Minimal K-Covering Set Algorithm based on Particle Swarm Optimizer

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1 87 JOURAL OF ETWORKS, VOL. 8, O., DECEMBER 3 Mnmal K-Coverng Set Algorthm based on Partcle Swarm Otmzer Yong Hu Chongqng Water Resources and Electrc Engneerng College, Chongqng, 46, Chna Emal: huyong969@63.com Abstract For random hgh densty dstrbuton n wreless sensor networks n ths artcle have serous redundancy roblems. In order to maxmze the cost savngs network resources for wreless sensor networks, extend the lfe network, ths aer roosed a algorthm for the mnmal k-coverng set based on artcle swarm otmzer. Frstly, the network montorng area s dvded nto a number of grd onts. Utlzaton rate and the node mnmum are used as otonal objectve, and a combnatoral otmzaton mathematcal model s establshed. Then usng Partcle Swarm Otmzer to solve otmzaton model, thus the otmal network coverage and the utlzaton od sensor nodes are obtaned. Smulaton results that algorthm has reduced node redundancy and the energy consumton, and mroved the network coverage effectvely. Index Terms Wreless Sensor etworks (WS); Partcle Swarm Otmzer (PSO); The Mnmal K-Coverng Set; etwork Lfetme I. ITRODUCTIO Coverage and control roblem s one of the basc roblems n alcaton of wreless sensor network [] that often adots the aroach of random deloyment. Owng to hgh densty of sensor node, redundancy of a large quantty of nodes wll be caused f all sensor nodes of the wreless sensor network are n oeraton. Moreover, energy of the sensor node s lmted, so node redundancy wll undoubtedly reduce the servce effcency of network. ode control and densty control can save energy and extend lfetme of the entre wreless sensor network by reducng network redundancy. Lterature [] adots the node regulaton scheme of alternatng actve nodes wth dormant nodes. It can effectvely save energy and ncrease network lfetme, but t s a roblem of P dffculty to ut the fewest sensor nodes nto actve workng condton [3]. Artfcal ntellgent grou otmzaton algorthm shows qute sueror characterstcs when solvng the roblem of P dffculty; such algorthms have arallelsm, so they can adat to wreless sensor network well. In recent years, ntellgent grou otmzaton algorthm has been aled to the coverage roblems of wreless sensor network n many studes. Lterature [4] rases the otmzed coverage mechansm based on genetc algorthm and constraned genetc algorthm whch can work out quas-otmal sensor node set requred by the regon fully covered wth sensor network. In order to extend workng tme of wreless sensor networks, the node densty s controlled [], whch means that under the recondton of mantanng coverage roerty of the entre wreless sensor network, some sensor nodes are transferred nto the slee state of low-ower dssaton. In ths way, the requrement for coverage roerty of the network has been satsfed; meanwhle, the work node densty has been reduced, sensor node redundancy of wreless sensor network has been decreased, and nterference n wreless communcaton has been lessened. The ultmate urose of node densty control s to cover the target regon wth the fewest sensor nodes. It s a P-comlete roblem to seek the mnmal coverng set of wreless sensor network. A dstrbuted densty control algorthm based on detecton (PEAS) [6] [7] can control swtchover between actve state and dormancy of the node va the sensor erceton radus, and thus reach the urose of mnmal node coverng set. Lterature [8] rovdes a self-adaton and self-organzaton algorthm (ASCET) to allocate the toologcal structure of network node organzaton. Both of the above algorthms cannot guarantee effectve coverage rate for the target regon; meanwhle, number of nodes n the mnmal coverng set cannot be determned. Partcle swarm otmzer was adoted to solve P-comlete roblem n the above, and an algorthm of otmzaton selecton for mnmal node coverng set was rovded. Ths algorthm can solve the mnmal sensor node set by amng at dfferent coverage rates. II. PARTICLE SWARM OPTIMIZER Partcle swarm otmzer (PSO) [9] s an otmzaton method based on oulaton and t was rased by J. Kennedy and R. C. Eberhart [, ] for the frst tme. It has advantages of smle structure, easy alcaton and feasblty wthout gradent nformaton, so t has been wdely used n varous otmzaton roblems. Wth develoment of artcle swarm, Lterature [] rases the mroved algorthm of nerta factor lnear decrease, and artcle swarm otmzer wth nerta factor has been called standard artcle swarm otmzer nternatonally. Lterature [3] rovdes a modfed artcle swarm otmzer whch has effectvely overcome the shortcomng of oor otmzaton effect of hgh dmensonal functon n standard artcle swarm otmzer. Lterature [4] rases a clusterng artcle swarm otmzer based on collson theory whch has do:.434/jnw

2 JOURAL OF ETWORKS, VOL. 8, O., DECEMBER solved the remature roblem n standard artcle swarm otmzer. Suose that the artcle swarm s comosed of m artcles, the artcles are searchng n the target sace of D dmenson, z ( z, z,, zd ) s the oston vector of o. artcle, v ( v, v,, vd ) s the movement seed of o. artcle, (,,, ) s the otmal oston searched by D o. artcle, and g ( g, g,, gd ) s the otmal oston searched by entre artcle swarm. In the teraton, the standard artcle swarm wll udate velocty and oston accordng to the followng formula: v v c r ( z ) c r ( z ) () k k k k d d d d gd d z z v () k k k d d d In whch,,, m; d,,, D, and d s the current dmensons; k s the current teraton tme, and r and r are the random numbers n [,]. The nerta weght w s: w w k ( w w ) / ter (3) max max mn max In whch w max s the ntal weght; w mn s the ultmate weght; ter s the maxmum teraton tme; max k s the current teraton tme. III. PROPOSED SCHEME A. The Mnmal Coverng Set Problem Model The sensor node n hgh densty random dstrbuton n the coverage regon S { s, s, s,, sn}, n whch s s the sensor node by settng ( x, y ) as coordnate and r as erceton radus. A Boolean control vector X a a a (,,, ) was defned, and ths control vector descrbes the state of sensor network nodes. In whch a means that o. sensor node s n workng condton, and a ndcates that o. sensor node s n dormant state. In terms of coverage otmzaton for wreless sensor network, on the one hand, network coverage rate f ( X ) should be maxmzed; on the other hand, node utlzaton rate f ( ) X should be mnmzed. Therefore, algorthm for mnmal coverng set of wreless sensor network s a mult-objectve combnatonal otmzaton roblem. Lnear combnaton of objectves can be formed va weghtng, and the orgnal sub-objectve otmzaton functon can be transformed nto sngle objectve otmzaton functon. The overall objectve otmzaton functon can be defned as: F( X ) f ( X ) ( f ( X )) (4) In whch,,, and are corresondng weghts of sub-objectve functon, and ther weghts deend on the desgner s comrehensve requrement for ths network ndex. B. Objectve Functon Soluton In order to calculate k-coverage rate f ( X ), the coverage area was dvded nto m n small squares, and the barycentrc coordnate of each small square exresses the entre regon of small squares. Probablty for the target node ( x, y ) to be covered by node s k, ( x x ) ( y y ) R, others Then the multle number ( x, y ) coverage s k s () k of the target node k (6) Judge whether node ( x, y ) s under k-coverage of sensor node h,, k k others The aroxmate k-coverage rate of the regon s f (X) = h m n The comutatonal formula of node utlzaton rate functon f ( X ) s f ( ) X Then accordng to Formula (4), the comutatonal formula of the objectve functon s: h ( ) ( ) F X C. Algorthm Flow a m n a (7) (8) (9) () Suose that the surveyed area s m m square, and t s dvded nto grd onts wth the same sze and area of, D sensor nodes scatter randomly, there are m artculates n the artcle, and each artculate has D dmensons. v s ntalzed randomly wthn mn max v, v. The basc rocess of the mnmal k-coverng set algorthm based on artcle swarm otmzer s as follows: ) Postons of D sensors are ntalzed, and m artcles are ntalzed n the target regon. ) The corresondng objectve functon of each artcle s worked out accordng to the formula, to assgn

3 874 JOURAL OF ETWORKS, VOL. 8, O., DECEMBER 3 the maxmum artcle datum of the objectve functon to. g 3) Velocty and state of the artcle are udated accordng to Formula (3) and (4). 4) The regonal objectve functon of each artcle s re-calculated and then comared wth ; f the value of new objectve functon s greater, then should be reset. Then t s comared wth ; f the value of new objectve functon s greater, then value of ths artcle should be assgned to. g ) End condton s judged: (maxmum teraton tme or good objectve functon value), return to the best sensor state, or go back to Ste 3) contnue. IV. A. Exermental Smulaton SIMULATIO EXPERIMET g resectvely. Fg. (b-f) resents the node dstrbuton stuaton of the mnmal sngle coverng set selected after,,, and teraton algorthms va artcle swarm otmzer. Fg. (b-f) resents the node dstrbuton stuaton of the mnmal k-coverng set selected after,,, and teraton algorthms va artcle swarm otmzer. (a) (b) (a) (b) (c) (d) (c) (d) (e) (f) (e) (f) Fgure. Dstrbuton dagram of the mnmal node set of sngle coverage selected after teraton va artcle swarm otmzer Suose that the regon A s the gven target regon of m m, 3 sensor nodes randomly lay out n A, and the erceton radus of sensor node s m. Sngle coverage rate and k-coverage rate were smulated Fgure. Dstrbuton dagram of the mnmalnode set of k-coverageselected after teraton va artcle swarm otmzer B. Analyss on Algorthm Performance In order to further llustrate the stuaton, the smulaton results were further analyzed through the followng table. Table shows the coverage rate, node utlzaton rate and objectve functon of the mnmal sngle coverng node set selected after dfferent teraton tmes. Table resents the coverage rate, node utlzaton rate and objectve functon of the mnmal k (k=3)-coverng node set selected after dfferent teraton tmes. In order to rove valdty of the algorthm, Fg. 3(a) and Fg. 3(b) resent relaton among dfferent teraton tmes, sngle coverage rate, and node utlzaton rate resectvely. Fg. 4(a) and Fg. 4(b) resent relaton

4 JOURAL OF ETWORKS, VOL. 8, O., DECEMBER 3 87 coverage rate node utlzaton rate teraton tmes teraton tmes (a) (b) Fgure 3. Relaton schema among teraton tmes, coverage rate, and node utlzaton rate n sngle coverage coverage rate.9.8 node utlzaton rate teraton tmes (a) teraton tmes (b) Fgure 4. Relaton schema among dfferent teraton tmes, coverage rate, and node utlzaton rate n k-coverage among dfferent teraton tmes, k-coverage rate, and node utlzaton rate resectvely. TABLE I. Iteraton tme SIMULATIO RESULT OF THE MIIMAL ODE SET OF SIGLE COVERAGE Coverage rate ( f ) ode utlzaton rate ( f ) Objectve functon ( F ).%.%.3 98.% 7.% % 64.% % 6.% % 8.%.67 9.% 7.%.667 Relatons between coverage rate and node utlzaton rate reflected n Fg. 3 and Fg. 4 are contradctory. When the teraton ncreases, number of the sensor nodes n oeraton decreases, whch wll nevtably reduce energy consumton n wreless sensor network and ncrease network lfetme. However, reducton of node quantty wll also cause decrease of effectve coverage rate n the coverage regon. In ractcal alcaton, when the requrement of effectve coverage rate s hgh for wreless sensor network, weght of effectve coverage rate should be ncreased roerly, whch can ncrease number of nodes n oeraton and thus enhance effectve coverage rate of wreless sensor network. When there s strct demand on the lfetme of wreless sensor network, weght of effectve coverage rate should be decreased, to use fewer sensor nodes n oeraton to satsfy the coverage requrement of the target regon and save network energy. In order to adat to requrements of

5 876 JOURAL OF ETWORKS, VOL. 8, O., DECEMBER 3 ractcal envronment, lmters can be added nto artcle swarm otmzer, and the algorthm can be termnated when t meets the requrement of coverage rate or the node quantty of the mnmal coverng set. TABLE II. Iteraton tme SIMULATIO RESULT OF THE MIIMAL ODE SET OF K-COVERAGE Coverage rate f ) ( ode utlzaton rate ( f ) Objectve functon ( F ).%.% % 66.%.9 79.% 63.% % 6.% % 6.% % 6.%.49 There s dfference between the objectve functon obtaned after calculaton and the otmal objectve functon. Frstly, sensor nodes lay out randomly n the target regon, whle otmal soluton s the actve node.9 dstrbuton under deal condton; secondly, artcle swarm otmzer can only gve quas-otmal soluton; fnally, soluton of calculatng objectve functon adots the estmaton method of dscretzng coverage area n the algorthm, so there exst some errors. However, the hgher the dscretzaton degree s, the fewer the errors are. But ths wll nevtably ncrease comlexty of the algorthm. C. Comarson Among Varous Algorthms In order to measure suerorty of the algorthm roosed by ths aer, exerment was conducted to comare ths algorthm wth ant colony algorthm and genetc algorthm on matlab smulaton latform. Refer to Fg. and Fg. 6 for smulaton results of the three algorthms. PSO ACA GA.9 sensor node utlzaton rate dfferent algorthms teraton tmes Fgure. Comarson among three algorthms n sensor node utlzaton rate.9 PSO ACA GA.9 k-coverng coverage dfferent algorthms teraton tmes Fgure 6. Comarson among three algorthms n effectve coverage rate

6 JOURAL OF ETWORKS, VOL. 8, O., DECEMBER Fg. resents relaton between teraton tmes and sensor node utlzaton rate of three algorthms for the mnmal k (k=3)-coverng set of wreless sensor network. Fg. shows that under secfc algorthm teraton tmes, algorthm for the mnmal k-coverng set based on artcle swarm otmzer rased n ths aer has the hghest effcency and gans the fewest sensor nodes after soluton. Fg. 6 shows relaton between teraton tmes and effectve coverage of three algorthms for the mnmal k (k=3)-coverng set of wreless sensor network. Fg. resents that under secfc algorthm teraton tmes, algorthm rased n ths aer can obtan hgher effectve coverage rate, and 3-coverage rate reaches about 7%. The exerment shows that erformance of ths algorthm s better than other two algorthms. When effectve coverage rate s ncreased greatly, fewer nodes are requred, less energy s consumed, and lfetme of wreless sensor network s extended effectvely. V. COCLUSIO By amng at the roblem of huge redundancy n wreless sensor network, ths aer rased an algorthm for the mnmal k-coverng set based on artcle swarm otmzer. In ths algorthm, the montorng area s dvded nto a number of grd onts frstly. Then the comoste functon of effectve coverage rate and node utlzaton rate of the network s used as objectve functon; otmal soluton of the network s searched va artcle swarm otmzer; redundant nodes are reduced to the greatest extent on the condton that a certan k-coverage rate s guaranteed; thus extra energy consumton s reduced and network lfetme s extended. Fnally, smulaton exerment was conducted for the algorthm. The exermental result shows that such algorthm can obtan the hghest coverage rate wth the fewest wreless sensor network nodes. Ths has rovded relable evdence for node layout and adjustment, greatly reduced energy consumton, and effectvely mroved coverage roerty of the network. Moreover, t was comared wth other two algorthms and the result fully roves suerorty of ths algorthm. ACKOWLEDGMET Ths work was artally suorted by the atonal ature Scence Foundaton of Chna (O. 649). REFERECES [] SU Lmn, LI Janzhong, CHE Yu, ZHU Hongsong. Wreless Sensor etwork. Tsnghua Unversty Press,, 7 [] Sljecevc S, Potkonjak M. Power effcent organzaton of wreless sensor networks. In: Proc of the IEEE Int Conference on Communcatons (ICC). Helsnk,, [3] Sljecevc S, Potkonjak M. Power effcent organzaton of wreless sensor networks. In: ICC, Helsnk, Fnland,, [4] JIA Je, CHE Jan, CHAG Guran. Otmal Coverage Scheme Based on Genetc Algorthm n Wreless Sensor etworks. Control and Decson, 7, (7) [] JIA Je, FAG L, ZHAG Heyng, etc. Algorthm for the Mnmal Connecton Coverng Set of Wreless Sensor etwork Based on Vorono Dvson. Journal of Software, 6, 7 () [6] Ye F, Zhong G, Lu S, et al. Energy effcent robust sensng coverage n large wreless sensor networks. In: Techncal reort, UCLA,,. 6-. [7] Ye F, Zhong G, Lu S, et al. Peas: Arobust energy conservng rotocol for long-lved sensor networks. In: the 3nd Internatonal Conference on Dstrbuted Comutng Systems (ICDCS). IEEE ress, 3, [8] Cera A, Estrn D. Ascent: A datve self-confgurng sensor networks toologes. In: Proc. of IEEE Infocom. ew York,, [9] Kennedy J, Eberhart R C. A Dscrete Bnary Verson of the Partcle Swarm Algorthm. Proc.f IEEE Internatonal Conference on Systems, Man and Cybernetcs. Orlando, Florda, USA: 977. [] J.Kennedy, and J. Kenndy. A new otmzer usng artcle swarm theory. Proceedng of the 6th Internatonal Symosum on Mcro Machne and Human Scence. J: IEEE CS. 99, [] R. C. Eberhart, and Y. sh. Comarson between Genetc Algorthm and Partce Swarm Otmzaton. Lecture otes n Comuter Scence (Evolutonary Programmng VII). Srnger Press, 988, [] Sh Yuhu, Eberhart R C. A Modfed Partcle Swarm Otmzer. Proc. Of IEEE Conf. On Evolutonary Comutaton. Anchorage, USA: 998. [3] ZHU Harong, LI Png, CHEG Jan. Otmzaton Method for Wreless Sensor etwork Coverage Based on Imroved PSO Algorthm. Comuter Engneerng,, 37 (8) [4] FEG Zhbo, HUAG Hongguang, LI Y. Strategy of Wreless Sensor etworks Coverage Otmzaton by Imroved Partcle Swarm Algorthm. Alcaton Research of Comuters,, 8 (4) Yong Hu, born n Chongqng, Chna. He s currently an Assocate Professor n Chongqng Water Resources and Electrc Engneerng College. Hs research nterests nclude software engneerng, network engneerng.