Front. Electr. Electron. Eng. 2012, 7(1): 16–31 DOI 10.1007/s11460-012-0192-0 Jun ZHANG, Wei-Neng CHEN, Zhi-Hui ZHAN, Wei-Jie YU, Yuan-Long LI, Ni CHEN, Qi ZHOU A survey on algorithm adaptation in evolutionary computation c Higher Education Press and Springer-Verlag Berlin Heidelberg 2012 Abstract Evolutionary computation (EC) is one of the fastest growing areas in computer science that solves intractable optimization problems by emulating biologic evolution and organizational behaviors in nature. To de- sign an EC algorithm, one needs to determine a set of algorithmic configurations like operator selections and parameter settings. How to design an effective and ef- ficient adaptation scheme for adjusting the configura- tions of EC algorithms has become a significant and promising research topic in the EC research community. This paper intends to provide a comprehensive survey on this rapidly growing field. We present a classification of adaptive EC (AEC) algorithms from the perspective of how an adaptation scheme is designed, involving the adaptation objects, adaptation evidences, and adapta- tion methods. In particular, by analyzing the popula- tion distribution characteristics of EC algorithms, we discuss why and how the evolutionary state information of EC can be estimated and utilized for designing ef- fective EC adaptation schemes. Two AEC algorithms using the idea of evolutionary state estimation, includ- ing the clustering-based adaptive genetic algorithm and the adaptive particle swarm optimization algorithm are presented in detail. Some potential directions for the re- search of AECs are also discussed in this paper. Keywords evolutionary algorithm (EA), evolution- ary computation (EC), algorithm adaptation, parameter control Received October 14, 2011; accepted December 27, 2011 Jun ZHANG , Wei-Neng CHEN, Zhi-Hui ZHAN, Wei-Jie YU, Yuan-Long LI, Ni CHEN, Qi ZHOU Department of Computer Science, Sun Yat-sen University, Guangzhou 510275, China Key Laboratory of Digital Life, Ministry of Education, Guangzhou 510275, China Key Laboratory of Software Technology, Education Department of Guangdong Province, Guangzhou 510275, China E-mail: [email protected]1 Introduction Evolutionary computation (EC) algorithms are a class of optimization techniques inspired by biologic evolution and organizational behaviors of living creatures. Gen- erally, EC algorithms include genetic algorithm (GA), evolutionary programming (EP), evolutionary strategies (ES), differential evolution (DE), estimation of distri- bution algorithm (EDA), particle swarm optimization (PSO), ant colony optimization (ACO), and memetic algorithm (MA). Instead of providing all details for im- plementation, the description of a specific EC algorithm usually leaves a number of factors undetermined. These factors, known as the configurations of ECs, include the setting of a particular parameter, the implementation of an operator, the structure of the population, etc. Investi- gations have shown that these algorithm configurations are crucial to the performance and behavior of ECs [1–4]. Finding appropriate configurations for ECs has long been an interesting and significant research topic in the EC community. Traditionally, fixed settings are applied to ECs. The algorithm configurations (e.g., the parame- ters and operators) are determined before execution ac- cording to prior guidelines or are tuned manually [2,5]. However, there are drawbacks with fixed settings. Both theoretical and empirical studies have shown that the op- timal configurations of an EC algorithm are specific to the optimization problems [6]. Predefined guidelines are inadequate for that they cannot be applied to numerous different application problems. Besides, the most bene- ficial algorithm configurations of ECs might be different in different stages of evolution [1,5,7–9]. The above facts indicate that fixed algorithm configurations cannot sat- isfy the requirements of optimization. To overcome the drawbacks of fixed settings, much research attention has been paid on controlling the EC configurations dynamically, among which the algorithm parameters control is the most popular research topic in most of the existing work. In Ref. [10], the parameter
Transcript
Front. Electr. Electron. Eng. 2012, 7(1): 16–31
DOI 10.1007/s11460-012-0192-0
Jun ZHANG, Wei-Neng CHEN, Zhi-Hui ZHAN, Wei-Jie YU, Yuan-Long LI, Ni CHEN, Qi ZHOU
Abstract Evolutionary computation (EC) is one ofthe fastest growing areas in computer science that solvesintractable optimization problems by emulating biologicevolution and organizational behaviors in nature. To de-sign an EC algorithm, one needs to determine a set ofalgorithmic configurations like operator selections andparameter settings. How to design an effective and ef-ficient adaptation scheme for adjusting the configura-tions of EC algorithms has become a significant andpromising research topic in the EC research community.This paper intends to provide a comprehensive surveyon this rapidly growing field. We present a classificationof adaptive EC (AEC) algorithms from the perspectiveof how an adaptation scheme is designed, involving theadaptation objects, adaptation evidences, and adapta-tion methods. In particular, by analyzing the popula-tion distribution characteristics of EC algorithms, wediscuss why and how the evolutionary state informationof EC can be estimated and utilized for designing ef-fective EC adaptation schemes. Two AEC algorithmsusing the idea of evolutionary state estimation, includ-ing the clustering-based adaptive genetic algorithm andthe adaptive particle swarm optimization algorithm arepresented in detail. Some potential directions for the re-search of AECs are also discussed in this paper.
Evolutionary computation (EC) algorithms are a class ofoptimization techniques inspired by biologic evolutionand organizational behaviors of living creatures. Gen-erally, EC algorithms include genetic algorithm (GA),evolutionary programming (EP), evolutionary strategies(ES), differential evolution (DE), estimation of distri-bution algorithm (EDA), particle swarm optimization(PSO), ant colony optimization (ACO), and memeticalgorithm (MA). Instead of providing all details for im-plementation, the description of a specific EC algorithmusually leaves a number of factors undetermined. Thesefactors, known as the configurations of ECs, include thesetting of a particular parameter, the implementation ofan operator, the structure of the population, etc. Investi-gations have shown that these algorithm configurationsare crucial to the performance and behavior of ECs [1–4].
Finding appropriate configurations for ECs has longbeen an interesting and significant research topic in theEC community. Traditionally, fixed settings are appliedto ECs. The algorithm configurations (e.g., the parame-ters and operators) are determined before execution ac-cording to prior guidelines or are tuned manually [2,5].However, there are drawbacks with fixed settings. Boththeoretical and empirical studies have shown that the op-timal configurations of an EC algorithm are specific tothe optimization problems [6]. Predefined guidelines areinadequate for that they cannot be applied to numerousdifferent application problems. Besides, the most bene-ficial algorithm configurations of ECs might be differentin different stages of evolution [1,5,7–9]. The above factsindicate that fixed algorithm configurations cannot sat-isfy the requirements of optimization.
To overcome the drawbacks of fixed settings, muchresearch attention has been paid on controlling the ECconfigurations dynamically, among which the algorithmparameters control is the most popular research topic inmost of the existing work. In Ref. [10], the parameter
Jun ZHANG et al. A survey on algorithm adaptation in evolutionary computation 17
control strategies in ECs are classified into three cate-gories, namely, the deterministic control, the adaptivecontrol, and the self-adaptive control. The determinis-tic control modifies the parameters according to deter-ministic rules, and utilizes no feedback from the evolu-tion. In contrast, both the adaptive control and the self-adaptive control are related to certain form of feedbackof the algorithm. The latter two strategies are preferredto deterministic control for that they consider the ac-tual progress of evolution. In this paper, both adaptivecontrol and self-adaptive control are regarded as “adap-tive” since the latter can be regarded as a subset of theformer.
Various adaptive ECs (AECs) with controlled config-urations have been developed, and the results of empiri-cal studies have shown to be encouraging. For all AECs,three issues should be addressed when designing adap-tation schemes. First, we have to determine what ob-jects in the AEC are to be adapted. That is, whetherthe parameters, operators, or population structures areto be adaptively controlled? Second, we have to deter-mine what evidences are used to activate the adaptation.That is, when to execute the adaptation? The evidenceincludes different forms of information on the evolution-ary process, e.g., fitness values, positional distributionof population, or both of them. Third, we have to de-termine what methods are used for controlling the ECalgorithm configurations.
In this paper, we conduct a comprehensive survey onthe design of adaptation scheme in ECs. Correspondingto the above-stated three issues, the adaptation schemesare classified according to three different taxonomies,i.e., the objects of control, the evidences of control, andthe methods of control. To provide a more insightful viewon the topic, we focus on a class of advanced AEC basedon estimation of the evolutionary state. To help betterunderstandings on their effectiveness, we will explain themotivation of introducing the “evolutionary state”, fol-lowed by detailed descriptions of the adaptation schemesin an adaptive GA (AGA) [11] and an adaptive PSO(APSO) [12]. Besides, potential research directions inthe AEC research area are discussed.
The rest of this paper is organized as follows. Sec-tion 2 presents classification of AECs according to threedifferent taxonomies. Two advanced AECs based on es-timation of evolutionary state are introduced in Section3. In Section 4, potential research trends for the AECsare discussed. Conclusions are finally drawn in Section5.
2 Classification of adaptation schemes
When designing an adaptation scheme for ECs, three as-pects need to be taken into considerations. 1) We have
to decide the component to be adapted in an EC algo-rithm, i.e., the adaptation objects. Major components ofan EC algorithm contain control parameters, evolution-ary operators, population structure, etc. 2) We shoulddecide what is the adaptation based on, i.e., the adapta-tion evidences. There are many kinds of evidences thatcan be used for adaptation. Among them, deterministicfactors, fitness values of individuals, and population dis-tribution are most commonly used. 3) After determiningthe evidence for adaptation, finally we need to design anadaptation method to perform the adaptive control. Theadaptation methods may be designed based on some sim-ple rules, or co-evolving the adaptation components withthe population. Other methods such as entropy-basedcontrol and fuzzy control methods are also frequentlyused. In the following contexts, we classify the adapta-tion schemes from the above perspectives and discusseach item in detail. The classification can be illustratedby Fig. 1.
2.1 Adaptation objects
The first criterion for classification naturally concernsthe adaptation objects. Considering the major compo-nents of an EC, we classify the adaptation objects intofour categories as control parameters, evolutionary op-erator, population structure, and others.
1) Control parametersAn EC algorithm may be associated with a set of
control parameters. Examples of control parameters indifferent EC algorithms are the crossover probability px
and mutation probability pm in GA [13,14], the inertiaweight w and acceleration coefficients c1, c2 in PSO [15],and the pheromone evaporation rate ρ in ACO [16,17].Table 1 summarizes the major control parameters in dif-ferent ECs. These control parameters have significant ef-fects on the optimization performance of the algorithms.This is because the values of them greatly influence theconvergence speed and population diversity. However, itis a difficult task to choose the right parameter values.First, different types of problems may need differentsuitable parameter settings, and these control param-eters are not independent but they interact with eachother. Thus, it is time-consuming and impractical tofind an optimal parameter setting empirically for a spe-cific problem. Second, different stages of evolution mayrequire different parameter values to achieve the bestperformance. For example, in the PSO algorithm, usinga large inertia weight w in the early stage is helpful to ex-plore new regions of the search space, and using a smallinertia weight w in the late stage is good at exploitingthe promising solutions. Therefore, it is more appropri-ate to adaptively control the parameter values during the
ant colony optimization (ACO) pheromone evaporation rate ρ
memetic algorithm (MA) local learning strategy
evolutionary process.
2) Evolutionary operators
The procedure of an EC involves a sequence of evo-lutionary operators, e.g., the mutation, crossover, andselection in GA, EP, and DE, velocity and position up-dates in PSO, and solution construction in ACO. An evo-lutionary operator can usually be implemented in differ-ent ways. For example, there exist many mutation strate-gies in DE algorithms (e.g., DE/rand/1, DE/best/1, andDE/current-to-best/1). It is observed that different mu-tation strategies are required for different evolutionarystates and different optimization problems to achieve thebest DE performance [18]. For instance, the DE/rand/1strategy is more suitable for exploration state and mul-timodal problems, while the DE/best/1 strategy is moresuitable for exploitation state and unimodal problems.Therefore, the adaptation of mutation strategies in DE isdesirable to make the algorithms less sensitive to differ-ent optimization scenarios. Another example is an elitistlearning strategy (ELS) designed in the APSO proposedby Zhan et al. [12]. The ELS performs adaptively only inthe convergence state of the optimization process. This
approach is helpful to maintain population diversity andavoid premature convergence.
3) Population structure
The dynamic changes of population size and popu-lation topology are two main forms of the populationadaptation in ECs. Determining an appropriate popu-lation size is usually a difficult task for ECs. Computa-tional resources may be wasted if the population size istoo large. In contrast, if the population size is too small,ECs may lose diversity too early and be trapped in localoptima. Therefore, various methods have been proposedfor adaptively controlling the population size for differ-ent ECs, such as GA [19], MA [20], DE [21,22], and mul-tiobjective optimization algorithms [23]. Regarding thepopulation topology, we take the PSO as an example.The main static topologies of PSO include global-best,local-best, pyramid, star, von Neumann, etc. [24]. Theireffects on PSO have been systematically studied in Ref.[24]. Recent research suggests that adaptive topologiescan be more competitive. The adaptive hierarchical PSO[25] and Frankenstein’s PSO [26] which use time-varyingpopulation topologies are capable of performing better
Jun ZHANG et al. A survey on algorithm adaptation in evolutionary computation 19
than those using static ones.
4) OthersApart from the above three categories of adaptive
components, other adaptation objects have been madeon the local search methods in MAs and migration strat-egy in parallel ECs, etc.
MA is one kind of hybrid ECs that combines globalsearch and local search procedures. Extensive researchhas shown that the local search methods or memes inMAs greatly influence the search performance of the al-gorithms. Nevertheless, these memes are often problem-dependent and it consumes a lot of time to select one fora particular problem. To enhance the robustness of MAs,many adaptive MAs have been proposed, using multiplememes in the search and adaptively applying one on anindividual. A detailed survey of memes adaptation inMAs can be found in Ref. [27].
Parallel ECs consist of multiple populations whichcommunicate with each other usually by a migration pro-cess. The behaviors of these algorithms are affected byparameters such as migration rate, migration size, andcommunication topology. In Ref. [28], a pseudocoevolu-tionary GA using an adaptive migration strategy is de-signed for power electronic circuit (PEC) optimization.With the adaptive control of the migration frequency,the effectiveness and efficiency in optimizing the circuitparameters have been improved. Such an adaptive mi-gration strategy was also applied to PSO by Zhan andZhang [29], and the experimental results demonstrate itspromising performance.
2.2 Adaptation evidences
After discussing which component of an EC algorithmcan be adapted, we next consider what the adaptationcan be based on. The evidence for adaptation can beclassified into one of the four categories, i.e., determin-istic factors, fitness values, population distribution, andcombination of fitness value and population distribution.
1) Deterministic factorsThe simplest evidence for algorithm adaptation may
be some deterministic factors. These factors are not re-lated to any information derived from the evolution.The generation number and fitness evaluations numberare two such factors most commonly used. Due to theirsimplicity and low computational cost, a lot of controlmethods are developed based on these factors. For ex-ample, the inertia weight w of PSO [15] and scale factorF of DE [30] are linearly decreased based on the gener-ation number. Merkle et al. [31] proposed an ACO algo-rithm for resource-constrained project scheduling prob-lem. They decrease the value of β linearly after 50% of
all generations, while start ρ with a small value and thenset it to a larger value for the last 200 generations. Asthese simple deterministic factors can hardly capture theevolutionary behavior of EC algorithms, the effects ofdeterministic-factor-based adaptation schemes are usu-ally limited.
2) Fitness valuesInstead of using deterministic factors, other adapta-
tions are made based on some form of feedback fromthe search. Since the improvement of fitness values aredesired for all ECs, the fitness values of individuals areconsidered as one natural and direct form of feedback.The fitness values can be measured at two levels, i.e.,the individual level and population level.
For the individual level, each individual often main-tains its own parameters which are controlled accord-ing to the individual fitness value. In the adaptive DE(JADE) proposed by Zhang and Sanderson [32], eachindividual is associated with its own parameter F andCR. It is believed that better parameter values lead tobetter individuals and they should be propagated to thenext generation. The parameter values for each individ-ual are recorded if the fitness value of the individualis better than that of the previous generation. The pa-rameter control process is then performed based on therecord of parameter values that lead to better fitness val-ues. Cai et al. [16] and Hao et al. [17] proposed adaptiveACOs for the traveling salesman problem. In their algo-rithms, each ant maintains its own value of parameter ρ,which is updated according to the quality of its solution.The motivation of the adaptation is that better solutionscontribute more pheromone than the worse ones.
In other adaptation schemes, fitness values are mea-sured at the population level and the parameters are alsoadapted for the whole population. For example, the ad-justments of px and pm in Refs. [13] and [14] are basedon the relationship between the average and maximumfitness values of the population. Similarly, the parameterF of DE in Ref. [33] is adaptively adjusted based on theminimum and maximum objective function values overthe individuals in each generation. There are also someother examples found in the adaptive PSO algorithms[34–36].
3) Population distributionBesides the fitness values, population distribution in
the search space is another form of feedback for adapta-tion evidence. The population distribution is often usedto reflect the population diversity. In such cases, allthe population members are usually associated with thesame adaptive parameters. A number of adaptive GAscontrol the crossover probability px or mutation prob-ability pm based on the population diversity. In theseapproaches, population diversity can be measured by
metrics such as Hamming distance [37,38] and other sta-tistical information [39]. Another example is an adap-tive DE algorithm (ADEA) [40] proposed for multiob-jective optimization problems. In ADEA, the parameterF is decided by the number of Pareto-front and the rel-ative crowding distance of the current solutions. OtherAECs adjust the parameters for each individual based onits relative position. For example, the particles in someadaptive PSO adjust their own inertia weight or acceler-ation coefficients according to the relationship betweentheir current positions and their personally best position[41] or the globally best position [42].
4) Combination of fitness value and populationdistribution
Some other adaptation evidences take both the fitnessvalues and the population distribution information intoconsideration. In Refs. [11] and [12], such informationis used to estimate the optimization states of the evolu-tionary process for GA and PSO, respectively. For theAGA [11], the population is first partitioned into clus-ters. Each cluster contains those individuals with similarcomponent vectors. Then, the px and pm are adjustedbased on considering the relative size of cluster contain-ing the best individual and the one containing the worstindividual. For the APSO [12], the estimation of evolu-tionary state is based on the assumption that the meandistance from the globally best particle to other particlesvaries during the evolutionary process. In each genera-tion, the relative mean distance of the globally best par-ticle is calculated for evolutionary state estimation andthe parameters are controlled accordingly. Different fromthe above two AECs, based on considering the fitnessvalues and population distribution information, Nguyenet al. [43] proposed an adaptation mechanism for indi-vidual learning intensity and developed a probabilisticmemetic framework. The characteristics and efficaciesof this framework are demonstrated by both theoreticaland empirical studies.
2.3 Adaptation methods
Designing a method for adaptation is the last step whenwe develop an adaptation scheme for EC. In this part wewill introduce some commonly used adaptation methodslike rule-based adaptation methods, coevolution meth-ods, entropy-based control methods, and fuzzy controlmethods.
1) Simple rule-based adaptation methodsIn many adaptation methods for EC, the adaptation is
based on simple rules defined by the observations of run-time characteristics of the evolutionary algorithms. Forexample, in Ref. [44], the author proposed that the pm
in GA is changing in an exponential way. This methodis proposed based on the observation on the convergencetrends of GA algorithm. There are also many parameteradaptation methods based on the fitness values of eachindividual in the population. Different parameters areused for individuals according to their fitness values. InRef. [13], the authors proposed the px and pm adapta-tion rules based on the fitness information as follows (forminimization optimization problem):
px =
{px1 − (px1−px2 )(f ′
t−ft,avg)
ft,max−ft,avg, if f ′
t � ft,avg,
px1 , otherwise,(1)
where px1 and px2 are constant values which are used tocontrol the range of the crossover probability. The mo-tivation of Eq. (1) is that when the fitness value of anindividual is better than the average fitness value, thenthe individual will use a large crossover rate and viceversa.
There are also similar approaches in PSO algorithms.In Ref. [35], the authors proposed a fitness based methodto adjust the parameter w as
w = k1
∣∣∣∣ f ′ − fmin
fmax − fmin
∣∣∣∣ + ε · k2, (2)
where f ′ is the current fitness value of the particle, fmin
is the current best fitness value of the whole popula-tion, and fmax is the optimal fitness of the worst parti-cle at present. k1 and k2 are two constant factors usedto control the range of the generated parameter, and ε
is a random factor used to enhance the diversity of thegenerated parameter. With better fitness, the generatedparameter will be smaller. In Ref. [45], the authors alsoused the fitness information to define rules to control theparameter for PSO, but in a more complicated form:
ωti = ω1 · 2
(1 − cos
(π
2ξti
))+ ω2, (3)
where
ξti =
{(f t−1
i − f t−1G )/f t−1
i , f t−1i �= 0,
0, f t−1i = 0.
(4)
Different from the other fitness based methods usingdirect linear transformation, in the above method, thefitness information is normalized by a cosine function,which is nonlinear. Exponential transformation is alsoused to apply the fitness information to adjust the pa-rameter w in PSO [41].
Covariance matrix adaptation ES (CMA-ES) [46–49]is one of the most promising evolutionary algorithmswhich can be used to solve some very difficult functions.The key mechanism of CMA-ES is the covariance matrixadaptation (CMA). CMA is based on the observationthat the distribution model should be updated in an ac-cumulated way. The evolution path information is alsoused to adapt the covariance matrix in order to let thealgorithm explore along the current improving direction.
Jun ZHANG et al. A survey on algorithm adaptation in evolutionary computation 21
CMA-ES shows its efficiency on the complex functionsdue to the adaptation method.
2) Coevolution methodsCoevolution methods use some kind of parameter gen-
eration mechanisms and put these parameters into evo-lution process [50–52]. The parameters are co-evolvedwith the population in every generation. Usually, differ-ent parameters are generated for every individual. Theparameters of the better individuals will survive in theevolution process and will be used to generate the newparameters.
The self-adaptive methods usually directly encode theparameters of the EC algorithms into the evolution pro-cedure itself. The parameters are directly encoded intothe original individuals and goes through the evolutionprocedure as genes of the population with the samemethods as the original genes [32,53]. There are also dif-ferent approaches like that in Refs. [54,55], where theparameters go through a different evolution procedurefrom the original population. In Ref. [54], the param-eters are affected by a Gaussian random perturbationand in Ref. [55], the parameters of an ACO algorithmare self-adaptively adjusted by PSO. In Ref. [56], Zhanand Zhang applied the PSO learning strategy to the DEalgorithm so as to evolve the DE parameters during theevolutionary process. In Ref. [57], the authors proposeda fuzzy controller based on a co-evolving GA. The fuzzycontroller is going through a separate GA to adjust thefuzzy rules.
3) Entropy-based control methodsEntropy-based control methods are widely used in EC
algorithms for parameter adaptation [58–65]. In the in-formation theory, entropy is used to measure uncertaintywith a random variable. In EC algorithms, the genera-tion of new individuals often contains some random fac-tors and the probability of generating a certain solutioncan be analyzed based on the population information.Therefore, entropy can be used to analyze the popula-tion characteristic of EC algorithms and the parametersand operators can be adjusted accordingly. The mostcommon entropy-based control method is to computethe Shannon entropy according to the probabilities pi ofgenerating certain individuals:
S(t) =n∑
i=1
pi(t) log pi(t). (5)
From the above formula we can see that when theprobability of generating a certain solution becomeshigh, the entropy will become smaller. The maximumentropy Smax can be achieved when all the probabilitiesare equal. Thus this entropy value can be used as an indi-cator for population convergence. Usually the probabil-ities of generating different individuals can be achieved
by simple analysis. For example, in the ACO [60], theprobability of generating an individual in the currentpopulation is computed by the rate of pheromone onthe solution:
pi(t) =τi(t)∑
m∈pop τm(t), (6)
where pop is the current population.From the above analysis we can see that entropy is
just a measure of uncertainty of the current state basedon some kinds of pi. There are many different ways toevaluate the uncertainty of the probability distribution.For example in Ref. [66], the probability distribution ofgenerating different individuals is first computed basedon the pheromone trails. Then, the average value is cal-culated and the number of probability values larger thanthe average value is counted to be a state value to showthe balance state. If the count number is small, the prob-ability distribution is unbalanced and thus the popula-tion is more converged.
The entropy indicator can be used in many ways. Forexample, it can be used in some other controllers likethe fuzzy controller [11]. Besides, it can also be used di-rectly. In Ref. [60], the entropy information is used toadjust the evaporating rate of pheromone trails. The lo-cal pheromone evaporation rate is set to a small valueat the early stage of convergence (when the entropy islarge) and is set to a large value when the population be-comes converged to avoid stagnation. This can be doneeasily with the state evaluation quantity variable(s). Thestate evaluation variable can be used as a condition toperform adjustment or not [41,67], and can also be usedin linear transformation [60,68] and nonlinear transfor-mation [69].
4) Fuzzy control methodsFuzzy controllers have been widely used currently
[11,12,34,70,71]. A fuzzy controller converts an input(e.g., certain information on the population) to an out-put (e.g., actual actions for parameter control or opera-tor control) based on a set of fuzzy rules. In Ref. [57] theauthors summarized the fuzzy controller models usuallyapplied to EC algorithms. The fuzzy controller model isdifferent from the other parameter adaptation methodsfor its well defined process stages and forms. A fuzzycontroller often has three procedures in a row to do thecontrol work. First the input signals or other informationare mapped into the membership functions and truthvalues. Fuzzy logic theory defines the concept of fuzzyset, a kind of set which permits an element to partiallybelong to the set. The degree an element belongs to afuzzy set is indicated by the membership function valuedin real interval [0, 1]. The mapping by the membershipfunction is the fuzzification process of the original inputmessage. After the mapping some rules will be invoked
and the membership information can then be processedand the results of different rules will be combined. Theserules are in the form of “IF THEN” statement. The truthvalue of each rule will be computed. The defuzzificationprocess will then be applied to transform these truth val-ues and control actions into the actual actions to do thecontrol.
Using the fuzzy controller in EC algorithms is quitesimple. The membership functions are used to evaluatethe current state and then rules can then be proposedbased on the state considered. Finally the rules will beused to control the parameters. The design of the mem-bership function can be various according to the stateconsidered. For example in Ref. [66], a cloud model isused to evaluate the current state. Various state eval-uation methods can be applied as long as they can beadapted to the form of a fuzzy membership function.
After computing the membership functions, the con-trol rules can also be designed with great freedom. InRef. [66] the controller is used to decide whether to doan additional pheromone updating or not. In Ref. [11]the controller is used to increase or decrease the param-eter values.
3 AEC based on evolutionary state
As reviewed in Section 2, a lot of AECs have been pro-
posed. In this section, we pay more attention to theAECs based on the evolutionary state. Our motivationsof introducing the evolutionary state into ECs are basedon the following two considerations.
First, the population and the searching behavior of theEC algorithm exhibit different characteristics in differentstates of evolution. We take PSO as an example. Sim-ilarly to the investigations in Ref. [12], a time-varying2-D sphere function f(x − r) = (x1 − r)2 + (x2 − r)2,xi ∈ [−10, 10], is employed to help illustrate the dy-namic of particles distribution of PSO. The total gen-eration number is set as 100, and the minimum of thefunction initialized at (−5,−5) shifts to (5, 5) at the50th generation. When a global version PSO with 100particles optimizing function f , the particle distributionin different running phases is illustrated in Fig. 2 (referto Fig. 1 of Ref. [12]).
It can be observed in Fig. 2(a) that all the particlesdistribute uniformly in the search space at the begin-ning of the searching process. Later all the particles flytoward the global optimum at (−5,−5) as in Fig. 2(b).The whole swarm then gathers close around the bestparticle as in Fig. 2(c). In Fig. 2(d) when the global op-timum of function f is shifted, the best particle quicklyjumps out from the center of the swarm and guides theswarm toward the new optima as in Fig. 2(e). In Fig.2(f) the PSO reaches a second convergence. From Fig.2 we can see that the population distributions of PSO at
Fig. 2 Population distribution of PSO at different stages. (a) Generation = 1; (b) Generation = 25; (c) Generation = 49; (d) Generation= 50; (e) Generation = 60; (f) Generation = 80
Jun ZHANG et al. A survey on algorithm adaptation in evolutionary computation 23
different stages differ significantly from each other. Thebest particle is closely surrounded by the swarm whenthe algorithm has converged, whereas the best particle isfar away from the crowding swarm when a new promis-ing region is discovered. Otherwise, when the algorithmfocuses on exploration, the whole swarm makes a com-prehensive and scattered coverage of the search space.
The above observations suggest that the searchingprocess of PSO can be identified as in one of severalstates. These states are termed as evolutionary state asdefined in Ref. [12]. In each evolutionary state, the char-acteristics of population, e.g., the positional relationshipbetween the best particle and other particles, are differ-ent from the other states.
Second, the ECs in different evolutionary state needdifferent algorithm settings. We can still take the PSOas an example. At the state aiming at exploration, a pa-rameter setting which helps the particles to learn morefrom its self experience is preferred. Thus the PSO canmake a thorough search on as many optima as possibleand avoid being cheated by local ones. However, whenthe best particle jumps out from the local optima, theparameter setting should emphasize more on the socialcognition, which will guide the swarm toward the newlydiscovered promising region. In general, the parametersetting should follow the objective of ECs in differentevolutionary states.
Based on the above considerations, it is beneficial toadaptively adjust the algorithm configurations of ECsbased on the evolutionary state. When designing theadaptive algorithms based on evolutionary state, the twofollowing problems should be first settled.• How to determine the evolutionary state of the ECs?• How to control the algorithm configurations of ECs
based on the evolutionary state?By solving the above-stated problems, an implemen-
tation of AECs based on evolutionary state can be given.The AGA in Ref. [11] and the APSO in Ref. [12] are twosuccessful examples, both of which are designed throughstudies on population distribution characteristics and fit-ness information of the algorithm. The detailed descrip-tions of the two algorithms are presented as follows.
3.1 Clustering-based adaptive GA
The basic flow of the proposed AGA [11] is similar tothat of traditional GA, except that the values of px andpm are updated according to the proposed parameteradaptation scheme in each generation.
The parameter control in the proposed AGA mainlyinvolves three tasks. One is to depict the distribution ofpopulation using the clustering technique. Another taskis the design of a set of fuzzy rules for maturity state es-timation and parameter adjustment. The last task is to
identify the maturity state and control the parametersbased on the results of clustering and the fuzzy rules.
1) Clustering of populationThe K-means [72,73] algorithm is employed to depict
the population distribution by partitioning the popula-tion into K different clusters. Among the K clusters,the cluster containing the best individual is denoted asGB, and the cluster containing the worst individual isGW. For generalization, the sizes of the GB and GW
are normalized by the differences of |Gmax| (the size ofthe largest cluster) and |Gmin| (the size of the smallestcluster) as in Eqs. (7) and (8):
GB =|GB| − |Gmin||Gmax| − |Gmin| , (7)
GW =|GW| − |Gmin||Gmax| − |Gmin| , (8)
where GB and GW denote the relative size of GB andGW, respectively.
The relationship between individual fitness and posi-tional distribution in the search space is outlined by thenormalized sizes of GB and GW (i.e., GB and GW). Theseresults provide necessary information for the estimationof maturity state and parameter control.
2) Fuzzy rules for maturity state estimation andparameter control
Based on the results of clustering, the maturity stateof search is estimated. A set of fuzzy rules are designedfor the maturity state estimation and the adjustmentsof px and pm.
For each maturity state, mainly three questions aretaken into consideration in the design of rules. First, theneed to encourage or discourage the reproduction of pop-ulation outside the existing clusters is considered. Thisis largely related to the crossover probability px. Second,the need to encourage or discourage the reproduction ofpopulation within the existing clusters should be takeninto consideration. This is largely related to the muta-tion probability pm. Finally, the need to combine theabove two guidelines is considered.
The rules for the adjustments of px and pm are tabu-lated in Table 2 (Table II in Ref. [11]). These rules areexplained as follows.
Rule 1 — matured state: The best individual isin a large cluster, and the worst individual is in a smallcluster. In this situation, the values of px and pm arereduced.
The optimization process is considered to be in thematured state. This situation implies that a large num-ber of similar individuals are likely to swarm togetheraround the best solution. Chances of reproducing better
Rule 1 = (Rule (1,0)): if (GB is PB) and (GW is PS) then
θpx = NB
Rule 2 = (Rule (1,1)): if (GB is PB) and (GW is PB) then
θpx = PB
Rule 3 = (Rule (0,0)): if (GB is PS) and (GW is PS) then
θpx = PB
Rule 4 = (Rule (0,1)): if (GB is PS) and (GW is PB) then
θpx = NB
rule for θpm
Rule 1 = (Rule (1,0)): if (GB is PB) and (GW is PS) then
θpm = NB
Rule 2 = (Rule (1,1)): if (GB is PB) and (GW is PB) then
θpm = NB
Rule 3 = (Rule (0,0)): if (GB is PS) and (GW is PS) then
θpm = PB
Rule 4 = (Rule (0,1)): if (GB is PS) and (GW is PB) then
θpm = PB
individuals through crossover and mutation are rela-tively small. Thus the values of px and pm are reduced.
Rule 2 — maturing state: The best individual isin a large cluster, and the worst individual is in a largecluster. In this situation, the value of px is increased andthe value of pm is reduced.
The optimization process is considered to be matur-ing. Here both GB and GW are likely to be the largestcluster. The algorithm has to achieve two goals. First,since the direction for exploration is largely undeter-mined, new search directions should be explored. Sec-ond, the convergence of population should be encour-aged. To achieve the above two goals, the algorithm isexpected to reproduce more individuals in and aroundthe existing clusters, and to avoid breeding individualsoutside the current population. Thus the value of px isincreased and the value of pm is reduced.
Rule 3 — sub-maturing state: The best individ-ual is in a small cluster, and the worst individual is in asmall cluster. In this situation, the values of px and pm
are increased.
The optimization process is considered to be in thesub-maturing state. Both GB and GW are probably thesmallest cluster. The region containing global optimumhas not been located and the direction of search is un-determined. To explore new search directions, breed-ing more individuals outside the existing population isrequired. On the other hand, the population has notswarmed around the best solution. The algorithm is ex-pected to reproduce more offspring in and around GB
for local exploitation. Thus the values of px and pm areincreased.
Rule 4 — initial state: The best individual is in
a small cluster, and the worst individual is in a largecluster. In this situation, the value of px is reduced andthe value of pm is increased.
The optimization process is considered to be in the ini-tial state. The situation implies that the evolution hasjust started. In the initial stage of evolution, finding newsearch directions is necessary for the exploration of thewhole search space. Thus the value of pm is increasedand the value of px is decreased.
3) Fuzzy control of px and pm
The mechanism of adjusting the values of px and pm
is based on fuzzy control, which consists of three com-ponents, i.e., fuzzification of variables, rule-based fuzzyinference, and defuzzification.
Fuzzification of variables: Two input variables, i.e.,GB and GW, are mapped to linguistic values throughfuzzy membership functions. For each of the variables,two fuzzy subsets are defined, including positive small(PS) and positive big (PB). The membership functionsfor the two fuzzy subsets on each variable are given inEqs. (9) and (10):
μ0(G) = 1 − G, (9)
μ1(G) = G. (10)
Rule-based fuzzy inference: Based on the fuzzified in-put variables and the fuzzy rules in Table 2, the controlactions of parameters px and pm are inferred. The fuzzyinference considers all the four rules. Take Rule (1,0) forexample, the membership of the output fuzzy set m1,0
is calculated by multiplying μ1(GB) and μ0(GW), where
m1,0 = μ1(GB)μ0(GW). (11)
Defuzzification: To output the changes of the valuesof px and pm, the results of fuzzy inference should beconverted to crisp values. The actual values of px andpm are the sum of their values in the previous genera-tion (px,gen−1 and pm,gen−1) and the output of the fuzzycontroller, as given in Eqs. (12) and (13):
px,gen = px,gen−1 + Kxθpx , (12)
pm,gen = pm,gen−1 + Kmθpm . (13)
Here Kx and Km are used to control the changes of px
and pm to be within a reasonable level. The variablesθpx and θpm are the defuzzified fuzzy decisions derivedfrom the four fuzzy rules. The defuzzification is appliedaccording to the formulas (14) and (15):
θpx =
i=1∑i=0
j=1∑j=0
m1,0yij
i=1∑i=0
j=1∑j=0
m1,0
, (14)
Jun ZHANG et al. A survey on algorithm adaptation in evolutionary computation 25
θpm =
i=1∑i=0
j=1∑j=0
m1,0zij
i=1∑i=0
j=1∑j=0
m1,0
, (15)
where the values of yij and zij are either +1 or −1, whichare determined by the corresponding rule. For example,the action in Rule (1,0) for θpx is “NB”, and the valueof y10 is −1.
4) Experimental resultsIn Ref. [11], experiments are conducted on two groups
of problems to investigate the performance of the pro-posed AGA. The first group includes a set of mathe-matical functions, whereas the second group includes anapplication problem of PEC.
On all of the mathematical functions, the proposedAGA with controlled parameters consumes a smallernumber of evaluations to achieve the global optimumthan traditional GA. On the application problem, theproposed method significantly improves the performanceof GA in terms of search speed and solution quality.These results verified the effectiveness of the proposedparameter control strategy.
3.2 Adaptive PSO
The basic idea of APSO is to adaptively control the pa-rameter and strategy of PSO according to the currentstate revealed in the evolutionary process of PSO. Theadaptation procedure of APSO consist mainly two steps,the evolutionary state estimation (ESE) step and the pa-rameter and strategy control (PSC) step.• ESE step: evaluate the current evolutionary state of
APSO based on the population distribution and particlefitness.• PSC step: adaptively control the parameter and
strategy of APSO according to the current evolutionarystate.
1) Evolutionary state estimationZhan et al. [12] have proposed a novel ESE approach
by analyzing the search behavior and the population dis-tribution characteristic of the PSO. In Ref. [12], fourevolutionary states of PSO have been presented, namelyexploration, exploitation, convergence, and jumping-outstates. The authors indicated that the positional rela-tionship between the best particle and the other particlesis an efficacious measure to mark off the current evolu-tionary state of PSO as one of the four states. When thebest particle is surrounded by the swarm, the PSO ismore likely to be in the convergence state. At this point,the globally best particle obtains a minimal mean dis-tance to the whole swarm than any other particle. Other-wise, when the best particle is far away from the crowd-ing swarm, the PSO is more likely to be in the jumping-out state. At this point, the globally best particle obtainsa maximal mean distance to the whole swarm. Hence,a normalized evolutionary factor f reflecting the com-paratively distance from the best particle to the wholeswarm is defined as Eq. (16) to indicate the current stateof PSO:
f =dgbest − dmin
dmax − dmin, (16)
where di is the mean Euclidian metric between the ithparticle and the whole swarm which is formulized as
di =1
N − 1
N∑j=1
√√√√ D∑k=1
(xki − xk
j ), (17)
N and D are the population size and the problem di-mension respectively. Thus dgbest is the mean Euclidianmetric between the globally best particle and the wholeswarm, and dmax and dmin are the maximum and mini-mum distances of all di’s.
A fuzzy classifier is adopted to map the normalizedevolutionary factor f into the current evolutionary stateof PSO as in Fig. 3.
2) Parameter and strategy controla) Adaptive parameter control
Three parameters, i.e., the inertia weight w, andthe acceleration coefficients c1 and c2 are adaptively
Fig. 3 Fuzzy membership functions for the four evolutionary states
adjusted based on the normalized evolutionary factorf and current evolutionary state obtained in the ESEsteps. The details are as follows.
The inertia weight w is an important parameter whichplaces a vital influence on balancing the exploration andexploitation ability of PSO. A comparatively larger w
is preferred for PSO to make a more thoroughly searchin the exploration state and a comparatively smaller w
is preferred to accelerate the converging speed of PSOin the exploitation state. The adaptation of the inertiaweight w is illustrated as
w(f) =1
1 + 1.5e−2.6f∈ [0.4, 0.9], (18)
where f is the normalized evolutionary factor computedas Eq. (16).
The acceleration coefficients c1 and c2 are two param-eters deciding the relative weight that the particle learnsfrom its own experience, i.e., the self-cognition, or thewhole swarm’s experience, i.e., the social influence. PSOwith a larger weight of c1 is more likely to pull the par-ticle towards its historical best position, thus keeps thediversity and leads to a more thorough exploration ofall the local niches. On the contrary, PSO with a largerweight of c2 is more likely to push the swarm towards theglobal best region, thus enjoys a fast converging speed.Four operations, i.e., increase (++), slightly increase(+), decrease (– –) and slightly decrease (–) are em-ployed on acceleration coefficients c1 and c2 accordingto the evolutionary state. The operation increase (++)or slightly increase (+) on ci means that one “accelera-tion rate” δ or half of δ is added to ci, respectively. Thedecrease operations are analogous with the increase op-erations. The adaptations of the acceleration coefficientsc1 and c2 are detailed as shown in Table 3.
Table 3 Fuzzy control of the acceleration coefficients c1 and c2
evolutionary state adjustment on c1 and c2
jumping-out – – c1 and ++ c2
exploration ++ c1 and – – c2
exploitation + c1 and – c2
convergence + c1 and + c2
Jumping-out state: Decrease c1 and increase c2. Atthis state, the global best particle has jumped out of thecrowding swarms and obtained a better solution. By de-creasing c1 and increasing c2, much more emphasis isput on the social experience in the learning process ofthe particles, which can help the whole swarm to moveto the promising region as quickly as possible.
Exploration state: Increase c1 and decrease c2. Atthe exploration state, a thorough search on as many op-tima as possible is expected. Increasing the weight ofc1 forces the particles to fly close around their histori-cal best position and explore individually in a variety of
promising regions, instead of gathering together aroundthe current best particle.
Exploitation state: Slightly increase c1 and slightlydecrease c2. At the exploitation state, the particles aregrouping into different clusters around the correspond-ing local optima of their historical best positions. A fullexploitation of all the potential local niches is expectedat this state to avoid the deception of the local optima.Slightly increasing the weight of c1 can achieve this tar-get.
Convergence state: Slightly increase c1 and slightlyincrease c2. At this state, a global optima region seemsto be found. Slightly increasing c2 can attract the otherparticles to fly toward the probable optima region. Onthe other hand, by slightly increasing c1, the PSO canavoid too fast a converging speed which may lead toover-premature.
After the adaptive adjustment on the acceleration co-efficients c1 and c2, a bounding and normalization op-eration is performed on them to ensure a more stableperformance of APSO. Both c1 and c2 are clamped be-tween [1.5, 2.5], and their sum is bounded between [3.0,4.0]. If the sum of the two parameters exceeds the upperbound 4.0, c1 and c2 are normalized to
ci =ci
c1 + c2× 4.0. (19)
Note that after the bounding and normalization op-eration of c1 and c2, slightly increasing c1 and slightlyincreasing c2 in the convergence state will eventually leadto a slight decrease on c1 and a slight increase on c2 be-cause c1 and c2 will be drawn to 2.0 when they are bothbeyond the upper bound 4.0.
b) Adaptive strategy controlAs the global best particle of PSO has no exemplars
to follow, Ref. [12] proposed a perturbation-based elitistlearning strategy (ELS) to give some fresh momentumto the global leader. The ELS randomly chooses one di-mension of the best particle’s historical best position andperforms a Gaussian perturbation as follows:
P d = P d + (Xdmax − Xd
min) × Gaussian(μ, δ2), (20)
where [Xdmin, X
dmax] is the search bound of the problem.
Gaussian(μ, δ2) is a random number following the Gaus-sian distribution. The mean μ of the Gaussian distribu-tion is set as zero and the standard deviation δ is linearlydecreasing with the evolutionary generation as
δ = ∂max − (∂max − ∂min) × g
G, (21)
where g and G are the current generation and total gen-erations respectively. ∂max and ∂min are the upper andlower bound of ∂ which are empirically set as 1 and 0.1.
The employment of different strategies is also adap-tively adjusted according to the current evolutionarystate of PSO. The ELS is employed by the APSO only in
Jun ZHANG et al. A survey on algorithm adaptation in evolutionary computation 27
the convergence state to help the best particle to jumpout of the probable local optima regions and enhancethe globally search ability of APSO. Nevertheless, in theother states, the classical PSO learning strategy is em-ployed because the problem of jumping out from thelocal optima is not the critical issue in these states.
4 Potential research directions
Although during the last decades, research on the adap-tation of ECs has reached an impressive state, there arestill many open problems and exciting issues to be re-searched. Below, we unfold some important future direc-tions in the area of EC algorithm adaptation.
First, the relationship between the algorithm adap-tation (especially the parameters adaptation) and theperformance of ECs should be further investigated. Amore clear clarification on the mechanism of how the pa-rameters work should presented. This is very importantto design parameter adaptation methods. In addition,as there are strong similarities and connections betweendifferent EC algorithms, it is very interesting to studywhether there is a common parameter adaptation frame-work for all the EC algorithms.
Second, more researches should be carried out on thetheoretical analysis on the algorithm adaptation of ECs.Most techniques used to adapt the algorithm configu-rations in ECs are simple and based on the experienceof the designers. The theoretical studies can provide asolid foundation and a powerful guidance in designingthe adaptation strategies for ECs. Moreover, whetherthe ECs can still preserve the convergence characteristicby using algorithm adaptation is worth of studying.
Third, the techniques from machine learning (ML)and other domains should be introduced to the EC al-gorithm adaptation control methodology. The ML tech-niques, which have attracted a lot of interests fromresearchers all around the world, own firm theoreticalfoundation and show favorable performance on many ap-plications. Recent researches have also shown that incor-porating ML techniques into EC algorithms can improvetheir performance significantly [54,74]. For example, in-spired from the idea of ensemble learning in ML domain,Qin et al. [54] proposed a similar concept for DE to forman ensemble of mutation strategies and parameter val-ues which competes to produce successful offspring pop-ulation. In addition, reinforcement learning can be usedto design a new parameter reinforcement learning strat-egy which could benefit from the profound reinforcementlearning theory. Theory of automatic control should befurther used in current AECs.
Fourth, the algorithm adaptation methodology of ECsin complex environments should be further studied. Cur-rently, the researches on AECs are mainly focused on
normal discrete and continuous optimization problems.However, a lot of complex optimization, e.g., multiobjec-tive optimization, constrained optimization, large-scaleoptimization, dynamic and uncertain environment, hasdrawn more and more attention from researchers. Thealgorithm adaptation schemes which exhibit favorableperformance on normal optimization problems may actpoorly on complex optimization problems. Hence, howto design promising algorithm adaptation schemes basedon the special demands of these complex optimizationproblems is very meaningful and still leaves much to bedone.
5 Conclusion
In this paper, we have provided a comprehensive surveyon adaptation schemes in ECs. Following the steps of de-signing an adaptation approach, the taxonomy of workin this area has been defined. The proposed classifica-tion is based on three aspects: 1) adaptation objects,2) adaptation evidences, and 3) adaptation methods.Adaptation schemes found in the literature have beenclassified into corresponding categories and extensivelydiscussed. Such a survey provides an overall pictureof the relevant research in the area and can be servedas a guide when designing an adaptation scheme forECs. Moreover, a kind of promising adaptation meth-ods based on estimation of evolutionary state have beenfurther discussed. Two representative AECs using suchadaptation method are introduced in detail. In the endof this paper, some potential research directions havealso been suggested based on the survey of the existingapproaches.
Acknowledgements This work was supported in part by theNational Science Fund for Distinguished Young Scholars (No.61125205), the National Natural Science Foundation of China(NSFC) (Grant No. 61070004), and NSFC Joint Fund with Guang-dong under Key Project U0835002.
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Jun ZHANG (M’02–SM’08) re-ceived the Ph.D. degree fromDepartment of Electronic Engi-neering, City University of HongKong, Hong Kong, China, in2002.
He is currently a Professorwith the Department of Com-
puter Science, Sun Yat-sen University, Guangzhou,China. He has authored seven research books and bookchapters, and over 100 technical papers in his researchareas. His research interests include computational intel-ligence, operations research, data mining, wireless sensornetworks, and power electronic circuits.
Dr. Zhang received the National Science Fund for Dis-tinguished Young Scholars from the National NaturalScience Foundation of China in 2011. He received theFirst-Grade Award in Natural Science Research fromthe Ministry of Education, China, in 2009. Dr. Zhangis currently an Associate Editor for the IEEE Trans-actions on Industrial Electronics, and Associate Editorfor IEEE Computational Intelligence Magazine. He isthe founding and current Chair of the IEEE GuangzhouSubsection and the IEEE Beijing (Guangzhou) SectionComputational Intelligence Society Chapter.
Wei-Neng CHEN received theBachelor’s degree in network en-gineering in 2006 from the SunYat-sen University, Guangzhou,China, where he is currentlyworking toward the Ph.D. degreein the Department of ComputerScience. His current research in-
terests include evolutionary computation and its ap-plications on financial optimization and operations re-search.
Zhi-Hui ZHAN received theBachelor’s degree in computerscience and technology from SunYat-sen University, Guangzhou,China, in 2007, where he is cur-rently working toward the Ph.D.degree. His current research in-terests include particle swarm
optimization, ant colony optimization, differential evo-lution, genetic algorithms, and their applications in real-world problems.
Wei-Jie YU received his Bache-lor’s degree in network engineer-ing in 2009 from Sun Yat-senUniversity, Guangzhou, China,where he is currently working to-ward his Ph.D. degree in the De-partment of Computer Science.His current research interests in-
clude differential evolution, ant colony optimization,particle swarm optimization, and other evolutionary al-gorithms.
Yuan-Long LI received the B.A.degree in mathematics from SunYat-sen University, Guangzhou,China, in 2009. He is currentlyworking toward the Ph.D. de-gree in computer science fromthe Sun Yat-sen University,Guangzhou, China. Currently,
his main research areas are meta-heuristics and evolu-tionary computation, which includes differential evolu-tion, CMA-ES, and so on.
Jun ZHANG et al. A survey on algorithm adaptation in evolutionary computation 31
Ni CHEN received the Bach-elor’s degree in computer sci-ence from Sun Yat-sen Univer-sity, Guangzhou, China, in 2009,where she is currently workingtoward the Ph.D. degree withthe Department of Computer
Science. Her current research interests include particleswarm optimization, genetic algorithms, and other com-putational intelligence techniques.
