Abstract
We present a novel distributed heterogeneous multi-population evolutionary dynamics approach, which can be used in diverse engineering applications as a distributed optimization-based algorithm. We also provide stability certificates of Nash equilibria under the proposed approach. Finally, over the end of this paper, an example illustrates the performance of the aforementioned multi-population evolutionary dynamics.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 16852-16857 |
| Number of pages | 6 |
| Journal | IFAC-PapersOnLine |
| Volume | 53 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2020 |
| Event | 21st IFAC World Congress 2020 - Berlin, Germany Duration: Jul 12 2020 → Jul 17 2020 |
Keywords
- distributed learning
- Heterogeneous populations
- multi-population evolutionary dynamics
ASJC Scopus subject areas
- Control and Systems Engineering
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In: IFAC-PapersOnLine, Vol. 53, No. 2, 2020, p. 16852-16857.
Research output: Contribution to journal › Conference article › peer-review
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TY - JOUR
T1 - Heterogeneous Multi-Population Evolutionary Dynamics with Migration Constraints
AU - Barreiro-Gomez, Julian
AU - Obando, Germán
AU - Pantoja, Andres
AU - Tembine, Hamidou
N1 - Funding Information: 1. INTRODUCTION inrtootoaccoclosuwntitthhinatathsaermeemmuastssboefdaifgfeenretns.t Ftyopr ecsoonfvernevieinsicoen, TheevolutionarygamINeTdyRnOaDmUicCsThaIOveNbecomeapowerful protocols within a same mass of agents. For convenience, Theevolutionaryg1a.mINeTdyRnOaDmUicCsThaIOveNbecomeapowerful wnretootcooacncocsloisduewnrtitathhisnaotcaitehstaeyrmetehmamutasctsosbmoepfdraiifsgfeesnretnsh.teFtcyooprlelcesocontifvoernnevioeifnsicaoelnl, tTohoeleinvotluhteiomnaordyelginagmeofdystnraamteigcischianvteerbaecctioomnseaspionweHrfouf-l we consider a society that comprises the collection of all tool in the modeling of strategic interactions as in Hof-whreeotcohocenotselisdroewgrietanhoisnuoscaieastgayemnttehsamtinacsosamospftrraiasgteeesngtisch.eiFncotorelrlcaeocnttiivooennn.ioeFfnucaerl-l, The evolutionary game dynamics have become a powerful the heterogenous agents in a strategic interaction. Fur-bauer and Sigmund [1988], Barreiro-Gomez and Tembine theercmhoenotsreiedr,oegrtehaneorseuoscaireaetgyedntitfhfseartienncotamcspltarrsiassteeessgtiochfeimnctoaelsrlsaeeccsttiioothnna.otFfauarrle-l tool in the modeling of strategic interactions as in Hof-thermore, there are different classes of masses that are [2018a]. Recently, this approach has been implemented in tohhreemrmhineogtreerd,oigvtehenresoreusparoaepguednliatftfseiorinenns.taDcslutaresastetesogiotcfheimntfaeasrcsatecsttihotahnta.teFaaucrrhe-b2a0u1e8ra]a.nRdeSceignmtluy,ntdhi[s19a8p8p],roBaachrrehiaros-bGeoemneizmapnledmTenemtebdinine forming diverse populations. Due to the fact that each many engineering applications as in Quijano et al. [2017]. pohorepmrumilnaogtrieod,nivthevresorelvpeasroepduidflfiaeftfreieornnetnsl.ty,Dcilu.aees.s,etisotsotfhevemolfauastcsiteosnthtiahstagteivaaecrhne m20a1n8yae].nRgienceeenrtinlyg, tahpipsliacpaptiroonaschashians Qbeueinjanimopeltemale.n[t2e0d17in]. population evolves differently, i.e., its evolution is given Moreover, in Tian et al. [2019], authors propose dynamical poyorpmduiilnfafgteirodenivtevresovelovlpeusotpidouinflfaaertryieondtsly.yn,Daimu.ee.i,ctsio,tstheevnolfuattchiteontphirasotpgeoivasechnd many engineering applications as in Quijano et al. [2017]. by different evolutionary dynamics, then the proposed attacking strategies in the simulation of reputation man-apyopprduoilfaaftceihroenbteecvoeovmloveleusstaidominffauerrlytein-dptlyoynp, auim.lea.it,ciosi,ntstcheaevsneo.lutMthieoornepoirsvoepgro,ivsweende attoarcekoivnegr,sitnraTtieagnieestianl.t[h2e01s9im],ualuathioonrsopfroreppousteadtiyonammiacna-l approach becomes a multi-population case. Moreover, we agement scheme evaluation applying evolutionary games. aplylpowrdoifadfceifhrfenbretenctoevmpoelpusutailoamntiauornlytsi-tdpoyoinpnautmlearitacicost,nttcohaesanec.htMhoeothrepeorrvoweprio,tshweinde agteamckenintgscshtreamteegieevsaliunatthioensaimppullyaitniogneovfolruetpiountaatriyongamaens-. allow different populations to interact to each other within In Kawano et al. [2019], authors study the evolutionary ahpllepowrsoaadmcifhefebrseeoncctoiemptoye.psuIalnadmteiuoenldts,i-tpeovoeipnnutleatrhtaiocoutngthcoaestaehc.ehMoeovthroeeluorvtwieorin,thwionef thlleowsadmifeferseonctieptoy.puIlnadteioends, teoveinntetrhaocut gtho etahceh oevthoelurtwiointhionf In Kawano et al. [2019], authors study the evolutionary two different populations are described by the same evo-twheo sdaifmfeeresnotcipeotyp.ulIantdioeneds ,areevednestchroibuegdh btyhetheevosalumtieonevoo-f evyonlavminigcs of two different types of communities in an lutionary dynamics, they might have different structures beveohlavviniogr fernovmirohnomneynbt,eeasnwdairnmsStiselglaenaenradliBzeadutso d[2u0o1p9o]l,isa-ruetgiaorndairnyg dmynigarmatiicosn, tchoenystmraiginhts.haHveendceif,fesrternattesgtrieusctpulraeys behavior from honeybee swarms is generalized to duopolis-different roles. For instance, there are strategies that allow etivcolcuotmiopneatriytiodnynanmdicosp. inion dynamics in the conte∆t of tivcolcuotmiopneatriytiodnynaanmdicosp. inion dynamics in the conte∆t of the interaction to other populations known as migration Evolutionary dynamics represent the evolution of a pop-nhofedfeeirnse,tnebtruartoctlteihos.nerFetoorarionetshatealrsnocpeso,opmtuhleeartseitoranarsteeksgtnireoaswttenhgaiaets otmnhlaiygtraaltlioown Ee voolluuttiioonnaarryyddyynnaamicicss. represent the evolution of a pop-nodes, but there are also some strategies that only allow Evolutionary dynamics represent the evolution of a pop-thnoedieninst,eterbaruactctittoihonnerwetiotahroienthatelhrseopssoaopmueleaptsiotorpnaustleakgtniieoosnw.tnhats omnliygraaltlioown ulation composed of a large number of agents. In this an interaction within the same population. ruelvagotaliruodnt,iotcnhoaemryepvodosyleundtaimoonfiacasryrleadprygrneeasemnnuitcmstbhaeerreevoaoflnuaotgnieo-natso.mfIaincptaohnpids-anodienst,erbaucttitohnerweitahrienatlhseossaome psotrpautleagtiieosn.that only allow regard, the evolutionary dynamics are a non-atomic and Tnheinctoernatcritbiountiownithofinththisepsapmeer pisoapunlaovtieolnd.istributed het-ulation composed of a large number of agents. In this anheinctoernatcritbiountiownithofinththisepsapmeer pisoapunlaovtieolnd.istributed het-anonymous approach, i.e., the decisions of an individual Trhoegecnoenotursibumtuiolnti-opfotphuilsatpiaopnerevisolautnioonvaelrydisdtyrnibaumteicds haept-regard, the evolutionary dynamics are a non-atomic and erogeneous multi-population evolutionary dynamics ap-agent have a negligible influence over the whole popula-Trrhooegaeccnhoe,notiurnsibwumthuiiolcnthi-optfohtpehuielsavtpoialoupnteiorenvisoolauftnidooinvffaelrryednisdttyrpniboaupmtueilcdastihoaenpts--anonymous approach, i.e., the decisions of an individual proach, in which the evolution of different populations tion. Likewise, this approach implies that all the agents porromogapecnohes,ioniungs awmhuuinlcthiiq-putoehpesuoelcavitoeiltouyntiioesnvdooleusftcirdoiibnffeaedrryebndytypmnoaepmaunilcsastoioafnpas-tigoenn.t have a negligible influence over the whole popula-composing a unique society is described by means of a are homogeneous. Therefore, population dynamics assume coormuoappcleohds,inaingndawdhuiisncthirqibutuehteesodecvsioeyltsuytteiimosn.dWoesfecrdpiibrffeesdreenbtytstpmaobepaiulniltsaytoicofenras-airoenh.oLmikoegweniseeo,utsh.iTshaeprpefrooraec,hpoimpupllaietsiotnhdaytnalml tichseaasgsuenmtes coupled and distributed system. We present stability cer-that the switching rates, for a given pairwise interaction, cioofmuicpaplteoedsi,nasgnhdoawduiinsntgirqitbuhueattesodthcsieytmsyteuimlsti.-dpWeosepcrupilbraeetsdieonbtyasptmpabreoailanitcsyhocfearna-threathothmeosgwenitecohuins.gTrhaetreesf,ofroer, paogpiuvelantipoanirdwyinsaeminictseraascstuiomne, tificates, showing that the multi-population approach can have the same structure for all the decision makers within citofiuilclpablteedsu,assenhddofwodriinstghrietbhsuaattmedtehspeyumsrtpeuomltsi.e-spWaoesputphlraeetssieointgalsept-papbrooiplaiutclyhatcieoarnn-that the switching rates, for a given pairwise interaction, still be used for the same purposes as the single-population the population. In contrast, this paper suggests to take sitofiuilclnabteersup,saserhdto.fwoTriontghthetihssaaetmntedh,peuwmrepupoltsrie-speaonsptutahlanetsiooifnfg-lalienp-epproeopcaoucnlhaotmcioainnc hhaeve the same structure for all the decision makers within counterpart. To this end, we present an off-line economic the population. In contrast, this paper suggests to take ctoiisulplnabttecrhupsaperrdto.fboTlreomtht.heissaemned,puwrepposreesseansttahne soifnfg-llien-epoepcounlaotmioinc ★★thJuliane populBarreiro-Gomezation. In conandtrasHt,amidouthis paTempebrinesugacgknesotswledtogetasup-ke discoisupapnattteccrhhpapprrorto.blebTleommt..his end, we present an off-line economic ★ Julian Barreiro-Gomez and Hamidou Tembine acknowledge sup-doisupnattecrhpaprrto.bTleomt.his end, we present an off-line economic ★poJulianJrtulfiraonmBarreiro-GomezBtharerUei.rSo.-GAoirmFeozrcandaenOdfHHficamidouaemoifdSocuieTTneetimmfibbciiRnneeesaaeacckkrcnnhoowwunlleedddeggreegsup-sruanpt-ffiiosptaatticohn:pLroebtlRem, .R>0, R≥0 denote the set of real, positive p★ort from the U.S. Air Force Office of Scientific Research under grant ffiiosptaatticohn:pLroebtlRem, .R>0, R≥0 denote the set of real, positive npuoJmrtublfireraonmFBAtha9550-17rerUei.rSo.-GA-1-0259.oirmFeozrcaenAOdndresfHficaemoifdPSoacunietTnoetjimafibcaiRcnkeensoaewackrlcnehdogwuenlseddesuppgregsruaortnpt-rffeioatla,tiaonnd: LneotnR-n,eRga>t0iv,eR≥re0adlennuomtebtehres,sertesopfercetaivl,eplyo.siTtihve number FA9550-17-1-0259. Andres Pantoja acknowledges support real, and non-negat>0ive≥real0numbers,respectively.The nromuomrtbfprorerormFjectAth9550-17e5214,U50.S-1.C7A-1-0259.o1inr-0vF2oo5catoriar9c.eAOndresffdiColcienciascreesofPSacnietnotjiaf818/2018.icaRckensoewarlcehdguensdesuppurpgpraortnrt rffeioatla,tiaonnd: LneotnR-n,eRga>t0iv,eR≥re0adlenuomtebtehres,sertesopfercetaivl,eplyo.siTtihve puomrtbfreormtheU.S.AirForceOfficeofScientificResearchundergrant rffeioatla,tiaonnd: LneotnR-n,eRgativ,eRreadlennuomtebtehres,sertesopfercetaivl,eplyo.siTtihve nruommbperroFjeAct9525104-,1C7-o1n-0v2o5c9a.toArinadCreoslciPeanncitaosja81a8c/k2n0o1w8l.edges support real, and non-negative real numbers, respectively. The from project 214, Convocatoria Colciencias 818/2018. real, and non-negative real numbers, respectively. The Publisher Copyright: © 2020 Elsevier B.V.. All rights reserved.
PY - 2020
Y1 - 2020
N2 - We present a novel distributed heterogeneous multi-population evolutionary dynamics approach, which can be used in diverse engineering applications as a distributed optimization-based algorithm. We also provide stability certificates of Nash equilibria under the proposed approach. Finally, over the end of this paper, an example illustrates the performance of the aforementioned multi-population evolutionary dynamics.
AB - We present a novel distributed heterogeneous multi-population evolutionary dynamics approach, which can be used in diverse engineering applications as a distributed optimization-based algorithm. We also provide stability certificates of Nash equilibria under the proposed approach. Finally, over the end of this paper, an example illustrates the performance of the aforementioned multi-population evolutionary dynamics.
KW - distributed learning
KW - Heterogeneous populations
KW - multi-population evolutionary dynamics
UR - http://www.scopus.com/inward/record.url?scp=85119592186&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85119592186&partnerID=8YFLogxK
U2 - 10.1016/j.ifacol.2020.12.1190
DO - 10.1016/j.ifacol.2020.12.1190
M3 - Conference article
AN - SCOPUS:85119592186
SN - 2405-8963
VL - 53
SP - 16852
EP - 16857
JO - IFAC-PapersOnLine
JF - IFAC-PapersOnLine
IS - 2
T2 - 21st IFAC World Congress 2020
Y2 - 12 July 2020 through 17 July 2020
ER -