17. may be not a comprehensive review. From the articles that we [19] Tianshi Chen, Ke Tang, Guoliang Chen, Xin Yao, On the analysis of average time complexity of estimation of distribution algorithm, in: have summarized, it can be found that the theoretical foun- IEEE Congress on Evolutionary Computation (CEC, 2007, pp. 453e460. dation performed by Chinese researchers was significant to [20] Tianshi Chen, Ke Tang, Guoliang Chen, Xin Yao, IEEE Trans. Evol. advancement of basic theory of EC. 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[149] Chenlong Liu, Jing Liu, Zhongzhou Jiang, IEEE Trans. Cybern. 44 (12) Shanfeng Wang received the B.S. degree in elec- e (2014) 2274 2287. tronic and information engineering from Xidian [150] Lijia Ma, Maoguo Gong, et al., Knowledge-Based Syst. 85 (2015) University, Xi'an, China, in 2012. Now he is working e 196 209. towards the Ph.D. degree in Pattern Recognition and [151] Qing Cai, Maoguo Gong, et al., IEEE Trans. Evol. Comput. 19 (6) Intelligent Systems at the School of Electronic En- e (2015) 903 916. gineering, Xidian University, Xi'an, China. His cur- [152] Cheng Wang, Lili Deng, Gengui Zhou, Meixian Jiang, Inf. Sci. 267 rent research interests are in the area of computational e (2014) 101 118. intelligence, complex network analysis and recom- [153] Maoguo Gong, Chao Song, Chao Duan, Lijia Ma, Bo Shen, IEEE mender systems. Comput. Intell. Mag. 11 (3) (2016) 22e33. [154] Jing Liu, Yaxiong Chi, Chen Zhu, IEEE Trans. Fuzzy Syst. 24 (2) (2016) 419e431. [155] Yang Li, Adaptive learning evaluation model for evolutionary art, in: 2012 IEEE Congress on Evolutionary Computation, IEEE, 2012, pp. Wenfeng Liu received the B.S. degree in intelligence e 1 8. science and technology from Xidian University, Xi'an, [156] Yang Li, Changjun Hu, Leandro L. Minku, Haolei Zuo, Genet. Pro- China, in 2015. Now he is working towards the Ph.D. e gram. Evolvable Mach. 14 (3) (2013) 315 337. degree in Pattern Recognition and Intelligent Systems [157] Yue-Jiao Gong, Jun Zhang, Henry Shu-Hung Chung, Wei-Neng Chen, at the School of Electronic Engineering, Xidian Uni- Zhi-Hui Zhan, Yun Li, Yu-Hui Shi, IEEE Trans. Evol. Comput. 16 (6) versity, Xi'an, China. His current research interests e (2012) 801 816. include computational intelligence and network [158] Xiao-Min Hu, Jun Zhang, Yan Yu, Henry Shu-Hung Chung, Yuan- robustness analysis. Long Li, Yu-Hui Shi, Xiao-Nan Luo, IEEE Trans. Evol. Comput. 14 (5) (2010) 766e781. [159] Pu Wang, Michael Emmerich, Rui Li, Ke Tang, Thomas Back, Xin Yao, IEEE Trans. Evol. Comput. 19 (2) (2015) 188e200. [160] Haibin Duan, Qinan Luo, Yuhui Shi, Guanjun Ma, IEEE Comput. Intell. e Mag. 8 (3) (2013) 16 27. Jianan Yan received the B.S. degree in intelligence [161] Yi Zuo, Maoguo Gong, Jiulin Zeng, Lijia Ma, Licheng Jiao, IEEE science and technology from Xidian University, Xi'an, e Comput. Intell. Mag. 10 (1) (2015) 52 62. China, in 2015, where he is currently pursuing the [162] Xingsi Xue, Yuping Wang, IEEE Trans. Knowl. Data Eng. 28 (2) (2016) M.S. degree. His current research interests include e 580 591. computational intelligence and complex network e [163] Tao Gong, Zixing Cai, J. Intell. Robot. Syst. 51 (2) (2008) 187 201. analysis. [164] Fei Ding, Yun Liu, Bo Shen, Xia-Meng Si, Phys. A Stat. Mech. Appl. 389 (8) (2010) 1745e1752.

Maoguo Gong received the B.S. degree in electronic engineering (first class honors) and the Ph.D. degree in electronic science and technology from Xidian Licheng Jiao received the B.S. degree from Shanghai University, Xi'an, China, in 2003 and 2009, respec- Jiaotong University, Shanghai, China, in 1982, the tively. Since 2006, he has been a Teacher with M.S. and Ph.D. degrees from Xi'an Jiaotong Univer- Xidian University. In 2008 and 2010, he was pro- sity, Xi'an, China, in 1984 and 1990, respectively. moted as an Associate Professor and as a Full Pro- Since 1992, Dr. Jiao has been a Professor in the School fessor, respectively, both with exceptive admission. of Electronic Engineering at Xidian University, Xi'an, His research interests are in the area of computa- China. His research interests include image process- tional intelligence with applications to optimization, ing, natural computation, machine learning, and learning, data mining and image understanding. Dr. intelligent information processing. Gong received the prestigious National Program for the support of Top- Notch Young Professionals from the Central Organization Department of China, the Excellent Young Scientist Foundation from the National Natural Science Foundation of China, and the New Century Excellent Talent in Uni- versity from the Ministry of Education of China. He is the Vice Chair of the IEEE Computational Intelligence Society Task Force on Memetic Computing, an Executive Committee Member of the Chinese Association for Artificial Intelligence, and a Senior Member of the Chinese Computer Federation. Please see his homepage (http://see.xidian.edu.cn/faculty/ mggong) for more information.

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