Evolutionary Method of Population Classification According to Level of Social Resilience

Transcription

1 (JACSA) eraoal Joural of Advaced Compuer Scece ad Applcaos, Evoluoary Mehod of Populao Classfcao Accordg o Level of Socal Reslece Coulbaly Kpa Tekoura Research Laboraory Compuer Scece ad Telecommucaos (LART) Naoal Polyechc sue Houphoüe Bogy (NPHB) Abda, vory Coas Brou Koa Marcell Naoal Polyechc sue Yamoussoukro, vory Coas Babr Mchel Naoal Polyechc sue Abda, vory Coas Souleymae Oumaaga Naoal Polyechc sue Abda, vory Coas Absrac Followg he may aural dsasers ad global soco-ecoomc upheavals of he s ceury, he cocep of reslece s creasgly he subec of much research amed a fdg approprae resposes o hese raumas. However, mos exsg work o reslece s lmed o a broad cross-dscplary pael of o-operaoal heorecal approaches. Thus, he sudy of he processes of socal reslece s cofroed wh dffcules of modelg ad a lack of approprae aalyss ools. However, he exsg srafcao mehods are oo geeral o ake o accou he specfces of he reslece ad are dffcul o use for o-specalss modelg. addo, mos radoal mehods of paro research have lmaos cludg her ably o effecvely explo he research space. hs paper, we propose a classfcao algorhm based o he echue of geec algorhms ad adaped o he coex of socal reslece. Our obecve fuco, afer pealzao by wo crera, allows o explore wdely he space of research for soluos whle favorg classes ue homogeeous ad well separaed bewee hem. Keywords geec algorhm; Usupervsed classfcao; socal reslece; Parog mehod. NTRODUCTON Reslece s a polysemc cocep ha s suded several felds cludg socology, ecology, ecoomcs, compuer scece ad psychology. Resulg from he physcs of maerals where desgaes he ably of a sysem o resume s al eulbrum afer a deformao, reslece s he segme of may researches hese days. However, aalyss of he leraure hs area reveals a lack of operaoal approaches. Ths paper s a corbuo o he process of operaoalzg he cocep of socal reslece ha s defed by he Frech ehologs Bors Cyrulk as he ably of a perso, a socal group or a evrome o overcome sufferg or rauma []. Oe of he fudameal prcples of cluserg s o esure he parog of a se of obecs so ha he elemes of he same group are as smlar as possble ad ha he varous groups are dsc amog hemselves. There are several famles of classfcao mehods, he mos wdely used of whch are herarchcal classfcao mehods ad parog mehods. These mehods, however, prese a cera umber of o cosderable drawbacks. effec, herarchcal or agglomerave mehods are lmed o small ses of szes due o he fac ha hey sore memory a dssmlary marx whose sze s uadrac as a fuco of he umber of verces. As for paro-based classfcao mehods, addo o geerag sub-opmal resuls depede o he al paro, hey explo oly a small par of he soluo search space. Ths calls for he eed o develop oher mehods offerg more possbles for explorg hs research space. The geec algorhms developed by Joh Hollad [] respod o hs cocer. deed, hese algorhms, spred by he prcples of he eo-darwa aural evoluo are kow for her effecveess explorg ue large ad complex research spaces. They geerally allow o geerae good soluos followg he applcao of a cycle of operaos (seleco, crossg, muao). Oe of he eress of our proposal s s ably o defy dffere doma characersc groups a gve populao. hus adaps well o he coex of socal reslece [3] especally he sudy of socal srafcao wh a populao vcm of a raumac shock. oher words, a applcao of hs suao could be he defcao of he socal groupgs of a populao accordg o he degrees of reslece of he dffere dvduals facg a raumac shock. hs paper, afer a preseao of he geec algorhms ad some work doe, we prese our proposo followed by a cocluso.. GENETC ALGORTHMS A. Prcple Geec algorhms are par of he sochasc opmzao algorhms [4][5]. They represe a modelg of aural evoluo o solve a research problem. Ther goal s o evolve a se of soluos owards a opmal soluo. To do so, he algorhm radomly geeraes a populao of dvduals 39 P age

2 (JACSA) eraoal Joural of Advaced Compuer Scece ad Applcaos, (chromosomes) ad proceeds by successve erao o geerae ew dvduals by applyg dffere seleco, crossover ad muao operaors ul reachg a sop crero. A evaluao fuco makes possble o evaluae beforehad each chromosome caddae for he seleco. As a resul of he evaluao, a sub-populao whch s vcorous of chromosomes s reaed for reproduco. The crossover ad muao operaos are carred ou respecvely accordg o a crossg probably (Pc) ad a muao probably (Pm). B. Geec operaors - The seleco operaor: allows pares o be chose for reproduco accordg o a evaluao fuco called fess. Geerally, for a populao of dvduals, / s seleced for reproduco hrough he crossg sep. We dsgush several echues of seleco he leraure of whch he mos used are he echue of roulee or he "roulee-wheel", he echue of he ourame, he echue of he rak (rakg ) ad he uversal sochasc seleco [6][7][8]. - The crossover operaor: Ths operaor makes possble o cross he pre-seleced pares o geerae ew chldre who have characerscs of her pares. hus complemes he populao of dvduals o dvduals. The crossg s doe accordg o a probably Pc whch creases wh he umber of cross pos. Three ma crossover operaors are dsgushed: crossg a oe po, crossg a -pos ( ) ad uform crossg. - The muao operaor: Ths operao cosss modfyg, radomly, he value of a allele followg a muao probably P m, whch s geerally very low. A oo hgh muao probably could lead o a subopmal soluo.. STATE OF THE ART M. Merzougu e al. [9] propose a mproveme of he usupervsed classfcao algorhm sodaa hrough s ma parameers. deed, because he resuls of "sodaa" are rscally lked o a hreshold from whch a class s dvded ad aoher hreshold from whch wo classes are merged, he auhors use he geec algorhms o deerme hese wo opmal hresholds. Ths has mproved he ualy of hs algorhm. However, oher parameers are emprcally fxed, such as he bouds of he chromosome membershp erval of he al populao. Ths helps o always fluece he resuls of he algorhm despe some performace. Sephae Legrad [0] proposes a geec program o dscover subses of homogeeous ad dsc daa a fle called "Zoo". Thus, represes a dvdual he form of a ree of logcal formulas. Each logcal formula cosss of a varable umber of predcaes. evaluaes he dvduals from a evaluao fuco based o a measure of homogeey (H) ad a measure of he separably (S) of he daa subses ad eual o: fess = H + µ S. apples a coeffce µ o he measureme of separably order o vary he relave wegh of he wo measuremes. cosders he homogeey H as he weghed average of he homogeey of he varous subses ad he separably S as he weghed average of he dsaces bewee he cerods of he subses. The covergece of he algorhm s o proved. Moreover, he arbrary choce of he coeffce µ grealy flueces he ualy of he resuls. Maulk e al. [] propose a cluserg mehod based o a geec algorhm whch each eleme s assged o he eares cerod so as o form clusers. Each me, he cerods are recalculaed as he average of he elemes of he same group ad he verse of he ra-group era s he calculaed o reduce o a maxmzao problem. The auhors use a represeao of he dvduals he form of k uples ad ecode he coordaes of he k cerods by real umbers. ally, hey alze a al populao of P chromosomes radomly. Moreover, he seleco echue used s a els proporoal casor, whch allows o rea he bes caddae of he prevous geerao. Ulke he prevous algorhm, coverge owards he global opmum. However, does o solve he ueso of o-cosse classes (havg oe eleme) ad separably bewee classes. Greee [] proposes a mehod ha geeraes herarches of paros. begs wh a op-dow mehod by whch he al populao s subdvded o several subpopulaos. Evaluao cosss opmzg a fuco depede o ra-group ad er-group era ad o he sze of he cosued groups. To lm he fluece of al codos cludg he order of sero of obecs he ree, he auhor proposes o geerae he bes possble ree by applyg a geec algorhm. A al populao of rees s geeraed by choosg a radom order of sero of he obecs. The dffere seleco, crossg ad muao operaors are appled. The seleco s made by he els proporoal roller echue where he wo bes soluos are reaed afer evaluag he ualy of each ree. For crossg, chooses he bes braches of he frs level of each ree. The algorhm akes o accou ay obecs ha are repeaed wo classes or mssg he paro. he frs case, he obec s maaed he bes class ad he secod case, s smply resered. Ths algorhm uforuaely does o provde formao o he opmaly of he geeraed soluo. V. OUR PROPOSAL A. Movaos order o sudy he processes of socal reslece, researchers ofe use classfcao mehods ha are ofe poorly adaped o hs doma because hey do o respec cera specfces lked o he cocep, parcularly s uobservable, emporal ad dyamc aspec. Moreover, he mos wdely used classfcao mehods prese a cera umber of oable coveeces cludg her adeuacy o large daa ses (for herarchcal algorhms) ad he very lmed exploao of he soluo search space (For parog algorhms). All hese lmaos ca corbue o based resuls. Thus, we propose o develop a parog mehod hybrdzed wh he echue of geec algorhms for he classfcao of daa of socal reslece. Ths mehod, addo o akg o accou he specfces of socal reslece, has he ably o explore a large soluo P age

3 (JACSA) eraoal Joural of Advaced Compuer Scece ad Applcaos, seekg space ad ca be appled o larger ses of daa. addo, ca be adaped o ay feld of sudy. hs paper, he algorhm s appled o a real daa se, obaed from a survey of a sample of people relao o he rece poselecoral crss vory Coas. The obecve s o fd he ma socologcal groupgs caused by he rauma of hs crss wh he populao suded. a broader case sudy, he resuls of our algorhm ca be used by he acors o faclae he makg of cera decsos favor of he reslece of he raumazed dvduals. B. Noao : The umber of obecs o be classfed; T : The me horzo for esmag he reslece of dvduals; : The oal umber of classes; T : Ω : Se of obecs o be classfed accordg o he formao colleced over he perod from o T; Pop() : Populao of dvduals (chromosomes) a me ; ξ : Esmao of he reslece of he dvdual a me. [... ] C : The h class as [... ] P cr : Crossover probably; P mu : Muao probably; : Number of obecs class : h paro of he Se C ; T : Ω a me ; K : Populao sze (Number of paros); M : Maxmum umber of erao (geerao); Mar : Dssmlary marx; f () : al obecve fuco; f () : Obecve fuco afer pealzao; p f ( ) : Evaluao value of he dvdual p g : Ceer of gravy of he classc ; g : Ceer of gravy of he whole po cloud; d : Eucldea dsace; ; α δ : Perceage of classes whose umbers are less ha (mmum umber); β δ : Perceage of classes wh closely spaced classes; δ : The overall pealy raes; A : All classes whose sze s less ha or eual o ; B : All o-homogeeous classes; card( A ) : Cardaly of he se A. C. Represeao of dvduals A dvdual s a class paro ad s a poeal soluo o he problem. he coex of geec algorhms, s represeed by a chromosome composed of gees. Each gee represes a class ad cosss of a seuece of bary dgs (0, ). hs paper, we use a presece / absece codg where he presece of a obec a class s marked by he umber ad s absece by he umber 0. Example of codg of our chromosome: Eher a gve se of raumazed persos each represeed by s socal reslece value ξ : { ξ } Ω T : = A radom parog of hs se made possble o oba he followg wo paros: {( ; ; ; ; ),( ; ; ; ),( ; ; )} {( ; ; ; ),( ; ; ; ; ),( ; ; )} = ξ ξ 3 ξ 4 ξ 6 ξ 8 ξ ξ 5 ξ 9 ξ ξ 7 ξ 0 ξ = ξ ξ 5 ξ 9 ξ ξ ξ 3 ξ 4 ξ 6 ξ 8 ξ 7 ξ 0 ξ The codg of hese paros gves he followg chromosomes: = = {( )( )( )} {( )( )( )} D. Our evaluao fuco order o oba homogeeous classes, we propose a evaluao fuco whch mmzes he rao of ra class era by oal era. s as follows: d (, g ) ξ = ξ f ( ) = d ( ξ, g) = ( d ξ, g ) = ξ f ( ) = d ( ξ, g ) = () 4 P age

4 (JACSA) eraoal Joural of Advaced Compuer Scece ad Applcaos, Sce he classfcao ofe leads o empy classes or classes coag a sgle eleme, we propose o pealze he above evaluao fuco by a rae whch s he perceage of classes whose umbers are less ha or eual o oe. Moreover, order o oba homogeeous classes well separaed from each oher, we propose o pealze also he obecve fuco by he perceage of classes whose class ceers are relavely close. We oba he global pealzao rae δ such as: δ = { αβ, } δ () card( A) δ α = (3) β card( B) δ = ( ) / Therefore, he pealzed obecve fuco s calculaed as follows: (4) f ( ) = f ( ) δ f ( ) p f ( ) = ( δ ) f ( ) p ( d ξ, g ) = ξ f ( ) = ( δ ) p d ( ξ, g ) = E. The choce of parameers For he seleco, we use he roulee mehod whch s smlar o a loery wheel o whch each dvdual s represeed by a secor euvale o hs fess value. A each ur of he wheel, each dvdual has a probably of beg seleced proporoal o s fess value : prob( ) = f ( )/ f ( ) = For he crossg of he dvduals, we use he crossg a a po of cu chose radomly amog he l (5) (6) possble pos ( l represeg he legh of a chromosome). A hs level, we choose a crossg probably as advocaed by Goldberg [3]. our case, P = 0,6 cr For he muao, we op for a muao probably versely proporoal o he sze of our populao,.e. P = 0,08. mu As crero for soppg our algorhm, we rea he maxmum umber of eraos (or geeraos) fxed. F. Proposed Algorhm Algorhm: Sgfca group defcao algorhm (AlgoGee) NPUT: dssmlary marx ( Mar ), Maxmum umber of classes (), Populao sze (K) Maxmum umber of geeraos (J) OUTPUT: Paro = C,..., C, whch mmzes he mos fess fuco BEGN. //Radom geerao of he al populao.. Choose radom ceers of gravy g.. Assg each observao o he eares ceer: 0 0 = { C,..., C }.3. Calculae he ew class ceers g ξ ξ.4. Repea seps. ad.3 ul he al fxed populao sze (K).5. Reur he al populao o opmze 0 0 { 0 } pop(0),..., k. // Opmzao of he al populao.. Codg he al populao (pop (0)) o bary.. Evaluae he al populao Repea.3. Selec from he roulee wheel K/ pares dvduals (P () P (-)).4. Cross a a po he seleced dvduals wh a probably P cr..5. Makg a muao o he descedas obaed wh a probably P mu..6. Reurg he ew populao pop( ) pop( ) + descedas.7. Evaluae he ew populao foud ( d ξ, g ) = ξ f p ( ) ( δ ) d ( ξ, g ) = 4 P age

5 (JACSA) eraoal Joural of Advaced Compuer Scece ad Applcaos, Ul: Number of geeraos > M = C C Reur he bes paro,..., The followg fgures show he bes groupgs obaed respecvely for 3, 4, 5 ad 6 classes. END G. Resuls ad erpreaos For he applcao of our algorhm, we use a real daa se, obaed from a survey of a sample of oe hudred (00) dvduals (see Table ). Ths survey relaes o he rauma caused by he rece pos-eleco crss hese people. TABLE. EXTRACT FROM THE DATABASE USED Fg.. Groupg o 3 classes Fg.. Groupg o 4 classes The obecve s o defy he sgfca groupgs ha ca be obaed from hs populao order o make decsos. Afer smulaos, appears ha he bes classfcao resul s obaed for 3 classes wh a Rad dex of 0.89 afer 50 eraos (geeraos) (see Table ). Accordg o hs classfcao, 8 dvduals are he frs class, 3 dvduals are he secod class ad he oher 50 dvduals are he hrd class. TABLE. TABLE OF RAND NDCES OBTANED FOR, 3, 4, 5 AND 6 CLASSES Rad dex ,69 0,89 0,87 0,859 0,53 Fg. 3. Groupg o 5 classes 43 P age

6 (JACSA) eraoal Joural of Advaced Compuer Scece ad Applcaos, Bary codg absece / presece Tree Cerods (acual coordaes) Tree of logcal formulas Real umber ecodg Represeao Fg. 4. Groupg o 6 classes O he oher had, expermeao has show ha, from 50 eraos, he classes are more closely grouped ad dsc. V. COMPARSON OF OUR PROPOSAL WTH OTHER WORKS These hybrd algorhms are very dffere whch makes hem very dffcul o compare. However, he able below, we prese some pos of comparso. TABLE. Model Valdy classes Covergece Separably Merzougu e al Paro k fxed classes Overlap from 6 classes Coverge o global opmum No respeced a a cera level of classes COMPARATVE TABLE OF OUR ALGORTHM (ALGOGENE) WTH OTHER WORKS Sephae Legrad Paro k fxed classes Overlap bewee classes No dcao o covergece Much relaed o he parameer μ Maulk e al Paro k fxed classes Always vald Coverge o global opmum No respeced for cera classes Greee Paro Herarchy (free k) No vald (empy clases + duplcaes) No sadard, depedg o al codos Respeced AlgoGee Paro k fxed classes Always vald Coverge o global opmum Respeced V. CONCLUSON We proposed a hybrd-parog algorhm for he defcao of sgfca groups as a fuco of he levels of reslece. geeraes from a radoal mehod of parog paros, whch are he opmzed usg he echue of geec algorhms o gve he bes paro possble: oe ha mmzes he mos ra-class era ad promoes classes whle elmag classes ha have oly oe eleme. The resuls of our smulaos showed ha he algorhm coverges afer 50 eraos by provdg a soluo correspodg o he expeced obecve. The Rad dex (0.89) obaed whou doub raslaes he good performace of our algorhm. fuure work, we ed o exed hs algorhm o oher areas of sudy oher ha socal reslece o es s robusess. REFERENCES [] Bors Cyrulk «Mafese pour la réslece». Sprale /00, 8, p. 77-8, 00. [] J. H. Hollad. Adapao Naural ad Arfcal Sysems. Uversy of Mchga Press, A Arbor, M, USA, 975. [3] Bors Cyrulk. «Le murmure des faômes». Odle Jacob, 003. [4] Duflo, Mare. Algorhmes sochasues [5] Back, Thomas. Evoluoary algorhms heory ad pracce: evoluo sraeges, evoluoary programmg, geec algorhms. Oxford uversy press, 996. [6] Sea Luke. Esseals of Meaheurscs. Lulu, secod edo, 03. [7] T. Blckle & L. Thele. A comparso of seleco schemes used geec algorhms. Evoluoary Compuao, 4(): 3 347, 995. [8] D. E. Goldberg & K. Deb. A comparave aalyss of seleco schemes used geec algorhms. Foudaos of Geec Algorhms, pp Morga Kaufma, 99. [9] M Merzougu, M. Nasr, Ahmad El Allaou. sodaa e les algorhms gééues pour ue classfcao o supervsée. Préseé au Cogrès Méderraée des Télécommucaos (CMT 6), -3 ma 06, A Téhoua, Maroc. Répéré à hps:// rhmes_geeues_pour_ue_classfcao_o_supervsee. [0] Sephae Legrad, Résoluo de problème de classfcao par algorhmes évoluoares grâce au logcel DEAP, ocobre 04, repéré à hps://sephaelegrad.fles.wordpress.com/04/0/classfcao_algo_ evol.pdf [] U. Maulk ad S. Badyopadhyay. Geec algorhm-based cluserg echue. Paer Becogo, 33: , 000. [] Wllam A. Greee. Usupervsed herarchcal cluserg va a geec algorhm. Proceedgs of he 003 Cogress o Evoluo, pages , 003. [3] D. E. Goldberg. Geec Algorhms Search, Opmzao, ad Mache Learg. Sudes Compuaoal ellgece. Addso- Wesley Logma Publshg Co., c., s edo, 989. SBN P age