Distributed Search Systems with Self-Adaptive Organizational Setups

Transcription

1 Inenaional Jounal of Ineacive Mulimedia and Aificial Inelligence, Vol. 4, Nº4 Disibued Seach Sysems wih Self-Adapive Oganizaional Seups Fiedeike Wall Univesiae Klagenfu, Depamen of Conolling and Saegic Managemen, Ausia Absac This pape sudies he effecs of leaning-induced aleaions of disibued seach sysems oganizaions. In paicula, scenaios whee aleaions of he seach-sysems oganizaional seup ae based on a fom of einfocemen leaning ae compaed o scenaios whee he oganizaional seup is kep consan and o scenaios whee he seup is changed andomly. The esuls indicae ha leaning-induced aleaions may lead o high levels of pefomance combined wih high levels of efficiency in ems of eoganizaion-effo. Howeve, he esuls also sugges ha he complexiy of he undelying seach poblem ogehe wih he aspiaion level (which dives posiive o negaive einfocemen) consideably shapes he effecs of leaning. Keywods Agen-based Simulaion, Complexiy, NK Finess Landscapes, Reinfocemen Leaning. I. Inoducion he oganizaional seup of disibued seach sysems is a opic ha Tis invesigaed in many disciplines, such as conol heoy, complex sysems science o compuaional oganizaion heoy (fo exensive eviews cf. [], [2], [3]). The coheence of and he coodinaion wihin disibued seach sysems ae among he pedominan issues in his line of eseach, whee he fome is defined in ems of some of he sysems popeies (e.g., soluion qualiy) and he lae is concened wih acions and ineacions of agens collaboaing in a disibued seach sysem [4], [5]. Thus, he key opics of he oganizaional seup of disibued seach sysems addessed efe o he appopiae segmenaion of he oveall seach poblem ino sub-asks, he way sub-asks ae assigned o agens, and he mechanisms o consolidae he (paial) soluions o sub-asks ino an oveall soluion. The oveall soluion should be as saisfacoy as possible whee is qualiy is deemined on he basis of coheence meics (e.g., [4], [5], [6]). Hence, feasible consensus mechanisms, pefoman algo ihms fo seach and opimizaion, and he appopiae assign men of asks ae of paicula inees in his line of eseach [] in ode o conibue o impoving esuls wih espec o coheence meics of elevance. Howeve, his line of eseach (mosly implicily) assumes ha he designe of a disibued seach sysem decides which of hese mechanisms, algoihms and ways of assignmen ae employed in he oganizaional seup of he seach sysem. This pape follows an appoach ha, in a way, can be egaded as complemen o he afoemenioned line of eseach: no he designe of a seach sysem is allowed o (exogenously) decide on he sysems oganizaional seup bu he seach sysem s oganizaional seup evolves endogenously. In paicula, we allow fo self-adapaion of he seach sysems oganizaional seup, i.e., while seaching fo bee soluions fo he oveall seach poblem (duing un-ime ) he seach sysem is allowed o change is oganizaion, whee changes ae based on feedback [7]. The idea of self-adapive disibued seach sysems builds on pio sudies which povide evidence ha disibued seach pocesses could emakably benefi wih espec o soluion qualiy obained fom inducing oganiza ional dynamics while seaching fo bee soluions may i be in he oganizaional seup of collaboaing obos o swams of unmanned aeial vehicles o in he oganizaional design of a fim whee manages seach fo highe levels of fim pefomance [8], [9], [0], []. Appaenly, ogani za ional change pe se ends o enhance he pefomance of a seach sysem by inducing a shif owads moe exploaion, i.e., discovey of new soluions, and less exploiaion, i.e., sepwise impove men. Howeve, i is woh emphasizing ha hese sudies employ meely andom-diven oganizaional change in he sense ha he seach sysems do no lean which oganizaional seups ae moe successful han ohes. By invesigaing he effecs of leaning-based oganizaional dynamics, his pape goes a sep beyond eseach sudies ha employ andom-diven oganizaional changes. In paicula, his pape sudies he effecs of endowing disibued seach sysems wih some capabiliies o lean abou hei oganizaion s pefomance and o adap he oganizaional seup accoding o he seach sysems pefomance. This pape is an exended vesion of [2] which was pesened a he 3 h Inenaional Confeence on Disibued Compuing and Aificial Inelligence (DCAI). The exensions pe dominan ly elae o he dimensionaliy of he seach poblems unde invesigaion, o he ime hoizon of simulaions, and o a sensiiviy analysis wih espec o he numbe of seach agens. I appeas o be of paicula inees o invesigae whehe seach sysems which employ leaning-based oganizaional change oupefom sysems which make use of andom changes in hei oganizaional seup o sysems which do no change hei seup changes a all. This sudy inends o povide findings on he elaive poenial benefis of leaning-based oganizaional dynamics. Since, i is well known ha he ask envionmen (in ems of he ask complexiy) ends o affec he pefomance of seach, his pape paiculaly conols fo he complexiy of he seach poblems by employing an agenbased simulaion model which is based on he famewok of finess landscapes [3], [4]. The nex secion inoduces he key elemens of he simulaion model. Secion III gives an oveview of he pefomed simulaion expeimens. The esuls ae pesened in Secion IV whee, fis, an in-deph analysis of some baseline scenaios of oganizaional change modes fo diffeen levels of complexiy ae povided. Second, a sensiiviy analysis is pesened which pus paicula emphasis on he need fo coodinaion wihin he seach sysem whee his need is consideably affeced by he numbe of seach agens who cay ou sub-asks. II. Ouline of he Simulaion Model The sudy employs an agen-based simulaion model which capues wo inewined adapive pocesses: In () he sho-em, seach agens seek o find supeio soluions fo he seach poblem. The qualiy of a soluion is measued on he basis of sysem s oveall pefomance level DOI: 0.978/ijimai

2 Regula Issue achieved. We model seach agens o opeae on NK finess landscapes [3], [4]. In (2) he mid-em, he seach sysems ae allowed o adap majo feaues of hei oganizaional seup. Changes ae diven by einfocemen-leaning, which is based on pe fomance enhancemens achieved. A schemaic flow-cha of key feaues of he simulaion model is displayed in Figue. A. Sho-Tem Adapive Seach fo Highe Levels of Pefomance The sudy employs he famewok of NK-finess landscapes, which wee oiginally inoduced in he domain of evoluionay biology [3]. An advanage of NK finess landscapes is ha hey easily allow fo conolling he complexiy of he undelying seach poblem [5]. ) Seach Poblem In each ime sep of he obsevaion peiod T, he seach sysems face an N-dimensional binay seach poblem, i.e., hey seek fo a supeio configuaion (wih, i =,..., N ) ou of a se of possible soluions, which is given by N 2 diffeen binay vecos. Each of he wo saes conibues wih o finess V ( d ) of he seach sysem o in ohe wods o he pefomance achieved by he seach sysem. Accoding o he NK famewok, is andomly dawn fom a unifom disibuion wih. The paamee K capues he complexiy of he undelying seach poblem [5]: In paicula, finess conibuion migh no only depend on he single choice bu also on a numbe of ohe choices whee K indicaes he numbe of ha affec in addiion o. In case of no ineacions K is 0, and K equals N fo he case of maximum inedependence. Hence, conibuion esuls fom wih { i,... ik } {,..., i, i,..., N} +. The oveall pefomance V achieved by he seach sysem in peiod is compued as he nomalized sum of conibuions : V N = V ( d ) = C i N i= 2) Agens and hei Choices The seach fo highe levels of pefomance V is collaboaively pefomed by M seach agens. In paicula, he N-dimensional seach poblem is paiioned ino M disjoin paial poblems, and each of hese sub-poblems is exclusively delegaed o one seach agen, =,..., M. The paial seach poblems ae of equal size wih N N = = (,..., M ). Fom he pespecive of seach agen, he M seach poblem is segmened ino a paial seach veco d which conains he choices which ae unde he seach agen s pimay conol and ino a paial veco d,es, which capues he esidual choices ha he ohe seach agens q ae in chage of. Howeve, wih coss-segmen ineacions among he sub-poblems, choices of agen migh affec he conibuion of he ohe agens choices o oveall pefomance, and vice vesa. () (2) In each ime sep, a seach agen seeks o idenify he bes configuaion fo he own choices d assuming ha he ohe agens do no ale hei choices made in -. Each agen andomly discoves * wo alenaives in addiion o he saus quo choice d, whee, as compaed o he saus quo, one alenaive (named a) diffes in one and he ohe one (labelled a2) diffes in wo single choices d i. In consequence, in ime sep, agen has hee opions o choose fom,,a i.e., keeping he saus quo o swiching o d o,a2 d. Which of hese opions appeas o be favoable fom he seach agen s pespecive depends on he agen s objecive P. This objecive is shaped by paamee α which defines he exen o which he esidual pa of he decision poblem is consideed in addiion o he own paial seach poblem. The objecive funcion can be fomalized by, own, es P ( d ) = P ( d ) + α P wih and = p N fo s > and p = 0 fo =. s= (3) M, es q, own P = P whee q=, q Howeve, he agens ex ane evaluaions of alenaives do no necessaily need o be pefec. In paicula, agens migh misjudge he opions conibuions o objecive P ( d ). This may no only be an uninenional shocoming of, e.g., agens infomaion pocessing capabiliies bu may also be inenionally induced: Some evidence suggess ha impefec infomaion on he finess (pefomance) of opions could incease he effeciveness of seach pocesses (e.g., [6], [7]). Pevious eseach shows ha false-posiive evaluaions of opions incease he divesiy of seach. As a consequence, hee is a chance o end siuaions of ineia induced by sicking o a local peak and o each basins of aacions fo highe levels of finess. Hence, inenionally o no, ou agens may evenually be endowed wih slighly disoed infomaion abou he pefomance of opions. Disoions ae capued by adding eo ems as exemplaily shown in Eq. (4): ~, own, own ( ) ( ), own P d = P d + e ( d ) (4) Fo he sake of simpliciy, disoions ae modeled as elaive eos added o he ue pefomance (fo ohe funcions see [6]). The eo 2 ems follow a Gaussian disibuion N (0; σ ) wih expeced value 0 and sandad deviaions, own σ and, es σ. Vaiances ae assumed o be he equal fo all seach agens =,..., M and sable ove ime (if no aleed by self-adapaion as descibed subsequenly); all eo ems ae assumed o be independen fom each ohe. Apa fom he seach agens, he model capues a kind of cenal agen whose ole is a wofold: () In he sho-emed adapive seach, he cenal agen could depending on he paicula mode of coodinaion inevene in he selecion of choices. (2) In he mid-em, he cenal agen assesses pefomance enhancemens and leans abou successful oganizaional seups by einfocemen. The nex secion povides moe deails on he cenal agen s oles. B. Mid-Tem Adapaion of he Oganizaional Seup based on Reinfocemen Leaning The vey coe of his sudy is elaed o leaning on he pefomance conibuions of a seach sysem s oganizaion and, evenually, aleing he oganizaional seup accodingly. The following wo subsecions descibe he modelled mode of einfocemen leaning as well as

3 Inenaional Jounal of Ineacive Mulimedia and Aificial Inelligence, Vol. 4, Nº4 he dimensions of he oganizaional seup which may be subjec o oganizaional change. ) Mode of Reinfocemen Leaning. In each T*-h ime sep, he cenal agen faces an L-dimensional decision poblem elaed o he L dimensions of he oganizaional seup which can be aleed. In paicula, he cenal agen chooses a seup ( a ( ),..., a ( )) Ö = L of alenaives al Al fo all l =,..., L and wih A l giving he numbe of alenaives a l in se A. l The model employs a simple mode of einfocemen leaning (fo oveviews see [8], [9]) based on saisical leaning, i.e., a genealized fom of he Bush-Moselle model [20], [2]: In evey T*- h peiod, he popensiies of choices ae updaed based on he simuli esuling fom he evaluaion of he oucome (pefomance effecs) achieved unde he egime of pio choices of he oganizaional seup. The oucome ω of configuaion Ö is given by he maximal elaive pefomance enhancemen which is achieved wihin he las T* peiods of he adapive walk, i.e., ϖ ( Ö V ~ - V-T* ~ ) = max, =,...,( T * ) V-T* The evaluaion of he oucome can be egaded posiive () o negaive (-), whee he assessmen of ω depends on whehe o no i, a leas, equals an aspiaion level v. Hence, he simulus τ () esuls as Le p( a l, ) denoe he pobabiliy of an alenaive wihin dimension l of oganizaional seup o be chosen a ime (whee (, ) = 0 p( a l, ) and p a l ); a l A L a l () denoes he opion ou of se A l which is implemened a ime-sep. The pobabiliies of opions al Al ae updaed based o he following ule, whee l ( 0 l ) eflecs he einfocemen sengh [2]: (5) (6) fo all seach agens =,..., M. In he following we skip index. 2. The pecisions of ex ane-evaluaions made by seach agens and by he cenal agen as given by, own σ and, es σ, and cen σ, especively. 3. The mode of coodinaion as seleced ou of hee alenaives: (a) decenalized : wihou inevenion fom he cenal agen o any coodinaion which ohe seach agens, each seach agen auonomously decides on he own paial choices d ; (b) laeal veo : he seach agens infom each ohe abou hei pefeences and ae endowed wih muual veo powe; (c) cenalized : each seach agen infoms he cenal agen abou he wo mos pefeed opions fom *,a d, d and,a2 d ; he cenal agen chooses ha combinaion of pefeences which pomises he highes oveall pefomance V. III. Simulaion Expeimens and Paamee Seings In he simulaion expeimens, afe a pefomance landscape is geneaed, he iniial oganizaional seup (i.e., veco Ö = 0 ) of a seach sysem is deemined andomly wih unifom pobabiliies p( a l, = 0) ou of he opions in each dimension l as inoduced above and summaized in Table I. Nex, he seach sysems ae placed andomly in he pefomance landscape. Then, ove an obsevaion ime T of 500 peiods, he seach sysems ae obseved while seaching fo highe levels of pefomance. In each T*-h peiod, pobabiliies ae updaed and oganizaional configuaions ae (evenually) aleed (cf. Sec. B). Fig. displays he key evens duing a simulaion expeimen capuing leaning-based adapaion of he oganizaional seup. Paamee TABLE I Paamee Seings Values / Types Obsevaion peiod T = 500 Numbe of choices N = 2 Ineacion sucues block-diagonal (K = 2); full inedependen (K = ) Numbe and scope of seach agens Baseline scenaios: M = 4, wih d = (d,...,d3), d2=(d4,,d6), d3 = (d7,,d9), d4 = (d0,,d2) Sensiiviy analysis: M = 2 wih d = (d,...,d6), d2=(d7,,d2) M = 6 wih d = (d,...,d3) o d6=(d0,,d2) Afe he pobabiliies ae updaed accoding o Eq. 7, he oganizaional seup Ö o be implemened fom ime seps + o + T * is deemined andomly based on he updaed pobabiliies. 2) Oganizaional Seup. The veco of he oganizaional seup Ö is modelled o be heedimensional, i.e., L = 3. Wihin each dimension, hee opions ae given (i.e., = 3 l {,2,3 } Table I): A l (7) ). These dimensions elae o (see also. The objecive of he seach agens as conolled by paamee in Eq. 3. Fo he sake of simpliciy, α α is modelled o be he same Numbe of oganizaional dimensions Dimension l=: Agens objecive Dimension l=2: Pecision of evaluaion Dimension l=3: Coodinaion mode Ineval of change Reinfocemen sengh L = 3 α Î {0, 0.5, } (s,own, s,es, scen) Î {(0, 0, 0), (0., 0.5, 0.25), (0.05, 0.25, 0.25)} decenalized; laeal veo; cenalized T* = 25 and fo conasing o no change : T* > T l Î {0, 0.5} Aspiaion level v Î {0, 0.0}

4 Regula Issue wih K = 2 and K* = 0 whee each of he fou sub-poblems is assigned o one seach agen. In his seup, one agen s decisions do no affec he pefomance conibuions of he ohe agens choices. The second case is chaaceized by full inedependence, i.e., all single opions d i affec he pefomance conibuions of all ohe choices d j i and he seach poblem s complexiy is aised o is maximum, i.e., inensiy of ineacions K as well as he coss-subpoblem ineacions K* ae maximal (see Figue 2.b fo an example wih K = and K* = 9). a. Block-diagonal sucue (K =2, K *=0) Choice di Choice di -Agen Noes: X Pefomance Conibuion C j X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X b. Full inedependen Sucue (K =, K *=9) Pefomance Conibuion C j X X X X X X X X X X X X 2 X X X X X X X X X X X X 3 X X X X X X X X X X X X 4 X X X X X X X X X X X X 5 X X X X X X X X X X X X 6 X X X X X X X X X X X X 7 X X X X X X X X X X X X 8 X X X X X X X X X X X X 9 X X X X X X X X X X X X 0 X X X X X X X X X X X X X X X X X X X X X X X X 2 X X X X X X X X X X X X Scope of pimay conol of seach agen Choice i affecs pefomance conibuion j Choice i does no affec pefomance conibuion j Fig. 2. Ineacion sucues and assignmen of choices o seach agens fo he a. block-diagonal and b. full inedependen sucue. IV. Resuls Fig.. Schemaic epesenaion of one simulaion un ove T peiods including poenial changes of he seach sysem s oganizaional seup. In ode o oppose seach sysems wih leaning capabiliies (i.e., wih l > 0) o non-leaning sysems employing oganizaional change, simulaions fo l = 0 ae conduced. Moeove, seach sysems which do no ale hei oganizaion wihin he obsevaion ime T (i.e., wih T* > T) ae simulaed. In ode o capue he complexiy of he undelying seach poblem, simulaions fo wo ineacion sucues ae pefomed which, in a way, epesen wo exeme scenaios [22]: in he block-diagonal sucue he oveall seach poblem can be segmened ino disjoin pas wih maximal inense ina-sub-poblem ineacions bu no coss-sub-poblem ineacions (K*). An example is given in Figue 2.a The simulaion expeimens ae conduced fo wo baseline scenaios of complexiy (see Figues 2.a and 2.b) and fo fou modes of oganizaional adapion: (I) no change, (II) change wihou leaning, (III) leaning-based change wih low aspiaion level and wih (IV) high aspiaion level. These baseline scenaios ae, hen, modified in he numbe of seach agens. In he modified scenaios, wo o six seach agens ae employed insead of fou. A. Baseline Scenaios Table II displays condensed esuls of he simulaed scenaios. The final pefomance achieved in he end of he obsevaion peiod ( V = 500 ) and he pefomance achieved on aveage in each of he 500 peiods ( V [ 0;500] ) may seve as indicaos fo he effeciveness of he seach pocess. The same applies o he elaive fequency of how ofen he global maximum is found in he final peiod. The aio of aleaions of d infoms abou he divesiy of he sho emed seach pocesses, while he aveage numbe of aleaions of oganizaional dimensions infoms abou he divesiy of oganizaional seups ha ae implemened duing adapive walks and, evenually, modified wihin in he (mid

5 Inenaional Jounal of Ineacive Mulimedia and Aificial Inelligence, Vol. 4, Nº4 emed) seach fo appopiae oganizaional seups. Figue 3 depics he aveaged adapive walks fo he diffeen modes of change in he block-diagonal sucue of ineacions, and Figue 4 epos on he full inedependen sucue coespondingly. In paicula, Figues 3 and 4 show he pefomance diffeences of he change, no leaning mode and he wo modes employing leaning, agains he no change mode. Scenaio of leaning and change TABLE II Condensed Resuls of he Baseline Scenaios Final Pefom. V =500 a Aveage Pefom. a V[ 0;500 ] Fequ. glob. max a =500 Block diagonal ineacion sucue (K=5) b I. No change II. Change, no leaning III. Leaning low asp.lvl IV. Leaning high asp.lvl I. No change II. Change, no leaning III. Leaning low asp.lvl IV. Leaning high asp.lvl ± ± ± ± ± ± ± ± Raio of aleed configs. of d Aveage no. of aleed oganiz. dimens. ove T 36.08% 20.00% n/a 45.40% 22.97% % 9.85% % 43.9% 20.0 Full inedependen ineacion sucue (K=) b ± ± ± ± ± ± ± ± % 5.63% n/a 7.84% 0.24% % 8.74% % 5.98% 36.2 a Confidence inevals, a a confidence level of 99.9%, fo final pefomance ange beween and and fo aveage pefomance beween 0.00 and b Scenaios: no change : T* > 500; change, no leaning : λ = 0; v = 0.0; leaning, low aspiaion level : λ = 0.5; v = 0; leaning, high aspiaion level : λ = 0.5; v = 0.0. Fo fuhe paamee seings see Table I. Each daa ow shows he esuls of 2,500 adapive walks: 0 walks on 250 disinc landscapes. In he following, hee aspecs of he pesened esuls ae discussed in deail: () pefomance diffeences of scenaios in which he oganizaional seup is changed agains scenaios in which he oganizaional seup is modelled o be consan, (2) he effecs of leaning-based adapaion compaed o puely andom adapions of he oganizaional seup, (3) he inensiy of oganizaional change (which is capued by he aveage numbe of aleed dimensions. Concening he fis aspec, Table II as well as Figues 3 and 4 indicae ha wih one excepion pefomance levels of scenaios employing change pesisenly go beyond he level of pefomance achieved wihou change. This behavio can be obseved afe appoximaely 40 peiods. These esuls confim findings of eseach which indicae ha aleing he oganizaional seup in he couse of disibued seach pocesses may be favoable [8], [0], []: I has been agued ha his is diven by he inceased divesiy of seach which educes he peil of sicking o local peaks. This is boadly confimed by he aio of aleaions of configuaions d and he fequency of how ofen he global maximum is found in = 500 (cf. Table II). Howeve, esuls also sugges ha leaning by einfocemen wih high aspiaion levels is no univesally beneficial. Appaenly, he complexiy of he seach poblem ogehe wih he aspiaion level subly affecs he benefis of leaning. In case of he block-diagonal sucue, employing leaning-based change wih a high aspiaion level leads o pefomance levels ha ae emakably below he pefomances achieved wihou change houghou he adapive walk fom abou ime-sep 75 o 500 and he final pefomance V =500 is abou 4 poins of pecenage below he no change case. An explanaion why, in case of he block-diagonal ineacion sucue, a high aspiaion level appaenly induces such a ahe poo pefomance, may be based in he specific selecive effecs induced in his scenaio: Wih inceasing aspiaion level i becomes moe unlikely ha a posiive simulus τ () is achieved unde he egime of a ceain oganizaional seup even if he seup had bough some (lowe han v) pefomance enhancemens in he las T* peiods. Hence, even poenially appopiae oganizaional seups ae likely o eceive low pobabiliies o be e-chosen fo he nex T* peiods. In he blockdiagonal sucue wih is faily low level of ineacions (K = 2), i is ahe likely ha he global maximum is found [22]: of couse, no fuhe pefomance enhancemen is possible in hese cases and he aspiaion level is no eached. Wheneve he global maximum is found (wih aspiaion level v > 0) he oganizaional seup is likely o be modified. An aleed oganizaional seup also induces a modified evaluaion of he cuen configuaion d []. As a esul, a move away fom he global maximum in he pefomance landscape becomes likely. Fig. 3. Pefomance diffeences of adapive seach pocesses employing oganizaional change agains seach pocesses wihou aleaions of he oganizaional seup in case of he block-diagonal ineacion sucue. Each cuve epesens he diffeence of means of he aveage of 2,500 adapive walks, i.e., 250 disinc pefomance landscapes wih 0 adapive walks on each. Fo paamee seings see Table I. Fig. 4. Pefomance diffeences of adapive seach pocesses employing oganizaional change agains seach pocesses wihou aleaions of he oganizaional seup in case of he full inedependen ineacion sucue. Each cuve epesens he diffeence of means of he aveage of 2,500 adapive walks, i.e., 250 disinc pefomance landscapes wih 0 adapive walks on each. Fo paamee seings see Table I

6 Regula Issue The second aspec o be discussed in deail is elaed o he pefomance effecs of leaning-based adapaion compaed o he puely andom-diven aleaions. The esuls sugges ha leaningbased change is no univesally moe beneficial han puely andomdiven oganizaional change. Rahe, i appeas ha he aspiaion level v is of emakable elevance: in boh ineacion sucues, leaning-based adapaion employing a high aspiaion level leads o a level of final pefomance ha is infeio o he pefomances achieved unde puely andom-diven change. Employing a low aspiaion level pefoms bes in he block-diagonal sucue i leads o a medium pefomance in he case of high complexiy. As agued above, a high aspiaion level induces moe oganizaional aleaions which leads o moe divesiy of seach, i.e., moe aleaions of d, as compaed o he low aspiaion level. Fo highly complex ineacion sucues, a paicula peil is ha he seach pocesses may sick o a local opimum, and, hence, inceasing divesiy of seach pe se may be beneficial. This migh explain he good pefomance of he change, no leaning mode. Howeve, a high aspiaion level, in a way, penalizes paiculaly hose seach pocesses which have eached a good soluion fom which fuhe impovemens ae had o achieve: as agued above, he block-diagonal ineacion sucue is paiculaly pone o his effec; howeve, he ahe low pefomance in he full-inedependen sucue (Figue 4) migh also be caused by his effec. Wih he hid aspec o be discussed moe ino deail he inensiy of oganizaional change (igh-mos column in Table II), and, hus, he efficiency of he mode of change and leaning comes ino play. The aveage numbe of oganizaional dimensions in which aleaions occu duing he adapive seach may be egaded as an indicao fo he effo ( coss ), if any, of oganizaional dynamics. Obviously, he conex of he seach oganizaion is elevan fo whehe, o no, and, if so, in which shape coss of oganizaional change occu. Fo example, in case of a newok of unmanned aeial vehicles, collaboaively seving a ceain sevice aea, he swich fom one coodinaion mode o anohe migh no cause any coss (apa fom acivaing anohe of aleady available coodinaion mechanisms); howeve, in case of fim manages, collaboaively seaching fo bee configuaions of key pefomance dives, eoganizaions ae ahe cosly, including, fo example, leaning coss of new oganizaional pocedues o he adjusmen of incenive schemes. Hence, he aveage numbe of dimensions changed may be ahe ciical fo he efficiency of inducing oganizaional dynamics of seach. Resuls sugges ha, in boh ineacion sucues unde invesigaion, leaning wih a low aspiaion level yields good pefomance and a high level of efficiency as compaed o he ohe scenaios: In case of he block-diagonal ineacion sucue he final pefomance achieved wih a low aspiaion level exceeds he pefomance eached via puely andom-diven change by abou 7 poins of pecenage while he aveage numbe of oganizaional aleaions is emakably lowe (i.e., 6.9 aleed dimensions on aveage in case of leaning wih low aspiaion level vesus 38.2 in case of puely andomized change). If he complexiy of he seach poblem is high he pefomance of he change, no leaning scenaio exceeds he pefomance of leaning-based adapaion wih low aspiaion levels; howeve, his comes along wih, on aveage, 37.9 oganizaional aleaions compaed o 6.2 aleaions in he lae case. In sum, i appeas ha leaning wih low aspiaion level may povide ahe high pefomance levels combined wih few oganizaional aleaions. Thus, wheneve oganizaional ale aions do no come along wihou any cos, leaning wih low aspiaion level appeas o be paiculaly ineesing wih espec o he efficiency of seach. B. Sensiiviy Analysis In he sensiiviy analysis, he baseline scenaios ae modified wih espec o he numbe of seach agens: he simulaions addiionally ae conduced fo sysems wih wo and wih six seach agens. In paicula, he ineacions among decisions emain unchanged, bu he assignmen of decisions is modified. Figues 5.a and 5.b show he assignmen fo he case of wo agens and six agens, especively, in he block-diagonal sucue as compaed o Figue 2.a. a. Block-diagonal sucue wih 2 agens (K =2, K* =0 ) Pefomance Conibuion C j X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X Choice di b. Block-diagonal sucue wih 6 agens (K =2, K * {, 2}) Pefomance Conibuion C j X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X Choice di Agen Agen 2 Agen Agen Agen Agen Agen Agen Noes: X - Scope of pimay conol of seach agen Choice i affecs pefomance conibuion j Choice i does no affec pefomance conibuion j Fig. 5. Assignmen of fou independen sub-poblems o a. wo and b. six seach agens. In he simulaion model, wih inceasing (deceasing) he numbe of seach agens he divesiy of seach is inceased (deceased): in each ime sep, each seach agen discoves wo alenaives o he saus quo of he own paial sub-poblem (Secion II.A) one alenaive whee one bi is flipped and anohe wih wo bis flipped. Thus, in case of wo seach agens, a maximum fou bis of he enie configuaion d could be flipped in ime sep ; in conas, wih six agens a maximum 2 bis could be flipped. Thus, wih inceasing numbe of agens he need fo coodinaion is inceased oo, and vicevesa. Figues 6 and 7 plo he final pefomance V =500 achieved in he block-diagonal and he full-inedependen ineacion sucue, especively, wih wo, fou and six seach agens

7 Inenaional Jounal of Ineacive Mulimedia and Aificial Inelligence, Vol. 4, Nº4 Fig. 6. Sensiiviy of final pefomance o numbe of seach agens in he block-diagonal ineacion sucue. Each mak epesens he aveage of 2,500 adapive walks, i.e., 250 disinc pefomance landscapes wih 0 adapive walks on each. Fo paamee seings see Table I. Fig. 7. Sensiiviy of final pefomance o numbe of seach agens in he full inedependen ineacion sucue. Each mak epesens he aveage of 2,500 adapive walks, i.e., 250 disinc pefomance landscapes wih 0 adapive walks on each. Fo paamee seings see Table I. The esuls sugges ha he change, no leaning mode and leaning wih low aspiaion level ae leas sensiive o he numbe of agens. In conas, he final pefomance obained by leaning wih high aspiaion level vaies consideably wih he numbe of agens. Howeve, he no change mode appeas mos sensiive o an incease in he numbe M of seach agens compaed o he modes employing oganizaional change. Wih he ansiion fom wo o fou agens, he final pefomance shows ahe sligh de- o inceases depending on he mode of change and he ineacion sucue. Howeve, wih he ansiion fom fou o six agens he final pefomance obained deceases emakably in boh ineacion sucues. An ineesing quesion is wha migh cause hese effecs. A eason migh be given by he elaion beween assignmen of decisions o seach agens and he ineacions among agens decisions. Fo example, wih six seach agens in he block-diagonal sucue (Figue 5.b), cossagen ineacions among seach agens choices occu wheeas fo wo and fou agens no coss-agen ineacions show up (Figue 5.a.). Hence, in his ineacion sucue he need fo coodinaion among agens choices anges fom no need a all (i.e., K* = 0 fo M = 2 and M = 4) o some coodinaion need as capued by K* = o K* = 2 (see Figue 5.b). V. Conclusion The majo finding of his sudy is ha employing self-adapaion fo he oganizaional seup of disibued seach sysems via einfocemenbased leaning poenially leads o high levels of pefomance and his, in paicula, wih a ahe high level of efficiency, as given by he exen of eoga ni zaion. These findings ae paiculaly ineesing when eoganizing he seach sysem causes maginal coss may i be due o leaning of new oganizaional pocedues on he agens sie o adjusmens equied in insiuional aange mens. Howeve, he esuls also sugges ha he complexiy of he seach poblem ogehe wih he aspiaion level consideably shapes he effecs of einfocemen leaning which, a wos, may even be hamful if compaed o efaining fom any oganizaional aleaions. These findings may sensiize he designe of a disibued seach sysem o employing leaning by einfocemen as he level of he aspied pefomance enhancemens should no be ove seched in ode o avoid hype-acively and ineffecively alenaing seach sysems. Moeove, he sensiiviy analysis suggess ha leaning wih high aspiaion level is paiculaly sensiive o he need fo coodinaion among seach agens. These findings emphasize he need fo fuhe eseach effos. An obvious nex sep is o es he key idea of inducing leaning-based oganizaional change in moe pacical seings han he one pesened hee. Though some peliminay esuls obained fo leaning-based selecion of he coodinaion mode in ems of he job scheduling policy employed by a swam of unmanned aeial vehicles [23] povide some suppo fo he ideas pesened in his pape, fuhe applicaions ae definiely of inees. Moeove, fuhe sudies should pefom in-deph analyses of he ole of he aspiaion level and ohe paamees like he ineval beween of oganizaional aleaions o he leaning sengh which wee fixed in he simulaion ex peimens pesened in his pape. Fuhemoe, he basic seach poblem capued in his sudy is ahe unsucued in ems of andomized pefomance coni buions (apa fom he sucue of ineacions); hence, in fuhe eseach sudies leaning-based oganizaional adjusmens of he seach sysem may un ou o be even moe beneficial in case of moe sucued seach poblems. Refeences [] C. Yongcan, Y. Wenwu, R. Wei and C. Guanong, An oveview of ecen pogess in he sudy of disibued muli-agen coodinaion, IEEE Tans. on Indusial Infomaics, vol. 9, pp , Jan [2] T. Goss and B. Blasius, Adapive coevoluionay newoks: a eview, Jounal of he Royal Sociey Ineface, vol. 20, pp , Ma [3] K. M. Caley and L. Gasse, Compuaional oganizaion heoy, in: Muliagen sysems: A moden appoach o disibued aificial inelligence, G. Weiss, Ed., Cambidge: MIT Pess, 999, pp [4] A. H. Bond and L. Gasse, Chape Oienaion, in Readings in Disibued Aificial Inelligence, A. H. Bond and L. Gasse (Ed.), San Maeo: Mogan Kauffmann, 988, pp. 56. [5] M. Wooldidge, An Inoducion o Muliagen Sysems (2nd ed.), Chichese: Wiley, [6] F. von Maial, Coodinaing Plans of Auonomous Agens, Lecue Noes in Aificial Inelligence, vol. 60. Belin/Heidelbeg/New Yok: Spinge, epin 2008 (992). [7] Y. Bun, G. Di Mazo Seugendo, C. Gacek, H. Giese, H. Kienle, M. Lioiu, H. Mülle, M. Pezzè, and M. Shaw, Engineeing Self-Adapive Sysems hough Feedback Loops, in Sofwae Engineeing fo Self- Adapive Sysems, BHC Cheng, R. de Lemos, H. Giese, P. Inveadi, and J. Magee, Ed., Belin/Heidelbeg: Spinge, 2009, pp [8] O. Baumann, Disibued Poblem Solving in Modula Sysems: he Benefi of Tempoay Coodinaion Neglec, Sysems Reseach and Behavioal Science, vol. 32, pp , Jan./Feb [9] F. Wall, Oganizaional dynamics in adapive disibued seach pocesses: Effecs on pefomance and he ole of complexiy, in Fonies of Infomaion Technology & Elecical Engineeing, vol. 7, pp , Ap [0] F. Wall, Effecs of oganizaional dynamics in adapive disibued seach

8 Regula Issue pocesses, in Disibued Compuing and Aificial Inelligence, 2h In. Conf., S. Omau, Q.M. Malluhi, S. R. Gonzalez e al., Ed., Advances in Inelligen Sysems and Compuing vol. 373, Belin: Spinge, 205, pp [] F. Wall, Beneficial Effecs of Randomized Oganizaional Change on Pefomance, in Advances in Complex Sysems, vol. 8, 05n06:55009, Nov [2] F. Wall, Self-adapive oganizaions fo disibued seach: The case of einfocemen leaning, in Disibued Compuing and Aificial Inelligence, 3h Inenaional Confeence, S. Omau, A. Semala, G. Bocewicz e al., Ed., Advances in Inelligen Sysems and Compuing, vol 474, Cham: Spinge Inenaional Publishing, 206, pp [3] S. A. Kauffman and S. Levin, Towads a geneal heoy of adapive walks on ugged landscapes, Jounal of Theoeical Biology, vol. 28, pp. 45, Jan [4] S. A. Kauffman, The Oigins of Ode: Self-Oganizaion and Selecion in Evoluion. Oxfod: Oxfod Univesiy Pess, 993. [5] R. Li, M. M. Emmeich, J. Eggemon, E. P. Bovenkamp, T. Bäck, J. Dijksa and J. C. Reibe, Mixed-inege NK landscapes, in Paallel Poblem Solving fom Naue IX, T. Runasson, H.-G. Beye, E. Buke, J. Meelo-Guevós, L. D. Whiley and X. Yao, Ed., Lecue Noes in Compue Science, vol. 493, Belin: Spinge, 2006, pp [6] B. Levian and S.A. Kauffman, Adapive walks wih noisy finess measuemens. Molecula Divesiy, vol., pp , Jan [7] F. Wall, The (beneficial) ole of infomaional impefecions in enhancing oganisaional pefomance, in Pogess in Aificial Economics, 6h Aificial Economics, M. Li Calzi, L. Milone and P. Pellizzai, Ed., Lecue Noes in Economics and Mahemaical Sysems, vol. 645, Belin: Spinge, 200, pp [8] R. S. Suon and A. G. Bao, Reinfocemen Leaning: An Inoducion, 2nd ed., Cambidge (Mass.): MIT Pess, 202. [9] L. P. Kaelbling, M. L. Liman and A. W. Mooe, Reinfocemen leaning: a suvey, Jounal of Aificial Inelligence Reseach, vol. 4, pp , May 996. [20] R. R. Bush and F. Moselle, Sochasic Models fo Leaning, Oxfod (Engl.): Wiley, 955. [2] T. Benne, Agen leaning epesenaion: Advice on modelling economic leaning, in Handbook of Compuaional Economics, vol. 2, L. Tesfasion and K. L. Judd, Ed., Amsedam: Elsevie, 2006, pp [22] R. W. Rivkin and N. Siggelkow, Paened ineacions in complex sysems: Implicaions fo exploaion, in Managemen Science, vol. 53, pp , July [23] A. Lembache, The Applicaion of Leaning Algoihms in Job Scheduling Poblems Mase Thesis (supeviso F. Wall), Univesiae Klagenfu 205 (unpublished). Fiedeike Wall eaned he Diploma fo Business Economics in 988 and he Docoal degee in 99, boh a he Geog-Augus-Univesiä Göingen, Gemany. In 996 she eceived he venia legendi (Habiliaion fo Business Economics) fom he Univesiä Hambug, Gemany. Afe being a scienific Pojec Refeen fo Accouning in he conex of he implemenaion of SAP R/3 a Max-Planck Sociey, Munich, Gemany she became Full Pofesso of Business Adminisaion, esp. Conolling and Infomaion Managemen a he Univesiä Wien/Hedecke, Gemany. Since 2009 she is Full Pofesso and Head of he Depamen of Conolling and Saegic Managemen a he Alpen- Adia-Univesiä Klagenfu, Ausia. Pof. Wall s scienific wok is focused on disibued decision-making, managemen conol sysems and he qualiy of he infomaion povided by hese sysems. He main eseach appoach is defined by agen-based simulaion mehods and agen-based echnologies