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

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

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.

Evolutionary computation;Evolutionary algorithms;Optimization;Data mining

1.Introduction

Evolutionary computation(EC)uses computational models of evolutionary processes as key elements in the design and implementation of computer-based problem solving systems [1].It has become an important part of computational intelligence.EC has received significant attention in China during the last two decades.Professor Guoliang Chen of the University of Science and Technology of China published the first Chinese book on EC in 1996[2].This book played an important role in introducing EC to Chinese researchers. Professor Lishan Kang,Zongben Xu,Xin Yao,Licheng Jiao, Zixing Cai,Jun Zhang,Zhi-Hua Zhou,Ling Wang,Jinhua Zheng,Dunwei Gong,Yongsheng Ding,Yuhui Shi,Ying Tan, Yuping Wang,Haibin Duan and their collaborators and successors paid attention to EC field one after the other.They have published a lot of papers and books related to EC. Among them,the papers published in international journals and conferences can be obtained all over the world.Chinese can read papers in English easily for English is the most popular language in the world,but the papers written in Chinese are difficult to be recognized by non-Chinese speakers.According to our statistic,a large number of books on EC have been published in Chinese.For example,Guoliang Chen and his collaborator published a book focused on genetic algorithm in 1996[2];Haibin Duan published a book focused on ant colony Algorithms[3];Licheng Jiao et al.published a book focus on immunological computation[4];Jinhua Zheng published a book focus on evolutionary multi-objective optimization[5];Yuping Wang published a book focus on evolutionary algorithm[6];Yaonan Wang et al.published a book focus on dynamical dynamic differential evolution algorithm[7];Ying Tan published a book on the fireworks algorithm[8].The EC papers published in Chinese Journals and conferences are also massive.Most of them focus on modifying existing EC algorithms or combining different algorithms to solve specifically problems.In recent years,more and more Chinese researchers prefer to publish their approving works in international Journals,such as IEEE Transactions on Evolutionary Computation,Evolutionary Computation Journal,IEEE Transaction on System,Man and Cybernetics series, 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 these journals,which will be summarized in detail in the following sections.Furthermore,some international events related to EC,such as the International Workshop series onNature Inspired Computation and Applications since 2004,the annual International Conference on Natural Computation since 2005,the annual International Conference on Computational Intelligence and Security since 2005,the 2008 and 2014 IEEE world congress on computational intelligence(WCCI),and the Annual Workshop on Evolutionary Computation and Learning (ECOLE)since 2014,to list only a few,were held in China. All of these show that Chinese researchers are more and more active in EC field.

In this paper,we will summarize the main contributions of Chinese researchers in EC field.From 1995,lots of Chinese researchers have focused on evolutionary algorithms and have published a great number of papers about evolutionary algorithms.In this paper,we select classic works that are well known or published in top journals or conferences,such as IEEE Transactions on Evolutionary Computation,Evolutionary Computation,IEEE Computational Intelligence Magazine and IEEE Congress on Evolutionary Computation and so on.All selected papers are written in English.

The remainder of this paper is organized as follows:Section 2 summarizes the theoretical foundation research, including time complexity analysis,convergence and diversity analysis.Section 3 summarizes the research results in evolutionary optimization,including global optimization,multiobjective optimization,many-objective optimization,constrained optimization and dynamic optimization.Section 4 describes the EC-based real-world applications.Finally, concluding remarks are presented.

2.Theoretical foundation research

2.1.Time complexity analysis

In EC,time complexity analysis and convergence analysis are considered to be two important issues in the basic theoretical analysis.However,convergence describes the behaviors atlimitpoints of evolutionary algorithms(EAs).If an EA with convergence property has tremendous time complexity,it is useless for application.Therefore,it is important to develop a systematic theoretical tool invesztigating into the computational time or time complexity of EAs.

He and Yao introduced drift analysis in estimating average computational time of EAs[9].In their paper,one-step mean drift at thet-th generation was defined and it could be classified into positive and negative drift,where the positive drift is the rate of the gain of a population towards the optimum and the negative drift is that away from the optimum.The authors analyzed a(1+1)EA on a linear function and a(N+N)EA on One-Max function.The upper bound of the mean first hitting times of EAs were presented.Besides,by drift analysis, they divided optimization problems into two classes(easy and hard)based on the mean number of generations needed to solve the problems.By their analysis,we could obtain that drift analysis is a useful tool in estimating the computational time of EAs.Drift analysis reduces the behavior of EAs in a higher-dimensional population space into one-dimensional space.Therefore,it is much easier than analysis of the original Markov chain to analyze the one dimension random walk.However,this approach requires a distance function which does not naturally exist in EAs.

He and Yao described a general analytic framework for analyzing first hitting times(FHTs)of EAs[10].The FHT of EAs is the time that EAs find the optimal solution for the first time,while the expected first hitting time(expected FHT)is the average time that EAs require to find the optimal solution, which implies the average computational time complexity of EAs.The general framework they gave was based on a linear equation and its bounds of the FHT of an EA's Markov chain model.Under this framework,conditions under which an EA will need polynomial(or exponential)mean computational time to solve a problem were studied.A number of case studies were given to illustrate how different results can be established by verifying these conditions.They proved that hard problems to a simple(1+1)EA can be classified into two classes:“wide gap”problems and“long path”problems. In addition to(1+1)EAs,EAs with population size greater than 2 and EAs with and without crossover were also studied in their paper.However,since the analytical form was derived from homogeneous Markov chain models,only EAs with stationary reproduction operators could be analyzed,although EAs with time-variant operators or adaptive operators are very popular and powerful.

He and Yao also compared(1+1)EAs and(N+N)EAs theoretically by deriving their FHT on some problems[11].In their paper,by rigorous theoretical analysis,they concluded that a population may bring benefits to an EA in terms of lower time complexity,higher first hitting probabilities,and shorter FHT.It was also shown that a population-based EA may take only average polynomial time to solve a problem that would take a(1+1)EA average exponential time to solve,given the same mutation operator in both algorithms.

He and Yao[12]analyzed the time complexity of EAs based on the maximum cardinality matching in a graph,which is a famous combinatorial optimization problem.They proved that the EA can find a matching with the early maximum cardinality in polynomial time.This was noteworthy as it was the first time complexity results on classical combinational optimization problems.

Zhou and He presented a time complexity analysis of EAs for solving constrained optimization[13].The mean runtimes of the penalty function(1+1)EAs with local mutation and global mutation for two simple knapsack problems were analyzed respectively.In their paper,they concluded that EAs have benefited greatly from higher penalty coefficients in some examples,while in other examples,EAs benefit from lower penalty coefficients.The systematical analysis of the role of penalty coefficients in constrained optimization is original and beneficial for designing constraint optimization algorithms.However,we still can not predict how to choose penalty coefficients for various problems.

Yu and Zhou also established a bridge between the convergence rate and the expected FHT of EAs[14].In their paper,non-homogeneous Markov chain model was employed and the expected FHT was derived from the convergence rateof EAs.A pair of general upper and lower bounds of the expected FHT were deduced.

For constrained optimization,Yu and Zhou[15]analyzed whether infeasible solutions are helpful or not in the evolutionary search and theoretically deduced that under what conditions infeasible solutions were beneficial.More importantly,a sufficient condition and a necessary condition of an EA will reach the optimal solution faster and infeasible individuals being included were derived and discussed.Finally, two problems were employed to judge whether exploiting infeasible solutions is helpful or not.The up and low boundaries of expected FHT of the two problems were deduced.By this paper,we can find that infeasible solutions play an important role for some problem in constrained optimization, and by exploiting infeasible solutions in the search process,an EA-Hard problem can be transformed to be EA-Easy and the reverse.

Yu et al.[16]developed a switch analysis approach for running time analysis of evolutionary algorithms.The proposed switch analysis made use of another well analyzed algorithm and can lead to better results by contrasting them.In their paper,they defined the reducibility relationship to investigate the relationship between general analysis approaches for EAs.The results showed the superior of switch analysis for running time analysis of EAs.

Yu etal.[17]further proved that another running time analysis approach,convergence-based analysis,is reducible to switch analysis.They also showed in a case study thats witch analysis leads to a tighter result than convergence-based analysis.

Qian et al.[18]presented a running time analysis on genetic programming(GPs).The theoretical results on two classical combinatorial problems theoretically supported the usefulness of rich representations in evolutionary optimization.From the analysis,the authors also found the variable solution structure might be helpful for evolutionary optimization when the solution complexity can be well controlled.

Chen et al.[19]analyzed the mean FHTs of two early versions of Estimation of distribution algorithm(EDA),Univariate Marginal Distribution Algorithm(UMDA)and the Incremental UMDA(IUMDA).They generalized the concept of convergence to convergence time,and managed to estimate the upper bound of the mean FHTs of UMDA and IUMDA on LEADINGONES function.An EA on a problem converging to the global optimum only implies that the EA can find the global optimum.It does not mean that the EA always converges to the global optimum.Convergence could not measure the time complexity of almost all the EAs,while FHT could denote the time complexity of EAs.In principle,the convergence time is almost larger than FHT(for(1+1)EAs,they are equivalent).In their paper,they have obtained the upper bounds of the mean convergence times of UMDA and IUMDA on LEADINGONES function.The upper bounds are all linear functions of the problem size if the relation between population sizes and problem size is omitted.

Chen et al.[20]studied the FHT of a simple Estimation of distribution algorithm(EDA),called the univariate marginal distribution algorithm(UMDA).The authors utilized the FHT to measure the time complexity of EDAs.Based on the FHT measure,they proved a theorem related to problem hardness and the probability conditions of EDAs.After that,they proposed a novel approach to analyzing the FHT of UMDA using discrete dynamic systems and Chernoff bounds.In their paper, UMDAs were analyzed in depth on two problems:LEADINGONES and BVLEADINGONES.The experiment analysis showed that LEADINGONES is easy for the UMDA,and they proved theoretically that the UMDA with margins can solve the BVLEADINGONES efficiently.

The publications above represented a systematic comparative study of time complexity analysis among different EAs on different problems by their FHTs model.These contributions were significant to advancement of basic theory of EC.

2.2.Convergence and diversity analysis

In the EC community,premature convergence is an important issue and open problem.Roughly speaking,premature convergence occurs when the population in an EA reaches such a suboptimal state that most of the evolutionary operators can no longer produce offspring that outperform their parents.Several methods have been proposed to prevent premature convergence.Leung et al.[21]proposed a concept of a degree of population diversity and quantitatively characterize and theoretically analyze the problem of premature convergence in GA using the theory of Markov chains.In their paper,the degree of population diversity converged to zero with probability one with zero mutation probability.The relationships between premature convergence and the GA parameters such as population size,mutation probability,and relevant population statistics were also studied.

Leung etal.proposed a new simulated evolutionary computation model called the abstract evolutionary algorithm(AEA) [22].In their minds,the simulated evolutionary algorithms include genetic algorithms(GAs),evolutionary programming (EP),and evolution strategies(ESs).These algorithms simulate the principle of evolution,and maintain a population of potential solutions through repeated application of some evolutionary operators.The proposed AEA unified most of the currently known EAs and described the evolution as an abstract stochastic process composed of two fundamental operators:selection and evolutionary operators.Besides,the selection pressure,selection intensity,evolution aggregating rate,evolution scattering rate, and evolution stability rate were defined,which were used to quantitatively measure their functions and properties.By the model,we can geta novel convergence analysis and convergence rate estimation method,which is not based on the usual ergodicity analysis,and could be regarded as a nonergodicity approach, which is important both from the viewpoint of theoretical significance and from the perspective of parallel computation. However,the AEA model requires essentially a certain kind of full connectivity,which is an implicit limitation of their model.

Duan and Shi et al.developed a theoretical framework based on Markov chains to model the brain storm optimization algorithm[23].The creation of discrete Markov chain models approximated the behavior of a BSO.The theoreticalprobability of the occurrence of each possible population was given as the number of generation count goes to infinity.The convergence of the BSO was proved by Markov models.

Zheng et al.presented a theory analysis for fireworks algorithm[24].Fireworks algorithm was proved as an absorbing Markov stochastic process.The defined Markov stochastic process was used to discuss the global convergence and time complexity of fireworks algorithm.

3.Evolutionary optimization research

In this section,we summarize the main contributions of Chinese researchers in evolutionary optimization,including global optimization,multi-objective optimization,manyobjective optimization,constrained optimization,and dynamic optimization.

3.1.Global optimization

Global optimization,arising in many fields of science,engineering,and business,is widely used in EC field for testing the performance of EAs.In China,several EC researchers proposed their EC-based global optimization methods [25-44].

Jiao and Wang proposed an improved genetic algorithm based on immunity(IGA)[25].In their paper,the idea of immunity was mainly realized through two steps based on reasonably selecting vaccines(i.e.,a vaccination and an immune selection),of which the former was used for raising fitness and the latter was for preventing the deterioration.For vaccination,it meant modifying the genes on some bits in accordance with priori knowledge so as to gain higher fitness with greater probability.For immune selection,itwas based on an immune testand annealing selection.IGAwas validated by Traveling Salesman Problem(TSP)and function optimization. The results showed that IGA was not only feasible but also effective and was conducive to alleviating the premature convergence in the original GA.

Leung and Wang proposed an orthogonal genetic algorithm with quantization for global numerical optimization with continuous variables[26].In this paper,the orthogonal array specified a number of a small number of combinations that were scattered uniformly over the space of all possible combinations, and then,the orthogonal array was sampled evenly to generate an evenly distributed population.The former orthogonal design was applicable to discrete factors only.To overcome this issue,each variable of solutions were quantized into a finite number of values.With respect to orthogonal crossover,it acted on two parents.It quantized the solutions space defined these parents into a finite number of points,and applied orthogonal design to select a small and representative sample of solutions as the potential offspring.Finally,the proposed algorithm was validated based on 15 benchmark problems with 30 or 100 dimensions. The results showed that the proposed algorithm could find optimal or close-to-optimal solutions on all the test problems.

Zhong et al.[27]proposed a novel multiagent genetic algorithm(MAGA)to solve global numerical optimization.In MAGA,an agent,a,represents a candidate solution to the optimization problem in hand,and the value of its energy is equal to the negative value of the objective function,i.e.,a∈S, Energy(a)=-f(a).The purpose is to increase its energy asmuch as possible.Each agent carries all variables of the objective function to be optimized.In order to realize the local perceptivity of agents,the environment is organized as a lattice like structure. The authors thought that the real natural selection only occurs in a local environment,and each individual can only interact with those around it.That is,in some phase,the natural evolution is just a kind of local phenomenon.Therefore,each agent devised by them can only sense its local environment,its behaviors of competition and cooperation can only take place between the agent and its neighbors.There is no globals election at all,so the global fitness distribution is not required.An agent interacts with its neighbors so that information is transferred to them.In addition to the aforementioned behaviors of competition and cooperation, each agent can also increase its energy by using its knowledge.On the basis of such behaviors,four evolutionary operators are designed for the agents.The neighborhood competition operator and the neighborhood orthogonal crossover operator realize the behaviors of competition and cooperation,respectively.The mutation operator and the self-learning operator realize the behaviors of making use of knowledge.In[18],MAGA was applied to solve ten benchmark functions and the scalability with respect to dimension was also investigated.It is noteworthy that,when the dimensions are increased to as high as 10,000,MAGA still can find high quality solutions at a low computational cost.

Liu et al.proposed a novel organizational evolutionary algorithm(OEA)and applied it into global numerical optimization [28].In the real-world situation,to achieve their purposes,organizations will compete or cooperate with others so that they can gain more resources.As a result,the resources will be reasonably distributed among all organizations little by little. This process plays an importantrole in human societies,and can be viewed as a kind of optimization.In OEA,organizations are composed of members,and a population is composed of organizations,so thata structured population results.On the basis of such a structured population,all evolutionary operations are performed on organizations,and three evolutionary operatorsare developed for organizations,which are Splitting operator, Annexing operator,and Cooperating operator.An organization interacts with others so that the information can be diffused. Obviously,such a kind of population is more similar to the real evolutionary mechanism in nature than the traditional population.Experimental results illustrate that the OEA has an effective searching mechanism for global numerical optimization.

Wang and Dang proposed level-set evolution(LEA)and Latin square design for global optimization[29].LEA was based on the mean-value-level-set method(M-L method). Besides,since Latin-square design is one of the uniform design methods,which can generate points uniformly scattered in a domain,Latin-square was introduced to generate the initial population.Numerical experiments were performed for 20 standard test functions.The highest dimension of these test problems is 100 and some of them have many local minima. The performance of the proposed algorithm was comparedwith thatof eight EAs and the Monte Carlo implementation of M-L methods.The results indicate that LEA could find optimal or close-to-optimal solutions,and it was more competitive than almost all of the compared algorithms for these test problems.

Yang et al.proposed a cooperative coevolution framework [30]for large scale optimization problems.A random grouping scheme and adaptive weighting were introduced in problem decomposition and coevolution.The authors adopted a variant of DE,SaNSDE,which combine a neighbor search mechanism and self-adaptability of crossover rate and scaling factor.Combined with SaNSDE,they presented a novel cooperative coevolution optimization algorithm,called DECC-G.Theoretical analysis showed that the new framework can be effective for optimizing large nonseparable problems.Extensive computational studies were carried out to evaluate the performance of DECC-G on a large number of benchmark functions with up to 1000 dimensions.The results showed that the new framework and algorithm were effective and efficient for large scale optimization problems.

Jiao et al.proposed a novel immune clonal algorithm, called a quantum-inspired immune clonal algorithm(QICA) [31],which was based on merging quantum computing and clonal selection theory.There were three innovation points listed as follows.Firstly,antibody was proliferated and divided into a set of subpopulation groups.Antibodies in a subpopulation group were represented by multi-state gene quantum bits.The quantum bit representation had the advantage that it can represent a linear superposition of states(classical solutions)in search space probabilistically.Thus,the quantum bit representation had a better characteristic of population diversity than other representations.Secondly,in the antibody's updating,the general quantum rotation gate strategy and dynamic adjusting angle mechanism were applied to accelerate convergence.Quantum NOT gate was used to realize quantum mutation to avoid premature convergence.Each subpopulation group evolved independently and enlarged the search space. Thirdly,the proposed quantum recombination operator realized the information communication between the subpopulation groups so as to improve the search efficiency.The algorithm was validated by ten unconstrained optimization problems with the dimension of 100,200,and 1000.

Tsai et al.proposed a hybrid Taguchi-genetic algorithm to solve global numerical optimization with continuous variables [32].Taguchi method is an important tool for robust design.The fundamental principal of it is to improve the quality ofa product by minimizing the effect the causes of variation without eliminating them.The Taguchi method was inserted between crossover and mutation operations of traditional GA.The proposed algorithm was effectively applied to solve 15 benchmark problems of global optimization with 30 or 100 dimensions.

Zhang et al.proposed a fuzzy logic controlled scheme to adaptively adjust the probabilities of crossover and mutation [33].K-means algorithm was employ at each iteration to cluster the distribution of the population in the search space. The method was tested on eight global mathematical functions and a buck regular design.

Zhang et al.proposed a cloud model based evolutionary algorithm[34].The excellent traits of the cloud model in expressing and transforming non canonical knowledge were integrated into genetic algorithm.The inheritance and mutation of the population were modeled naturally and uniformly by the cloud model.The scale of them and the scope of search space were easily controlled by the algorithm.Eight global classical functions were used to validate its performance in the experiment.

An intelligent evolutionary algorithm IEAwas proposed by using a novel intelligent gene collector(IGC)[35].IGC was the main phase in an intelligent recombination operator of IEA.Based on orthogonal experimental design,IGC used a divide-and-conquer approach,which consists of adaptively dividing two individuals of parents into pairs of gene segments,economically identifying the potentially better one of two gene segments of each pair,and systematically obtaining a potentially good approximation to the best one of all combinations using at most 2 fitness evaluations.Empirical studies showed that IEA had high performance in solving benchmark functions comprising many parameters,as compared with some existing EAs.The authors also proposed the multiobjective optimization version in the same paper.

Ding et al.introduced a histogram-based estimation of distribution algorithm for continuous optimization[36].Histogram probabilistic model was employed to represent multiple local optima by different bins with different heights. Besides,a surrounding effect and shrinking strategy were proposed and incorporated with histogram probabilistic model.The hybrid estimation of distribution algorithm was validated by Schwefel,Griewank and two-peak functions.

Gong et al.proposed the ranking-based mutation operators for the differential evolution algorithm[37].Individuals were assigned the probabilities according to their rankings,which are measured by the fitness of the individual.Some of the parents in the mutation operators were proportionally selected according to their rankings.Experiments on the benchmark functions and five real-world problems demonstrated the performance of the proposed algorithm.

Gong et al.introduced a multioperator search strategy for evolutionary optimization[38].A cheap surrogate modelbased multioperator search strategy was proposed.In this algorithm,multiple offspring reproduction operators are used to generate a set of candidate offspring solutions,and the best one is chosen according to the surrogate model.30 benchmark functions and 28 functions presented in the CEC 2013 were used to test the performance of the proposed algorithm.

Hu et al.first presented a new way of extending ant colony optimization(ACO)to solving continuous optimization problems[39].An effective sampling method was used to discretize the continuous space and then ACO could be used for continuous optimization.The proposed algorithm consisted of three major steps,i.e.,the generation of candidate variable values for selection,the ants' solution construction, and the pheromone update process.Experiments demonstrated that the proposed algorithm performed better than some state of-the-art algorithms,including traditional ant-basedalgorithms and representative computational intelligence algorithms for continuous optimization.

Chen et al.presented a novel set-based PSO(S-PSO) method for discrete optimization problems[40].The proposed S-PSO is based on a set-based representation scheme and the scheme enabled S-PSO to characterize the discrete search space of combinatorial optimization problems.The candidate solution and velocity were defined as a crisp set,and a set with possibilities,respectively.All related arithmetic operators in the velocity and position updating rules were replaced by the operators and procedures defined on crisp sets and sets with possibilities.Experiments showed that the discrete version of the PSO variants algorithm based on S-PSO was promising.

Zhan et al.proposed an orthogonal learning(OL)strategy for particle swarm optimization[41].The OL strategy constructed a much promising and efficient exemplar,and discovered useful information from a particle's personal best position and its neighborhood's best position.OL could guide particles fl y in better directions.Moreover,the OL strategy can be applied to the global and local versions of PSO,respectively.16 benchmarks including unimodal,multi modal,coor dinaterotated,and shifted functions were used to test the performance of the proposed algorithm.

Chen et al.proposed a novel particle swarm optimization [42].A growing age and a lifespan are assigned to the leader of the swarm.In this way,the leader had a long lifespan to lead the swarm.The lifespan of the leader was adaptively tuned based on the leader's leading power.Once the leader obtained a local optimum,the other individuals will challenge the leadership which can bring in diversity.17 benchmark functions were used to test the performance of the proposed algorithm.

Li et al.proposed an information sharing mechanism(ISM) for particle swarm optimization[43].In the proposed ISM,each particle could share its best search information,so that all the other particles could use the shared information by communicating with each other.A competitive and cooperative(CC) operator was designed in the proposed algorithm for a particle to utilize the shared information properly and efficiently.The proposed algorithm could prevent the premature convergence when solving global optimization problems.16 benchmark functions were chosen to test the performance of the proposed algorithm.

Peng etal.[44]presented a population-based algorithm portfolio(PAP)for solving numerical optimization problems.PAP is easy to implement and can accommodate any existing population based search algorithms.After that,they proposed a pairwise metric to compare the risks associated with two algorithms.The experiment results showed that PAP outperformed its constituent algorithms.Further analysis indicated that PAP was capable of increasing the probability of finding the global optimum and was insensitive to control parameters of the migration scheme.

Li and Tang[45]proposed a history-based topological speciation(HTS)method.In their paper,the proposed HTS is parameter-free and can be integrated into a variety of niching techniques for solving multimodal problems.The experiment results demonstrated that HTS clearly outperforms existing topology-based methods when the fitness evaluations budgetis limited.

Yang et al.[46]proposed a novel multiple sub-models maintenance technique(MAPS)to improve the performance on multimodal problems.The proposed MAPS can explicitly detect the promising areas,which can accelerate the optimization speed.Besides that,MAPS can be combined with any EDA that adopts a single Gaussian model.The experiments results showed that MAPS based EADs outperformed the compared algorithms with a faster optimization speed and more stable solutions on most tested problems.

Tang et al.[47]proposed a new EA,namely negatively correlated search(NCS),to solve multi modal optimization problems.The proposed NCS is featured by its information sharing and cooperation schemes to explore more effectively in the search space.The experiment results indicated the advantages of NCS in comparison to other existing EAs on different problems.

3.2.Multi-objective optimization

In real-world optimization applications,it is often necessary to optimize multiple objectives in a problem at the same time.The simultaneous optimization of multiple objectives is different from single-objective optimization in that there is no unique solution to multi-objective optimization problems (MOPs).Multi-objective optimization involves many conflicting,incomparable and non-commensurable objectives. Therefore,a set of optimal trade off solutions known as the Pareto-optimal solutions should be obtained.During the past two decades,EAs have been obtaining an increasing attention among the multi-objective optimization community mainly because of the fact that they can be suitably applied to deal simultaneously with a set of possible solutions.Chinese researchers have made a very positive contribution to the development of the domain.A number of evolutionary algorithms have been developed by them for multi-objective problems[38,48-59].

Zeng et al.proposed an orthogonal multi-objective evolutionary algorithm(OMOEA)for MOPs with constraints[48]. Firstly,with respect to constraints in MOPs,a strict partial ordered relation was defined to simplify the Pareto dominance.Then,the orthogonal design and the statistical optimal method were generalized to MOPs.In OMOEA,an original niche evolves first,and splits into a group of sub-niches according to the output niche-population of the evolution.Then every sub-niche iterates the above operations so as to enhance the precision of the solutions.Itis noteworthy that,a niche is a hyper-rectangle in the decision space.The main component of the new technique is the niche evolution procedure which consists of quantizing niches into discrete niches and producing an initial niche-population.OMOEA was validated on ZDT1,ZDT2,ZDT3,ZDT4,three problems with linkages among the variables:FON,modified DTLZ3,and W. Compared with SPEA,it performed better results in terms of convergence and diversity.However,as the authors indicated, if the modelis additive and quadratic,itis valid to compute an optimum in the crossover operator.For a general model,fewer nondominated levels may be eliminated from thenondominated level set,and some dominated levels near a nondominated level may exist in the nondominated level set.

Evolutionary multi-objective optimization usually deals with the problems with low number of objectives.Multi-objective problems with four or more objectives are often viewed as many-objective optimization problems.Zou etal.[49]proposed a new evolutionary algorithm for solving the problems of this type.In order to improve the convergence of the traditional multi-objective optimization,thermodynamic based dynamical multi-objective evolutionary algorithmwas studied in this paper. Besides,L-optimality was proposed to provide reasonable solutions for decision making.The algorithm was tested by DTLZ1,DTLZ2 and DTLZ6 with 3-9 objectives.

Jiao et al.proposed an immune dominance clonal multiobjective algorithm(IDCMA)[50]which maintained three different populations of solutions.The firstpopulation denoted as the immune dominance population which is used to store the set of non-dominated solutions with the best immune differential degree.In every generation,the set of recombined antibodies form the second population which is denoted as the generic antibodies population.The rest of the antibodies will constitute the third population known as the immune energy antibodies population.Besides,the authors introduced a new similarity measure between antibodies,based on distances in the objective space:the immune differential degree.Again, this similarity measure was used to reduce the size of the offl ine population in the update step.The algorithm also presented a different selection mechanism for cloning.In this mechanism,one antibody was randomly selected from the first population in the beginning at each generation.The quality value of each individual in the second population was computed based on the antibody-antibody affinity,that was, similarity in the representation of the solutions.

Gong et al.proposed a multi-objective immune algorithm with nondominated neighbor-based selection[51].The new algorithm,Nondominated Neighbor Immune Algorithm(NNIA), consisted of a novel nondominated neighbor-based selection technique,an immune inspired operator,two heuristic search operators,and elitism.The main contribution ofthis algorithm to MO field was its unique selection technique.The selection technique only selected minority isolated nondominated individuals based on their crowding-distance values.The selected individuals were then cloned proportionally to their crowdingdistance values before heuristic search.By using the nondominated neighbor-based selection and proportional cloning, the new algorithm realized the enhanced localsearch in the lesscrowded regions ofthe currenttrade-offfront.Depending on the enhanced localsearch realized by clonal proliferation,hypermuation and recombination,NNIA can solve MOPs with a simple procedure.The experimentalstudy on NNIA,SPEA2,NSGA-II, PESA-IIand MSIA in solving three low-dimensionalproblems, five ZDT problems and five DTLZ problems has shown that NNIAwas able to converge to the true Pareto-optimalfronts in solving most of the test problems.More importantly,for the complicated problems DTLZ1 and DTLZ3,NNIA performed much betterthan the otherfouralgorithms.Besides,with respect to DTLZ1 and DTLZ3,when the number ofobjective increases to 7,NNIAstillcould obtain the approximate minimum values of convergence and spacing metrics.

Zhang proposed an immune optimization algorithm for constrained nonlinear multi-objective optimization problems [52].A novel constraint-handling scheme designed in uniform form,specialized antibody affinity design,adaptive antibody evolution mechanism,immune selection,memory pool,antigen pool and dynamically variable sizes of evolving populations are the main techniques in the paper.

Li et al.proposed a running metric that could evaluate uniformity of obtained solutions at every generation[53].Besides, the metric could compare the population with different size and different number of objectives.They presented a new multi objective evolutionary algorithm based on minimum spanning tree[54],which was employed to update the solutions in the external population.It was observed intuitively that good performance in convergence and uniformity were obtained.

Yang et al.presented an adaptive hybrid model(AHM) based on nondominated solutions for solving MOPs[55].In this model,three search phases were devised according to the number of nondominated solutions in the current population. In order to exploit local information efficiently,a local incremental search algorithm was merged into the model.The algorithm obtained comparatively good performance in solving MOPs with 2-9 objectives.

Ke et al.proposed a novel multiobjective evolutionary algorithm based on decomposition and ant colony[56].Multiobjective optimization problem is decomposed into a number of single-objective optimization subproblems.Each ant is responsible for one subproblem.All the ants are divided into several groups and each group maintains a pheromone matrix. New solution is constructed for an antby information from its group's pheromone matrix,its own heuristic information matrix,and its current solution.

Ke et al.proposed a multiobjective evolutionary algorithm by combining evolutionary algorithm,decomposition and local search[57].In the decomposition based multiobjective evolutionary algorithm,Pareto local search and a single objective localsearch were adopted to update populations.The proposed algorithm performed better than some other state-of the art algorithms on the multiobjective traveling salesman problem and the multiobjective knapsack problem.

Zhan et al.proposes a novel coevolutionary technique named multiple populations for multiple objectives(MPMO) [58].In MPMO,each population corresponded with only one objective,so that the fitness assignment problem could be dealt with.Based on MPMO,a coevolutionary multiswarm PSO(CMPSO)is develop,which used many swarms as the objectives number and each swarm focused on optimizing one objective.These swarms worked cooperatively and communicated with each other by an external shared archive.An external shared archive for different populations was to exchange search information by using two novel designs, including the modified velocity update equation and an elitist learning strategy.Experimental results demonstrated that the proposed algorithm had superior performance in solving different sets of MOPs.

Gong et al.proposed a surrogate model-based multi-operator search strategy for evolutionary optimization[38].The model was used to implement multi-operator ensemble which can improve the algorithm performance.Each operator generated its own candidate point,so no operator will be lost when generating the new candidate points in the subsequent running stages.An ensemble of differentoperators can also be implemented into different EAs.Experimental results have indicated that this approach could improve the performance for the single operator-based methods,and it could also be applied to multi-objective optimization.

Zhou et al.proposed a generalized resource allocation strategy for decomposition-based MOEAs[59].In this algorithm,each subproblem was chosen to invest by using a probability of improvement vector.An offline measurement and an online measurement of the subproblem hardness were used to maintain and update this vector.Utility functions were proposed and studied for implementing a reasonable and stable online resource allocation strategy.Thirty benchmark functions and the functions presented in the CEC 2013 were chosen to test the performance of the proposed algorithm.

Many objective optimization problems are the problems have more than three objectives.In China,several researchers proposed several many-objective evolutionary algorithms for many optimization problems[49,60-62].

Zou et al.proposed a novel algorithm(MDMOEA)for many-objective optimization problem[49].In this algorithm, an L-optimality was defined and in this definition,allobjectives were assumed equally important.L-optimal solutions were subsets of Pareto-optimal solutions.Experiments demonstrated that MDMOEA could converge to the true L-optimal frontand maintained a widely distributed set of solutions.

Wang et al.proposed an improved two-archive algorithm for many-objective optimization[60].In the proposed algorithm,two main innovations,including assigning different selection principles to the two archives,designing a new Lpnorm-based(p＜1)diversity maintenance scheme were introduced.Experiments showed that the proposed algorithm could deal with many-objective optimization(up to 20 objectives)with good convergence,diversity,and complexity.

Xu et al.[61]proposed a novel evolutionary algorithm to deal with many-objective optimization.The fitness evaluation scheme in MOEA/D was used to improve the convergence of the algorithm and atthe same time the diversity was preserved. In this algorithm,a new dominance relation was introduced.In the designed dominance,solutions were represented by welldistributed reference points and allocated into different clusters.The solutions have the competitive relationship if they are within the same cluster.80 instances of 16 testproblems were used to show the performance of the proposed algorithm.They also introduced two enhanced algorithms(MOEA/D-DU and EFR-RR)for many objective optimization problems[62].The perpendicular distance from a solution to the weight vector in the objective space was used to improve MOEA/D and ensemble fitness ranking algorithm(FR).In MOEA/D-DU,a distance-based updating strategy was used to update solutions. In EFR-RR,a ranking restriction scheme was adopted.In the ranking restriction scheme,each solution involves in the ranking on a part of aggregation functions could be better than on all.Experiments demonstrated that these two algorithms performed well in balancing the convergence and diversity in many-objective optimization.

3.3.Constrained optimization

Constrained optimization is another important topic in EC. Many science and engineering disciplines encounter a larger number of constrained optimization problems(COPs).Researchers have done much work in this domain.

Cai and Wang proposed a multi-objective optimization based evolutionary algorithm for constrained optimization [63].As multi-objective EAs have two goals(convergence to the true Pareto optimal set,and maintenance of a uniform distribution of the Pareto front),constrained optimization evolutionary algorithms(COEAs)also have two definite objectives(landing in or approaching the feasible domain promptly,and reaching the globaloptimal solution in the end). COPs are therefore recast as biobjective optimization problems.The authors introduced a nondominated individual replacement scheme for transforming COPs to MOPs.On the basis of the nondominated individual replacement scheme, two models were devised for the generation of individuals in a population.The difference between these two models was that model 1 used all information provided by nondominated individuals,while model 2 only used partial information provided by nondominated individuals.Furthermore,they realized the effects of infeasible solutions on finding the global optimum in feasible regions.Therefore an infeasible solution archiving and replacement mechanism was devised.Finally, they evaluated the performance of their algorithm on thirteen well-known benchmark functions.Experimental results showed that the proposed approach outperformed six compared algorithms in terms of the best,mean,and worst objective function values and the standard deviations.

Wang et al.proposed a hybrid constrained optimization evolutionary algorithm(HCOEA)[64].In HCOEA,a given COP is converted into a biobjective optimization problem. Two models were devised and merged into the algorithm.The first model was a niching GA based on tournament selection for global search,which could reduce selection pressure and maintain the diversity of the population.While the second model used local search through clustering and multiparent crossover.The population was split into disjoint subpopulations according the location of individuals in the solution space.Offspring were generated by in each subpopulation.In order to utilize infeasible individuals for COPs,a simple best infeasible individual replacement scheme was devised.Wang et al.[65]also proposed an adaptive tradeoff model(ATM)for COP.In this model,in order to obtain an appropriate tradeoff between objective function and constraint violations,three main issues were considered according to how many individuals in the population were feasible versus infeasible.In[66],the authors introduced an experimental design method,orthogonal design,to theirconstrained optimization evolutionary algorithm.An experimental design is orthogonal if each factor can be evaluated independently of all the other factors.In the evolutionary process,several individuals were chosen from the population as parents and orthogonal design was applied to pairs of parents to produce a set of representative offspring.

Zeng et al.presented a lower dimensional search evolutionary algorithm and applied it to constrained optimization [67].The main characteristic of the algorithm was their crossover operator,which searched a space with dimensions lower than 3 no matter how many dimensions the decision space of the optimization problem is.They concluded thattheir algorithm converged fast especially for the higher-dimensional problems studied.However,for some complicated problems,it was trapped in local optima.Zou et al.described a dynamic evolutionary algorithm(DEA)for constrained optimization [68].In the dynamic evolutionary algorithm,each solution, called particle,was assigned a momentum and an activity.A selection operator was based on the above two quantities.Zhou et al.presented a new approach to simple convert the constrained optimization to minimization of two objective functions[69].By their method,one objective was the original objective function and the other was the degree function violating constraints.A concept of measuring the Pareto strength of each individual was introduced.Finally,a new realcoded genetic algorithm based on Pareto strength and Minimal Generation Gap(MGG)model was devised to solve COPs.

Zhang et al.proposed a novel search biases selection strategy for constrained optimization[70].The shortcomings of stochastic ranking[71]were analyzed and the explicit search biases ability in the feasible regions was enhanced.The current best feasible solutions in the population were selected with a high probability in order to accelerate convergence speed and enhance numerical accuracy.

Yu et al.proposed a new constrained evolutionary algorithm to solve maintenance-costview-selection problem in online analytical processing queries[72].Uniform crossover, gene bit based mutation and stochastic ranking were used in this paper.The experiment results showed this algorithm can provide significantly better solutions in terms of minimization of query processing cost and feasibility.

Liu et al.proposed a novel hybrid algorithm(PSO-DE)for constrained numerical and engineering optimization[73].The proposed algorithm integrated particle swarm optimization (PSO)with differential evolution(DE).Only half of particles are updated by PSO,in which Deb's feasibility-based rule was used to judge whether the pbest is updated or not.After the PSO evolution,DE is used to update pBest.Each pbest in pBest could produce three offspring by using DE's three mutation strategies.The offspring that has a better fitness value and lower degree of constraint violation was selected as the new pbest.Experiments on 11 well-known benchmark test functions and five engineering optimization functions showed the performance of PSO-DE.

Wang et al.proposed an improved CW algorithm (CMODE)[74].CMODE combined multiobjective optimization with differential evolution.CMODE used differential evolution as the search engine and a novel infeasible solution replacementmechanism based on multiobjective optimization. 24 benchmark test functions were used to demonstrate the performance of CMODE.

Wang etal.presented a dynamic hybrid framework(DyHF) for constrained optimization problems[75].Two models are designed in this framework:global search model and local search model.In these two models,differential evolution served as the search engine,and Pareto dominance used in multiobjective optimization was used to compare the individuals in the population.Global and local search models were executed dynamically according to the feasibility proportion of the current population.The performance of DyHF was tested on 22 benchmark test functions.

Wang et al.proposed an evolutionary optimization for constrained optimization problems[76].The proposed algorithm consisted of a(μ+λ)-differential evolution and an improved adaptive trade-off model.In(μ+λ)-differential evolution,the offspring population was generated by three mutation strategies and binomial crossover.The improved adaptive trade-off model included three main situations:the infeasible situation,the semi-feasible situation,and the feasible situation.Different constraint-handling mechanisms were designed for each situation.24 well-known benchmark test functions demonstrated that the proposed algorithm was competitive compared with other algorithms.In[77],Jia et al. improved the algorithm in[76].The improved algorithm consisted of an improved(μ+λ)-differential evolution and a novel archiving-based adaptive tradeoff model.Offspring was generated by several mutation strategies and the binomial crossover of differential evolution in the improved(μ+λ)-differential evolution.The proposed algorithm could maintain a good balance between the diversity and the convergence of the population during the evolution.In[78],Wang et al.proposed an algorithm to balance constraints and objective function in constrained evolutionary optimization.The proposed algorithm incorporated the objective function information into the feasibility rule by the DE operators,the replacement mechanism and the mutation strategy.

Wang et al.imposed some constraints on the subproblems of decomposition-based multi-objective evolutionary algorithms[79].In this algorithm,a further strategy which uses information collected from the search was also proposed to adaptively adjust constraints.Experimental results demonstrated the good performance of the proposed algorithm in balancing the population diversity and convergence.

3.4.Dynamic optimization

Many real world optimization problems are actually dynamic.Optimization methods capable of continuously adapting the solution to a changing environment are needed.EC is suitable for problems with dynamically changing environment. When a problem's environment is constantly changing,the current best solution becomes unacceptable and another solution,which fits the current environment better,may exist.In China,Researchers have done some work on this topic.

Zeng et al.proposed an orthogonal evolutionary algorithm (ODEA)for dynamic optimization problems[80].Its population consisted of niches,and a niche is defined to be a small hyper-rectangle.To evaluate the fitness of a niche,each niche selects its best solution found so far as its representative.The fitness value of the representative was defined to be the fitness of the niche.ODEA algorithm divided its population into two groups.One group of niches,called observer niches,was for local search.The other group,called explorer niches,explored new peaks for global search.Zeng et al.also proposed another orthogonal evolutionary algorithm(ODHC)[81]for dynamic optimization problems,which incorporated hill-climbing algorithm.The niche and orthogonaltechnique are same to[45]. An archive was used to store the latest found higher peaks for the ODHC algorithm learning from the past search.The operator of climbing to a peak for a niche in the ODHC algorithm consisted of two stages:At the first stage,the niche does not cover a peak.It repeated a moving operator to approach a potential peak.At the second stage,a shrinking operator was repeated to obtain a“close-to-peak”with a higher precision until the niche size less than threshold.The experiments in[80,81]showed that ODEA and ODHC performed better than self organizing scouts algorithm(SOS)on one moving peaks benchmark function.The authors also extended their algorithm to solving dynamical MOPs[82].For Dynamic TSP,Kang et al.proposed some benchmarks and provided an example of the use of the benchmark[83].Zhou et al.[84]devised three dynamic operators,insert operator, delete operator,and change operator,to modify a static TSP algorithm to Dynamic TSP algorithm.Besides,the inver-over algorithm combined the three operators was used to solve the Dynamic TSP with size of 100.A Dynamic TSP is harder than a general TSP,which is a NP-hard problem,because the city number and the cost matrix are time varying.

Tang et al.[85]proposed a self-adaptive mechanism for EAs with immigrantschemes to address dynamic optimization problems.In their paper,they examined the impact of replacement rate on the performance of EAs with immigrant schemes in dynamic environments.The experiment results on a series of dynamic problems showed that the proposed approach could avoid fine-tuning the parameter and outperformed other immigrantschemes using a fixed replacement rate.

Li et al.proposed a dynamic neighborhood multi-objective evolutionary algorithm(DNMOEA/HI)to balance convergence and diversity of solutions[86].The fitness of each individual is evaluated by tree neighborhood density and the Pareto strength value.A novel algorithm was proposed to optimize the hypervolume contribution of a single individual. Compared with six other multi-objective evolutionary algorithms,the efficiency of our proposed algorithm is demonstrated.

Peng and Zheng et al.proposed a novel prediction and memory strategies for dynamic evolutionary algorithm(PMS) [87].The proposed algorithm contained three parts:exploration operator based on population evolutionary direction, exploitation operator based on the direction of nondominated solutions linkage and memory strategy based on the optimal solution set.By adopting these operators,PMS is with better performance than other algorithms.

4.Real-world applications

EC techniques have been successfully applied to many realworld problems since the early 1960s.In this section,we summarize the contributions of EC-based applications obtained by Chinese researchers.

4.1.EC based methods applied in data mining

Data mining is an importantstep in knowledge discovery in database(KDD)as the volume of data grows rapidly in modern times.To the best of our knowledge,EC-based methods are suitable for solving complex or ill-defined problems and have been applied into data mining and knowledge discovery by some researchers.

Jiao et al.proposed an organized coevolutionary algorithm for classification(OCEC)[88].OCEC causes the evolution of sets of examples,and at the end of the evolutionary process, extracts rules from these sets.These sets of examples form organizations.Three evolutionary operators and a selection mechanism are devised to simulate the interaction among organizations.OCEC dose not put emphasis on forming the appropriately sized organizations,but on simulating the interacting process among organizations.Besides,OCEC adopts a bottom-up search mechanism to avoid generating meaningless rules.In[88],OCEC was compared with several well-known classification algorithms on 12 benchmarks from the UCI repository datasets and multiplexer problems.The 20-and 37-multiplexer problems are used.OCEC was also applied to radar target recognition problems.All results showed that OCEC achieved a higher predictive accuracy with a lower computational cost and obtains a good scalability.

Gong etal.performed unsupervised image classification by using a novelevolutionary clustering method,named manifold evolutionary clustering(MEC)[89].In MEC,the clustering problem was considered from a combinatorial optimization viewpoint.Each individual was a sequence of real integers representing the cluster representatives.Each datum was assigned to a cluster representative according to a novel manifold-distance-based dissimilarity measure,which measured the geodesic distance along the manifold.In[89], the authors applied MEC to solve seven benchmark clustering problems on artificial data sets,three artificial texture image classification problems,and two synthetic aperture radar image classification problems.The experimental results showed that in terms of cluster quality and robustness,MEC outperformed the K-means algorithm,a modified K-means algorithm using the manifold-distance-based dissimilarity measure,and a GA-based clustering technique in partitioning most of the test problems.

Au et al.presented a novel evolutionary data mining algorithm for churn prediction[90].For churn prediction,it did not only need to predict whether a subscriber would switchfrom one carrier to anther,also require that the likelihood of the subscriber's doing so be predicted.In[90],the proposed algorithm had the following characteristics.First,the initial population consisted of a set of first-order rules.Higher-order rules were obtained by the iterating the initial population. Besides,an objective interestingness measure was employ for identifying interesting rules.Probability based function was used to evaluating the fitness of chromosomes.Finally,seven databases were used for validating the techniques in the algorithm.

Ma et al.proposed a novel evolutionary algorithm called evolutionary clustering(EvoCluster)[91]to uncover inherent clusters in gene expression microarray data.EvoCluster encoded the entire cluster grouping in a chromosome so that each gene encodes one cluster.And it had a set of crossover and mutation operators that facilitated the exchange of grouping information between two chromosomes.Besides,the interestingness of a particular grouping of data records was measured by the fitness.In this algorithm,there was no requirement for the number of clusters to be decided in advance.The experiment results showed that patterns hidden in each cluster can be explicitly revealed and the algorithm is very robust in noise environment.

Wong and Leung introduced a novel data mining approach that employed an evolutionary algorithm to discover knowledge represented in Bayesian networks[92].The algorithm embodied two phases:the first phase was the conditional independence test for reducing the size of search space,and the second one was the search phase,in which good Bayesian network models were generated by a GA.Finally,the hybrid algorithm was applied to two data sets of direct marketing and comparative better prediction accuracy was obtained.

Query reweighting is a very important research topic of document retrieval.Chang and Chen presented a new method for query reweighting to solve document retrieval[93].GA is employed to reweight user's query vector.The query vectors were encoded into chromosomes and the optimal weights of query terms are searched by genetic algorithm.Finally,the National Science Council document database,Taiwan,was used in the experiment.The average recall rate and average precision rate of the top ten retrieved documents and the top twenty retrieved documents were improved.

Time series are an important class of temporal data objects and can be easily obtained from financial and scientific applications.Chung et al.proposed an evolutionary time series segmentation algorithm[94].It allowed a sizeable set of pattern templates to be generated for mining or query.With respect to application in times series of selected Hong Kong stocks,a perceptually important point-based subsequencematching were introduced.

Xiao et al.proposes a quantum-inspired genetic algorithm for k-means clustering(KMQGA)[95].Without knowing the exact number of clusters beforehand,KMQGA could obtain the optimal number of clusters as well as providing the optimal cluster centroids.A Q-bit based representation was applied for exploration and exploitation in discrete 0-1 hyperspace by using rotation operation of quantum gate as well as the typical genetic algorithm operations.The experimental results on both the simulated datasets and the real datasets showed that KMQGA could obtain promising results.

Gong etal.[96]proposed a multiobjective model for sparse feature learning in deep neural networks.A multiobjective induced learning procedure which consisted of fast updating step and multiobjective inducing step was designed to optimize the model.In the multiobjective inducing step,MOEA/D was improved by incorporating with self-adaptive differential evolution.The individuals in the population are updated by differential operators in order to adapt to the properties of network parameters.

Gong etal.introduced a multiobjective learning process for self-paced learning[97].The objective function of the selfpaced learning was decomposed into two terms,i.e.,loss term and the self-paced regularizer.In the learning process, MOEA/D was used to learn from easy region to complex region of the objective space.Differential evolution operators were utilized to generate the offspring.

Though many works of evolutionary algorithms on data mining have been done,this application has not been drew widespread attention.Nowadays,machine learning and deep learning are very hot study direction.Combing EAs and machine learning and deep learning are very interesting.

4.2.EC based methods applied in VLSI floorplanning

Floorplanning is a criticalphase in physicaldesign of VLSI circuits and it consequence has an important relation with performance of the final chip.The goal of VLSI fl oorplanning is to find a fl oorplan for the modules such that no module overlaps with another and the area of the floorplan and the interconnections between the modules are minimized.The methods of floorplanning could be classified into two categories:slicing structure and nonslicing structure.Because of the generality of nonslicing fl oorplanning,it was obtained more attention and popularity.EAs employ methods of perturbing the fl oorplan and searching for better solutions,and have become an efficient method in solving fl oorplanning.In China,Tang and Yao[98],Liu etal.[99]have done research in this domain.

Tang and Yao proposed a memetic algorithm for VLSI fl oorplanning[98].The novelmemetic algorithm combined an effective genetic search method to explore the search space,an efficient local search method to exploit information in the search region,and a novel bias search strategy to maintain tradeoff between them.The most efficient nonslicing representation,the ordered tree(O-tree)was adopted.A subtree of the O-tree represents a compact placement of a cluster of modules.Hence,subtrees were used as memes in their memetic algorithm.The memes were transmitted and evolved through one crossover operator and two mutation operators.In [98],two hard rectangle models,ami33 and ami49,were used to test the performance of the algorithm.

Liu et al.proposed a new nonslicing floorplan representation,moving block sequence(MBS)[99].With respect to MBS,four moving rules were described corresponding to fourinitial positions.In MBS representation,allblocks can only be moved in the first quadrant to form a left-bottom compact fl oorplan sheet,that is,any block in the chip can notbe moved left or down any more.The MBS is suitable for evolutionary algorithms since no extra constraints are exerted on the solution space.Besides,an organizational evolutionary algorithm incorporated the intrinsic properties of MBS was designed (MBS-OEA).With the intrinsic properties of the MBS in mind,three new evolutionary operators were designed in the MBS-OEA.The results showed that the MBS-OEA was not only suitable for solving a wide range of problems,but also competent for solving large-scale problems.

VLSI fl oorplanning is an NP-hard problem.EAs are with good performance of solving NP-hard problem.Designing effective global and local search strategies are needed in dealing with this problem.

4.3.EC based methods applied in DS-CDMA multiuser detection

In recent years,Direct-Sequence Code-division Multipleaccess(DS-CDMA)systems have emerged as one of prime multiple-access solutions for 3G and future wide-band wireless systems.In the DS-CDMA framework,multiple-access interference(MAI)existing at the received signal creates“near-far”effects and constitutes the main limitation of DSCDMA systems.Multiuser detection(MUD)techniques can efficiently suppress MAI and substantially increase the capacity of CDMA systems,so ithas gained significant research interestsince the Optimal MUD(OMD)was proposed.Butthe computational complexity of OMD increases exponentially with the growth of user number.From a combinatorial optimization viewpoint,OMD is an NP-complete problem and EC based methods have been introducing in solving the problems. In China,Gong etal.[100],Wang etal.[101],Soo etal.[102] have done some work in this domain.

Gong et al.presented a novel clonalselection algorithm for multiuser detection(CAMUD)[100].In their paper,an antigen was defined by the problem and its constraints,antibodies were represented by the limited-length character strings. Except the normal clonal mutation operator and clonal selection operator,it is noteworthy that,a novel clonal death operator was devised by the authors.Theoretical analysis and Monte Carlo simulations showed that the algorithm could significantly reduce the computational complexity and achieve good performance in MAI suppression and“near-far”resistance.

Wan et al.presented a(1+λ)evolution strategy method to solve asynchronous DS-CDMA multiuser detection[101].The main contribution of this paper is the analysis of the offspring sizeλand the mutation probabilityPm.As their suggestion,the value ofλis approximately equal tonlnnin all instances, wherenis equal to the product of the number of active users and the packetsize.Besides,they have validated thatPmis 0.2, which makes the proposed ES escape local optima effectively and improves the quality of solutions.Experimental study showed that their method performed well for small number of users,while for larger number of users,it performed a little worse.

In[102],particle swarm optimization was developed to find sub-optimal multi-user detection.A de-correlating detector or linear minimum mean square error detector was used as the first stage to initialize the detector.Then,the PSO algorithm was applied to detect the received data bit by optimizing objective function.Simulation showed that the performance of the proposed method was promising.

Though few works have been done on this problem,EAs were good methods to deal with this problem.With the development of wide-band wireless systems,DS-CDMA may be out of date nowadays.Future works will focus on other problems in the communication research community,for example,multiple-input-multiple-output(MIMO)systems.

4.4.EC based methods applied in hardware-software partitioning

Hardware-software partitioning is one of the most important issues of Codesign of embedded systems because it is made at the beginning of the cycle of design.In terms of costs and delays,final results will strongly depend on partitioning.A good partitioning scheme is a tradeoff under some constraints, such as power,size,performance,and so on.

In China,Zhang et al.applied artificial immune principals based on negative selection algorithm towards solving this problem[103].In contrast to prior work with negative selection in artificial immune systems(AIS),in their paper,it did not have a precise self-definition,and the worst candidate solutions in every generation are added into the self-setstep by step,while the oldest individuals in the self-set are removed when the self-set is full.Therefore,it is a dynamic scheme, namely first-in-first-out updating strategy.According to their experimental results,they concluded that their algorithm was more efficient than traditional evolutionary algorithm.

Hardware-Software partitioning is difficult problem for engineering.This direction is popular with embedded system in recent years.However,the methods proposed and standard benchmark test functions are fewer,and metrics used for optimized are partial.Therefore,there should be much work in this domain.

4.5.EC based methods applied in solving equations

Many problems come down to linear equations or nonlinear equations.Solving equations are of great importance in many systems.Traditional methods for equations solving are with many constraints,for example,differentiable,unisolution and so on.

He et al.presented a novel application of evolutionary computation techniques in solving linear and partial differential equations[104].Several combinations of evolutionarycomputation techniques and classical numericalmethods were proposed.The experimental results showed that the proposed hybrid algorithms outperformed the classical numerical methods significantly in terms of effectiveness and efficiency.

Wu and Kang presented a parallel elite-subspace evolutionary algorithm(PESEA)for solving system of non-linear equations[105].The PESEA ran on the parallel computer with 2 processors and share memory.Elite-preserve strategy is adopted in their paper to conduct multi-processor crossover.It is a simple parallel algorithm applied into solving non-linear equations.

Song et al.proposed a simple and generic transformation technique based on multiobjective optimization for nonlinear equation systems[106].The proposed algorithm transformed a nonlinear equation system into a bi-objective optimization problem and then the transformed problem could be solved by MOEAs.The experimental results have demonstrated the performance of the proposed algorithm compared with another state-of-the art multiobjective optimization based transformation technique and four single-objective optimization based approaches.

Compared with classic methods,EAs are more efficientand robust in solving equations.In reality,many systems are nonlinear equation systems and they are with many solutions, such thatpowerful MOEAs are suitable for nonlinear equation systems solving.Designing effective MOEAs for nonlinear equation systems will be an interesting research.

4.6.EC based methods applied in solving multiple destination routing problems

Multiple destination routing(MDR)problems well up with the advance and development of network and information technology in modern society.Multiple destination routing enables widespread usage of multipointservices ata lowercost than networks using point-to-point routing.An MDR problem can be stated as the determination of the bestrouting in a given communication network for the delivery of a message from the source(one or more)to multiple destination nodes with reference to certain criteria,such as time delay and network bandwidth.However,the MDR problem itself is very complex. Furthermore,its optimal solution,the Steiner tree problem,is NP-complete and thus not suitable for real-time applications.

Leung et al.proposed a new genetic algorithm for MDR problems without constraints[107].The method made use of the genetic operators to search the intermediate nodes for an MDR problem.Besides,with respect to the algorithm,four basic components:representation ofindividuals,determination of the fitness function,design of the genetic operators,and determination of the probabilities controlling the genetic operators were devised accordingly.The algorithm was applied to solve the B problem set of the Steiner tree problem on graphs in the OR-library and problems with randomly generated dense networks.By their experiment,we can obtain that this method is robust and can find the optimal solutions with high probability.However,the computational time is not suitable for application.

4.7.EC based methods applied in path planning in mobile robot system

Path planning is one of the most important problems in mobile robot control system.Environmental model of path planning is difficult in its physical and dynamic properties. There are already some methods that solve path planning problems,such as artificial potential method and grid method. Cai and Peng[108],Duan and his collaborators[109-114] have done much work in this domain.

By dividing a complicated problem into several relatively simple sub-problems and assigning them to each singleagent,multi-agent systems can effectively solve complicated problems with modularity,maintainability,extendibility,faulttolerance and robustness.In order to maintain the relation of the agents,Cai and Peng proposed a cooperative multi-mobile robot system based on genetic algorithm (CCAGA)for path planning[108].In a multi-mobile robot system,the performance of it is improved by the cooperation and coordination relation among those mobile robots.A main characteristic of CCAGA is that potential solutions of each sub-problem form their own sub-population,and evolve only in their own sub-population.Besides,a novel fixed-length decimal encoding mechanism for paths of each mobile robot is also proposed in their paper.The algorithm was validated on a cooperation two-mobile robot system and it obtained robust convergence.

Duan et al.have done some investigations on ant colony algorithms and apply it into global trajectory planning of unmanned aerial vehicle[109-114].In[109],several hybrid improvement strategies were introduced and combined with basic ant colony algorithm for alleviating its limitation of stagnation and prematurity.In[110],satisficing decision algorithm was hybridized with ant colony optimization for solving the uninhabited combat air vehicle path planning in complicated combat field environments.An acceptance function and rejection function are used for selecting the next node from the current candidate path nodes.In[111],a new hybrid meta-heuristic ant colony optimization(ACO)and differential evolution(DE)algorithm was proposed for UCAV three dimension path planning problem.Aк-trajectory was adopted to make the optimized UCAV path more feasible.In[112], an improved artificial bee colony(ABC)optimization algorithm was introduced for UCAV path planning.In the proposed improved ABC algorithm,chaotic variable was introduced preventing the ABC algorithm falling into the local optimum.Duan et al.proposed an improved constrained differential evolution algorithm for path planning[113].A novel satisfactory level update strategy was introduced to improve the searching ability of the proposed algorithm.Duan et al. applied artificial bee colony algorithm to deal with reentry trajectory optimization[114].The algorithm consisted of two processes.First,the control variables of the hypersonic reentry vehicle were discretized at a set of Legendre-Gauss collocation points.Second,artificialbee colony algorithm was used to solve this problem.The feasibility and the superiority of the proposed method were proved by simulations.

Yang et al.[115]presented an EA-based UAV path planner based on a novel separate evolution strategy for solving the UAV path planning problems.In their paper,eight commonly used constraints and objective functions were decomposed, and the waypoints of candidate paths were separately evaluated and evolved.The performance of the proposed approach was validated by comparison with the other state-of-the-art EA-based planners.

Path planning problem is always a hot topic.Recent researches have shown that EAs were very useful in path planning problem under different constraint conditions,while these researches are offline planning.The online planning and cooperative planning may be research topics because they are more practical than offline planning.

4.8.EC based methods applied in power system

Many optimization problems in power systems are combinatorial optimization problem.They are difficultto deal with by traditional mathematical programming algorithms.EC based methods could provide near optimal oroptimal solutions for these problems under reasonable time.Several scholars from Taiwan,Hongkong,and Chinese Mainland have done work in this domain.

Lin et al.proposed a hybrid algorithm by integrating evolutionary programming,tabu search and quadratic programming methods to solve the non-convex economic dispatch problem[116].The problem is solved in two phase,the costcurve-selection sub-problem was solved with a hybrid evolutionary programming and tabu search.The typical economic dispatch sub-problem was settled by quadratic programming.

Lin developed an improved tabu search algorithm for economic dispatch with non-continuous and non-smooth cost functions[117].The method adaptively regulates the tabu list size,the number of mutated and recombined individuals.The performance was validated by its obtained accurate solutions and great potential application in the power system.

Short-term load forecasting of electric power plays an important role in operation scheduling and secure operation of power systems.Liao and Tsao proposed a fuzzy network combined with a chaos-search genetic algorithm and simulated annealing to the issue[118].A fuzzy hyperrectangular composite neural network was adopted for initial load forecasting,afterward,the genetic algorithm and simulated annealing are used to find the optimal parameter setting of the network.In[119],particle swarm optimization was employed to identify the autoregressive moving average with exogenous variable model for short-term load forecasting.The global and parallel search abilities are emphasized in this article.The performance of the method is validated by Taiwan Power load data.

Network reconfiguration problem is important in power system for enhancing service reliability and reducing power losses.Itis a complex nonlinear combinatorial problem.Hsiao proposed a multi-objective evolution programming method for distribution feeder reconfiguration[120].Four objectives were introduced in this algorithm,which were minimizing power losses,ensuring voltage quality,service reliability assurance, and minimizing switching operations.

It still receives a great deal of attention of EAs on power system.There should be much works on applying EAs to deal with more problems or solving economic dispatch problems with different constraint by EAs.

4.9.EC based methods for image processing

Image processing includes several important issues,for example image segmentation,image classification,and sparse reconstruction et al.It is difficult for traditional algorithms to deal with image processing in the adjustment of parameters and get the best solution.Some image processing problems can be modeled as single optimization problems or multiobjective optimization problems.EAs perform well in these optimization problems.

Liu and Tang presented an autonomous agent-based image segmentation approach[121].From the paper,we can obtain that a digital image is regarded as the environment in which the agentinhabitand act.By some effective reactive behaviors such as breeding and diffusion,the agent could succeed in labeling homogeneous segments.Once the agents find the pixels of a specific homogeneous segment,they will breed offspring agents inside their neighboring regions.Finally,the distributed behavior-based agents in searching and labeling various homogeneous regions in a brain-scan image are studied.Besides,Liu et al.introduced a new evolutionary autonomous agent based approach to image feature extraction [122].The agent environment is also a digital image.The agent behaviors include self-reproduction,diffusion and cease to exist in this paper.And the most distinct traits of this method is its bottom-up,decentralization and distributing in nature and relying on local agent behavior.

Zhong et al.introduced a novel multiple-valued immune network based supervised classification algorithm for remotesensing imagery[123].By their literature,samples in interesting regions were employed to train the immune network. The trained immune network was used for classifying the imagery.The performance of this method was validated by comparison with maximum likelihood,back-propagation neural network,and minimum distance.

Li et al.[124]proposed a new soft-thresholding evolutionary multiobjective algorithm for sparse reconstruction in image processing.This algorithm optimized two competing cost function measurementerror and a sparsity-inducing term. Besides a soft-thresholding technique,the algorithm incorporated two additional heuristics.Optimal solutions were found in knee regions on the Pareto front.Compared with five commonly used sparse reconstruction algorithms,the algorithm was demonstrated effective for practical applications.

A multiobjective model was built for band selection in hyperspectral image processing[125].In this model,the band selection problem was modeled as a multiobjective optimization problem(MOP),and two objective functions with a conflicting relationship were designed to describe the information contained in the selected band subsets and the numberof selected bands.A multi-objective evolutionary algorithm based on decomposition was proposed to find a balance between these two objectives and generate a set of band subsets with different numbers of bands in a single run.

Gong et al.introduced a multi-objective sparse unmixing (MOSU)model for hyperspectral sparse unmixing[126].A novelmulti-objective cooperative coevolutionary algorithm was proposed to optimize confl icting objectives:the reconstruction term,the sparsity term and the totalvariation regularization term. Arandom group strategy based on sparsity and the non-uniform mutation operatorwere designed to obtain more sparse solutions. Experiments on simulated and real hyperspectral data sets demonstrated the effectiveness of the proposed algorithm.

Duan et al.proposed an elitist chemical reaction optimization for contour-based target recognition in aerial images [127].In this algorithm,Contours were described by edge potential function and contour-based target recognition was formulated as an optimization problem.To optimizing this problem,an improved chemical reaction optimization algorithm was adopted.The elitistselection procedure was used to improve the efficiency.Experimentalresults demonstrated that the algorithm performed well in enhancing the accuracy and robustness of target recognition for aerial images.

Lots of works of EAs for image processing have been done in recentyears in China.Illposed problems or inverse problem are frequently encountered problems.MOEAs are with good performance in solving these problems.It will be an interesting and effective topic by applying EAs to solve ill posed problems in image processing in the future.

4.10.EC based methods for electronic circuits

Electronic circuit design and optimization are hard problem in circuit system.Several EC based methods have been proposed for power electronic circuitoptimization,combinational logic circuits,and digital filter design by Chinese scholars.

Zhang et al.studied an asynchronous migration scheme by pseudo coevolutionary genetic algorithm for power electronic circuit optimization[128].Component values of power conversion stage and feedback network were optimized by two coadapted evolutionary training processes.An illustrative example showed that the optimized values gave a higher fitness value because of the interaction between the parallel conversion stage and feedback network.

Cheang et al.developed a combinational logic circuit learning system,named genetic parallel programming logic circuit synthesizer[129].A variable length parallel program structure was employed to represent combinational circuit. Two stages were divided in the program.The firststage aimed atfinding 100%functional program,while in the second stage, the method used another set of genetic operators guiding by a fitness function to improve the qualities of correct programs. The method was performed on two-and four-input lookuptable-based combinational logic circuits.

In[130,131],a hybrid Taguchi genetic algorithm and Taguchi immune algorithm were introduced to solve optimal digital infinite-impulse response filters design.The Taguchi method was inserted between crossover and mutation operations of a traditional genetic algorithm in[130].The systematic reasoning ability of the Taguchi method was incorporated in the crossover operation for better gene selection.In[131], the clonal proliferation performed by hypermutation and recombination were integrated to improve the search ability of the algorithm.The two algorithms were tested on seven global numerical optimization problems and designing the digital low-pass,high-pass,band-pass,and band-stop filters.

Lin et al.modeled the electronic circuit design with uniform search range,and proposed an efficient orthogonal learning particle swarm optimization[132].It used a novel orthogonallearning strategy which can find usefulinformation in each particle's best position and its neighborhoods'best position.The predictive solution strategy was also used to save computational burden.The effectiveness in a practical circuit of their algorithm has been validated.

Previous works all formulated power electronic circuit optimization as single optimization problem.In the future, power electronic circuit optimization will be extended to multi-objective optimization model and solved by MOEAs.

4.11.EC based methods for signal processing

There are many applications in signal processing,such as time-delay estimation,blindly separating unobservable independent source signals.In these applications,a set of parameters should be optimized under a restrictive bounded area. Objective functions of these applications are usually linear or nonlinear,equality or inequality,smooth or nonsmooth.EAs have been used for signal processing in China.

Evolutionary algorithmsalso have been introduced to deal with signal processing.Tang etal.[133]presented a brief summarization of EC based methods in signal processing.Firstly,they discussed two traditional optimization techniques including calculusbased optimization techniques and dynamic programming and presented their shortcomings.Afterward,the basic framework of genetic algorithm was described in detail,including encoding scheme,fitness techniques,genetic operation,and scheme theory. Then,applications in signal processing were presented,such as IIR adaptive filtering,nonlinear model selection,time-delay estimation,active noise control,and speech processing.

Tan and Wang proposed a novel EC and neural network based method for blindly separating unobservable independent source signals from their nonlinear mixtures[134].A parameterized neural network was employed to model the demixing system and the statistical dependence of the output signals were measured by higher order statistic based cost functions. Importantly,genetic algorithm was employed to minimize the highly complicated cost function.

Tang et al.utilized a parallel on-line genetic structure to solve time-variantdelay problem[135].Time delay estimation is present in signal processing applications,including sonar, radar,electronic circuitdesign and so on.In this paper,on-line time-delay estimation problem was viewed as a finite impulse response(FIR)filter and a new genetic algorithm was employed to optimize the coefficients of the filters.

There are lots of applications in signal processing,while few works have focused on signal processing.In the future,it is foreseen that more EAs will be launched for signal processing applications.

4.12.EC based methods for control system design

Control system design has been widely viewed as constrained optimization problems,therefore,EC could be employed for design and optimize the control system.Several EC based methods have introduced for this problem.

Tang et al.proposed a structured genetic algorithm for robustH∞control system design[136].H∞optimization is a type of effective method for control system design and several development has been the use of method to design robust control system.One such method was the loop-shaping design procedure(LSDP).In[132],the proposed algorithm is developed to optimize simultaneously over the structures and coefficients of the weighting functions in LSDP.Besides,a multiple objective ranking approach was introduced for achieving the design criteria of extreme plants.

Ho and Chou proposed a direct computational algorithm for solving the Takagi-Sugeno(TS)fuzzy-model-based feedback dynamic equations[137].Orthogonal functions were used for expressing the state variables by use of its elegant operational properties.A novel algebraic computational algorithm with two terms of expansion coefficients for solving the TS fuzzy control system was proposed in this study.Then,the introduced computational algorithm was integrated with the hybrid Taguchi-genetic algorithm for quadratic optimal PDC and non-PDC controller design.

Lau and Wong introduced an immunity based distributed multi-agent control framework[138,139].The framework tried to supply an integrated solution to control and coordinate complex distributed systems with large number of autonomous agents.The actions of different agents in a dynamic environment were defined and allowed them to cooperate strategically by simulating the ability of immune system to fight against antigens with different immune responses.Memory scheme of agents consisted of long-term and short-term memories.Long-term memory stored information for completing all the tasks in the workplace,and the short-term one stored data for temporary use.

4.13.EC based methods for capacitated arc routing problems

The capacitated arc routing problem(CARP)is a challenging combinatorial optimization problem.CARP is with many real-world applications,e.g.,salting route optimization and fleet management.Several evolutionary algorithms have been proposed to solve CARP in China.

Mei et al.[140]proposed a decomposition-based MA with extended neighborhood search(D-MAENS)for solving MOCARP.In their paper,a MO-CARP that considers minimizing the total cost and the makespan as two objectives was investigated.Then they proposed a decomposition-based framework.After that,a competitive algorithm for SOCARP and a novel algorithm D-MAENS were integrated into the proposed framework.The superiority of D-MAENS was validated by comparison with LMOGA and NSGA-II.

Mei et al.[141]proposed a new MA for solving PCARP.A new solution representation scheme and a novel crossover operator were used in their paper,and a Route-Merging(RM) procedure was devised and embedded in the algorithm.The experiment results showed that the proposed MARM could obtain better solutions than the existing meta-heuristic approaches in much less time.

Wang et al.[142]proposed an estimation of distribution algorithm(EDA)with stochastic local search(SLS)to tackle this problem.The proposed method integrated an EDA with a two phase SLS procedure to minimize the maximal total cost. Experiment results showed that the proposed method outperformed existing state-of-art algorithms.

Previous works dealt with capacitated arc routing problems of different scenes.In reality,uncertainties will occur.It is more important and interesting to take uncertainties into account and solve these problems by EC-based methods.

4.14.EC based methods for social networks analysis and mining

Social networks analysis problems are formulated as optimization problem.These problems are always NP-hard problem.Lots of EC based algorithms are adopted for networks analysis and mining,such as network community detection [143-149],network structure balance[150,151],network influence maximum[152,153]and gene regulatory network reconstruction[154].

In[143-145],single objective evolutionary algorithms or swarm optimization algorithms were introduced to discover network community.Gong et al.proposed a novel memetic algorithm to discover communities in networks[143].The proposed algorithm,which isa synergy ofa genetic algorithm with a hill-climbing strategy as the local search procedure,is used to optimize modularity density.Two-way crossover and neighbors based mutation operations based on network structure are used to explore the search space.Experiments on computer-generated and real-world networks show the effectiveness and the multiresolution ability of the proposed method.In[144],a multilevel learning based memetic algorithm was proposed for community detection.The proposed algorithm combines genetic algorithm and multi-level learning strategies to optimize modularity.The multi-level learning strategies are designed based on the knowledge of the node,community and partition structures of networks,respectively.Extensive experiments demonstrated that the proposed algorithm could detect community in large scale networks.Agreedy discrete particle swarm optimization was proposed in[145]for community detection in large-scale networks.In the proposed algorithm,the particle statuses are redefined in discrete form.The status updating rules are reconsidered and consider a greedy strategy.

In[146-149],community detection was formulated as multi-objective optimization problem and solved by multiobjective evolutionary algorithms.In[146],multiobjectiveevolutionary algorithm based on decomposition was employed. Two-pointcrossover and neighbor-based mutation are designed based on the network structure.The proposed algorithm can divide the network into communities at different hierarchical levels.Shi et al.introduced a multi-objective evolutionary algorithm for community detection[147].This algorithm is designed based on PESA-II.The uniform two-point crossover and neighbor-based mutation are also adopted.Shi et al.also proposed two model selection methods to select solutions on pareto front.Gong et al.[148]introduced a multiobjective discrete particle swarm optimization algorithm for community detection.The proposed algorithm first decomposes our multiobjective network community detection into a number of scalar problems,and then it optimizes them simultaneously using a newly proposed discrete PSOframework.The proposed algorithm also was extended to detect communities in signed networks.Liu et al.adopted multiobjective evolutionary algorithm to detect communities in signed networks[149].Two contradictory objective functions were designed for community detection in signed networks.A direct and indirect combined representation was used,and this algorithm can detect both separated and overlapping communities from signed social networks based on the proposed representation.

Ma et al.proposed a novel memetic algorithm to compute and transform structural balance in signed networks[150].A general energy function is designed to compute the structural balance of signed networks both in strong and weak definitions. This energy function can evaluate the transformation costin the transformation of positive and negative edges.To solve this problem,a multilevellearning based memetic algorithm,which incorporates network-specific knowledge such as the neighborhoods of node,cluster and partition,was proposed.Experimental results showed that this method can resolve the potential confl icts of signed networks with the minimum cost. Cai et al.[151]introduced a two-step algorithm to compute structural balance in signed networks.In the first step,the network is divided into several communities by multiobjective evolutionary algorithm.In the second step,energy function is adopted to select the best results on the pareto front.

Wang et al.devised a set-based coding genetic algorithm for influence maximum problem in network analysis[152].In the set-based coding genetic algorithm,the chromosome is coded as a set and genetic operators are redesigned based on the set operators.The convergence of this algorithm is studied through schema analysis and Markov chain analysis.Gong et al.proposed a novel memetic algorithm for influence maximization in social networks[153].The algorithm consists of three steps.Firstly,the network is divided into several communities by community detection algorithm.Secondly, candidate seeds are selected based on the community structure.Finally,the ultimate seeds are selected by memetic algorithm.Experimental results showed that the proposed memetic algorithm could speed up the convergence and find the promising solutions in a low running time.

Liu etal.[154]proposed a dynamic multiagent genetic algorithm to reconstruct large-scale gene regulatory networks from time-series expression profiles based on fuzzy cognitive maps.In the algorithm,four genetic operators,namely the neighborhood competition operator,the neighborhood orthogonal crossover operator,the mutation operator,and the self-learning operatorare used to explore the evolutionary process.Experimental results demonstrated thatthe proposed algorithm can proficiently handle the large search space ofreconstructing gene regulatory networks.

Lots of EC-based methods for network analysis and mining have been proposed in the past decades.Previous works focused on theory analysis and may not be suitable for practicalapplications,for networks in realworlds are in large scale and dynamic.It is more useful if EC-based methods are used for large scale networks or dynamic networks.

4.15.EC based methods for evolutionary arts

The goal of evolutionary arts is to investigate computational methods which can make applicable aesthetic decisions as humans can.Judging beauty is a highly subjective task,but certain features are considered importantin aesthetic judgment. Chinese researchers have done many works on evolutionary arts.

Lietal.introduced an adaptive learning evaluation modelto guide the evolutionary process[155].The model selected the certain aesthetic features from internalevolutionary images and realworld paintings.Compared with multi-layerperceptron and C4.5 decision tree,the results showed that the adaptive model was efficientatpredicting user's preference.

Li et al.introduced an adaptive model to learn aesthetic judgments in the task ofinteractive evolutionary art[156].They then reduced features to a relevantsubsetusing feature selection, and extracted the features from previous interactions by building the model.An evolutionary artsystem was builtby adopting this model to test the efficacy of the approach.The results showed thatthe use ofthe learning modelin evolutionary artsystemswas sound and promising for predicting users'preferences.

In the future,more external images are needed to explore stylistic changing.Different features are needed to help us to understand the aesthetic criteria.

4.16.EC based methods for other real applications

Except for applications above,EC-based methods were used for other real-world applications by researchers in China.

Gong et al.proposed a novel particle swarm optimization (PSO)for resource allocation problems[157].To solve resource allocation problems(RAPs)effectively,a novel representation of each particle in the population and a comprehensive learning strategy for the PSO search process were designed.

Hu et al.proposed a hybrid approach by combining a genetic algorithm and schedule transition operations(STHGA) [158].The proposed algorithm aimed to find the maximum number of disjoint complete cover sets of sensors,in order to maximize the lifetime of wireless sensor networks.A forward encoding scheme for chromosomes in the population and some effective genetic and sensor schedule transition operations were designed in STHGA.

Wang et al.introduced a new convex hull-based multiobjective genetic programming(CH-MOGP)to maximizereceiver operating characteristic problem[159].In CH-MOGP, two novel convex hull-based strategies,namely CWR-sorting and area-based contribution indicator were introduced.Population was parted into severalrank levels by CWR-sorting and the area-based contribution indicator was used to select the survivors in the same level.

Duan et al.proposed a hybrid particle swarm optimization and genetic algorithm(HPSOGA)for the multi-UAV formation reconfiguration problem[160].The multi-UAV formation reconfiguration problem was formulated as an optimal control problem with dynamical and algebraic constraints.HPSOGA could find time-optimal solutions simultaneously.

Zuo and Gong et al.proposed a novel multiobjective evolutionary algorithm for recommendation[161].The proposed multiobjective evolutionary algorithm was used to optimize two objectives of recommendation:accuracy and diversity.The proposed algorithm could return a set of different recommendations for users.

Xue and Wang et al.proposed a memetic algorithm for instance coreference resolution[162].A similarity measure was introduced for the instance coreference resolution and then a problem-specific memetic algorithm was proposed to solve instance coreference resolution problem by optimizing this measure.

Gong and Cai proposed a novel tri-tier immune system (TTIS)and applied it to anti-virus problem and software fault diagnosis of mobile robot[163].TTIS was a novel artificial immune system,which was comprised of three computing tiers:inherent immune tier,adaptive immune tier and parallel immune tier.The first two tiers were inspired from the natural immune system and the third tier was based on the parallel computer technique.Finally,the simulation of the immune application to the mobile robot simulator showed that,the immune technique was effective in the non-self detection,the non-self recognition,the non-self elimination and the failover of the useful system files.

Ding et al.presented game theory methods to model the formation of binary opinions[164].Cooperative games and minority games were proposed to model the interaction rules of general people and the behaviors of contrarians,respectively.The majority voter model could be restored from the proposed games.The game theory models could get similar evolutionary results to traditional opinion models.

5.Conclusion

We have attempted to summarize the main contributions of EC performed by Chinese researchers.However,due to the limitation of our knowledge,some important work in EC in China may be not covered in this review.Therefore,this is may be nota comprehensive review.From the articles that we have summarized,it can be found that the theoretical foundation performed by Chinese researchers was significant to advancement of basic theory of EC.On the other hand,many Chinese researchers paid attention to the domain of evolutionary optimization,including global optimization,multiobjective optimization,many-objective optimization,constrained optimization,and dynamic optimization.However, the research results in EC-based data mining obtained by Chinese research were less.The real-world applications of EC were also widely studied in China.In a word,Chinese researchers are more and more active in EC field.

Acknowledgements

This work was supported by the National Natural Science Foundation of China(Grant nos.61273317,61422209, 61473215),the National Program for Support of Top-notch Young Professionals of China,and the Specialized Research Fund for the Doctoral Program of Higher Education(Grantno. 20130203110011).

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Maoguo Gongreceived the B.S.degree in electronic engineering(first class honors)and the Ph.D.degree in electronic science and technology from Xidian University,Xi'an,China,in 2003 and 2009,respectively.Since 2006,he has been a Teacher with Xidian University.In 2008 and 2010,he was promoted as an Associate Professor and as a Full Professor,respectively,both with exceptive admission. His research interests are in the area of computational intelligence with applications to optimization, learning,data mining and image understanding.Dr. 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 Talentin University 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.

Shanfeng Wangreceived the B.S.degree in electronic and information engineering from Xidian University,Xi'an,China,in 2012.Now he is working towards the Ph.D.degree in Pattern Recognition and Intelligent Systems at the School of Electronic Engineering,Xidian University,Xi'an,China.His currentresearch interests are in the area of computational intelligence,complex network analysis and recommender systems.

Wenfeng Liureceived the B.S.degree in intelligence science and technology from Xidian University,Xi'an, China,in 2015.Now he is working towards the Ph.D. degree in Pattern Recognition and Intelligent Systems at the School of Electronic Engineering,Xidian University,Xi'an,China.His current research interests include computational intelligence and network robustness analysis.

Jianan Yanreceived the B.S.degree in intelligence science and technology from Xidian University,Xi'an, China,in 2015,where he is currently pursuing the M.S.degree.His current research interests include computational intelligence and complex network analysis.

Licheng Jiaoreceived the B.S.degree from Shanghai Jiaotong University,Shanghai,China,in 1982,the M.S.and Ph.D.degrees from Xi'an Jiaotong University,Xi'an,China,in 1984 and 1990,respectively. Since 1992,Dr.Jiao has been a Professorin the School of Electronic Engineering at Xidian University,Xi'an, China.His research interests include image processing,natural computation,machine learning,and intelligent information processing.

Available online 12 November 2016

*Corresponding author.

E-mail address:gong@ieee.org(M.Gong). URL:http://web.xidian.edu.cn/mggong/

Peer review under responsibility of Chongqing University of Technology.

http://dx.doi.org/10.1016/j.trit.2016.11.002

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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/).