1、New Ways to Calibrate EvolutionaryAlgorithmsA.E. Eiben, M.C. SchutDepartment of Computer Science, Faculty of Science,VU University, Amsterdam, The Netherlands.fae.eiben,mc.schutgfew.vu.nlSummary. The issue of setting the values of various parameters of an evolutionaryalgorithm (EA) is crucial for go
2、od performance. One way to do it is controlling EAparameters on-the- y, which can be done in various ways and for various parameters.We brie y review these options in general and present the flndings of a literaturesearch and some statistics about the most popular options. Thereafter, we providethre
3、e case studies indicating a high potential for uncommon variants. In particular,we recommend to focus on parameters regulating selection and population size,rather than those concerning crossover and mutation. On the technical side, thecase study on adjusting tournament size shows by example that gl
4、obal parameterscan also be self-adapted, and that heuristic adaptation and pure self-adaptation canbe successfully combined into a hybrid of the two.Key words: Parameter Control, Self-Adaptive, Selection, Population Size1 IntroductionIn the early years of evolutionary computing the common opinion wa
5、s that EAparameters are robust. The general claim was that the performance of an EAdoes not depend heavily on the right parameter values for the given probleminstance at hand. Over the last two decades the EC community realised thatsetting the values of EA parameters is crucial for good performance.
6、 One wayto calibrate EA parameters is controlling them on-the- y, which can be donein various ways and for various parameters 13, 18, 16. The purpose of thispaper is to present a general description of this fleld, identify the main streamof research, and argue for alternative approaches that do not
7、fall in the mainstream. This argumentation is based on three case studies published earlier6, 15, 17.The rest of the paper is organised as follows. Section 2 starts ofi withgiving a short recap of the most common clasiflcation of parameter controltechniques. Then we continue in Section 3 by an overv
8、iew of related work,2 A.E. Eiben, M.C. Schutincluding some statistics on what types of parameter control are most commonin the literature. Section 4 presents three case studies that substantiate ourargument regarding the choice of the parameter(s) to be controled. The paperis flnished by a number of
9、 conclusions in Section 5.2 Classiflcation of Parameter Control TechniquesInclassifyingparametercontroltechniquesofanevolutionaryalgorithm,manyaspects can be taken into account 1, 13, 18, 16, 54. In this paper we considerthe three most important ones:1. What is changed? (e.g., representation, evalua
10、tion function, operators, se-lection process, mutation rate, population size, and so on)2. How the change is made (i.e., deterministic heuristic, feedback-basedheuristic, or self-adaptive)3. The evidence upon which the change is carried out (e.g., monitoring per-formance of operators, diversity of t
11、he population, and so on)Each of these is discussed in the following.2.1 What is Changed?To classify parameter control techniques from the perspective of what com-ponent or parameter is changed, it is necessary to agree on a list of all majorcomponents of an evolutionary algorithm, which is a dicult
12、 task in itself.For that purpose, let us assume the following components of an EA: Representation of individuals Evaluation function Variation operators and their probabilities Selection operator (parent selection or mating selection) Replacement operator (survival selection or environmental selecti
13、on) Population (size, topology, etc.)Note that each component can be parameterised, and that the number ofparameters is not clearly deflned. For example, an ofispring v produced by anarithmetical crossover of k parents x1;:;xk can be deflned by the followingformula:v = a1x1 +:+akxk;where a1;:;ak, an
14、d k can be considered as parameters of this crossover. Pa-rameters for a population can include the number and sizes of subpopulations,migration rates, and so on for a general case, when more then one populationis involved. Despite the somewhat arbitrary character of this list of compo-nents and of
15、the list of parameters of each component, the what-aspect“ isone of the main classiflcation features, since this allows us to locate where aspeciflc mechanism has its efiect.New Ways to Calibrate Evolutionary Algorithms 32.2 How are Changes Made?Methods for changing the value of a parameter (i.e., t
16、he how-aspect“) can beclassifled into: parameter tuning and parameter control. By parametertuning we mean the commonly practised approach that amounts to flndinggood values for the parameters before the run of the algorithm and then run-ning the algorithm using these values, which remain flxed durin
17、g the run.Parameter control forms an alternative, as it amounts to starting a run withinitial parameter values that are changed during the run.We can further classify parameter control into one of the three followingcategories: deterministic, adaptive and self-adaptive. This terminology leadsto the
18、taxonomy illustrated in Figure 1.Deterministic parameter control This takes place when the value ofa strategy parameter is altered by some deterministic rule. This rule flres atflxed moments, predetermined by the user (which explains the name deter-ministic“) and causes a predeflned change without u
19、sing any feedback fromthe search. Usually, a ime-varying schedule is used, i.e., the rule is used whena set number of generations have elapsed since the last time the rule wasactivated.Adaptive parameter control This takes place when there is some formof feedback from the search that serves as input
20、s to a mechanism used to de-termine the direction or magnitude of the change to the strategy parameter.The assignment of the value of the strategy parameter may involve creditassignment, based on the quality of solutions discovered by difierent opera-tors/parameters, so that the updating mechanism c
21、an distinguish between themerits of competing strategies. Although the subsequent action of the EA maydetermine whether or not the new value persists or propagates throughout thepopulation, the important point to note is that the updating mechanism usedto control parameter values is externally suppl
22、ied, rather than being part ofthe standard“ evolutionary cycle.Self-adaptive parameter control The idea of the evolution of evolu-tion can be used to implement the self-adaptation of parameters 5. Here theparameters to be adapted are encoded into the chromosomes and undergo mu-tation and recombinati
23、on. The better values of these encoded parameters leadbefore the run during the runParameter settingParameter tuning Parameter controlDeterministic Adaptive SelfadaptiveFig. 1. Global taxonomy of parameter setting in EAs.4 A.E. Eiben, M.C. Schutto better individuals, which in turn are more likely to
24、 survive and produceofispring and hence propagate these better parameter values. This is an im-portant distinction between adaptive and self-adaptive schemes: in the latterthe mechanisms for the credit assignment and updating of difierent strategyparameters are entirely implicit, i.e., they are the
25、selection and variation op-erators of the evolutionary cycle itself.2.3 What Evidence Informs the Change?The third criterion for classiflcation concerns the evidence used for determin-ing the change of parameter value 49, 52. Most commonly, the progress ofthe search is monitored, e.g., by looking at
26、 the performance of operators, thediversity of the population, and so on. The information gathered by such amonitoring process is used as feedback for adjusting the parameters. Fromthis perspective, we can make further distinction between the following twocases:Absolute evidence We speak of absolute
27、 evidence when the value of astrategy parameter is altered by some rule that is applied when a predeflnedevent occurs. The difierence from deterministic parameter control lies in thefact that in deterministic parameter control a rule flres by a deterministictrigger (e.g., time elapsed), whereas here
28、 feedback from the search is used.For instance, the rule can be applied when the measure being monitored hitsa previously set threshold this is the event that forms the evidence. Exam-ples of this type of parameter adjustment include increasing the mutation ratewhen the population diversity drops un
29、der a given value 38, changing theprobability of applying mutation or crossover according to a fuzzy rule set us-ing a variety of population statistics 37, and methods for resizing populationsbased on estimates of schemata fltness and variance 53. Such mechanismsrequire that the user has a clear int
30、uition about how to steer the given param-eter into a certain direction in cases that can be specifled in advance (e.g., theydetermine the threshold values for triggering rule activation). This intuitionmay be based on the encapsulation of practical experience, data-mining andempirical analysis of p
31、revious runs, or theoretical considerations (in the orderof the three examples above), but all rely on the implicit assumption thatchanges that were appropriate to make on another search of another problemare applicable to this run of the EA on this problem.Relative evidence In the case of using rel
32、ative evidence, parameter val-ues are compared according to the fltness of the ofispring that they produce,and the better values get rewarded. The direction and/or magnitude of thechange of the strategy parameter is not specifled deterministically, but rel-ative to the performance of other values, i
33、.e., it is necessary to have morethan one value present at any given time. Here, the assignment of the value ofthe strategy parameter involves credit assignment, and the action of the EAmay determine whether or not the new value persists or propagates through-out the population. As an example, consi
34、der an EA using more crossoversNew Ways to Calibrate Evolutionary Algorithms 5with crossover rates adding up to 1.0 and being reset based on the crossoversperformance measured by the quality of ofispring they create. Such methodsmay be controlled adaptively, typically using bookkeeping“ to monitor p
35、er-formance and a user-supplied update procedure 11, 32, 45, or self-adaptively4, 23, 35, 47, 51, 54 with the selection operator acting indirectly on operatoror parameter frequencies via their association with flt“ solutions.2.4 SummaryOur classiflcation of parameter control methods is three-dimensi
36、onal. Thecomponent dimension consists of six categories: representation, evaluationfunction, variation operators (mutation and recombination), selection, re-placement, and population. The other dimensions have respectively three(deterministic, adaptive, self-adaptive) and two categories (absolute, r
37、elative).Their possible combinations are given in Table 1. As the table indicates, deter-ministic parameter control with relative evidence is impossible by deflnition,and so is self-adaptive parameter control with absolute evidence. Within theadaptive scheme both options are possible and are indeed
38、used in practice.Deterministic Adaptive Self-adaptiveAbsolute + + Relative + +Table 1. Reflned taxonomy of parameter setting in EAs: types of parameter con-trol along the type and evidence dimensions. The entries represent meaningless(nonexistent) combinations.3 Related workWe conducted a literature
39、 review to get an overview of the work that has beendone on the various parameters of evolutionary algorithms of the last decade.Our aim was not to deliver a fully annotated bibliography, but rather to illu-minate some examples from the literature on this topic. The literature spansthe conference pr
40、oceedings of three major EC conferences today: the GECCO(1999-2006), CEC (1999-2006) and PPSN (1990-2006). In total we found 235papers that were concerned, in any way (thus not necessarily (self-)adaptive),with one of the parameters of EAs mentioned above: representation, initiali-sation, evaluation
41、 function, variation operators, selection and population size.(In addition, we found 76 papers about adaptive EAs in general.) We cate-gorised the 235 papers, of which the result is shown in Figure 2. We consider6 A.E. Eiben, M.C. SchutFig. 2. Publication histogram.this a preliminary overview giving
42、 some indication of the distribution of re-search efiort spent on these issues. The histogram clearly shows that much re-search efiort is spent on the variation operators (in general: 25, mutation: 54,crossover: 30). Also, the population parameter is researched much. However,we are aware of the fact
43、 that this number is biased, because it includes papersthat are somewhat out of the scope of this paper: for example, on populationcontrol in genetic programming, on the island-model of (sub)populations andon distributing (sub)populations in parallel evolutionary algorithms. We didnot include papers
44、 on co-evolution.We brie y discuss each EA parameter here, where we focus on the papersthat explicitly look at (self-) adaptivity of the parameters. If possible, we makea distinction between deterministic, self- and adaptation within the discussionof a parameter.3.1 RepresentationConcerning represen
45、tation, the genome length can be taken as a variable dur-ing an evolutionary run 28, 43, 36, 57. Consider Ramsey et al. 43 whoinvestigate a variable length genome under difierent mutation rates. To thesuprise of the authors, the length of inidividuals self-adapts in direct responseto the applied mut
46、ation rate. When tested with a broad range of mutationrates, the length tends to increase dramatically in the beginning and thendecrease to a level corresponding to the mutation rate.In earlier work, Harvey 28 presents an important property of variable-length genomes: the absolute position of some s
47、ymbols on the genotype canNew Ways to Calibrate Evolutionary Algorithms 7usually no longer be used to decide what feature those symbols relate to“.Harvey sketches SAGA: a framework that was constructed to investigate thedynamics of a GA when genotype lengths are allowed to increase. The frame-work i
48、ncludes a particular crossover operator (SAGA cross) that has the re-quirement that the similarities are maximised between the two left segmentsthat are swapped and beteen the two right segments that are swapped. Thisresults in a computationall ecient algorithm where populations largely con-verge.St
49、ringer and Wu 57 show that a variable-length GA can evolve to shorteraverage size populations. This is observed when: 1) selection is absent fromthe GA, or 2) when selection focuses on some other property not in uencedby the length of individuals. The model starts with an integer array of 100elements, where each element represents an individual and the value denotesan individuals chromosome length. A simulated crossover produces childrenfrom two random parents, where the value of the flrst child equals the flrst(random) crossover point
