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The Cuckoo Search Algorithm: A review.
Shaunak Shiralkar1 , Atharv Bahulekar2, Samidha Jawade3
1 School of Mechanical Engineering, Dr Vishwanath Karad MIT World Peace University, Pune - 411038, Maharashtra, India
2,3 School of Mechanical Engineering, Dr Vishwanath Karad MIT World Peace University, Pune - 411038, Maharashtra, India*** - -
Abstract
Today’sworldisefficiencydriven.Allorganizationsirrespectiveofthetypeofindustrytheybelongto,strivetoachieve maximum efficiencies in their processes, this is where optimization comes into picture. It is mainly concerned with finding the optimum values for several decision variables to form a solution to an optimization problem . This paper aimstoreviewtheconceptofCuckooSearchAlgorithm(CSA),whichisametaheuristicnaturallyinspiredoptimization algorithm. Further, the major improvements in the traditional CSA have also been reviewed. Finally the recent applications of the cuckoo search in optimization problems have also been presented in the form of a bibliographic review.Thispaperaimstobeaone-stoparticleforresearchersorreaderswhowanttogainanoverviewoftheconcept ofCSAandunderstandtheconceptthoroughly.
Keywords: Meta-heuristic,LiteratureReview,Optimization,CuckooSearchAlgorithm
1. Introduction
Optimization is nothing but employing a maximising or minimising type decision making algorithm, adapted to methods of approximation[1]. The principle of decision making involves choosing between various alternatives. The result of this is to choose the best solution/decision from all the choices. These optimization algorithms are based on nature-derived concepts that deal with choosing the best alternative in the sense of the given objective function. An Optimization algorithms are mainly classified as: evolutionary algorithms (EAs), swarm-based algorithms, and trajectory-basedalgorithms.Thesealgorithmsemulatetheprinciplecalled,Thesurvivalofthefittest.Thisstartswith an initial group of individuals, called population[2]. At every generation, preferred characteristics of the current populationarecombined,anda newpopulation,whichisselectedonthenasisoftheprincipleofnaturalselection[1]. On the other hand, swarm-based algorithms mimic the behaviour of a group of animals when searching for food. Solutions are constructed normally, based on previous data collected by previous generations. At each iteration, that solution will be moved to its neighbouring solution, which resides in the same search space region, using a specific neighbourhoodstructure.Inthispaper,wewillbefocusingontheCuckoosearchalgorithm[3].Therearethousandsof birdspeciestoday,butthemostcommonlyobservedtraitinbirdsisthewayofreproduction.Birdsreproducebylaying eggs.Sincetheseeggsarerichinprotein,andaretheultimatesourceofnourishmentforpredators,henceitisofutmost importance for the parent bird to protect its egg. The cunning behaviour shown by some bird species to secure or increasethesurvivalrateoftheirnextgeneration,isknownasbroodparasitism.Cuckoosshowthistypeofbehaviour. Theynevermaketheirownnestsbutlaytheireggsinotherbird’snestsandthusiftheeggshatch,thehostbirdtakes careofthecuckoochicks.Cuckoomothersshowcharacteristicsofstealthandspeed.Themothercuckoolayshereggin thehostbird’snestandremovesonehosteggandfliesoffwithinafewseconds.Thisentireprocessisextremelyfast, which allows cuckoos to parasitise hundreds of bird species. Cuckoos specialise in a particular type of bird species. Theyaccuratelymimic their eggsize,shapeandcolour, makingitdifficultforthehostbirdtoidentifythecuckooegg. Exactly how the cuckoos manage to mimic the host bird is not known and rather is one of nature’s many unsolved mysteries. The host birds slowly learn to identify the cuckoo eggs and thus destroy them, hence the cuckoos have to continuously improve their strategy to lay their eggs in the host birds nests. Obligate brood species look for good environmentswheretheirchicksgetwell nourished.Afterthesechicksgrowintoadults,theyagaincarryonwiththe samelifecycle.Hencethisbroodparasitismispassedontothenextgenerations.
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2. Concept of Cuckoo search algorithm
The cuckoo search was developed in recent times ( in the year 2009) by Xin-she yang and Subhash Deb. The cuckoo optimization algorithm was later developed by Rajabioun in 2011.Before getting into the details, let us understand what the word‘meta-heuristic’ means.Firstly a heuristic algorithm means algorithmisonethatisdesignedto solvea problem in a faster and more efficient manner as compared to traditional methods[1]. Heuristic algorithms are most often used when approximate solutions are sufficient and exact solutions are necessarily computationally expensive. The Cuckoo optimization algorithm is based on the life cycle of the Cuckoo bird species. i.e. the characteristic brood parasitismofthesebirds.Thecuckoobirdslaytheireggsinnestsmadebyotherbirds.Theeggsthatthecuckooslayin thehostnests,mayormaynotsurvive,thiswillhappenwhenthehostbirdidentifiestheforeigncuckooegg.Hostsmay throw this egg out of its nest or may altogether abandon its nest and make a new one. To avoid this, cuckoos try to mimic the colour, size etc of the hosts eggs and place their eggs in the host nest very carefully so that the host won’t recognise the eggs laid by the cuckoo. This aggressive reproduction strategy inspires the CS algorithm. Thus the key point to note here is that the cuckoo must be very accurate to mimic the hosts eggs and the host must be vigilant enough to identify a parasite egg this is the fight of survival. We can very meaningfully compare this system to an optimizationproblem.Theeggsinthenestrepresentsolutionsandthecuckooeggsrepresentnewsolutions.Theaim hereistoreplaceaverage/notasgoodsolutionswithbettersolutions. Theprobabilitythatthehostwillrecogniseand throw away the cuckoo birds egg is given by pa ε[0,1]. If the host bird is unable to identify the cuckoo eggs, then the cuckoo eggs tend to hatch early as compared to the host eggs. When the chicks hatch, the host destroys its own eggs. Thisincreasesthecuckoobirdschancesofsurvivalbygettingmoreshareoffood.Followingarecertainbasicconcepts usedintheCSalgorithm:
2.1 Basic concepts
Optimization in simple words means betterment or improvement of a process, achieved by tweaking or changing the inputparametersofaprocess,mathematicalequation,experimentetctogettheoutputasmaximumorminimum. The input comprises of variables, where the process as a whole is known as a function, also known as cost function/objectivefunction/fitnessfunction Similarly,theoutputiscalledascostorfitness.Therearevariousmethods which can be used to solve optimization problems. The most common of all of these methods are nature-inspired algorithms. For example, PSO or Particle Swarm Optimization. This is inspired by bird flocking or fish schooling. The Genetic Algorithm (GA) is another very popularly used method to solve optimization problems[5]. It uses operators similar to the natural genetic variation and natural selection. Other examples include Ant Colony Optimization (ACO) whichisanevolutionaryoptimizationalgorithm.SincewewillonlybefocusingontheCuckooSearchAlgorithm,(CSA), weneedtounderstandthatthemaingoalofthecuckoomotherbirdistoplaceheregginonlythosenestsinwhichher eggswillhatch,thusinoptimizationtermstheprofitabilityofthatnestmustbehigh.Cuckooshaveacunningstrategy when it comes to reproduction. After the cuckoo egg is placed, one host egg is thrown off from the host nest by the cuckoo so that the host cannot make out the difference in the number of eggs. Also when the cuckoo egg hatches, the chickisabitlargerthatthehostchick.Hence,theyconsumealargeportionofthefoodbroughtinbythehostbird.Asa result, the host bird’s chicks might die of insufficient food. Also cuckoo chicks try to imitate the other host birds chirps/soundstoattractthemotherhostbirdtogetmorefood.Thusthecunningtraitincuckoosispassedonfromone generationtothenext.CuckooSearchAlgorithmisgenerallyusedincombinationwithLevy’sflight.
Levy Flights- `whenanimalsgooutinsearchoffoodorotherresources,theywalkrandomly.Theirwalkisrandomin nature because their next step depends upon their current location/position and the probability of transition to the next position. This random walk can be modelled mathematically, almost all insects/birds/animals follow the levy flightsprinciple.SowecansaythattheLevyflightsisarandomwalkshownby(inthiscontext)Cuckoos inwhichthe step length can be determined by using a heavy tailed probability distribution. Heavy-tailed probability distributions are the ones in which their tails are not bounded exponentially hence having heavy tails than the rest of the distribution.
3. Cuckoo Search Algorithm framework.
Metaheuristics exhibitthecharacteristic ofimitatingthebestfeaturesofthenature,thatisthebiologicalsystemsthat have evolved over a long period of time due to natural selection. These systems show two main points of interests. Theseare-adaptationtotheenvironmentandsurvival/selectionofthefittest.Inmodernmetaheuristics,thesefeatures canbeutilisedintodefiningthetermsintensificationanddiversification.Diversificationenablesthealgorithmtosearch
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theentirespaceefficiently.Ontheotherhand,intensificationdealswiththesearch aroundcurrent bestsolutionsand theselectionofthebestsolutionsamongstthem.TheCSAisbasedonthreesimplerulesorassumptions.Theseare:
1) Eachcuckoolaysonlyoneegganddumpsitinarandomlyselectednest.
2) Thebestnestswithhighqualityofeggswillpassonorcarryontothenextgenerationofcuckoos.
3) Thenumberofhostnestsarefixed,hencetheprobabilitythatthehostidentifiesthecuckooeggisgivenbythe probability of Pa ∈ [0,1] Hence as mentioned before, the host can throw away the cuckoo egg or simply abandonthenestandbuildanewone.
Now,incaseofmaximizationproblems,thequalityofthesolutionisproportionaltotheobjectivefunction.Thecuckoo searchalgorithmcanalsobeappliedtocaseswithmorethanonecuckooegginthehostnesti.e.,multipleeggspernest. Butwewillconsiderthesimplestformofthisalgorithm,whichisaccordingtotheabovementionedrules.Eachcuckoo only lays one egg. In order to generate a new function, denoted by: x(t+1) for a cuckoo ‘i’. then the Levy flights is performedas:
x(t+1)=x(t)+α⊕Levy(λ), [1]
Intheaboveequation,αdenotesthesteplengthwhichisgreaterthan0.Generallyorinmostofthecases,thevalueof stepsizeistakenasunity.i.e. α=1.Astochasticequationistheoneinwhichoneormoretermsarestochasticandthe resulting solution is also a process which is stochastic in nature. A random walk is a Markov chain. Hence the next locationorthestatus dependson the current positionandthe probabilityof transition. The firsttermin equation[1] denotes current position and the second term of the equation denotes the probability of transition. ⊕ denotes entry wise multiplication. The Levy flights is used to obtain the random walk, but the random step length is given by Levy distribution.
Levy∼u=t λ , (1<λ≤3), [2]
This has infinite mean and variance. These steps essentially create a random walk, as mentioned earlier, the random walkprocessisgeneratedwithapower-lawstep-lengthdistributionwithaheavytail.Nowwecanlookataverysimple flowchartdepictingthecuckooalgorithm.
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Fig.1 Cuckooalgorithmflowchart[Shehabet.al.2017]
TheCuckoosearchalgorithmcanberepresentedusingthefollowingpseudocode: begin
Objectivefunctionf(x),x=(x1,...,xd)T
Generateinitialpopulationof nhostnestsxi(i=1,2,...,n) while (t<MaxGeneration)or(stopcriterion)
GetacuckoorandomlybyLevyflights evaluateitsquality/fitnessFi
Chooseanestamongn(say,j)randomly
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if (Fi>Fj), replacejbythenewsolution; end
Afraction(pa)ofworsenests areabandonedandnewonesarebuilt; Keepthebestsolutions (ornestswithqualitysolutions); Rankthesolutionsandfindthecurrentbest end while Postprocessresultsandvisualization end
Themostimportantadvantageofthecuckoosearchalgorithmisthatitusesveryfewcontrolparameters.Thefollowing tableshowstheseparametersandthecommonlyusedvaluesforthem.
PARAMETER SYMBOL RANGE COMMONLYUSED NEST N [15,50] N=15 FRACTION Pa [0,1] Pa=0.25 STEPSIZE a a >0 a=1
Table.1.CSAparametersandcommonvalues.
4. CS algorithm suggested by Rajabioun:
AbetterCuckooalgorithmapproachwassuggestedby Rajabioun in2011.Initially,thealgorithmstartswithaninitial population ofcuckoos.Thesecuckooshaveeggsthattheywill layinsomeotherbird’snest.The eggs whichare more similartothoseofthehostbird’seggs,willhaveagreaterchanceofsurvival. Thatis,theywillhatchandbecomeadult cuckoos.Othereggsthatthehostidentifies,willbethrownawayandkilled.Theeggsthatsuccessfullyhatch,depictthe suitability of that area for cuckoo breeding. Areas where large number of eggs survive, are more profitable outcome wise. The Cuckoo algorithm will optimize the positions where more eggs survive. Cuckoos will aim to search for the bestareastolayeggs,soasto,maximisethesurvivalrateoftheireggs.Themostsuitableorappropriateareaiswhat cuckoobirdssearchfor,soastomaximisethesurvivalrateoftheireggs.Oncetheeggsthatsurvivegrow,andturninto afullygrowncuckoo,theystartmakingsocieties.Here,everysuchsocietyhasitshabitatareatolivein.Finally,thebest habitat amongst all these, will be the one which will be aimed for by all cuckoos from other societies. Then they immigrate toward this best habitat. The number of eggs laid by cuckoos, and its distance to the goal point, the egg layingradiusisdecided.Accordingly,thebirdstarts tolayeggsintotallyrandomnestswhicharewithintheegglaying radius.Thisiscontinueduntilthebesttargetwiththehighestprofitvalueisreached[1].
According to the theory explained in cuckoo algorithm this is stochastic algorithm, means it has random probability, anyone cannot predict further step. This type of algorithm can be analysed statistically but may not be predicted precisely.ThecuckooalgorithmisImmuneEvolutionaryAlgorithm.
ImmuneEvolutionaryalgorithmisbasedonimmunesysteminspiredbydefenceprocess ofbiologicalimmunesystem andevolutionarymeanscontinuousevolutionsoralterationsaremadeincurrentproducttoobtainmostapproximate orfittestsolutionforproblem.Thisgoesaccordingto Darwin’stheorySURVIVALOFFITTEST.Someoftheadvantages ofevolutionaryalgorithmare:
1) Beingrobusttodynamicchanges
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2) Broadapplicability
3) Hybridizationwithothermethodispossible
4) Solveproblemsthathavenosolutions(nohumanexpertiserequired)
Wecanobservewiderangeapplicationofevolutionaryalgorithmsinfollowingregionsofstudy: Power system operation and control, NP-hard combinational problem, Chemical Process, Job scheduling problems, Vehicle routing, Mobile networking, Batch process scheduling, Multi objective optimization problem, Modelling optimizedparameters,Imageprocessingandpatternrecognitionproblem
Cuckoo species uses STEALTH, SURPRISE AND SPEED strategy for its survival. Cuckoo’s majority species occur in forests and woodland and in evergreen rain forests. Most species of cuckoo are sedentary, but several species undertakepartialmigrationovercompleterange.Forspeciesbreedingathigherlatitudesfoodavailabilitydictatesthat they migrate to warmer climates during the winter, and all do so. Long migration flights which are also observed, include the Lesser Cuckoo which takes its flight journey from India to Kenya across the Indian ocean. Whereas the commoncuckoobirdsmainlytheEuropeanones,flynonstopovertheMediterraneanSeaandtheSaharanDesertover toSouthAfrica[1,2,6]
Cuckoooptimizationalgorithmisgoingtooptimizewheremorecuckooeggsaregrown.Cuckoo’ssearchisbasedonto layeggsinordertomaximiseeggsurvivalrate.Ifbabycuckoogrowsandithatchestheeggandbecomematurecuckoo, thentheycreatetheirsociety inthatrespectivearea.Inthisprocesscuckoomakecertainhabitatwhereprobabilityof survival of cuckoo is highest. In other words, cuckoo makes that certain region CUCKOOPRONE OR FIT FOR CUCKOO SURVIVAL.Accordingly,othercuckoosinhabitnearthe besthabitat.Accordingtonumberofcuckooeggseachcuckoo has cuckoo lay eggs in some radius around best habitat (which is created by some other cuckoos). This process continuestillbestregionwithmaximumprofitoutcomeisobtained.
Cuckooalgorithmpseudocode[1]
1. Initialisecuckoohabitatswithsomerandompointsontheprofitfunction.
2. Dedicatesomeeggstoeachcuckoo.
3. DefineELRforeachcuckoo.
4. LetthecuckooslayeggsinsidetheircorrespondingELR.
5. Killeggswhicharerecognisedbyhostbirds.
6. Lettheeggshatchandthechicksgrow.
7. Evaluatehabitatofeachnewlygrowncuckoo.
8. Limitcuckoosmaximumnumberinenvironmentandkillthosewholiveintheworsthabitats.
9. Clustercuckoosandfindbestgroupandselectgoalhabitat.
10. Letnewcuckoopopulationimmigratetowardgoalhabitat.
11. Ifstopconditionissatisfied,thenstop,ifnotgotostep2.
Oneinterestingandspecific factaboutcuckoois,theylaytheireggsinrandombird’snestintheirrespectiveELR,but eggs whichcan’t match with characteristicsofhost bird’s eggs arekilled byhostbird [1].Fromthe remaining eggsof cuckooonlyoneegghaschancetogrow.Asifonecuckoochiccomesoutofegg,firstitwillthrowallothereggsoutside the nest. And if cuckoo comes outside the later then it eats all the food given by host bird, it results in death of remainingchickduetohunger.
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Oncethecuckoochickisoutsidethetheyliveinthatsociety,feedthemselvesinthatsocietyuntilegglayingperiod.AS egglayingperiodapproachestheyfindbetterplaceorareawheretherewillbesufficientfoodfornewyoungsters.After thesecuckoogroupsareformedindifferentsocietiestheonesocietywithmaximumprofitvalueissetasgoalforother cuckoostoimmigrate.Whilemigratingallcuckoosdonotflyallthewaybuttheygetdeviatedorsomeflyhalftheway.
ItisobservedeachcuckooflyOnlyl%distancetowardsthegoalandhasФ%deviation.ThesetwoparameterslandФ helpthecuckoostofindmuchmorenewpositionsinallenvironment Foreachcuckoo l~U(0,1) =itisrandomnumberbetween0and1 Ф~U(-w,w)=itlimitsthedeviationcuckoos
Asitisknown naturealwayshasequilibrium maximum numberof cuckoosarealways restricted inthe environment. Aftersomeiterationandtrialsallcuckooswillmovetoonebesthabitatwithgoodfoodresourceandhavingmaximum eggresemblancewithhostbirdeggs.Thishabitatwillproducemaximumoutput.Convergenceofmorethan95%ofall cuckoosinsamehabitatgiveyoutheendofcuckooalgorithm.
5. A bibliographic review of major applications of CSA.
MajorresearchandimprovementisdoneonCSalgorithmasimprovisedandsuperiorresultsobtainedafterapplication of CS algorithm to various fields of engineering. In 2010 design of spring and welded beam were improvised after applicationofCSalgorithmtodesignprocessby YangandDeb.YangandDeb(2010)[25]appliedCSalgorithmtosolve various problems in field of engineering. Objective was to reduce weight and to reduce overall cost of fabrication. CS algorithm was proved to be very efficient among Genetic algorithm and particle swarm optimization. Model with CS algorithmofaccuracymeasurementforspikingneuroninpatternrecognitionwasprovedbetterthansamemodelwith Differential evolutionalgorithm.This comparisonwasdone byVazquez(2011).Burnwal andDeb(2012)[8]testedCS algorithm for scheduling optimization of flexible manufacturing system by minimizing penalty cost and maximizing machineutilization time. CS was proved to be better than other algorithms. Enhanced CS algorithm was proposed for optimization of bloom filter in spam filtering by Natarajan and Subramanian (2012)[9]. Enhanced cuckoo algorithm was employed to minimize the total member ship invalidation cost of bloom filters by finding optimal false positive ratesandnumberof elementsstoredineverybin. CSwasimplementedinobjectorientedsoftwareforunconstrained optimizationproblems.Inproposedtestthissoftwareperformedwell.Cuckoobasedparticleapproachwasappliedto achieve energy efficient and wireless sensor networks. This implementation was done by Dhivhya, Sundarambal and Anand(2011)[7] Resultsobtained were comparable withLEACH andHEED protocols Inthe paperauthored by Sang Dang Ho, Ve Song, Toan Minh Le and Thang Trung Nguyen [12] two modified versions of CSA were proposed, where new solutions were obtained using two distributions including Gaussian and Cauchy distributions which were proposed for economic emission load dispatch (EELD) problem with multiple fuel options. The advantages of Cuckoo searchalgorithmwithGaussiandistribution(CSA-Gauss)andCuckoosearchalgorithmwithCauchydistribution(CSACauchy)overCSAwithLévydistributionarefewerparametersandfewerequationsandshortercomputationalprocess. Theproposedmethodwastestedononetestsystemconsistingoftengeneratingunitswithvariousloaddemandsand compared to other methods Similarly, Mareli et.al.[13] proposed the Adaptive Cuckoo search algorithm for optimisation (2017). This paper also emphasizes on dynamic parameter switching in cuckoo algorithm and 3 new models of cuckoo algorithm. These new models with dynamic switching parameters are compared with CS algorithm withconstant parameters. ManyotherpapersalsocompareLevyflighttechnique withsome traditional techniquesto getbetteroneforoptimisationoftheprocess.
6. Conclusions.
In this paper, the concept of cuckoo search algorithm was reviewed, along with it, significant improvements over the traditionalCSAwerealsoseen.ThesemethodsaimedtoincreasetheconvergencerateoftheCSAtogetmoreaccurate andefficientresults.AfterunderstandingtheconceptofCSAtheoretically,itisofgreatimportancethatthereadersof this article get insights about the applications of CSA in real world optimization problems. This was achieved by providinganindepthbutaptbibliographicreviewabouttheapplicationsandfruitfuloutcomesof CSA.Optimizationis the key to efficiency in any process or task which needs to be executed. Meta-heuristic algorithms do prove to be a solutiontoincreaseefficiency,andstillhavealotofscopeforimprovements,whichshouldbefocusedupon.
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7. References.
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