IMPROVING THE SPEED OF DYNAMIC CLUSTER FORMATION IN MANET VIA SIMULATED ANNEALING

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1 IMPROVING THE SPEED OF DYNAMIC CLUSTER FORMATION IN MANET VIA SIMULATED ANNEALING. Manousaks* and J.S. Baras Electrcal and Computer Engneerng Department and the Insttute for Systems Research Unversty of Maryland College Park College Park, MD 074 A.J. McAuley and R. Morera Telcorda Technologes Inc. One Telcorda Drve Pscataway, NJ ABSTRACT Future mltary systems, such as FCS, requre a robust and flexble network that supports thousands of ad hoc nodes. Therefore, networkng protocols for MANETs must be made to scale. The use of herarchy s a powerful general soluton to the scalng problem. We have prevously proposed methods based on Smulated Annealng (SA) to optmze herarchy n MANETs. The challenge, however, s to mprove the slow convergence tme of SA, so t can be used n dynamc envronments, wthout penalzng optmalty. In prevous work the mportance of parameters such as coolng schedule, state transton probabltes and convergence condton are nvestgated. Ths paper proposes a new approach to decrease SA convergence tme. SA s an optmzaton technque based on an teratve process that takes an ntal soluton, or map, to start the process. In ths paper we analyze the effect that ths ntal soluton has on the SA convergence tme as a functon of the network sze. We beleve that the combned modfcatons to SA can speed the optmzaton process to the pont that t can quckly generate very effcent clusterng solutons n large dynamc networks. 1. INTRODUCTION In recent years Moble Ad Hoc Networks (MANETs) have become very popular, due to ther nfrastructure-less characterstcs. Ther mportance n the mltary world has been hghlghted from many researchers and mltary planners. However, there are stll many unresolved problems that make them neffcacous n scenaros such as the large scale ad hoc networks envsoned n Future Battlefeld Networks. Then, networkng protocols (e.g., routng, securty and QoS) must be made to scale. Prepared through collaboratve partcpaton n the Communcatons and Networks Consortum sponsored by the U.S. Army Research Laboratory under the Collaboratve Technology Allance (CTA) Program, Cooperatve Agreement DAAD The U.S. Government s authorzed to reproduce and dstrbute reprnts for Government purposes notwthstandng any copyrght notaton thereon. 1 The use of herarchy s a powerful general soluton to the scalng problem, snce t allows networkng protocols to operate on a lmted number of nodes, as opposed to the entre network. Herarchy also provdes other mportant benefts, such as smplfyng network management and provdng more effcent support for heterogenety. In the lterature, there are many research proposals for dynamcally creatng and mantanng an optmal herarchy n large dynamc networks (Ln and Gerla, 1997; Baker et al., 1984; Chatterjee et al., 00; Basagn, 1999). Whle local mantenance algorthms are essental to provde fast robust performance, the use of a global optmzaton has been shown to be crtcal on provdng good overall clusterng. In partcular, Smulated Annealng (SA) can optmze the network for a wde varety of metrcs smultaneously (Manousaks et al., 004; Manousaks and Baras, 004). In (Manousaks et al., 004) SA was optmzed for the specfc applcaton of clusterng by a) modfyng the termnaton condton of the algorthm, b) selectng faster coolng schedule and c) modfyng the state transton probabltes n accordance to the cost functon beng optmzed. These technques produced an order of magntude mprovement n performance compared to standard SA. Despte the mproved performance, the applcaton of SA s stll lmted to clusterng hundreds of nodes. Other technques (e.g., mn-cut) are avalable for larger networks, but they are unable to solve the requred complex mult-metrc, mult-layer optmzatons. Ths paper proposes new technques to provde further sgnfcant reducton n SA convergence tme that wll allow applyng SA n networks wth thousands of nodes. Our approach s based on provdng a clusterng map better than a random map as the ntal cluster confguraton for SA to start the optmzaton process. Although ths s a well founded ntutve soluton, t has not been shown how much reducton n convergence tme can be acheved and how much loss n optmalty results for typcal clusterng cost functons. Even though SA wanders randomly around the surface of feasble

2 Report Documentaton Page Form Approved OMB No Publc reportng burden for the collecton of nformaton s estmated to average 1 hour per response, ncludng the tme for revewng nstructons, searchng exstng data sources, gatherng and mantanng the data needed, and completng and revewng the collecton of nformaton. Send comments regardng ths burden estmate or any other aspect of ths collecton of nformaton, ncludng suggestons for reducng ths burden, to Washngton Headquarters Servces, Drectorate for Informaton Operatons and Reports, 115 Jefferson Davs Hghway, Sute 104, Arlngton VA Respondents should be aware that notwthstandng any other provson of law, no person shall be subject to a penalty for falng to comply wth a collecton of nformaton f t does not dsplay a currently vald OMB control number. 1. REPORT DATE 00 DEC 004. REPORT TYPE N/A 3. DATES COVERED - 4. TITLE AND SUBTITLE Improvng The Speed Of Dynamc Cluster Formaton In Manet Va Smulated Annealng 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TAS NUMBER 5f. WOR UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Electrcal and Computer Engneerng Department and the Insttute for Systems Research Unversty of Maryland College Park College Park, MD 074; Telcorda Technologes Inc. One Telcorda Drve Pscataway, NJ PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR S ACRONYM(S) 1. DISTRIBUTION/AVAILABILITY STATEMENT Approved for publc release, dstrbuton unlmted 11. SPONSOR/MONITOR S REPORT NUMBER(S) 13. SUPPLEMENTARY NOTES See also ADM001736, Proceedngs for the Army Scence Conference (4th) Held on 9 November - December 005 n Orlando, Florda., The orgnal document contans color mages. 14. ABSTRACT 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU a. REPORT unclassfed b. ABSTRACT unclassfed c. THIS PAGE unclassfed 18. NUMBER OF PAGES 8 19a. NAME OF RESPONSIBLE PERSON Standard Form 98 (Rev. 8-98) Prescrbed by ANSI Std Z39-18

3 solutons, f t starts from a soluton that s closer to optmal t s more probable to reach the optmal faster and stay there for the approprate number of teratons untl fnal convergence. Any optmal soluton must work wthn the constrants that any par of nodes n the same cluster can reach each other usng only lnks and nodes that are nternal to the cluster. We call clusters havng ths pathwse property feasble clusters; they fall wthn the category of topologcal clusters as defned below: Defnton (Topologcal Cluster): A cluster consstng of the set S of nodes s called topologcal f node, node S and j, there s always a path P j from node to node P j node j such that nodek S holds that k j. All the members of a cluster can communcate between them wthout the need to use ntercluster lnks, whch are lnks that nvolve non-member nodes. The ntal cluster map that s fed nto the SA must be feasble. In (Manousaks et al., 004), the ntal confguraton map s generated by randomly assgnng nodes to clusters, wth the constrant that the generated clusters are feasble. We propose here two ways of generatng better ntal clusters ether by applyng some fast heurstc related to the optmzaton metrc of SA, or, when SA runs perodcally, by usng the exstng or prevously optmzed clusterng (so we do not start from scratch each tme). The use of a modfed SA soluton s partcularly attractve n dynamc networks whch must be reoptmzed relatvely often. Obvously, due to the moblty of nodes, clusters may become nfeasble. Therefore we must force feasblty before a prevously generated cluster confguraton can be nput to SA. Alternatvely, we can drectly use the current soluton produced by local mantenance algorthms. Dfferent approaches can be used (Manousaks et al., 004b) that can have dfferent effects on the rate of degradaton, but all mantan feasble solutons that can be fed n drectly nto SA.. SIMULATED ANNEALING Smulated annealng (SA) has been wdely used for tacklng dfferent combnatoral optmzaton problems (rkpatrck et al., 1983). The process of obtanng the optmum confguraton s smlar to that followed n a physcal annealng schedule. In SA, however, the temperature s merely used as a control parameter and does not have any physcal meanng. Fgure 1. Smulated Annealng algorthm for network parttonng Fgure 1 hghlghts the general steps n the algorthm. The objectve of the algorthm s to obtan the cluster network partton confguraton, C*, that optmzes a partcular cost functon. The process starts wth an ntal temperature value, T 0, whch s teratvely decreased by the coolng functon untl the system s frozen (as decded by the stop functon). For each temperature, the SA algorthm takes the current champon confguraton C * and apples the recursve functon to obtan a new confguraton C and evaluates ts cost, E. If E s lower than the cost of the current E *, C and E replace C * and E *. Also, SA randomly accepts a new confguraton C even though E s greater than E * to avod local mnma. In the latter case C and E replace C * and E * respectvely. One of the key characterstcs of smulated annealng s that t allows uphll moves at any tme and reles heavly on randomzaton (Johnson and McGeoch, 1997). The hgher the temperature, the hgher the probablty of acceptng a confguraton that worsens E * nstead of mprovng t. Indeed, f the temperature s suffcently hgh, SA wll smply take a random walk around the soluton space. The lower the temperature, the lower the probablty of acceptng worse confguratons.

4 The number of teratons requred to reach equlbrum s defned by the equlbrum functon. The functon can be a smple constant (e.g., 100) or a functon of the temperature and other parameters specfc to the optmzaton problem, such as number of network nodes. 3. COST FUNCTIONS SA s one of many global optmzaton algorthms that we can utlze to obtan optmal or suboptmal clusterng decsons (Manousaks et al., 004; Manousaks and Baras, 004). The goodness of the clusterng decsons depends prmarly on the cost functons and constrants provded for optmzaton, not on the optmzaton algorthms themselves. We have found the careful desgn and selecton of cost functons s very mportant for the qualty of clusterng decsons, wth respect to the mposed network objectves (e.g., mnmum overhead or mnmum latency). The cost functons are based on varous metrcs of nterest that can be measured from the network. Table 1 lsts ten example cost functons have been shown to meet dfferent clusterng objectves (Manousaks et al., 004; Manousaks and Baras, 004). Lnks among cluster members have long expraton tme estmates. Improves the lfetme of the generated herarchy Cluster members move wth smlar drecton and velocty, so we expect more stable cluster membershp. Lke (6),(7),(8) capturng more node dynamcs (e.g., drecton and velocty) C z (9) J( C) = mn Iz( LETj) z= 1, j= 1 Cz U z, j r, j 1*max( S ) (10) = J( C) = mn C z= 1 z θ r, j +, j= 1180 Table 1 Example Objetves and assocated Cost Functons Objectve Cost Functon Balanced Sze JC ( ) mn Clusters ( Var( C1,..., C )) Balanced Dameter Clusters Balanced Sze Clusters wth the least number of Border Routers Cluster members move n a smlar drecton, so we expect longer duratons of stable cluster membershp Cluster members have smlar velocty, so we expect more stable cluster membershp = (1) 1 J ( C) = mn C () J( C) mn ( dc ) 1 ( ) mn ( ( C,,..., )) 1 C C ( ) = mn ( 1,..., ) + C = (3) J C = Var d d d (4 ) JC VarC C BR 1 Cz JC ( ) = mn θr, j z= 1, j= 1 JC ( ) mn Varθ (,..., θ = ) z z r1, rc z 1, C z z= 1 ( ) mn U z r, J C (5) (6) (7) Cz = (8) j z= 1, j= 1 3 Parameter C C dc BRC θ r, j U r, j LETj S Defnton Cluster Sze of cluster Dameter of cluster Number of border routers of cluster Relatve drecton of nodes,j Relatve Velocty of nodes,j Expraton Tme of Lnk between nodes,j Scalar speed of node 4. IMPROVING THE SPEED OF SA The most domnant characterstc of the network envronments under consderaton s the dynamc topology. The SA algorthm, due to ts slow convergence tme, has only been consdered for statc problems. Due to ts smplcty of mplementaton, ts ablty to handle complex cost functons, and optmalty of the solutons t provdes, we have attempted to modfy t approprately, so that the convergence tme s mproved sgnfcantly. Ths way, convergence tme s not a lmtaton for applyng SA n dynamc networks. These mprovements are not comng for free, but affect the optmalty of the clusterng solutons provded by SA. So, our task becomes twce as dffcult snce we have to speed up SA to the pont where t can be appled n dynamc envronments but also we have to be careful so that the qualty of the clusterng solutons remans unaffected.

5 In (Manousaks et al., 004) we ntroduced three modfcatons for mprovng the speed of SA. In ths secton we wll brefly revew them pror to the ntroducton of the new modfcaton. The three prevously presented modfcatons are related to the followng parameters of SA algorthm: a. Coolng Schedule b. Termnaton Condton c. State Transton Probabltes A more detaled descrpton of these modfcatons and ther effect on the convergence tme of the algorthm s gven n the followng paragraphs. 4.1 Coolng Schedule The SA algorthm has been proven to convergence n probablty to the global optmal under the assumpton of the logarthmc coolng schedule utlzaton. where, T T 1 lnt 0 t = (11) + T 0 : Intal Temperature t : Number of teratons Even though the logarthmc coolng schedule produces hgh qualty clusterng solutons, t also results n slow convergence tmes. Our objectve was to select another coolng schedule, whch could result n much faster convergence tmes but also mantan the qualty of the clusterng solutons. The geometrc coolng schedule met our objectve, snce t s much faster and we obtaned clusterng solutons of the same qualty as the logarthmc coolng schedule. The geometrc coolng schedule s descrbed from the followng expresson: where, Tt t = α T0 (1) T 0 : Intal Temperature t : Number of teratons α : Constant value ( 0.90 α 0.99 ) 4. Termnaton Condton The theoretcal verson of the algorthm termnates when the temperature T t reaches zero, because ths s when the algorthm converges to the global optmal value. In practce the algorthm reaches the zero temperature n nfnte number of teratons, so we cannot utlze ths termnaton condton n a realzable verson of SA. Obvously, the larger the number of teratons are, the better the qualty of the clusterng soluton and the larger the runnng tme of the algorthm (.e., slower convergence tmes). 4 Our objectve s to trade off optmalty wth convergence tme, such that the qualty s satsfyng and the convergence tme of the algorthm s mproved. The parameter we ntroduced to control the termnaton condton s called StopRepeats. Ths value determnes the number of consecutve tmes we have to observe the same optmal value before we stop the algorthm and accept ths optmal value as the clusterng soluton. In (Manousaks et al., 004) we measured the effect of varous values of StopRepeats on the qualty of the clusterng solutons. We observed that the utlzaton of small values O(100) does not affect notably the qualty of the clusterng soluton and at the same tme mproves sgnfcantly the convergence tme of the algorthm. 4.3 State Transton Probabltes The functonalty of SA s based on the random generaton of a new clusterng map n each teraton. Ths clusterng map s compared wth the optmal at that tme n order to be decded f the new clusterng map takes the place of the optmal or the prevous optmal s mantaned. The clusterng maps that are used for the comparsons wth the optmal are generated by randomly movng nodes between clusters. The generaton of a new clusterng map conssts of three random selectons: 1. Cluster from where we wll move a node. Node from the above cluster 3. Cluster where we wll move the new node Tradtonally the selecton process for each one of the three elements above utlzes the unform dstrbuton. Our objectve was to boost the ablty of SA to reach a good clusterng soluton as fast as possble. Instead of relyng on the unform dstrbuton for the elements 1 and 3 we decded to bond the selecton probabltes on the cost functon we want to optmze and study the effect that t has on the convergence tme of the algorthm. Ths modfcaton s expected to result n faster convergence tmes snce t assgns hgher probabltes to the potentally better clusterng maps wth respect to the cost functon beng optmzed. For a better understandng of the state transton probabltes modfcaton, assume cost functons (1) and () for the generaton of balanced sze clusters. For ths clusterng objectve (e.g., balanced sze clusters) nstead of utlzng the unform dstrbuton for selectng 1 and 3 to generate a new clusterng map, we ntroduced the followng state transton probabltes: For selectng the cluster from where we wll mgrate a node:

6 ("from" cluster ) P = C (Total Number Of Nodes) For selectng the cluster where the node wll mgrate to: (Total Number Of Nodes)- C P( "to" cluster ) = (Number of Clusters - 1)x(Total Number Of Nodes) The selecton of the above transton probabltes ams on the mgraton of nodes from larger clusters to smaller ones. By gvng hgher probablty to ths type of transtons we force the earler generaton of clusterng maps wth balanced sze clusters. In combnaton wth the modfcaton related to the termnaton condton we force the faster convergence of the SA algorthm. 4.4 Intal Soluton The new modfcaton we propose here s to use better ntal solutons used to bootstrap the SA algorthm. Pror the ntroducton of ths modfcaton the ntal soluton was generated randomly subject to the constrant of topologcal clusters. The successful applcaton of the modfcaton depends on two factors: 1. The level of the mprovement we get wth respect to the qualty of the ntal soluton.. How we can generate ntal solutons that wll provde us wth large convergence tme mprovements. In ths work we wll go nto the detals of the frst factor. Due to the random nature of SA, t s not straghtforward that by startng from a better than a random ntal soluton wll provde us wth any convergence tme mprovement at all. We wll answer to the latter by quantfyng the convergence tme effect subject to the qualty of the ntal soluton. Intutvely, we would expect that the closer the value of the ntal soluton to the resultng optmal one, the faster the convergence tme of the algorthm. The results that wll be presented later provde also some ndcatve values of the mprovement percentage. By showng that the random character of SA algorthm quest to the optmal soluton does not elmnate the effect of startng from a good ntal soluton, ndcates that we have to provde answers for the second factor. What are these methods that can be used to determne qualty ntal solutons? Even though we do not deal wth ths problem n ths paper, the approaches depend on the clusterng objectves we set. Good ntal solutons can be generated from heurstc methods customzed to the clusterng objectves (.e., for the generaton of balanced sze clusters we can generate ntal solutons utlzng a customzed mn-cut algorthm). Also, modfed 5 optmzaton algorthms can be useful for the generaton of qualty ntal solutons. Apart from the applcaton of other methods we can also utlze a feasble, prevously generated optmal soluton from SA. Due to the dynamcs of the MANETs envronment, the clusterng decsons have to undergo correctons n order to retan ther optmalty subject to the topology changes. In the case where we have to reapply SA, then nstead of generatng a new ntal soluton we can use as a bootstrappng clusterng map the prevously optmal one, under the condton that t s stll feasble wth respect to the new topology. The latter approach can provde qualty ntal solutons especally when the topology s slowly changng wth respect to the reapplcaton frequency of SA algorthm. In any case what we have to take nto consderaton when we deal wth the approach wll follow for the generaton of ntal soluton, s that the combned tme of the generaton of the ntal soluton and the convergence of SA has to be smaller that the convergence tme of SA when we start from a randomly selected ntal soluton. In other words, the followng nequalty has to be satsfed at all tmes f we want the effect of ntal soluton to be vsble on the convergence tme of the algorthm. where, T T t + t t + t ' nrs rs gnrs SA grs SA t t t t t t ' gnrs grs SA SA gs SA nrs : Non-random ntal soluton rs : Random ntal soluton T : Complete process tme t : Partal process tme The results that wll be presented n the next secton can be utlzed to suggest the order of the quanttes on the expressons above for dfferent qualty levels of the ntal soluton. These results can be very helpful when we desgn or modfy the methods for the generaton of ntal solutons. 5. PERFORMANCE EVALUATION Ths secton shows the benefts receved from better ntal solutons n example networks. Specfcally, by bootstrappng SA wth a better than a random ntal clusterng soluton, ts convergence tme s mproved, whch s not straghtforward due to ts random search character. Also, we can quantfy ths mprovement on the convergence tme by lookng at some ndcatve results related to the convergence tme of the algorthm subject to varous qualtes of ntal solutons. The followng results collected for two networks of dfferent szes 100 nodes

7 and 00 nodes. The topology of these two networks appears n the followng fgures. Network Confguraton (100 nodes 500m x 500m) modfcaton. The followng results have been averaged O. out from a large number of runs ( 1000) Convergence Tme Speedup Startng from a Fracton of a Random Intal Soluton (100 nodes) 0.5 meters Convergence Tme (secs) meters Fgure 100 node network n an area of 500m x 500m meters Network Confguraton (00 nodes 1000m x 1000m) meters Fgure 3 00 node network n an area of 1m x 1m The methodology we appled for the collecton of results t s based on the networks presented above and the SA clusterng algorthm presented n secton. We utlzed cost functon (1) for the generaton of balanced sze clusters. We computed the cost of a random generated soluton wth respect to ths cost functon and then we generated clusterng solutons wth a cost that was a fracton of the cost of ths random soluton. The y-axs of the followng fgures represents the convergence tme n seconds for varous qualtes of ntal solutons, whch are characterzed from the fracton of ther cost compared to the random ntal soluton. The x-axs s marked wth the value of ths fracton. The convergence tme values represented from the followng graphs are ndcatve for the cost functon (1) but they provde some very useful conclusons for the proposed Fracton of the Cost of a Random Intal Soluton Fgure 4 SA convergence tme mprovement wth the qualty of the ntal soluton for 100 nodes network Convergence Tme (secs) Convergence Tme Speedup Startng from a Fracton of a Random Intal Soluton (00 nodes) Fracton of the Cost of a Random Intal Soluton Fgure 5: SA convergence tme mprovement wth the qualty of the ntal soluton for 00 nodes network The most mportant concluson can be drawn from the above fgures s that the bootstrappng of SA algorthm wth a better than a random ntal soluton has advantageous effect on the convergence tme of the algorthm. Both curves n fgures 4 and 5 respectvely present a droppng tendency wth the mprovement of the ntal soluton compared to the random one. Furthermore, we can draw mportant conclusons also from the quantfcaton of the convergence tme mprovement. By comparng the curves of fgures 4 and 5 respectvely, we observe that the larger the network, the larger appears to be the mprovement of the convergence tme. For the specfc case we present, for the network of 100 nodes, the convergence tme drops ~100ms as we utlze nstead of a random soluton, a clusterng map that has a cost 75% better. For the network of 00 nodes the convergence tme s mproved by ~4.8s when we utlze an ntal clusterng 6

8 soluton that s 75% better than a random one. To quantfy better ths decrease of convergence tme we provde the percentage of mprovement nstead of the actual tmes. Table : Percentage mprovements of convergence tme Network sze Actual Tme Improvement Percentage of Improvement s 19.% s 8.8% By lookng at the correspondng percentages of mprovement wth reference to the convergence tme when SA starts from a random soluton, t s obvous that the larger the network, the slower the convergence tme of SA, whch results n larger space of mprovement. The proposed modfcaton s suffcent to mprove enough the convergence tme and consttute a tradtonally slow convergence algorthm, realzable even n dynamc envronments lke the MANETs. We showed that better than a random ntal soluton results nto faster convergence tmes for the modfed SA. The remanng open ssue s how we can generate these ntal solutons, so that we can make the modfcaton applcable n real world problems. As we mentoned above we can take varous approaches for the desgn of methods that can produce qualty ntal solutons wth respect to the clusterng objectves we set. After the dscusson we had n ths paper, the desgned methods can be characterzed and compared usng the fracton of the produced clusterng soluton cost compared to a random generated soluton. Ths fracton n accordance wth the network sze can be ndcatve of the mprovement on the convergence tme as we showed from the demonstrated results. 6. CONCLUSIONS Smulated Annealng s a well known method for the global optmzaton of complex cost functons. Tradtonally, ts slow convergence tme was prohbtve for ts utlzaton n dynamc envronments and n real tme problems. In ths paper we overvewed prevously presented modfcatons but also we have suggested and revewed a newly ntroduced modfcaton, whch s related to the bootstrappng soluton that s provded to SA algorthm durng ts ntalzaton. Due to the random search character of SA t s not straghtforward that by startng from a good ntal soluton, ths wll result n faster convergence tmes. Here we prove ths and also we quantfy the mprovement we get wth respect to the level of qualty of the ntal soluton (e.g., the fracton of the cost compared to a random ntal soluton). The results we collect regardng the proposed modfcaton along wth the mprovements we have gotten from the applcaton of the prevous modfcatons ndcate that SA can be realzable n dynamc envronments lke the MANETs. Also, we have shown that the proposed modfcatons do not affect the qualty of the clusterng solutons, even though these solutons mght not be anymore global optmal. The latter s not mportant n such envronments where the topology s constantly changng and the clusterng solutons provded by the modfed SA are temporary. Even though we have demonstrated the effect of the ntal soluton to the convergence tme of SA, there s stll a very mportant ssue to be resolved for the completon and realzaton of the approach. Ths ssue s related to the methods that we have to apply n order to obtan qualty ntal solutons. Our objectve s to present such methods and prove that the combnaton of these methods wth SA stll provdes better convergence tme compared to the SA, whch reles on a random ntal soluton. REFERENCES Baker D., Ephremdes A., and Flynn J., The desgn and smulaton of a moble rado network wth dstrbuted control, IEEE Journal on Selected Areas n Communcatons, SAC-(1):6--37, 1984 Basagn S., Dstrbuted and Moblty-Adaptve Clusterng for Multmeda Support n Mult-Hop Wreless Networks, VTC 1999-Fall, Vol., pp Chatterjee M., Das S.., Turgut D., WCA: A Weghted Clusterng Algorthm for Moble Ad hoc Networks, Journal of Cluster Computng (Specal Issue on Moble Ad hoc Networks), Vol. 5, No., Aprl 00, pp Johnson D.S. and McGeoch L.A., The Travelng Salesman Problem: A Case Study n Local Optmzaton, n E. H. Aarts and J.. Lenstra (eds.), Local Search n Combnatoral Optmzaton, John Wley and Sons, Ltd., pp , 1997 rkpatrck S., Gelatt C.D.Jr., and Vecch M.P., Optmzaton by Smulated Annealng, Scence 0 (13 May 1983), Ln R. and Gerla M., Adaptve Clusterng for Moble Wreless Networks, IEEE Journal on Selected Areas n Communcatons, pages , September 1997 Manousaks., Baras J.S., "Dynamc Clusterng of Self Confgured Adhoc Networks Based on Moblty ", Conference on Informaton Scences and Systems (CISS) 004, Prnceton, New Jersey, March 17-19, 004 Manousaks., McAuley A. J., Morera R., Applyng Smulated Annealng for Doman Generaton n Ad Hoc Networks, Internatonal Conference on Communcatons (ICC 004), Pars, France, 004 7

9 Manousaks., McAuley A. J., Morera R., Baras J.S., Rate of Degradaton of Centralzed Optmzaton Solutons and ts Applcaton to Hgh Performance Doman Formaton n Ad Hoc Networks, MILCOM 004, Monterey, CA, USA, November 004. Manousaks., McAuley A.J., Morera R., Baras J.S., Routng Doman Autoconfguraton for More Effcent and Rapdly Deployable Moble Networks, Army Scence Conference 00, Orlando, FL Su W., Lee S.-J., and Gerla M., "Moblty Predcton and Routng n Ad Hoc Wreless Networks," Internatonal Journal of Network Management, 000 The vews and conclusons contaned n ths document are those of the authors and should not be nterpreted as representng the offcal polces, ether expressed or mpled of the Army Research Laboratory or the U.S. Government 8