Evolutionary Control of an Autonomous Field

Transcription

1 Evolutionary Control of an Autonomous Fiel Mar W. wen SPAWAR System Center San Diego Coe D7 San Diego, CA, U.S.A. Dale M. Klamer & Barbara Dean rinon Corporation San Diego, CA, U.S.A. Abstrat - An autonomous fiel of sensor noes nees to aquire an tra targets of interest traversing te fiel. Small etetion ranges limit te etetability of te fiel. As etetions our in te fiel, etetions are transmitte aoustially to a master noe. Bot etetion proessing an aousti ommuniation rain a noe s power soure. In orer to maximize fiel life, an approa must be evelope to ontrol proesses arrie out in te fiel. In tis paper we evelop an aaptive tresol ontrol seme. Tis tenique will minimize te power onsumption wile still maintaining te fiel-level probability of etetion. Te power onsumption of te fiel of sensor noes is riven by te false alarm rate an target etetion rate at te iniviual sensor noes in tis problem formulation. Te ontrol law to be evelope is base upon a stoasti optimization tenique nown as evolutionary programming. At te en of te paper, a set of results are presente tat will sow tat by ynamially ajusting sensor tresols an routing strutures, te ontrolle fiel will ave twie te life of te fixe fiel. Keywors: Fiel level ontrol, evolutionary programming, etetion teory, battery power, istribute system, aaptive tresol ontrol. Introution Te ffie of Naval Resear (NR establise te Deployable Autonomous Distribute System (DADS program as sown in Figure to emonstrate te feasibility of inrease performane for an avane Figure. Fiel of DADS Autonomous Sensor Noes tatial/surveillane system tat operates as a fiel of unerwater istribute sensor noes. Te goal of DADS is to emonstrate te feasibility of a ooperative fiel level etetion an ata fusion system tat inreases performane at a reue ost. Given limite power, te objetives are to use istribute etetion an ata fusion to inrease te life time of te fiel (reue power onsumption, erease te false alarm rate of te fiel over tat of te iniviual noes, inrease te fiel-level etetion, inrease te probability of orret lassifiation, an inrease te auray of target position estimates [,, 3]. A DADS fiel onsists of iniviual sensor noes operating autonomously. Ea sensor noe uses a set of aousti an eletromagneti sensors to provie overage of a small area of interest. Ea DADS sensor noe uses a mate-fiel traing algoritm to provie target etetions onsisting of position, veloity, an lassifiation information. ne a etetion is onstrute at a sensor noe, te ata is transferre to a DADS master noe were fiel-level ata fusion is performe.. Detetion teory In te DADS program, a nee exists to ientify wat onstitutes target etetions from te fiel of autonomous sensor noes. Te DADS program also requires an optimization algoritm to route ommuniation messages effiiently using as little power as possible. A fiel-level ontrol/etetion seme is sougt to etet targets of interest at a given fiel-level probability an to route messages optimally by using a minimal amount of power. Control of an autonomous set of sensor noes is neee to meet a esire probability of etetion for te fiel an to exten te life of te fiel. To onstrut a fiel level etetion, we now efine wat is require to all out a fiel level etetion. Ea sensor noe ontains an aousti sensor suite an an eletromagneti sensor suite. To report a etetion, bot te aousti an magneti sensors must etet a target at a sensor noe. ne one noe as etete te target, a seon noe nearby is ue an anoter sensor noe must etet te target. ne tis seon sensor noe etets an reports te target, a fiel level etetion is alle an reporte out by te master noe for fiel level fusion. Ea sensor noe as a tresol for te sensor suite given by an operating point on a reeiver operating

2 arateristi (RC urve as sown in Figure. Te operating points on te figure are labele R an R an represent ifferent signal-to-noise ratio (SNR levels for te sensor suite. Coosing ifferent operating points on P R R te etetion ypotesis. Te tresol T is use to etermine weter or not te signal to noise ratio (SNR is ig enoug to all out a etetion. Te SNR in te figure is labele γ. Uner te two Gaussian urves, a probability of etetion an a probability of false alarm an be etermine. Integrating te H0 probability ensity funtion (pf from T to, te false alarm probability is alulate. Integrating te H pf from T to, te probability of etetion is alulate. Figure 4 sows several signal-to-noise ratios from a osen RC urve operating point. Te objetive of te fiel-level ontroller is to aapt te sensor noe tresols to aquire a target of interest an etet it suessfully troug te fiel. In te figure, te grap labele nominal is sown to emonstrate a osen operating point for te sensor noe. Te next two graps sow a erease in SNR an an inrease in SNR, respetively. As SNR levels vary, a target may beome easier or more iffiult to etet altoug te probability of false alarm remains onstant aross all tree graps. nly te probability of etetion ereases or inreases ue to te Pfa Figure. Typial Reeiver perating Carateristi (RC Curve te RC urve yiels ifferent probabilities of etetion an probabilities of false alarm. A onstant fiel level probability of etetion is esire for operation of te fiel of sensor noes. By ajusting tresol levels at te sensor suite, tat is, moving up an own operating points on te RC urve at ea sensor noe, a onstant fiellevel probability an be aieve. Besies ontrolling te tresols at te iniviual sensor suites at ea noe, anoter problem is to minimize te power onsumption of te iniviual sensor noes wile meeting te fiel-level probability onstraint. Tis issue aresses te routing of ommuniation messages troug te istribute fiel of sensor noes. As messages are passe from sensor noe to sensor noe an finally arrive at te master noe, te battery level is raine by te amount of ommuniation power spent transmitting an relaying etetions aoustially. A fiel-level ontroller will ajust te etetion tresol levels at ea sensor noe to meet te esire fiel-level probability of etetion an to perform optimal routing of messages troug te fiel. A typial example of a point on a RC urve is sown in Figure 3. Figure 3. A Single Point from a RC Curve A brief overview of etetion teory is provie below [4]. In Figure 3 two possible ypoteses, labele H0 an H are sown. H0 is te false alarm ypotesis an H is Figure 4. Possible Detetion Curves signal-to-noise ratio of te target. ur tas is to ajust tresols ynamially to mae sure te target is aquire an trae as it passes troug te fiel. To o tis, we will lower tresols for subsequent ue etetions to inrease te etetion range at a sensor noe, but at te same time we inrease te number of false alarms from a sensor noe. Wen ajusting tese tresols at ea sensor noe, we must maintain a onstant fiel-level probability of etetion. A simple example of tis tresol ajustment is to use a battub analogy. If one sie of te battub water is puse own, water on te oter sie of te tub will rise. Tis example sows wat we will o wen aapting tresols: we will lower a ertain set of sensor noe tresols, wile raising anoter set.. Tresol aaptation Figure 5 sows a ooie utter example of a fiel of sensor noes. Ea sensor noe as a efine etetion range given in re (small irles for a ig tresol (low false alarm rate, ig signal-to-noise ratio an anoter

3 etetion range sown in blue (large irles for a low tresol (ig false alarm rate, low signal-to-noise ratio. Tis figure emonstrates te aaptive proess tat must our for te DADS fiel of sensor noes to etet an ontinue to etet a target as it passes troug te fiel. Figure 5. Sensor Noe Tresol Ajustments via Fiel- Level Control If te fiel were stati, te small re irles woul itate te area of overage tat te fiel oul pi up etetable targets. In te figure, a ypotetial target as been rawn by a bla line wit an arrow at te tip. If te tresol were el at tis iger level, only one possible etetion migt our as tis target traverse te fiel of sensor noes. By lowering te tresols (larger blue irles wi is one by ueing te fiel, a broaer overage of te fiel is aieve. Te figure sows tat up to four possible etetions on a target of interest an our by lowering te sensor noe tresols. Tis improve etetability onept will improve te overall fiel level ata fusion by proviing more ontat information tan previously apable wit a stati set of sensor noe tresols. By lowering te tresol toug a larger number of false alarms an our ausing power to be raine from te sensor noes. False alarms also mae te ata fusion problem at te master noe more suseptible to misorrelation. Terefore, ropping all of te sensor noe tresols is not aeptable beause it will limit te system operation. As explaine previously, we will lower tresols an raise tresols at iniviual sensor noes to maintain te esire fiel-level probability of etetion, wile maximizing te life of te fiel..3 Two of two fiel etetor To ajust tresols, we propose to use a baseline moel of a two-of-two etetor. Te etetor will utilize ommuniation osts, probabilities of etetion an false alarm, noe spaing of te fiel, an signal proessing parameters use at te sensor noe sensor suite. Tis formulation sows tat false alarms as well as target etetions rain te power at ea sensor noe. We will now present our baseline moel equation for fiel level ontrol as erive in [5]. Tis formulation will allow te omplete fiel to be ontrolle by te master noe in te DADS system. Te baseline moel equation is as follows. P n Te estimate power $ ( onsume over a perio of time T at ea noe n, n =,..., N, is given by ρ T ( ( ( ( n on = ( n ( n N p ( n + F F C ( n n R s $ n n n N p P ( T = C + F F C ( n n B ( n n B L NM ( n ( n N F L ( n NM N p n ( / n ( N n n n n n p + F ( N ρsδtn + π p P[ sd r ] ( n n ( ( ( n ( n F F F F C ( n p + ( n n R ( n ( n ( n ( n ( n ( T T T ( n n R e F F e j C ( ρ δtn + π P[ sd r ] ( ( ( ( ( ( ( n r P P F F C D ( n n n n n ( ( ( ( p s p + ρ r P P F F C D + ρ ( / + ρ L NM T ( n n B r ( ρsδtn π p P[ sd r ] ( + ( n ( n ( n ( n ( n P P F F C D ( n n B ( P P F F e j ( / + ρ ( P P F F N p n n n n ( ( ( ( ( n n R L ( P NM P F F e j Q PC / D ( ρsδtn π p P[ sd r ] ( + n n n n ( ( ( ( ( n were ρ s is te basi sample rate an T is te time perio of te estimate life of te noe. Te first term represents te power onsume C on from te proessor in te noe. If te sensor noe is on, a ertain amount of proessing power is raine from te battery. Te seon term represents te ase tat an initial false alarm is generate ( n ( n at noe n, were F, F are te probabilities of false alarm tat are ontrolle by tresols T n N p ( j ( n ( ( an T n, ( n an C is te ommuniation power use to transmit from noe n to te next upstream noe speifie by te ( n urrent ommuniation route R at time. N p te size of te parameter spae over wi te etetors must test, e.g. if te etetor must loo over a isrete set of spee (say N s an losest point of approa (CPA, say N CPA, tus giving N = N N. Tis is te seon p s CPA etetion require for elaring a fiel level etetion from te fiel. Te tir term represents te ase of a ownstream noe n tat generates a false alarm an noe n is simply a passtroug; te ommuniation route ( n for noe n at time is speifie by R. Te fourt term represents te ase tat a false alarm is generate at noe n as te result of being ue by anoter noe n in a set ( n of neigboring noes B. Speifially, P is te ovariane of te tra estimate at te time of te etetion at te first noe, [+sd ] is te expansion fator for te tra ovariane until te seon etetion at te next noe etetion, π r b g e j is te area of te etetion spae for te seon sensor noe, an D is te lengt of te sensor fiel. Te fift term represents te ase of a ownstream noe n tat generates a false alarm as a result of being ue, an noe n is simply a passtroug. Te last four terms eal wit te ases of a target present; ρ T is te target rate. Te sixt term represents a target ( n ( n etetion at noe n, were P, P are te probabilities of etetion, again ontrolle by te ( tresols T n ( an T n. Tis is a true target etetion an not a false alarm. Te sevent term represents te ase of a ownstream noe n etetion were noe n is simply a passtroug for te initial onition. Te eigt term represents te ase tat a target etetion is

4 generate at noe n as te result of being ue by anoter noe n. Te final term represents a ownstream noe n tat generates a target etetion as te result of being ue, an noe n is simply a passtroug. Given te urrent power P ( n available at ea noe, te estimate remaining power is ε ( n ( n ( $ ( n T = P P ( T. Te objetive funtion for maximizing te life of te fiel is maximize T, subjet to te onstraints tat ea of te estimates of te remaining power is positive ε ( n ( T 0, n =,..., N an te fiel level probability of etetion is speifie by PD = N ( ε, ε,..., ε π r P P F F L NM ( ( ( ( N p N ρδtn P( + sd / eπr j ( ( ( ( p P P F F A( D were N ( ε, ε,..., ε N is te number of noes wit nonzero power remaining an π r A D is te area ( overe by an iniviual noe. Te objetive is to maximize fiel life T subjet to meeting te fiel-level onstraint by ajusting PD/PFA tresol levels an ( n varying ommuniation routes (troug R. By oosing appropriate tresols at ea sensor suite, te fiel-level probability of etetion onstraint an be met an te fiel life extene. An algoritm tat will oose tresols to meet te probability of etetion onstraint an exten te fiel life is now isusse..4 Evolutionary programming Evolutionary programming (EP is a stoasti optimization tenique tat is applie in tis paper to optimize routing of te sensor noe message traffi at minimal power ost an to meet a fiel-level probability onstraint. EP falls uner te omain of Evolutionary Computation tat ontains oter algoritmi teniques su as geneti algoritms (GAs, geneti programming, as well as oters [6]. ne of te main ifferenes between EP an GAs is tat EP performs a mutation operation wile GAs perform a mutation operation as well as a rossover operation. Geneti algoritms also operate from te bottom up wen fining a solution. Evolutionary programming is a top own approa to fining optimal solutions. An evolutionary algoritm is sown in Figure 6. In simple terms, an evolutionary algoritm starts out wit a population of possible solutions to a problem. A population onsists of parent solutions an teir orresponing offspring solutions. Tis stoasti optimization tenique allows te wole parameter spae to be seare an evaluate for a best fitting solution. In te figure, te initial solutions are alle parents. Ea parent solution an be a goo first guess at te orret answer or a ranomly osen solution tat may be very poor. Ea parent as te ability to reate a set of offspring solutions by mutation or by rossover if a geneti approa was utilize. Ea parent solution is mutate by anging its state to form an offspring solution. Tis mutation an be Gaussian or some oter linear or non-linear eviation. ne te population of parents as been mutate an te offspring Parents Mutation an Crossover Evaluation an Soring Seletion Figure 6. Evolutionary Algoritm solutions are reate, te population onsisting of parents an offspring solutions is ten sore, as sown in te figure. Soring or evaluation of te population for our purpose is one to mae sure te fiel of sensor noes meet a efine fiel level probability onstraint wit teir efine tresol settings. A seletion proess is ten performe wereby te next generation of parents are selete to evolve better an better solutions. Tis seletion proess ooses te solutions tat passe te onstraint in te soring proess by seleting te solutions tat yiel te largest amount of fiel life. Te stanar EP approa onsists of several steps (initialization, mutation, soring, an seletion [6]. Initialization is performe by assigning tresols to ea sensor in te sensor suite (magneti, aousti an using tese tresols, te sonar equation, an an error funtion to evaluate te probability of etetion an probability of false alarm of te sensor noe. Tis is one for ea sensor noe in te fiel given by ( n = / * (. 0 erf ( T ( n SL( n NL( n P + ( an P n = / *. 0 erf T n + NL n (3 ( ( ( ( ( were Equation ( initializes te probability of etetion P for sensor noe n given its tresol T, te target soure level SL, an te noise level at te sensor NL. Equation (3 initializes te probability of false alarm Pfa for sensor noe n given its tresol T, an te noise level at te sensor NL. Tis is performe for ea sensor noe until all tresols an probabilities of etetion an false alarm ave been initialize. Tis fully initialize fiel of sensor noes is eeme as a parent solution in te EP language an is a possible solution for te fiel life problem. Possible solutions are efine as parents an are given as ( S( P ( n, Pfa( n, T ( n R( n P, = (4 were P( are te number of parents in te population solutions. Ea solution S is mae up of a fiel of sensor

5 noes wit inepenent tresols T, wi itate a P an Pfa for te sensor noe, an a routing table R for ommuniation wit oter noes in te fiel. ne te population of parent solutions as been initialize, te EP algoritm is able to perform te next tree steps (mutation, soring, an seletion iteratively to onverge to te best possible solution given time onstraints an memory requirements of te system. Te first step is te mutation proess wereby parent solutions generate offspring solutions. ffspring solutions ave te possibility of generating a better solution tan teir parents. Tis is te evolutionary step in te EP proess. ne of te mutation steps is to ange te tresol at ea sensor at a sensor noe to yiel a better solution. Tis is efine by [ T ( m, n ] P[ T (, n ] N( 0, + = (5 were [T(m,n] is te mutate tresol at offspring m for sensor noe n, P[T(,n] is te tresol at parent for sensor noe n, an N(0, is a Gaussian ranom variable wit zero mean an unit variane. Equation (5 anges ea parent s tresol to generate an offspring s tresol. Anoter mutation step is to ange te routing table for ommuniations at ea noe. Tis is efine by [ R( m, n ] P[ R(, n ] ± Urv * = (6 were [R(m,n] is te mutate ommuniation routes at offspring m for sensor noe n, P[R(,n] is te ommuniation routes at parent for sensor noe n, Urv is a Uniform ranom variable, an is te number of possible noes for sensor noe n to ommuniate wit. Te number of ommuniation routes an inrease or erease aoring to equation (6. Equation (6 anges ea parent s ommuniation route to generate an offspring s ommuniation route. Ea parent an perform tese mutation steps an generate as many offspring as esire. ne tis is one, te new population of parents an offspring are sore an evaluate against te system onstraints. For example, if te esire fiel-level probability of etetion is 0.8, ea solution is evaluate using PD = N ( ε, ε,..., ε π r P P F F L N M ( ( ( ( N p N ρδtn P( + sd / eπr j ( ( ( ( p P P F F A( D wi is te probability of etetion for a fiel of sensor noes efine in setion.3 above. We will use a simulate annealing approa to meet tis onstraint. For example, if 0.8 is esire, we may allow solutions to lie between (0.7,0.9 in te beginning an slowly onverge towar 0.8 wile we iterate. All solutions tat pass tis fiel-level probability onstraint are ten passe to te seletion proess. Seletion is one by piing te best solutions tat meet te onstraint an minimize te power onsumption efine from te baseline moel from Equation (. Tese best solutions ten beome te parents for te next iteration. Te proess ontinues until te best solution is foun. Tis evolutionary proess (7 extens te fiel life by optimizing te tresols of te fiel an planning te optimal routes for message passing. Results Now we present some results of our evolutionary programming solution to te aaptive tresol ontrol problem. Tese results are for a omplete fiel of sensor noes. Ea noe as a set of tresols solve for by te EP algoritm as well as te optimal routes for ommuniation to exten fiel life.. Simulation verview As state previously, te laim of tis paper is tat it an be sown tat fiel life an be ouble by using a fiel level ontroller to ynamially ajust tresols an routing strutures, as ompare to a fixe fiel wi uses stati tresols an routing strutures. Te EP software written for tis paper generates solutions tat are representative of a fiel uner te ontrol of a fiel level ontroller. In orer to o te omparison to a fixe fiel, a fixe fiel implementation a to be generate.. Te Fixe Fiel Te fixe fiel require a nominal routing struture an a set of sensor tresols, wi woul meet te fiel level probability of etetion. To generate te nominal routing strutures a fiel initialization seme was emulate. Te emulation of tis fiel initialization seme onsists of te following steps:. Te Master Noe broaasts a Waeup Message.. Any noe, wi an ear, respons wit a Waeup Response message. In tis ase any noe witin te ooie utter range an ear. 3. Noes, wi respone to te Master Noe, will be iret ommuniation routes. Tis means tat tese noes will relay teir paets iretly to te master noe. 4. Noes tat ear te Master Noe will broaast to teir neigbors. 5. Any noe, wi an ear witin te ooie utter range, will respon. 6. If te noe wi respons oes not ave a estination noe yet, te noe wi broaast will beome te estination noe. 7. Tis sequene is repeate until every noe in te fiel as been assigne exatly one estination noe. Te above sequene generate a nominal routing struture for a fixe fiel as sown in Figure 7. In 56 units Master Noe Figure 7. Fixe Fiel Routes 8 units

6 onjuntion wit te routing strutures, sensor tresols, wi met te fiel level P require. To get tese tresols, te EP moel was run, an te tresols from te optimal solution were use..3 Te Controlle Fiel In te simulations two types of results are generate for te ontrolle fiel. Te first type is referre to as a "single optimize" solution. Tis solution is generate using te EP software. ne te EP algoritm fins an optimal ombination of tresols an routing strutures, it uses tat solution for te life of te fiel. Figure 8 sows te optimal routes foun for te single optimize solution. 56 units Master Noe 8 units.6 Simulation Results Te results from te simulation are given in te table below. Te results are provie in units of ays. Table. Simulation Results in Days Fiel Detetor Fixe Fiel Single Vetor ptimize LayDown ptimize : 3 45 of : of Figure 9 sows te results from running te fixe fiel simulation. In te fixe fiel te routing assignment was performe by using te minimum number of ops between te master noe an ea noe in te fiel. Tis result is for te of etetor proessing for te seon fiel layown. It sows tat running no optimization algoritm an just a greey algoritm to assign a route for te fiel only yiels a fiel life of 74 ays. As sown in figure 9 one single noe begins to lose its power immeiately. Tis noe is te main ommuniation noe to te master noe. ne one noe in te fiel loses all of its power te fiel is onsiere to be ea. Figure 8. Single ptimize Fiel Routes Te seon type of a ontrolle fiel solution is referre to as a "vetor optimize" solution. As wit te "single optimize" solution, te EP algoritm fins a solution set, wi maximizes fiel life. However, in tis solution, te routes an tresols an be ajuste every 4 ours, tus resulting in a vetor of solutions. Sine ea ay te ontrol algoritm is run an te routes are potentially ange it is not possible to sow ea aily grapial solution in tis paper..4 Fiel Lay Down Simulations were run for two fiel lay owns. In ea lay own, te fiel onsists of 30 sensor noes an master noe arrange in a (56x8 unit gri. Te ifferene between te lay owns is te plaement of te master noe. In te first fiel lay own, te master noe is a square box on te ege of te fiel as sown in figures 7 an 8. In te seon lay own, te master noe is in te enter of te fiel of sensor noes. Power Days Figure 9. Fixe Fiel Life Figure 0 sows te results from te single optimize fiel simulation. Te routes for tis result were alulate by running te EP algoritm one for te wole life of te fiel. Tis optimization result yiele a fiel life of 06 ays for te of etetor for te seon fiel layown. As seen in tis figure a single noe still rives te fiel to eat, but tere are several oter sensor noes tat are also losing power at a similar rate Detetor Types Te objetive funtion presente in setion.3 is for a of etetor. Tis paper also efine an objetive funtion for a - etetor. Te - etetor requires an initial etetion from te magneti sensor on one noe followe by a onfirme etetion from te aousti sensor on a seon noe. Results for bot te of etetor an te - etetor are reporte below. Power Days Figure 0. Single ptimize Fiel Life

7 Te fiel life was extene over te fixe fiel implementation by using at least one planne optimal route te wole simulation. Figure sows te results from te vetor optimize fiel simulation. Tis result as its routes realulate ea ay by running te EP optimization algoritm. Tis optimization result yiele a fiel life of 54 ays for te of etetor for te seon fiel layown. As seen in tis figure a group of sensor noes all lose power similarly at te same rate. Approximately /3 of te sensor noes in te fiel ie on te 54 t ay. Tis result more tan ouble te life of te fiel over te fixe fiel result of figure 9. It also inrease te life of te fiel from 06 ays for te single optimize solution sown in figure 0 to 54 ays for te vetor optimize solution. Power Days Figure. Vetor ptimize Fiel Life.7 bservations Te following observations are mae regaring te simulation results:. Te vetor optimize solution more tan ouble fiel life as ompare to te fixe fiel solution.. Te of etetor as a longer life tan te - etetor. Tis is beause te of etetor as stringent initial etetion rules, wi translates to less reports an less ommuniation as sown in Table. 3. Fiel life inrease wen te master noe was move from te ege of te fiel to te enter of te fiel for te seon fiel layown. Tis is beause wen te master noe is in te enter of te fiel, tere are more iret routes to te master noe, wi spreas out battery rain. 4. Te vetor optimize solution as a longer fiel life tan te single optimize solution. Tis is beause anging te routes every 4 ours allows te battery rain to be sprea more evenly aross te fiel. Wit te vetor optimize solution, approximately /3 of te fiel will ie on te same ay were an analyti solution is not attainable matematially. Ea sensor noe in te two-of-two etetor ontaine two tresols to aapt yieling four total tresols to ompute. Te four tresols are ombine to meet a fiel level probability of etetion onstraint an exten te life of a fiel of sensor noes. A set of results sow te benefits of aaptive tresol ontrol in an autonomous sensor fiel by reuing ommuniation osts an extening te life of te fiel by two. Referenes [] Mar Hat, Mar wen, et al, Data Fusion Metoologies in te Deployable Autonomous Distribute System (DADS Projet, Proeeings of te International Conferene on Multisoure-Multisensor Information Fusion, Las Vegas, Nevaa, pp , July, 998. [] E Jan, Joan Kaina, Mar Hat, Fusion of Multi- Sensor Information From an Autonomous Unersea Distribute Fiel of Sensors, Proeeings of te Seon International Conferene on Multisoure-Multisensor Information Fusion, Sunnyvale, California, pp. 4-, July, 999. [3] Peter Sea, Mar wen, Fuzzy Control in te Deployable Autonomous Distribute System, to appear in Proeeings of SPIE: Signal Proessing, Sensor Fusion, an Target Reognition VIII 999, volume 370, Ivan Kaar, eitor, rlano, Floria, April, 999. [4] Carl W. Helstrom, Statistial Teory of Signal Detetion, Pergamon Press, New Yor, 968. [5] Dale Klamer, Mar wen, Aaptive tresol ontrol in an autonomous sensor fiel, to appear in Proeeings of SPIE: Signal an Data Proessing of Small Targets 000, volume 4048, liver Drummon, eitor, rlano, Floria, April, 000 [6] Davi B. Fogel, Evolutionary Computation, IEEE Press, New Yor, Conlusions In tis paper, we ave applie a stoasti optimization tenique to aapt te tresols of an autonomous sensor fiel an plan te ommuniation routes. Tis stoasti optimization algoritm is nown as evolutionary programming. Te evolutionary program aapte te tresols of a two-of-two etetor for a set of sensors as well as a one-two etetor. Te algoritm is an evolutionary omputation tenique for NP ar problems