Avalabl onln at www.scncdrct.com Procda Computr Scnc 19 (2013 ) 106 115 Th 4 th Intrnatonal Confrnc on Ambnt Systms, Ntworks and Tchnologs (ANT 2013) Mnmzng Enrgy Consumpton n Wrlss Ad hoc Ntworks wth Mta hurstcs Ibukunola. A. Modup a, Oludayo. O. Olugbara b, Abodun. Modup c a,c partmnt of Softwar Engnrng, Tshwan Unvrsty of Tchnology, Prtora, 0001, South Afrca b partmnt of Informaton Tchnology,urban Unvrsty of Tchnology,urban, 4001, South Afrca Abstract Th objctv of ths study s to dscrb an nrgy functon modl bas on Gographc Adaptv Fdlty (GAF), whch s on of th bst known topology managmnt schms usd n savng nrgy consumpton n ad-hoc wrlss ntworks. In wrlss ad-hoc ntwork, th nods rsponsbl for th transmsson of data ar battry-opratd and as a rsult, thr s a nd for nrgy to b consrvd n ordr to prolong th battry lfspan. Gntc Algorthm (GA) and Smulatd Annalng (SA) mtahurstcs ar compard to mnmz th nrgy consumpton n ad-hoc wrlss ntworks modlld by rctangular GAF. Rsults show that GA and SA mta-hurstcs ar usful optmzaton tchnqus for mnmzng th nrgy consumpton n ad-hoc wrlss ntworks. 2013 2011 Th Publshd Authors. by Publshd Elsvr by td. Elsvr Slcton B.V. Opn accss undr CC BY-NC-N lcns. and/or pr-rvw undr rsponsblty of [nam organzr] Slcton and pr-rvw undr rsponsblty of Elhad M. Shakshuk Kywords: Ad-hoc Ntworks, Mtahurstcs, Gographc Adaptv Fdlty, Gntc Algorthm and Smulatd Annalng 1. Introducton A wrlss ad-hoc ntwork nvolvs th ntrconncton of wrlss nods wthout th us of a cntral bas staton to achv flblty n th ntwork structur. Nods n ad-hoc wrlss ntworks ar usually battry-opratd and ar mostly dployd n crtcal nvronmnts such as mltary zons, hostl, hazardous, floodd aras and n an mrgncy halthcar stuaton whr t s almost mpossbl to rplnsh th battrs. Ths maks t ncssary to consrv battry nrgy for th sustanablty of opraton and for th ntwork lfspan to b prolongd. Th rats at whch nods n th ntwork consum nrgy dffr dpndng on whthr th nods ar n transmttng, rcvng, lstnng or slpng stat [1]. Th last nrgy s consumd whn a nod s n slpng stat, but all nods wll not always b n th slpng stat. Th nrgy rato btwn nods n lstnng, rcvng and transmttng s ndcatd as 1:1.05:1.4 and 1:1.2:1.7 [1], [2]. Th work rportd n [1] dscrbs th optmzd nrgy consumpton n 1877-0509 2013 Th Authors. Publshd by Elsvr B.V. Opn accss undr CC BY-NC-N lcns. Slcton and pr-rvw undr rsponsblty of Elhad M. Shakshuk do:10.1016/j.procs.2013.06.019
Ibukunola. A. Modup t al. / Procda Computr Scnc 19 ( 2013 ) 106 115 107 ad-hoc wrlss ntworks by comparng thr paramtr mtrcs such as qual-grd, adjustabl-grd and gntc algorthm. Th rsults show that gntc algorthm sav mor nrgy n th ntr ntwork whn compard to qual and adjustabl grd modls. Bhondkar t al [3] opratd on a hgh numbr of snsors for GA to gnrat ts dsgn. Th unformty of th snsng ponts was mad optmal and th communcaton nrgy consumpton was mnmzd wth th constrants mt. Sajd t al [4] optmz nrgy by usng GA to dtrmn th nrgy-ffcnt clustrs and to dntfy th clustr hads for th transmsson of data. Th rsult shows that GA rtans small nrgy for a largr duraton of tm. Wang t al [5] and Jang t al [6] usd SA to optmz nrgy n wrlss snsor ntworks. Spcfcally, Wang t al [5] achv nrgy mnmzaton by proposng dstrbutd Partcl Swarm Optmzaton (PSO) and SA for nrgy ffcnt covrag to fnd th bst dploymnt of mobl wrlss snsor. Sgnfcant nrgy consrvaton was obtand wth both PSO and GA combnd to fnd th global optmal soluton. Jang t al [6] achv nrgy mnmzaton n wrlss snsor by prsntng a ntwork topology constructon mthod that can handl th formaton of clustrs among nghborng nods so as to flu th data collctd from th snsors. Clustr hads ar thn slctd wth th us of SA for ach clustr to collct and flu th data from ts clustr mmbrs unto th bas staton as wll as to optmz nrgy. An optmal nrgy cannot b guarantd n ths approach bcaus of larg numbr of clustr hads n th ntwork. In ths study, w dscrb th Gographcal Adaptv Fdlty (GAF) nrgy modl to optmz nrgy consumpton n ad-hoc wrlss ntworks. W compar nrgy mnmzaton procsss usng two mtahurstcs tchnqus of GA and SA to gnrat nrgy n both drctons of and of ad-hoc wrlss ntworks. GAF s dscrbd as a topology managmnt schm that s usd to sav nrgy n a wrlss ntwork by groupng ntwork nods nto vrtual grds. Th nods that fall wthn th sam grd ar smlar and rsponsbl for data transmsson. As a rsult, only on nod that rcvs and transmts data to th nt grd can b actv at a gvn tm and th rmanng nods ar mad rdundant to sav nrgy. Th smlarts of ths nods ar computd usng locaton nformaton such as Global Postonng Systm (GPS) to partton th ntwork ara nto grds. Th consumpton of nrgy can thn b balancd by rotatng th transmttng data among th nods n ach grd to facltat actv nods to corrspond ffctvly durng th broadcast of data from a sourc nod to a dstnaton nod [1]. Howvr, th study dscrbs how nrgy consumpton n a wrlss ad-hoc ntwork can b mnmzd usng nrgy modl basd on GAF protocol. Our modl was smulatd usng GA and SA toolbos n MATAB. Ths two mthods (GA and SA) ar parts of mta-hurstcs us for solvng convolutd optmzaton problms. A comparson s thn mad on th mnmal nrgy gnratd by th mta-hurstcs toolbos basd on SA and th GA modls. Th modls of nrgy mnmzaton dscrb n ths papr ar smulatd usng GA and SA toolbos n MATAB. An prmntal comparson s thn mad btwn th mnmal nrgs gnratd by th two mta-hurstcs tchnqus. Howvr, Tabl 1. shows th summary of th ltratur for dffrnt nrgy modls wth mthods to dstngush ach study. Th rmandr of ths papr s succnctly summarzd as follows. In Scton 2, w dscrb th analyss of nrgy consumpton basd on th GAF formulaton. In Scton 3, w dscrb th tchnqus of GA and SA for nrgy mnmzaton. In Scton 4, w prsnt th prmntal rsults of th mta-hurstcs tchnqus. In Scton 5, w gv a concludng rmark and provd motvaton for futur work.
108 Ibukunola. A. Modup t al. / Procda Computr Scnc 19 ( 2013 ) 106 115 Tabl 1. Estng Modls to Mnmz Enrgy n Wrlss Ntworks Mnmum Enrgy Not Rportd Not Rportd 4.68% of nrgy was achvd Not Rportd Enrgy Modl Gntc Algorthm (Bhondkar t al, 2009) Gntc Algorthmbasd hrarchcal clustrs usng rado modl (Hussan t al, 2007) Partcl swarm optmzaton (PSO) and smulatd annalng (SA) (Wang t al, 2007) Total nrgy consumpton for ach clustr, rsdual nrgy of th clustr hads and applcaton of SA to optmz th nrgy consumpton (Jang t al, 2006) 8.6590J Gographc Adaptv Fdlty (GAF), qual and adjustabl grds (Fng t al, 2009) scrpton monstrat th us of GA basd on a nod placmnt mthodology to mnmz th opratonal and communcaton nrgy consumpton n wrlss snsor ntworks. Ths can b achvd by usng GA systm to dtrmn th snsors that wll b actvly nvolvd n th transmsson of data, transmt n low transmsson rang and also th ons that wll b th clustr-n-charg Optmzaton nrgy consumpton by usng GA to dtrmn th nrgy-ffcnt clustrs for th transmsson of data. GA also dntfs th nods sutabl to b th clustr hads n th ntwork. Th clustr formaton phas s compltly don wth th broadcast and rcpton of mssags to and from th bas staton. Combn th usag of both PSO and SA to fnd th global optmal soluton of a dsgnd objctv functon to mnmz nrgy consumpton and also to guarant covrag spcfcaton. Prsnt a ntwork topology constructon mthod that can handl th formaton of clustrs among nghborng nods so as to flu th data collctd from th snsors and choos th approprat clustr hads wth th hlp of SA for ach clustr forward and flu th data from ts clustr mmbrs unto th bas staton as wll as to optmz nrgy savng. Analyz nrgy consumpton n ad-hoc wrlss ntwork by usng thr GAF modls to achv nrgy ffcncy n th ntwork. Mthod Hypothtcal applcaton on a sngl ftnss functon. Hrarchcal clustrng tchnqu WSNs Clustrng Tchnqus Analytc for qual grd to gntc algorthm 7.65J GAF adjustabl grd (Our study) W dscrb an nrgy functon basd on a rctangular GAF modl. Two mta-hurstcs (GA and SA) ar usd to mnmz th nrgy functon gnratd to dtrmn f mta-hurstcs ar usful optmzaton tchnqus that can b usd to achv optmal nrgy consumpton n wrlss ad hoc ntworks. Gntc Algorthm and Smulatd Annalng Algorthm 2. Gographc Adaptv Fdlty (GAF) Th GAF protocol consrvs nrgy by parttonng th nods n th ntwork ara nto vrtual grds as llustratd n Fg.1 [1]. In th modl, an ad hoc wrlss ntwork wthn a rctangular ara of lngth and
Ibukunola. A. Modup t al. / Procda Computr Scnc 19 ( 2013 ) 106 115 109 bradth B s dvdd nto grds so that data can b forwardd grd by grd to th dstnaton nod Th total nrgy consumd n a grd E s th addton of th nrgy gnratd by th nod whn n th transmttng, rcvng, lstnng and n slpng stats rprsntd as follows [1]: Fg. 1. (a) Enrgy consumpton n adjustabl rctangular GAF Modl E ttt rtr 1 T1 sts (1) whr s th powr gnratd whn th nod s transmttng, r s th powr gnratd whn th nod s rcvng, 1 s th powr gnratd whn th nod s n lstnng stat and s s th powr gnratd by th nod whn n slpng stat. T t, T r, T 1 and T s rprsnt th duraton of th ntwork n transmttng, rcvng, lstnng and slpng stats rspctvly as compard to th ntwork stats n [7]. t r 1 s a a a d cr b n (2) whr a, b, c, and d ar constants that ar dtrmnd by lctronc componnts of a nod wth a corrspondng valus of a = 0.083 (J/S), b = 0.017 (J/S), c = 0.00002 (J/S) and d = 0.013 J/S/m2. Th valu of n rprsnts th powr nd for communcaton path loss wth a valu of 3. R rprsnts th nomnal rang that nsurs that any two nods that ar n adjacnt grds can drctly communcat. Th paramtrs s and l ar quvalnt bcaus t has bn shown that d has a vry small valu that s clos to zro compard to a and b [8]. As a rsult, th nrgy consumd by th grd E s computd as th summaton of powrs n transmttng t, rcvng r and slpng s stats multpld by tm duraton T t and Tr. Howvr, w substtut Equaton (2) nto Equaton (1) to obtan a modl that dscrbs th amount of nrgy consumd n th ntr grd as follows. n E a btr cr Tt (3) whr th duratons for transmttng and rcvng th traffc data rspctvly s gvn as: t T T t r r (4) Th paramtr s dfnd as th transmttd or rcvd data rat n bts pr scond wth a gvn valus of 250kps (klobt pr scond). Th data traffc dmand n wrlss ntworks s usually assumd to
110 Ibukunola. A. Modup t al. / Procda Computr Scnc 19 ( 2013 ) 106 115 b statc, but rcnt studs hav ndcatd that th data traffc dmand n wrlss ntwork s hghly dynamc and unprdctabl n natur [7]. Th varabl ntnsty of th ad-hoc ntwork s dscrbd as th rato of th traffc data to th ntwork ara masur n bt/sc. Thus, B (5) Th actv nods n a grd that ar closr to th dstnaton nods wll hav mor data to b transmttd than thos that ar far from t. Ths mpls that ths nods wll hav a shortr transmsson rang than th thos that ar far for nrgy ffcncy. Th transmttd and th rcvd data traffc n th grd can b obtand by dductng th grd lngth (for both transmssons and rcvng) n th th poston of th grd from th lngth of th ntr ntwork. Th dstanc btwn th nods n ach grd for transmttng t and rcvng r data to and from th dstnaton nod s obtand by subtractng th summaton of th grds lngth from th ntwork lngth to gv th followng. t r m 1 2 m 1 B B (6) W substtut Equaton (6) nto Equaton (5) to gv th transmttd traffc data traffc data for th th grd as follows. r t and rcvd t r m 1 m 2 B B whr th paramtr m rprsnts th total numbr of nods n th ntwork and as shown n Fg.1, th nomnal rang R nsurs drct communcaton btwn th nods n th adjacnt grds and th nomnal rang for th grd n th ntwork s dtrmnd as: (7) R 2 2 X X 1 B (8) th Equatons (4), (7) and (8) ar substtutd nto Equaton (3) to obtan th nrgy grd of th ntwork as follows. E consumd n th E a b whr 0 whnvr 1. r c n 2 2 1 B t (9)
Ibukunola. A. Modup t al. / Procda Computr Scnc 19 ( 2013 ) 106 115 111 3. Mthodology In ths study, w mbddd GA and SA mta-hurstcs nto GAF nrgy modl gnratd n Equaton (9) to obtan th mnmum nrgy consum n th ntr wrlss ad-hoc ntwork. Ths mta-hurstcs ar brfly dscrbd n ths scton for th sak of lucdty. 3.1. Gntc Algorthm Mthod GA s oftn dscrbd as on of th most ffctv mta-hurstcs wdly usd for solvng convolutd optmzaton problms by mmckng th bologcal voluton of computng modl to fnd th possbl optmal soluton [9]. GA mnmzs th ftnss functon or th objctv functon of th optmzaton modl usng ts oprators. Th thr paramtrc oprators dfnd n GA algorthms ar as follows. Slcton: Ths functon chooss parnt chromosoms for th nt gnraton basd on thr scald valus from th ftnss scalng functon Mutaton: Ths functon maks small random changs btwn th ndvdual chromosoms n th populaton, whch provd gntc dvrsty and nabl th GA to sarch a broadr soluton spac Crossovr: Ths functon combns two ndvdual or parnt chromosoms to form a nw ndvdual or chld chromosom for th nt gnraton. Thus, th GAF nrgy modl gvn by Equaton (9) s appld as th ftnss functon so that a GAF/GA-basd constrant optmzaton problm s obtand by mnmzng th total nrgy n th ntr ntwork as follows: Mnmz E m 1 a b Subjct to th followng constrant m 1 r c n 2 2 1 B t (10) whr s th lngth of th ntr ntwork and ach s rprsnts th GA varabl. Th GA gnrats th bst ftnss functon by choosng th approprat oprator as summarzd n Tabl 2. Th total nrgy gnratd by th GA functons shows that stochastc unform, Gaussan and scattrd functons can gnrat th bst ftnss functons whn compard to othr functons. Tabl 2. Enrgy Consumpton Gnratd by GA Oprators Oprators Eprmntal Rsult Slcton Mutaton Crossovr Enrgy(J) Is Constrant M? (Y/N) Stochastc Unform Gaussan Scattrd 7.7163 7.7163 Rmandr Unform Sngl Pont 7.65 7.65 Unform Adaptv Two Pont 13.3358 13.3358 Fasbl Roultt Gaussan Intrmdat 15.537 15.537 Tournamnt Gaussan Hurstc 9.7332 9.7332 Th mannr n whch ths functons wr usd n GA MATAB toolbo to gnrat th mnmum nrgy as wll as mtng th constrant of th ftnss functon s dscrbd as follows. Th slcton functons that ar avalabl n GA toolbo of MATAB nclud stochastc unform, rmandr, unform, roultt and tournamnt. Th stochastc unform gnratd th mnmum nrgy by layng out a ln n (11)
112 Ibukunola. A. Modup t al. / Procda Computr Scnc 19 ( 2013 ) 106 115 whch ach parnt corrsponds to a scton of th ln of lngth proportonal to ts pctaton. Th algorthm movs along th ln n stps of qual sz, on stp for ach parnt. At ach stp, th algorthm allocats a parnt from th scton t lands on. Th frst stp s a unform random numbr lss than th stp sz. Th mutaton functons avalabl n GA toolbo of MATAB nclud Gaussan, unform, adaptv fasbl. Gaussan functon wth th scal and shrnk factor of 1 gav th dsrd mnmum nrgy by addng a random numbr to ach vctor ntry of an ndvdual. Ths random numbr s takn from a Gaussan dstrbuton cntrd on zro. Th varanc of ths dstrbuton can b controlld wth two paramtrs. Th scal paramtr dtrmns th varanc at th frst gnraton. Th Shrnk paramtr controls how varanc shrnks as gnratons go by. If th shrnk paramtr s 0, th varanc s constant. If th shrnk paramtr s 1, th varanc shrnks to 0 lnarly as th last gnraton s rachd. Th crossovr functons avalabl n GA toolbo nclud: scattrd, sngl pont, two ponts, ntrmdat, hurstc and arthmtc. Scattrd functon gnrats th mnmum lowst mnmum nrgy compard to othr functons by cratng a random bnary vctor. It thn slcts th gns whr th vctor s a 1 from th frst parnt and th gns whr th vctor s a 0 from th scond parnt and combns th gns to form th chld. Th applcaton of ths oprators was dmonstratd n GA toolbo to mplmnt Equatons (10) and (11) to gv th optmal nrgy of 7.7163J (Jouls) compard to th optmal of nrgy of 8.6590J obtand n [3], w obtand a lowr nrgy n our dsgn modl. 3.2. Stmulatd Annalng Mthod Th SA s anothr powrful mta-hurstc tchnqu usd for solvng convolutd optmzaton problms. Th tchnqu s basd on th prncpl of hatng a sold substanc tll t rachs th mltng pont and slowly cools down th tmpratur of th lqud substanc from ts hghst tmpratur untl t convrgs to a stady and frozn stat. In optmzaton prspctv, annalng allows th substanc to plor, scap from a local mnmum and at th nd and sttl on a global mnmum. Th GAF/SA modl s basd on solvng th constrant optmzaton modl gvn by Equaton (10). Th SA was mplmntd n MATAB toolbo usng th followng procdur. Stp (1) - start by sttng th ntal tmpratur hgh and slct th varabls 1 randomly to gnrat th corrspondng valu of th objctv functon. g Th tmpratur s thn slowly coold or lowrd as th numbr of traton ncrass. Stp (2) - a nw objctv functon 1 objctv functon. g s gnratd at ach traton and compard to th currnt Stp (3) f g 1 g thn g 1 rplacs g and th numbr of traton s ncrasd untl th tmpratur valu s consdrably rducd. 4. Eprmntal Rsults Th GA fnds ts optmal nrgy valu for th optmzaton problm consdrd by optmzng th corrspondng varabls of th ftnss modl gvn by Equatons (10) and (11). W startd th prmnt by dtrmnng th approprat populaton sz for th ftnss valu. Aftr svral runs, a populaton sz of 350 was achvd. Th 350 populaton sz was run alongsd wth GA oprators as shown n Tabl 2 to dtrmn th bst ftnss valu (that s th mnmum nrgy consumd). Th bst ftnss valu was obtand wth th slcton of stochastc unform (slcton functon), followd by
Ibukunola. A. Modup t al. / Procda Computr Scnc 19 ( 2013 ) 106 115 113 Gaussan (mutaton functon) wth a scal and shrnk factor of 1 and fnally followd by scattrd (crossovr functon). Th prformancs of ths functons yldd th bst ftnss valu as dscussd n Scton 3. Fg. 2 (a) shows th mnmum nrgy obtand. Th rsult shows that at ach gnraton, nrgy s consumd. Whn th gnraton was at ts ntal (btwn 0 and 3), th nrgy consumpton gnratd was ncrasng, but as th gnraton stadly progrsss, nrgy consumpton rachs ts mamum and startd dcrasng as th gnraton progrsss untl a constant valu s rachd whn th gnraton was at 5. Th nrgy consumpton thn bgan to fluctuat as th gnraton progrsss untl t rachs th mnmum nrgy consumd. Fg. 2 (a). Mnmzaton of th ntwork nrgy by GAF/GA Modl ;( b) Currnt nrgy obtand by GAF/SA Modl. Th nrgy mnmzaton was amnd for th nw objctv functon g 1 to rplac th currnt objctv functon g as dscussd n scton 3.2. It was obsrvd durng th prmnt that as th tmpratur of th substanc s slowly coold and th traton valu s ncrasd, th nrgy consumd s rducd untl th currnt nrgy consumd s rachd. Fg.2 (c) shows th nw or bst nrgy consumpton that rplacs th nrgy consumd n Fg.2 (b). Whn th traton was at zro, th nrgy consumd was hgh and ths start dcrasng as th traton ncrass untl th bst mnmum nrgy of 7.650J s obtand. Fg. 2(c). Bst nrgy obtand by GAF/SA modl
114 Ibukunola. A. Modup t al. / Procda Computr Scnc 19 ( 2013 ) 106 115 5. Concluson Ths papr dscrbs an prmntal comparson of GA and SA mta-hurstcs to obtan th mnmum nrgy consumd n ad-hoc wrlss ntworks. urng th prmnt, th approprat populaton sz was dtrmnd and usd wth th slctd GA oprators (stochastc unform, Gaussan and scattrd) to gt th bst ftnss functon valu. Th nw objctv functon n SA rplacs th currnt objctv functon f ts valu s lssr. Ths was prformd n ordr to achv th mnmum nrgy consumpton. Th mnmum nrgy consumpton gnratd by th GAF/GA s 7.716J whl GAF/SA gnratd mnmum nrgy of 7.650J. From ths rsults, th mnmal nrgs gnratd by both modls ar smallr whn compard to th ftnss functon (8.6590J) gnratd by W t al. [1]. W can thrfor nfr that mta-hurstcs optmzaton mthods ar hghly ffctv for solvng nrgy mnmzaton problm n wrlss ad-hoc ntwork. Rsults show that th nrgy gnratd by GAF/GA modl s not sgnfcantly dffrnt from that gnratd by GAF/SA modl. Ths shows that mtahurstcs basd optmzaton mthods ar ffctv and usful for mnmzng nrgy consumpton n ad-hoc wrlss ntworks. Futur study wll b conductd to compar othr mta-hurstcs lk th ant colony optmzaton and Tabu sarch to vrfy f thy can qually mnmz nrgy consumpton n ad-hoc wrlss ntworks ffctvly th way GA and SA achvd n ths study. Acknowldgmnts I wsh to prss my sncr grattud to all staff mmbrs of th partmnt of Appld anguags, Faculty of Humants, Tshwan Unvrsty of Tchnology (TUT) for thr support.
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