Emergence of altruism behavior in army ant-based social evolutionary system

12 Pages·2014·1.66 MB·English

Ichimuraetal.SpringerPlus2014,3:712
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a SpringerOpen Journal
RESEARCH OpenAccess
Emergence of altruism behavior in army
ant-based social evolutionary system
TakumiIchimura1*†,TakuyaUemoto1†,AkiraHara2†andKennethJMackin3†
Abstract
Armyantsperformthealtruismbehaviorthatanantsacrificesitsownwell-beingforthebenefitofanotherants.They
buildbridgesusingtheirownbodiesalongthepathfromafoodtothenest.Wedevelopedthearmyantinspired
socialevolutionarysystembyusingSwarmlibrary.Thesystemhas2kindsofantagents,‘Majorant’and‘Minorant’.
Theycommunicatewitheachotherviapheromones.Armyantcanrecognizethemasthesignalsfromtheotherants.
Thepheromonesevaporatewiththecertainratioanddiffusedintothespaceofneighborsstochastically.Ifthe
optimalbridgeisfound,thepaththroughthebridgeistheshortestroutefromthefoodtothenest.Wedefinethe
probabilityforananttoleaveabridgeastothenumberofneighboringants.Theconstructingmethodoftheoptimal
routehasbeenproposed.Inthispaper,thebehaviorsofantundertheenvironmentwithtwoormorefeedingspots
wereobserved.Someexperimentalresultsshowthebehaviorsofgreatinterestwithrespecttoaltruismofants.The
knowledgediscoveryofsocialevolutionaryprocessfromsomecomputersimulationresultsisdescribedinthispaper.
Keywords: Artificiallifesimulationsystem;Armyant;Altruismbehavior
Introduction thedaytocaptureinsects,spiders,andsoon.Thestation-
In animal societies, self-organization is the theory of aryphasestartswhenthelarvaepupateforafewweeks.
how minimal complexity in the individual can generate Moreover, army ants build a living nest with their bod-
greater complexity at the population. The rules specify- iesinsteadofbuildinganestlikeotherants.Eachantwill
ingtheinteractionsamongthecomponentsinthesystem hold on to the other legs and form a linked chain or a
are implemented by using only local information with- ballstructure.Thisbehaviorisknownasabivouac.This
out global information. In the study of social evolution, allowsthebridgingofanemptyspace.Inordertoaddress
armyantperformsaltruismasonebehaviorofcomplex- theself-assembledstructureasaparticulartypeofaggre-
ities, where each individual reduces its own fitness but gation, Deneubourg et al. defined the probability of an
increasesthefitnessofotherindividualsinthepopulation. antenteringorleavingchainin(Deneubourgetal.2002).
Such behaviors seem to be involved acts of self-sacrifice Moreover,theyshowedthatthegregariousbehaviorfacili-
in order to aid the others. In evolutionary biology, such tatescooperationbyBlattellagermanicainsheltersduring
abehavioriscalledreciprocalaltruism.Theconceptwas therestingperiod.Theprobabilitytoleavetheshelterwas
initiallydevelopedtoexplaintheevolutionofcooperation defined.
asmutuallyaltruisticacts(Trivers1971).Thebasicideais Ishiwata et al. (2011) developed the simulation sys-
closetothestrategyof“equivalentrelation”inthestudyof tem for the foraging behavior and the altruism of army
strategicdecisionmaking. ants by using Swarm library, Swarm-2.2 (Lancaster et al.
Army ants are characterized by their two different 2002).(Theoriginalwebsitewww.swarm.orgisinthepro-
phases of activities, a nomadic phase and a stationary cessofbeingrebuilt.)Theprobabilitiestoformthechain
phase.Duringthenomadicphase,armyantsmoveduring defined in (Lioni et al. 2001) was used in their simula-
tionexperiments.Thenumberofneighboringactiveants
*Correspondence:[email protected] isconsideredastheconditionforaltruisticbehavior.Their
†Equalcontributors
1FacultyofManagementandInformationSystems,PrefecturalUniversityof simulationresultsshowamimicaltruisticbehavior.
Hiroshima,1-1-71,Ujina-Higashi,Minami-ku,734-8558Hiroshima,Japan By inspiring Ishiwata’s study, Ichimura et al. devel-
Fulllistofauthorinformationisavailableattheendofthearticle oped the multi-agent simulation system to execute more
©2014Ichimuraetal.;licenseeSpringer.ThisisanOpenAccessarticledistributedunderthetermsoftheCreativeCommons
AttributionLicense(http://creativecommons.org/licenses/by/4.0),whichpermitsunrestricteduse,distribution,andreproduction
inanymedium,providedtheoriginalworkisproperlycredited.
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realistic altruistic behavior where two or more kinds of Simulationenvironment
agentsrealizethedivisionofrolesinarmyants(Ichimura Theswarmisthebasicunitofsimulationforacollection
and Douzono 2012). According to the environment in ofagentsexecutingascheduleofactions.TheSwarmpro-
(Ichimura and Douzono 2012), the simulation results videsobjectorientedlibrariesofreusablecomponentsfor
reportedthattheoptimalpathfromthefoodtothenest buildingmodelsandanalyzing,displaying,andcontrolling
cannot be always found, because two or more chains in experiments on those models. We executed the altruism
theenvironmentwereformed.Althoughmoreemergence simulationsystembypheromoneevaporationanditsdif-
ofaltruisticbehaviorswasobserved,butthecapabilitiesof fusion in army ant multi agent systems. The developed
formingchainwasdispersed.Asaresult,theperformance system is depicted in 100 × 100 2D space as shown in
of foraging decreases and some ants took a circuitous Figure 1. The solid-filled rectangle, which consists of 3
route.Onthecontrary,Ichimuraetal.definedtheevap- kindofbars:‘leftbar’,‘rightbar’,and‘centerbar’,dividesthe
oration rate of pheromone dues to normal distribution spaceinto2parts.Theinnerpartisthenestregionandthe
probability and the probability to leave from the chain bottompartundertherectangleisthefoodsourcepart.
when the ants in its neighbor region depart gradually in The 4 coordinates (x,y) of leftbar, rightbar, and center-
(Ichimura and Douzono 2012). The altruism simulation barare{(30,30),(33,30),(30,70),and(33,70)},{(70,30),
resultsarereportedtofindmoreoptimalpathsfromfood (73,30),(70,70),and(73,70)},and{(30,70),(73,70),(30,
tothenest. 73),and(73,73)},respectively.Eachbarrepresentsaditch
In this paper, we observed the behaviors of ant agents and the width of ditch is 3. The center rectangle of the
under the multi feeding spots in the same environment space is ‘nest’ and the bottom rectangle under the bar is
of(IchimuraandDouzono2012).Someexperimentswith ‘foodsource.’Sinceanantcannotcrosstheditchbyitself,
different ratio of feed size were investigated. In general, someantsbeginaltruisticbehaviortocooperatewitheach
antagentstakeanactiontobeconcentratedinthelargest other. The two hypotheses were proposed as the judg-
feedingspot.Theshortestpathfromthespottothenest mentcriteriaforaltruisticactivity,Model1:Basedonthe
is constructed and the ants bring feed to the nest. Then, PresenceofNeighboringAntsandModel2:Basedonthe
thefeedingspotswillbedisappearedintheorderoflarger Presence of Pheromone (Ishiwata et al. 2011). In Model
spot. However, it has turned out that there is a certain 1,anantwillstartformationoflivingbridgeoveragully
tendencywithoutregardtothesizeoffeed.Thealtruism only when neighboring ants are present. Hypothetically,
behaviordoesnotworkwellandthebridgewillbebroken, thisapproachwillbemoreefficientcomparedtoforming
if enough ant agents are not gathered into the ditch. As abridgeblindly.InModel2,theplaceswherepheromone
aresult,thefoodatthespotsremainstotheendofsim- concentrationsarehigherthanafixedlevelaretheloca-
ulation.Moreover,thegroupofagentswasautomatically tionsthatmanyantshavepassedand/orwillpassthrough
constructedduringsearch.Theexperimentalresultswith infuture.
the different number of agents show the building group Figure2showstheareaofactivitiesandthevisualfield
fortheeffectivesearch. byanarmyant.Inthispaper,antagentscanmoveinthe
Suchbehaviorsarealsoseeninthecollaborativesocial diagonal direction, but the scattered pheromone dimin-
networks. Especially, a research framework for studying ishescomparedtotheadjacentpositionsonupanddown,
social systems uses agent based modeling and simula- leftandright.Thedistancefromapositiontotheneighbor
tion. Madey et al. (2002, 2003) describe the simulation is defined Distance. For example, the distance to ‘A’ and
results for the collaborative social network composed of ‘C’inFigure2a√re1Distanceand2Distance,respectively.
opensourcesoftware(OSS)developersandprojects.The Practically,‘B’is 2Distance.However,forthesakeofease,
obtained knowledge in this paper will be useful for the wedefine‘B’as1Distanceinthediagonaldirection.
collaborativesocialnetworks.
The remainder of this paper is organized as follows. Agentbehaviors
ThesectionSimulationenvironmentdescribesthesimu- The actions include foraging for foods and transport of
lationenvironmentwithSwamlibrary.ThesectionAgent them and communications with neighboring ants using
behaviors defines the behaviors of agents such as search pheromone.Thepheromoneisreleasedbyanagentwhen
phase, homing phase (return to the nest), and altruism it finds food. Once the pheromone is attenuated and
phase. The section Proposed method describes the pro- is dispersed, the information about the food position is
posedmethodrelatedtopheromoneandtheleavingprob- disseminatedamongtheants.
ability from chain. Experimental results for simulations The system has 2 kinds of ant agents, ‘Major ant’ and
aredescribedinthesectionExperimentalresultsforaltru- ‘Minorant’andtheantscommunicatewitheachothervia
ismandthesectionExperimentalresultsfortheformation pheromones. Major ant scatters pheromones and moves
of group. In the section Conclusive discussion, we give throughoutintheenvironment.Ontheotherhand,Minor
somediscussionstoconcludethispaper. ant makes a mimic altruistic behavior to foraging and
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Figure1Environmentinarmyantsimulationsystem.
transporting. Ichimura et al. shows the numerical supe- 4. Searchaditch
riority in case of the 2 variants of ants (Ichimura and Searchaditchwithin1Distance.Ifthereisaditch,
Douzono2012).Inthispaper,theexperimentalsimulation transittoAltruismState.otherwisegoto6).
related to the altruistic behaviors has the 2 kinds of ant 5. Move
agents. Movetotheotherpositionaccordingtothe
Aminorantagentaimstofindafoodsourceandthen scatteredpheromonedescribedinthe
toreturntothenest.Ifthereisaditchinthepathamong section“Pheromoneupdate”.
them,theantwillbuildabridge.The3kindofstatesare 6. Randomselectionofwalkingdirection
defined according to the behavior of ants (Ishiwata et al. Checkwhethertheotheragentstaysoraditchexists
2011). atthenextpositionexceptgoingstraightahead.The
nextpositionisselectedwithanarbitraryprobabilityα.
Searchstate
Ifthepositionisempty,gobackto1).Otherwise,
Search state is an initial condition of agents to seek the
selectanotherposition.Moreover,iftheagentis
food source by random walk. Once an agent reaches the
surroundedbyotheragentsoraditch.itstaysatthe
food,itmovesintoReturnstate.Theanttakesafoodon
samepositionuntiltheneighborbecomesempty.
the way back to the nest until the food source becomes
empty.Belowshowsthesearchalgorithm.
Returnstate
1. Searchoffoodsecure In Return state, an agent comes back to the nest carry-
First,searchafoodsourcewithin1Distance.Ifthe ingthefood.Afterreachingthenest,theagentmovesinto
agentfindsagoodatthedestination,movinginto Searchstate.Belowshowsthereturnalgorithm.
Returnstate.
2. Perceptionofpheromone 1. Currentposition
Perceivingpheromonewithin2Distances. Checkthecurrentpositionofanagent.Itisinthe
3. Searchtheotheragents nest,gotoSearchstate.Otherwise,itgoestonext
Checkingtheotheragentswithin2Distances.Ifthe steptomovetothenest.
otheragentsstay,goto4).Otherwisegoto6). 2. Searchaditch
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C
B
A
Figure2Theareaofactivities.
Ifthereisaditchwithin1Distance,goto3). Pheromoneupdate
Otherwise,itmovesanextpositiontothenextand In many works related ant systems, the ants commu-
goto1). nicate with each other via the pheromone dissemina-
3. Randomwalk tion.However,theresearchershavediscussedonlyabout
Checkwetherthetheotheragentstaysorditch the pheromone on the ground. We consider that the
existsattherandomlyselectednextpositionexcept pheromone evaporates and spreads into the space. The
goingstraightahead.Ifthepositionisempty,go ant in this study can recognize the volatilization of
backto1).Otherwise,selectanotherposition. pheromoneinthespace,butnotknowthepheromoneon
Moreover,iftheagentissurroundedbyotheragents the ground. Based on such an idea, pheromone update
oraditch,itstaysatthesamepositionuntilthe processisexecutedbyEq.(1)andEq.(3).
neighborbecomesempty.
Altruismstate space(cid:3)(x,y)(t) = rA×sp⎛ace(x,y)(t) ⎞
(cid:4)
Some agents stop walking before a ditch and come
togetherasflock.Twoormoreagentswillbuildabridge. +rB×⎝ space(ip,jp)(t)−4space(x,y)(t)⎠
belowshowsthealtruismalgorithm. ⎛ p ⎞
(cid:4)
1. Sifetahrecrhetahreeonthaegrenatgsenwtithin2Distances,theagent +rC ×⎝ space(iq,jq)(t)−4space(x,y)(t)⎠
q
stayswithanarbitraryprobability1-P describedin
1
thesection“Themodelofarmyant”andcontinues
(x ,y ) = {(x,y+1),(x,y−1),(x+1,y),(x−1,y)}
tocheckitssurroundedsituation.Otherwise,goto ip jp
2)withtheprobabilityP1. (xiq,yjq) = {(x+1,y+1),(x+1,y−1),
2. Gotosearchstate (x−1,y+1),(x−1,y−1)} (1)
Selectapositionwithin1Distanceinthepartof
chain.Ifthepositionisempty,gotoposition,and space(x,y)(t+1)=space(cid:3)(x,y)(t)+re∗groundx,y(t) (2)
thenmakethetransitiontoSearchstate.Otherwise,
theantisembeddedinthechain. ground(x,y)(t+1)=ground(x,y)(t)−re∗ground(x,y)(t) (3)
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where space(x,y) means the amount of pheromone in the Table1Thesizeoffeedingspots
space over the position (x,y) in Eq. (1). rA is the decay Env. Agents A:B:C Env. Agents A:B:C
ratio. r is the diffusion rate in the direction of up and
B 1-1 2:1:1 2-1 2:1:1
down,leftandright.r isthediffusionrateinthedirec-
C
tion of the diagonal. ground (t) means the pheromone 1-2 Major:3 1:2:1 2-2 Major:3 1:2:1
amountonthegroundatthexp,yosition(x,y)inEq.(2).r is 1-3 Minor:100 1:1:2 2-3 Minor:50 1:1:2
e
theevaporationrate. 1-4 4:2:1 2-4 4:2:1
Multifeedingspots
Figure3showstheenvironmentwithmultifeedingspots
toextendthesimulationsystem.AsshowninTable1,we pheromone in simulation environment partially. The sit-
investigate the behaviors of ant for some ratios of food uationincreasestheagentsswarmingaroundthem.Asa
size. result,itbecomeseasytoenterAltruismStateandtwoor
more bridges are built without the shortest path from a
Proposedmethod foodsourcetothenest.
The simulation system mainly focuses two parts, In order to avoid such a situation, the ratio of
‘PheromoneEvaporationandItsDiffusion’and‘Probabil- pheromone evaporation is defined based on the nor-
ity for leaving from chain’. In this paper, the pheromone mal distribution probability as shown in Figure 4.
evaporation method and a new probability for leaving Figure 5 shows the transverse plane of Figure 4. The
fromchainaredefinedasfollows. rate of pheromone in 3D space is set to ‘r ’: ‘r ’:
A B
‘r ’=0.788:0.043:0.010inFigure5.
C
Pheromoneevaporationanditsdiffusion
As for the former part, Pheromone Evaporation and Its Themodelofarmyant
Diffusion, the method in (Ichimura and Douzono 2012) Theprobabilitiesofanantenteringachain(P )orleaving
e
assumedtheimproperrateofevaporationanddiffusionof a chain (P) are depending on the size of the chain. The
l
pheromoneintheagentanditsbehavior.Theparameter chain is a small part of constructing bridge. Lioni et al.
settingcausesabiasfortheflock.Thatis,thereismuch (2001)definedtheseprobabilitiesasfollows.
Figure3Theenvironmentformultifeedingspots.
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Figure4Thedistributionofpheromone.
C X that of the initial group. ν is a parameter of the growing
P =C + e1 i (4)
e e0 C +X rateofgroupduringtheconstructionofchain.Thevalues
e2 i
oftheseprobabilitiesshouldbeintherangeof0and1.
C
Pl =Cs0+ C +s1Xν (5) The function Pe expresses the idea that the probabil-
s2 i ityforananttojointhechaingrowsthenumberofnest
whereXiisthenumberofantsinthechaini.Ce0,Ce1,and matesalreadypresentedandreachesaplateauvalueequal
Ce2 are parameters for entering the chain. Cs0, Cs1, and toCe0+Ce1.Ce0isthevalueofspontaneoushangingwhen
Cs2 are parameters for leaving the chain. The size of the Xi = 0. The function Pl expresses the probability for an
agent group when they leave a chain will be larger than anttoleavethechaindecreaseswithX.
i
r
r
B
C
r
A
Figure5Theevaporationrateofpheromone.
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The ant in the chain does not always stay in the same sectionAltruismStateforenteringachainandEq.(6)for
chain. A certain probability for leaving from the chain leavingthechain.
isrequiredtorealizeAltruismStatus.Duetointeraction
between ants, the probability decreases with the num- Experimentalresultsforaltruism
berofcon-specificsinthechain.Thephenomenaisruled Thebehaviorofarmyantsateachenvironmentasshown
byempiricalequationverysimilartothatforOecophylla inTable1wasobserved.Parametersettingsareasfollows:
(Deneubourgetal.2002).Theprobabilityforleavingfrom n = 2, a = 0.4, and re = 0.05. At each environment
chainisgivenbyEq.(6). inthispaper,10trialsforeachsetwereexecutedandthe
behaviorofantswererecordedasthemotionvideo.There
a are 2 kinds of ants at each environment, Major ants to
Pi = 1+bX2 (6) makearandomsearchandMinorantstofollowthescat-
i
tered pheromone. In this paper, for almost trials we can
where X is the number of ants in the chain i. a is observe the following simulation results. During the ini-
i
the probability of leaving a chain under a disregard tialphaseasthesearchofanareaforprey,themovement
for the number of other agents. b is the parameter of of Major agent will be a key in the change of course to
depending the amount of pheromone in chain i: b = searchthesubspace,becausetheMajoragentscattersthe
min{η(log(space(x,y) + 1)) + (cid:5),1}. A theoretical model pheromone while moving in a space. After the discovery
suggests that these basic mechanisms account for the offood,theMinoragentcatchesthefoodandscattersthe
clustering of insects (Deneubourg et al. 2002; Lioni and pheromoneonthewayfromthespottothenest.Thepath
Deneubourg2004;Lionietal.2001). becomes congested since there is an obstacle of a ditch.
Ichimuraetal.(2012)reportstheagentsinaltruismsit- Such situation causes the construction of the bridge on
uation perform the shortest path by construction of the theditch,sincetheantssearchtheshortestpathfromthe
bridge.Figure6showstheconstructedbridgeontheway feeding spot to the nest. Moreover, the agent swarming
fromthefeedingspottothenest.Inthispaper,weinves- around the food increases with the size of food, because
tigatethealtruismsituationbyusingtheconditioninthe morepheromoneisscatteredwhiletheagentbringsafood
Figure6Thediscoverofshortestpath.
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tothenest.Thatis,thelargerthefoodintheenvironment IntheexperimentastoFigure8(A),agentsgatheredto
has,themorepheromonetheagentsscattered. area B too much. As a result, the wide bridge was con-
structed between area B and the nest. Because almost
Transitionof100agents agentswereinaltruismstateandonlyafewagentscould
Figures 7 show the number of agents in each area, A, B, carry the food to the nest, it took a long time to finish
andC,with100agentsintheenvironment.Incaseof100 theworkinareaBandtheycouldnotproceedtothearea
agents,theyaredividedintosomegroupsandeachgroup A. Some agents in area B moved to area C according to
cansearchthearea,respectively.Figure7(A),Figure7(B), pheromonescatteredbyMajorants.Aftertheagentsfin-
Figure7(C),andFigure7(D)showthetransitionofagents ishedtheworkinareaC,theycouldmovetoareaAatlast.
withA : B : C = {2 : 1 : 1, 1 : 2 : 1, 1 : 1 : 2, 4 : 2 : When ant agents concentrated superfluously, the search
1},respectively.Thetransitionofagentsasshowninthese mightnotprogress.
figuresemerged7or8timesof10trialsineachsituation. IntheexperimentastoFigure8(B),agentsgatheredto
We can observe that ant agents carry the food from the area B and the bridge between area B and the nest was
nearestfoodspotorthelargestsizeoffoodspot.Notethat constructed.SomeagentsinareaBwereattractedbythe
evenifthefoodsizeofareaAisthelargest,thefoodofarea largestsizeofareaA.Asaresult,becausetherewerenot
AremainsuntilareaBorareaC isdisappeared.Because almost agents in area C, the bridge was not constructed
antagentsfindareasBorCandbringallfoodfromareaB in area C and the agents avoided the ditch to carry the
orareaC,respectively. food.
On the contrary, Figure 7(C) (A : B : C = 1 : 1 : 2), Wesummarythecharacteristicbehaviorsunderthe100
Figure 8(A) (A : B : C = 2 : 1 : 1), and Figure 8(B) agentsasfollows.
showthattheresultsarebeyondourexpectations.Inthe
experimentastoFigure7(C),moreagentsgatheredtothe 1. Mostagentsgathertotheleftareaandtheright
areasBandCthantheareaAattheinitialphase.Andthen areanearfromthenest.Theymovetothe
agentsmovedtoareaClargerthanareaBandtheymadea bottomareaaftertheyfinishtheworkateach
bridgeintheareaC.AfterthefoodwaslostinareaC,the area.
antsinareaC movedtoareaA.WeexpectedareaBthan 2. PheromonescatteredbyMajoragentsattractsthe
area A will be disappeared, because some agents visited minoragentsandtheymovetooneoftheleftarea
area B and they knew the existence of area B. However, andtherightarea.Theymovetothebottomarea
most agents moved to A, because the pheromone at the aftertheyfinishedtheworkatthearea.
initialphasewasdisappeared.Therefore,thefoodofBwas 3. Someagentsmakeabridgeonthewayfromthenest
carriedtothenestafterareaAwaslost. tothefoodspot.
Figure7Transitionof100Agents.(A)A:B:C=2:1:1,(B)A:B:C=1:2:1,(C)A:B:C=1:1:2and(D)A:B:C=4:2:1.
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Figure8Transitionof100Agents(othercase).(A)A:B:C=2:1:1and(B)A:B:C=4:2:1.
Transitionof50agents nest,howeververyfewagentscannottakeallofthem.The
Figures 9 show the number of agents in each area, A, B, scattered pheromone was smaller than the evaporated
and C, with 50 agents in the environment. The situation pheromone.Therefore,thepheromonearoundthebridge
has50agentsintheenvironment,theycannotsearchthe disappears and then the bridge was destroyed, because
spacesufficiently.Theantsdidnotdivideintosomesearch the agents in altruism situation depart the bridge in the
groupandthenthesearchofareawasprocessedsequen- conditionoflesspheromone.Theagentleavingfromthe
tiallysuchas A → B → C.Figure9(A)andFigure9(D) bridgemovestoareaA,butthereareonlyafewagentsin
showthetransitionofagentsincaseofA : B : C = {2 : the area. From such results, only few agents in the envi-
1:1,4:2:1},respectively.Asshowninthesefigures,we ronment with large size of food cannot get the altruism
can observe general behaviors in the search space. That situationeasily.
is,thefeedingspotsaredisappearedintheorderoflarger Wesummarythecharacteristicbehaviorsunderthe50
spot.Onthecontrary,Figure9(B)(A : B : C = 1 : 2 : 1) agentsasfollows.
and Figure 9(C) (A : B : C = 1 : 1 : 2) show that the
resultisbeyondourexpectations.IncaseofFigure9(B), 1. Mostagentsgathertotheleftareaandtherightarea
theconstructedbridgeswerenotintheshortestpathon nearfromthenest.Theymovetothebottomarea
the way to the nest as shown in Figure 8(B). In case of aftertheyfinishtheworkateacharea.
Figure9(B),itisaninterestingcase,andalmostagentswill 2. Ifthefoodsizeisthelargestinthebottomarea,the
makebridgesplacetoplaceintheditchfromareaCtothe agentsgatherthereregardlessofthedistancefrom
nest.Theremainingagentsshoulddeliverthefoodtothe thefoodspottothenest.Theyseparatetomovethe
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Figure9Transitionof50Agents.(A)A:B:C=2:1:1,(B)A:B:C=1:2:1,(C)A:B:C=1:1:2,and(D)A:B:C=4:2:1.
Figure10Theconstructionof3bridgessimultaneously.