Fuzzy Logic Resource Management and Coevolutionary Game-based Optimization

Transcription

1 Naval Reseach Laboatoy Washington, DC NRL/FR/ Fuzzy Logic Resouce Management and Coevolutionay Game-based Optimization JAMES F. SMITH III ROBERT D. RHYNE II Suface EW Systems Banch Tactical Electonic Wafae Division Septembe 28, 2001 Appoved fo public elease; distibution is unlimited.

2 Fom Appoved REPORT DOCUMENTATION PAGE OMB No Public epoting buden fo this collection of infomation is estimated to aveage 1 hou pe esponse, including the time fo eviewing instuctions, seaching existing data souces, gatheing and maintaining the data needed, and completing and eviewing this collection of infomation. Send comments egading this buden estimate o any othe aspect of this collection of infomation, including suggestions fo educing this buden to Depatment of Defense, Washington Headquates Sevices, Diectoate fo Infomation Opeations and Repots ( ), 1215 Jeffeson Davis Highway, Suite 1204, Alington, VA Respondents should be awae that notwithstanding any othe povision of law, no peson shall be subject to any penalty fo failing to comply with a collection of infomation if it does not display a cuently valid OMB contol numbe. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT DATE (DD-MM-YYYY) 2. REPORT TYPE 3. DATES COVERED (Fom - To) Septembe 28, 2001 Fomal 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Fuzzy Logic Resouce Management and Coevolutionay Game-based Optimization 6. AUTHOR(S) 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 5d. PROJECT NUMBER James F. Smith III and Robet D. Rhyne II 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Naval Reseach Laboatoy Tactical Electonic Wafae Division Washington, DC e. TASK NUMBER 5f. WORK UNIT NUMBER 8. PERFORMING ORGANIZATION REPORT NUMBER NRL/FR/ SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) Naval Reseach Laboatoy 4555 Ovelook Ave., SW Washington, DC SPONSOR / MONITOR S ACRONYM(S) 11. SPONSOR / MONITOR S REPORT NUMBER(S) 12. DISTRIBUTION / AVAILABILITY STATEMENT Appoved fo public elease; distibution is unlimited. 13. SUPPLEMENTARY NOTES 14. ABSTRACT A fuzzy logic expet system has been developed that automatically allocates electonic attack (EA) esouces in eal-time. This expetise-based esouce manage is made up of fou tees: the isolated platfom tee, the multiplatfom tee, the fuzzy paamete selection tee, and the fuzzy stategy tee. The initial vesion of the algoithm was optimized using a genetic algoithm using fitness functions constucted based on expetise. A new appoach is being exploed that involves embedding the esouce manage in an electonic game envionment. The game allows a human expet to play against the esouce manage in a simulated battlespace with each of the defending platfoms being exclusively diected by the fuzzy esouce manage and the attacking platfoms being contolled by the human expet o opeating autonomously unde thei own logic. This appoach automates the knowledge discovey poblem. The theoy of coevolutionay optimization is intoduced, eoptimization citeia and stopping citeia ae discussed, an algoithm fo automatically constucting coevolutionay fitness functions is intoduced, and examples ae povided to show the effectiveness of coevolutionay optimization. A measue of effectiveness (MOE) fo validation is discussed. Finally, the effectiveness of the esouce manage and the optimization pocedues is shown though a demanding example. 15. SUBJECT TERMS Fuzzy logic, esouce management, genetic algoithms, expet systems, distibuted AI algoithms, knowledge discovey 16. SECURITY CLASSIFICATION OF: a. REPORT b. ABSTRACT c. THIS PAGE Unclassified Unclassified Unclassified 17. LIMITATION OF ABSTRACT UL 27 i 18. NUMBER OF PAGES 19a. NAME OF RESPONSIBLE PERSON James F. Smith III 19b. TELEPHONE NUMBER (include aea code) Standad Fom 298 (Rev. 8-98) Pescibed by ANSI Std. Z39.18

3 CONTENTS 1. INTRODUCTION A BRIEF INTRODUCTION TO FUZZY SETS, LOGIC, AND DECISION TREES Fuzzy Set Theoy Fuzzy Decision Tees OPTIMIZATION OF THE ROOT CONCEPT S PARAMETERS USING A GENETIC ALGORITHM THE SUBTREES OF THE RM The Isolated Platfom Decision Tee The Multiplatfom Decision Tee The Fuzzy EA Decision Algoithm The Fuzzy Paamete Selection Tee The Fuzzy Stategy Tee COEVOLUTION AND SOFTWARE TOOLS Coevolution The Stategy Tee Appoach to Coevolutionay Data Mining Tools fo Visualization of Data-mined Infomation Citeion fo Reoptimization Stopping Citeion fo Coevolution Automatic Constuction of a Fitness Function fo Coevolution A Simple Example of Coevolutionay Optimization Using the Fuzzy Concept Close EXAMPLES OF MULTIPLATFORM RESPONSE Input Scenaios and Output of the Fuzzy RM A Battle Ceated Using the Scenaio Geneato MEASURES OF EFFECTIVENESS, COMBINATORIAL EA, AND A GAME-THEORETIC APPROACH TO RULE INVERSION A Multiplatfom MOE Combinatoial EA Game-theoetic Appoach to Automatic Multiplatfom Doctine Invesion fom Physics SUMMARY ACKNOWLEDGMENTS...22 REFERENCES...22 iii

4 FUZZY LOGIC RESOURCE MANAGEMENT AND COEVOLUTIONARY GAME-BASED OPTIMIZATION 1. INTRODUCTION Moden naval battle foces geneally include many diffeent platfoms, e.g., ships, planes, and helicoptes. Each platfom has its own sensos, e.g., ada, electonic suppot measues (ESM), and communications. The shaing of infomation measued by local sensos via communication links acoss the battlegoup should allow fo optimal o nea optimal decisions. The suvival of the battlegoup o membes of the goup depends on the automatic eal-time allocation of vaious esouces. A fuzzy logic algoithm has been developed that automatically allocates electonic attack (EA) esouces in eal-time. In this epot, electonic attack efes to the active use of electonic techniques to neutalize enemy equipment such as ada [1]. The paticula appoach to fuzzy logic that is used is the fuzzy decision tee, a genealization of the standad atificial intelligence technique of decision tees [2]. The contolle must be able to make decisions based on ules povided by expets. The fuzzy logic appoach allows the diect codification of expetise foming a fuzzy linguistic desciption [3], i.e., a fomal epesentation of the system in tems of fuzzy if-then ules. This will pove to be a flexible stuctue that can be extended o othewise alteed as doctine sets, i.e., the expet ule sets change. The fuzzy linguistic desciption will build composite concepts fom simple logical building blocks known as oot concepts though vaious logical connectives: o, and, etc. Optimization has been conducted to detemine the fom of the membeship functions fo the fuzzy oot concepts. The algoithm is designed such that when the scenaio databases change as a function of time, the algoithm can automatically eoptimize, allowing it to discove new elationships in the data. Altenatively, the esouce manage (RM) can be embedded in a compute game that EA expets can play. The softwae ecods the esult of the RM and expet s inteaction, automatically assembling a database of scenaios. Afte the end of the game, the softwae makes a detemination of whethe o not to eoptimize the RM using the newly extended database. To be consistent with teminology used in atificial intelligence and complexity theoy [4], the tem agent is sometimes used heein to mean platfom; also, a goup of allied platfoms is efeed to as a meta-agent. Finally, the tems blue and ed efe to agents o meta-agents on opposite sides of a conflict, i.e., the blue side and the ed side. Section 2 biefly intoduces the ideas of fuzzy set theoy, fuzzy logic, and fuzzy decision tees. Section 3 discusses optimization with a focus on genetic algoithms. Section 4 discusses five majo components of the RM. Section 5 examines coevolutionay theoy, esults, and softwae tools. Section 6 povides an example of the RM s esponse fo a multiplatfom scenaio. Section 7 discusses a method of validating the esouce manage and an algoithm that automatically invents new multiplatfom EA techniques, ules, and stategies. Finally, Section 8 povides a summay. Manuscipt appoved August 29,

5 2 Smith and Rhyne 2. A BRIEF INTRODUCTION TO FUZZY SETS, LOGIC, AND DECISION TREES The RM must be able to deal with linguistically impecise infomation povided by an expet. Also, the RM must contol a numbe of assets and be flexible enough to apidly adapt to change. The above equiements suggest an appoach based on fuzzy logic. Fuzzy logic is a mathematical fomalism that attempts to imitate the way humans make decisions. Though the concept of the gade of membeship, fuzzy set theoy and fuzzy logic allow a simple mathematical expession of uncetainty. The RM will equie a mathematical epesentation of domain expetise. The decision tee of classical atificial intelligence povides a gaphical epesentation of expetise that is easily adapted by adding o puning limbs. Finally, the fuzzy decision tee, a fuzzy logic extension of this concept, allows easy incopoation of uncetainty as well as a gaphical codification of expetise. This section develops the basic concepts of fuzzy sets, fuzzy logic, and fuzzy decision tees. The paameteization of oot and composite concepts is discussed. 2.1 Fuzzy Set Theoy This subsection povides a basic intoduction to the ideas of fuzzy set theoy. Fuzzy set theoy allows an object to have patial membeship in moe than one set. It does this though the intoduction of a function known as the membeship function, which maps fom the complete set of objects X into a set known as membeship space. Moe fomally, the definition of a fuzzy set [5] is as follows. If X is a collection of objects denoted geneically by x, then a fuzzy set A in X is a set of odeed pais: A = {( x, A( x)) x X}. ( x) A is called the membeship function o gade of membeship (also degee of compatibility o degee of tuth) of x in A which maps X to the membeship space M. The logical connectives and, o, and the modifie not ae defined as 2.2 Fuzzy Decision Tees o : A B and : A B not B : B A B B ( x) = max[ A B ( x) = min[ ( x) = 1 The paticula appoach to fuzzy logic used hee is the fuzzy decision tee. The fuzzy decision tee is an extension of the classical atificial intelligence concept of decision tees. The nodes of the tee of degee one, the leaf nodes, ae labeled with what ae efeed to as oot concepts. Nodes of degee geate than unity ae labeled with composite concepts, i.e., concepts constucted fom the oot concepts [6] using and, o, and not. Each oot concept has a fuzzy membeship function assigned to it. The membeship functions fo composite concepts ae constucted fom those assigned to the oot concepts using fuzzy logic connectives and suitable modifies. Each oot concept membeship function has paametes that ae detemined by optimization as descibed below. Figue 1 offes an example of a decision tee. The logical connective and is denoted on the tee as a vetex with a line, the logical connective, o by a vetex without a line, and the logical modifie not as an edge with a cicle though it. B A ( x). ( x), A B ( x), ( x)] B ( x)]

6 Fuzzy Logic Resouce Management and Coevolutionay Game-based Optimization 3 ATTACKING DANGEROUS BEARING-IN- ATTACK UNCERTAIN-ID BEARING-IN CLOSE LETHAL FRIEND UNCERTAIN-ID Fig. 1 A significant subtee of the isolated platfom tee 3. OPTIMIZATION OF THE ROOT CONCEPT S PARAMETERS USING A GENETIC ALGORITHM The paametes of the oot concept membeship function ae obtained by optimizing the RM ove a database of scenaios using a genetic algoithm (GA). A genetic algoithm [7] can be descibed as follows. A genetic algoithm is an optimization method that manipulates a sting of numbes in a manne simila to how chomosomes ae changed in biological evolution. An initial population made up of stings of numbes is chosen at andom o is specified by the use. Each sting of numbes is called a chomosome and each numbeed slot is called a gene. A set of chomosomes foms a population. Each chomosome epesents a given numbe of taits that ae the actual paametes that ae being vaied to optimize the fitness function. The fitness function is a pefomance index that is to be maximized. The opeation of the genetic algoithm poceeds in steps. Beginning with the initial population, selection is used to choose which chomosomes should suvive to fom a mating pool. Chomosomes ae chosen based on how fit they ae (as computed by the fitness function) elative to the othe membes of the population. Moe fit individuals end up with moe copies of themselves in the mating pool so that they will moe significantly effect the fomation of the next geneation. Next, two opeations ae taken on the mating pool. Fist, cossove (which epesents mating, the exchange of genetic mateial) occus between paents. The final opeation is mutation, which is the andom change of a gene in a chomosome. Afte cossove and mutation, the next geneation is fomed, and the pocess is epeated until a stopping citeion is met [7]. The optimization pocedues used hee ae a component of a knowledge discovey opeation. Knowledge discovey o data mining is defined as the efficient discovey of valuable, non-obvious infomation embedded in a lage collection of data [8]. The genetic optimization techniques used hee ae efficient, the elationship between paametes extacted and the fuzzy ules ae cetainly not a pioi obvious, and the infomation obtained is valuable fo decision-theoetic pocesses. Also, the RM is designed such that when the scenaio databases change as a function of time, the algoithm can automatically eoptimize, allowing it to discove new elationships in the data.

7 4 Smith and Rhyne The application of the genetic algoithm is actually pat of the second step in a thee-step data mining pocess. The fist step is the collection of data and subsequent filteing by a domain expet to poduce a scenaio database of good quality. The second step involves the use of vaious data mining functions such as clusteing and association. Duing this step, the genetic algoithm-based optimization is used to mine paametes fom the database. These paametes allow the fuzzy decision tee to fom optimal conclusions about esouce allocation. In the thid and final step of the data mining opeation, a domain expet analyzes the RM s decisions to detemine thei validity. Data mining to eoptimize the RM and eal-time opeation of the RM may occu simultaneously on diffeent computes. Since the RM is designed to opeate on a collection of platfoms, even duing vey active use of the RM, some compute esouces may be available fo additional optimization and othe data mining elated activities. Thus, the multiplatfom scheme allows fequent eoptimization of the RM, while the peviously optimized vesion of the RM continues to function in eal-time. Typically the database is constucted fom data taken fom sensos of diffeent types. The data will be spase, intemittent, and noisy. To assemble a epesentative database, the domain expet must eliminate unacceptable data followed by the use of vaious data mining functions such as clusteing [9-12] and association [13-20]. Clusteing can be used fo such tasks as oganizing the data and suppessing outlies. Association detemines when data measued on diffeent sensos coespond to the same obsevable. An altenate appoach to constucting a database fo eoptimization involves embedding the RM in a compute game. The game is designed so human EA expets can play it in eal-time against the RM. The game softwae ecods the expet s selections. This ecod contibutes to a database fo eoptimization. Such a database is pue than one bon of senso data since such factos as envionmental noise and senso defects ae not contaminating the data. This offes the advantage that the filteing stage of the data mining opeation is simplified. The obvious disadvantage is that the database will be less epesentative of events in the eal wold than one bon of eal senso data taken duing battle. 4. THE SUBTREES OF THE RM The esouce manage is made up of fou decision tees: the isolated platfom decision tee (IPDT), the multiplatfom decision tee (MPDT), the fuzzy paamete selection tee, and the fuzzy stategy tee. The EA decision algoithm, which can be called by the IPDT o the MPDT, is an expet system fo assigning electonic attack techniques. The IPDT povides a fuzzy decision tee that allows an individual platfom to espond to a theat [6]. The MPDT allows a goup of platfoms connected by communication links to espond to a theat in a collaboative fashion [6]. The communications model used fo simulation puposes is descibed elsewhee [6]. The fuzzy paamete selection tee is designed to make optimal o nea optimal selections of oot concept paametes fom the paamete database assembled duing pevious optimization with the genetic algoithm. Finally, the stategy tee is a fuzzy tee that an agent uses to ty to pedict the behavio of an enemy. This section discusses the fou majo decision tees that make up the RM, the fuzzy EA decision algoithm and how they make efficient use of the Netwok-Centic paadigm. The Netwok-Centic paadigm efes to stategies that make optimal use of multiple allied platfoms linked by communication, multiple esouces distibuted ove diffeent platfoms, and decentalized command. 4.1 The Isolated Platfom Decision Tee The IPDT allows a blue platfom that is alone o isolated to detemine the intent of a detected platfom. It does this by pocessing data measued by the sensos, e.g., ESM, ada, and IFF. Even when an incoming platfom s ID is vey uncetain, the IPDT can still establish intent based on kinematics.

8 Fuzzy Logic Resouce Management and Coevolutionay Game-based Optimization 5 When faced with multiple incoming platfoms, the IPDT can establish a queue of which platfoms to attack fist. Figue 1 (pesented in Section 2) shows a significant subtee of the IPDT. The oot concepts, those nodes of the tee of degee one, ae epesented as boxes with gay coloation. The othe nodes o boxes ae composite concepts. The tee contains thee classes of oot concepts, all of which depend on measued infomation: those that make diect use of physics, those elated to uncetainty in ID, and those elated to infomation that is a function of ID and stoed in databases. Some of the functions of ID consideed ae infomation-theoetic in oigin. The oot and composite concepts of the subtee of the IPDT depicted in Fig. 1 ae simila to those found in the senso management liteatue [2]. They diffe in fuzzy membeship functions, intepetation, and application. Additional concepts on the IPDT not found in the liteatue will be the subject of a futue publication Root Concepts Related to Physics The oot concepts close and beaing-in belong to the fist class, i.e., they ae diectly elated to physics. The oot concept close has been descibed in detail elsewhee [6, 21-22]. Beaing-in uses the same membeship function as close with ange eplaced by beaing. Each oot concept fuzzy membeship function is dependent on a physical obsevable O and fequently, its fist deivative in time, do/dt. If the oot concept is only dependent on O, then the membeship function togethe with a theshold defines an inteval, such that if a measued value of O falls outside this inteval, the membeship function takes on a cetain value that may tigge an action by the RM. The two-dimensional space esulting fom plotting do/dt vs O is a phase space. The inequality between the oot concept membeship function and its theshold upon invesion will give inequalities in O and do/dt, typically. The esulting system of inequalities defines a egion of phase space efeed to as the admissible egion whee ed can engage in activities without signaling its intent to blue. The membeship function paametes that ae found though data mining detemine the boundaies of the admissible egion of phase space. The admissible egion cannot in geneal be bought to zeo aea; othewise, blue will cay out an action against eveything it detects, esulting in faticide and wasting valuable esouces essential to its suvival Root Concepts Related to ID Just as quantities elated to geomety and kinematics such as ange, beaing, and elevation ae all inputs to the IPDT, it is assumed that an ID classification is also an input. The ID is epesented as a classification vecto. The thee ID subclasses making up the ID classification vecto ae fiend_type, neutal_type, and foe_type. Ideally, these would be non-fuzzy o cisp concepts, i.e, the ID of an incoming platfom would be cetain as to if it is a fiend, neutal o foe. The RM has the ability to deal with uncetain ID, so each of the ID subclasses coesponds to a fuzzy set of the same name and each incoming platfom has a fuzzy degee of membeship in each of these fuzzy sets. This geneally poves to be a vey valuable appoach and even in the case of vey good ID infomation this fomalism still is vey effective since elevent gades of membeship can be assigned values of unity o zeo. Each time new input data ae povided to the RM by sensos, the ID infomation is povided in the following fomat. The RM at input update time t is povided with the ID uncetainty vecto U ( i, t), whose elements ae the gade of membeship of the i th emitte in the fuzzy subsets fo fiend_type, neutal_type, and foe_type, i.e., U ( i, t ) = ( fiend ( i, t), neutal ( i, t), foe type 2 ( 1)( i, t ), foe type ( )( i, t ),..., foe type ( n )( i, t )),

9 6 Smith and Rhyne whee the subscipts foe-type(1), foe-type(2),, foe-type(n), indicate that thee can be n foe types that can theaten a blue platfom. The elements of the ID uncetainty vecto ae defined such that thei sum is less than o equal to unity. The RM can also deal with input elating to moe than one fiend-type and neutaltype, but that is beyond the scope of this discussion Root Concepts that ae a Function of ID It has also poven valuable to define additional oot concepts that ae a function of the fuzzy gades of membeship of the elements of the ID classification vecto. A useful concept that is a function of ID is lethal. The membeship function fo the concept lethal is defined in tems of the sum given below: lethal n ( i, t ) = Σ ( )( i, t ). j = 1 foe type j Given the gades of membeship fo lethal, fiend, and neutal, the fuzzy membeship function fo the concept unknown is defined as follows: ( i, t) = 1 [ ( i, t) + ( i, t) + ( i, t)]. unknown lethal fiend neutal This is the fuzzy complement of the sum of the elements of the ID uncetainty vecto. The concept unknown quantifies the the degee to which the ID of the incoming emitte is unknown. One fequently used measue of global uncetainty is the fuzzy entopy [5], which is defined as S k ( i, t ) ln ( i, t ). =. k k To apply the fuzzy entopy as a measue of global uncetainty fo ID, it is useful to make the following definition, k ( i, t) = fiend lethal neutal unkown ( i, t) ( i, t) ( i, t) ( i, t) k = 1 k = 2 k = 3 k = 4. The oot concept uncetain-id, which povides a measue of global uncetainty in ID, is defined as 4 uncetain ID k k, k= 1 ( i, t ) K ( i, t ) ln ( i t ) =, with K a constant defined so that the fuzzy membeship function does not exceed unity. 4.2 The Multiplatfom Decision Tee The IPDT made limited use of the Netwok-Centic paadigm, using the othe netwoked platfoms fo suveillance and electonic intelligence. Howeve, the pupose of the Netwok-Centic paadigm is to use multiple platfoms to gain geometic, physical, and tactical advantage by using multiplatfom techniques that ae moe effective than standad techniques. Such techniques equie coodination and communication fom platfom to platfom, as well as some command and contol stuctue.

10 Fuzzy Logic Resouce Management and Coevolutionay Game-based Optimization Platfom-to-Platfom Inteactions The IPDT allowed an isolated platfom to espond to an incoming emitte. The RM unning on the isolated platfom based its decisions and, hence, esponse on standad senso output, e.g., ange, angeate, and beaing. The isolated platfom s esponse can ange fom simply continuing to monito the envionment to deciding to engage in EA. If a decision to engage in EA is made by the RM, a call is made to the fuzzy EA decision algoithm, which is discussed in Section 4.3. As it stands, the IPDT cannot take full advantage of the Netwok-Centic paadigm. To do this, anothe decision tee, the MPDT, is equied. Using senso output, the MPDT allows a goup of platfoms, connected by a communications netwok to wok togethe in an optimal fashion, to take advantage of the full potential of the Netwok-Centic paadigm. Figue 2 depicts a significant subtee of the MPDT. The MPDT equied many new ules, some analogous to ules found on the IPDT, but most quite distinct. The following will examine at a coase level some of these ules and thei elated fuzzy concepts. AVAILABLE ATTACKER NEED EFFECTIVE ATTACKER DESTRUCTIVE SELF-HELP- EFFECTIVE ADJACENT THREATENED ALLY-CLOSE HELP-EFFECTIVE Fig. 2 A significant subtee of the multiplatfom decision tee Some Root and Composite Concepts on the MPDT The fist ule to be defined is the fuzzy concept of a platfom s need. If the RM aboad a blue platfom detemines a theat is attacking by using the IPDT, then the detecto should alet othe platfoms to its need fo assistance. A platfom s need is a function of its ability to espond to a theat and how destuctive the theat is peceived to be. The composite concept need is constucted using the membeship functions fo the oot concepts self-help-effective and destuctive, as shown in Fig. 2. The membeship function fo selfhelp-effective is a function of the EA esouces aboad the i th platfom, whee need is being detemined.

11 8 Smith and Rhyne The composite concept destuctive is constucted fom the oot concepts potentially destuctive and kinetic-enegy destuctive (not pictued). The fuzzy membeship function fo potentially destuctive is actually an index between zeo and one, assigned by expets detailing how theatening the emitte is peceived to be in tems of its onboad hadwae. The fuzzy membeship function fo kineticenegy-destuctive is a function of the emitte s estimated tanslational and otational kinetic enegy. In actual application thee ae othe oot concepts contibuting to destuctive, the concept has been simplified hee due to space limitations. The composite concept of need educes the amount of data that has to be sent ove the netwok. It does this by sending pocessed infomation, as opposed to aw data, ove the netwok. The composite concept adjacent checks platfom/theat disposition, along with esouces onboad the potential helpe platfom. A helpe platfom is one that is not theatened but has eceived a communication message that anothe platfom is theatened, i.e., the theatened platfom is communicating to the helpe that it has need. The fuzzy oot concept ally-close elates to how close the theatened ally is to the platfom that is evaluating its ability to help in tems of the concept adjacent. The oot concept help-effective elates to how effective the helping platfom might be if it should come to the assistance of the theatened platfom that has need. The composite concepts effective attacke and need ae combined though an and connective to constuct the composite concept available attacke. If the membeship function fo available attacke exceeds a cetain theshold, the helping platfom comes to the assistance of the platfom with need. Note that the pats of the tee leading up to need ae calculated on the theatened platfom; the subtee fo effective attacke and the final and opeation between need and effective attacke ae calculated on the helping platfom. This allows the RM to take advantage of multiple computes within the blue platfom goup. 4.3 The Fuzzy EA Decision Algoithm Once the IPDT o the MPDT detemines an action is equied, the fuzzy EA decision algoithm becomes active. This fuzzy algoithm allows the RM to pick the best EA technique(s) to use against the incoming emittes. The RM s decision is based on the emittes ID, uncetainty in ID, available assets within the blue goup, blue asset eliability, logistics fo esupplying blue assets, battlespace geomety, intelligence epots elated to ed assets, ed asset eliability, logistics fo esupplying the ed foces, weathe and atmospheic conditions, etc. The fuzzy EA decision algoithm is an expet system based patially on militay doctine obtained by inteviewing expets, pefeed techniques found in the liteatue, and entiely new classes of techniques invented to exploit the Netwok-Centic paadigm. A new class of algoithms has been developed specifically fo the pupose of inventing optimal EA techniques fo use unde the Netwok-Centic paadigm. These ae efeed to as combinatoial EA algoithms. The name combinatoial EA deives fom the appoach. Fo a given militay scenaio, the vaious blue and ed platfoms and thei assets ae simulated. Each platfom in the blue platfom goup can use cetain EA techniques. The diffeent combinations of techniques ove the blue platfom goup ae enumeated and stoed as a vecto; each element of the vecto coesponds to a technique a blue platfom in the goup can use. The value of using such a technique combination is detemined using a measue of effectiveness (MOE). The numbe of possible combinations of techniques fo multiplatfom engagements is typically lage, so an efficient seach algoithm is equied. The cuent appoach to seach and evaluation uses a genetic algoithm with a modified vesion of the MOE acting as a fitness function. When blue selects an EA technique o a combination of EA techniques, thee is always the dange that ed will make use of a countemeasue designed to cicumvent blue s deception. This pobability of

12 Fuzzy Logic Resouce Management and Coevolutionay Game-based Optimization 9 ed s success against blue can incease if blue uses the same EA techniques each time simila ed stategies ae encounteed. Two algoithms that automatically invent new multiplatfom EA techniques, ules, and stategies ae unde development. They ae discussed in geate detail in Section The Fuzzy Paamete Selection Tee The fuzzy paamete selection tee can be called by the IPDT, MPDT, the fuzzy stategy tee, and the fuzzy EA algoithm. Fo each tee, it allows the selection of the best paametes detemined offline using genetic optimization. The selections ae a function of such data as emitte ID, uncetainty in ID, intelligence epots, battlespace geomety, geogaphy, and weathe. These paametes can include pobabilities fo the best stategy calculated using game theoy. By selecting specialized paamete sets fo diffeent situations, the RM can use the same decision tees and functional foms fo the fuzzy membeship functions. This also allows the RM to be used on many diffeent types of blue platfoms and deal with vey geneal ed theats. 4.5 The Fuzzy Stategy Tee A stategy tee is an agent s concept of an opposing agent s decision tee. If an agent has sufficient knowledge of the enemy s past behavio, the stategy tee can be vey useful fo pedicting futue behavio. To make this idea moe concete, conside the oot concept close on the blue decision tee. This oot concept deals with the ideas of how nea the ed platfom is to the blue platfom and how fast the ed platfom is appoaching the blue platfom. If ed is nea o appoaching fast, the close membeship function will assume a value nea one. If the membeship function exceeds a cetain theshold, even though ed s ID infomation has a high degee of uncetainty, the RM will engage in an action, i.e., it will execute EA against the incoming ed platfom. Red desies to get sufficiently nea blue so that a ed action can occu. If ed knows the mathematical fom of the membeship function fo close exactly and has appoximate knowledge of the elated paametes, then ed can get vey nea to blue without tiggeing an action. Red s vesion of close on his stategy tee, togethe with the associated theshold and the gade of membeship that it must not exceed to avoid an action by blue, detemines inequalities. These inequalities detemine a egion of the ange-ate vs ange-phase space, efeed to as the admissible egion of phase space as defined in Section If ed emains in that egion and ed s paametes fo close depat little fom those of blue, then ed will not alet blue as to his intention. Thus ed can use a stategy tee to get vey nea blue befoe executing an action. Moe geneally, as descibed in Section 4.1.1, each oot concept gives ise to an admissible egion of phase space. If ed s ID is highly uncetain, and though his stategy tee ed has a good notion of the geomety of each admissible egion of each phase space associated with each of blue s oot concepts, then ed can exploit this knowledge to geatly incease his likelihood of beating blue. Just as with ed, blue typically has a stategy tee and uses it to exploit knowledge of ed s past behavio. 5. COEVOLUTION AND SOFTWARE TOOLS This section discusses coevolutionay data mining and its elation to stategy tee theoy, the stopping citeia fo coevolutionay data mining, the eoptimization citeia, and an algoithm fo automatically constucting the coevolutionay fitness function. Softwae tools ae discussed that allow the full solution of the data mining poblem using the scenaio geneato. Finally, a detailed example fo the oot concept close is given.

13 10 Smith and Rhyne 5.1 Coevolution In natue, a system neve evolves sepaately fom the envionment that contains it. Both biological system and envionment evolve simultaneously. This is efeed to as coevolution [23-27]. Similaly, the fuzzy esouce manage should not evolve sepaately fom its envionment, i.e., enemy tactics should be allowed to evolve simultaneously. Cetainly, in eal-wold situations, if the enemy sees the esouce manage use a cetain ange of techniques, the enemy will evolve a collection of counte techniques to compete moe effectively with the esouce manage. A pevious epot [6] exploed an appoach to coevolution involving aveaging ove a database of militay scenaios. The cuent appoach involves both blue and ed meta-agents, each having fuzzy decision tees and stategy tees. Both types of tee will adapt duing optimization. A stategy tee diffes fom a decision tee in that it is one meta-agent s model of anothe meta-agent s decision tee. Duing coevolution, as a meta-agent leans the behavio of its enemy, the paametes in its stategy tee will be adjusted, finally duplicating those in the enemy meta-agent s decision tee. 5.2 The Stategy Tee Appoach to Coevolutionay Data Mining The appoach to coevolution is as follows. A theshold is defined fo each oot concept membeship function on the ed stategy tee, such that if the membeship function exceeds this theshold and if ed s stategy tee is a good epesentation of blue s decision tee, then ed s intention is signaled to blue, esulting in an action by blue. The membeship function is typically a function of some physically measuable quantity O and its fist deivative in time, do/dt. The two-dimensional space esulting fom plotting do/dt vs O is a phase space. The inequality between the oot concept membeship function and its theshold, upon invesion, will give inequalities linea in O and do/dt, typically. The esulting system of inequalities defines a egion of phase space efeed to as the admissible egion whee ed can engage in activities without signaling its intent to blue. The membeship function paametes that ae found though data mining detemine the boundaies of the admissible egion of phase space. The admissible egion cannot in geneal be bought to zeo aea; othewise, blue will cay out an action against eveything it detects, esulting in faticide and wasting valuable esouces essential to its suvival. The concept close efes to how nea the taget/emitte on tack i is to the ship, o moe geneally the platfom of inteest [22]. The univese of discouse will be the set of all possible tacks. Each tack i has membeship in the fuzzy set close based on its ange R (nmi) and ange ate dr/dt (ft/s). The fuzzy membeship function fo close takes the fom The paametes to be detemined by optimization ae 1 close( i) =... 1 α Ri Rmin / max( Ri, Rmin) α, R min, and R min. The paametes fo close wee initially detemined using a genetic algoithm [21, 22]. The fitness function used fo initial optimization (i.e., befoe the beginning of the coevolutionay pocess) is descibed in Refs. 21 and 22. This fitness function is the zeoth ode fitness function fo coevolution. The gay egion of Fig. 3 is the admissible egion of the ange-ate vs ange-phase space detemined using the above pocedue fo the oot concept close on ed s stategy tee. It is assumed ed knows the exact mathematical fom of blue s fuzzy membeship function fo close, but ed only knows the paametes fo close appoximately. Quantities with an supescipt ae those assumed by ed, i subscipts efe to the i th tack, the k subscipts indicate values at the k th time step, and 0 subscipts ae.

14 Fuzzy Logic Resouce Management and Coevolutionay Game-based Optimization 11 used on ed s initial values of ange and ange-ate. The symbol τ is the theshold that ed s gade of membeship in close should not exceed so as to not signal ed s intent to blue. The quantity d H is the desied distance ed would like to be fom blue befoe executing an action. Once the admissible egion of phase space is detemined it is staightfowad to find tajectoies fo ed that ae optimal accoding to some citeion and at the same time allow ed to appoach blue without indicating its intent. Fo example, the tajectoy that allows ed to spend the minimum amount of time in the admissible egion of phase space is collinea with the line segment detemined by points A and B in Fig. 3. The associated acceleation is R&& i,k = ( Rmin Ri k, ) α τ 1 τ This tajectoy allows ed to tavel at the maximum absolute ange-ate at each time step. It is also a high isk tajectoy fo ed, since if ed has been even slightly ovely optimistic about blue s paametes, ed will depat fom the admissible egion and signal its intent to blue. 2 R & R 1 1 α τ i, k 1 R & min + R min blue R& min A P d H R ( R i R ) O = 0 i, 0,, & R& i, k ( R R ) min i, k α τ 1 τ B Fig. 3 The gay shaded aea is the admissible egion of phase space that ed seeks to occupy It is impotant to ealize that the fitness functions used fo initial optimization, i.e., pio to the beginning of coevolution, ae bon of expetise. The fitness functions ae highly nonlinea and lack deivatives at many points. The esulting optimization poblem is a natual candidate fo application of a genetic algoithm. When it can be established that only small changes in paametes ae equied, then faste appoaches to eoptimization can be used. 5.3 Tools fo Visualization of Data-Mined Infomation To facilitate data mining, coevolution and validation of the RM, a softwae tool known as the scenaio geneato (SG) has been ceated. It automatically ceates simulated blue and ed platfoms with use-defined assets. It also ceates a map o battlespace and automatically places the ed and blue platfoms in this space whee they can inteact. Each blue platfom is contolled by its own copy of the fuzzy RM.

15 12 Smith and Rhyne The SG has two modes of opeation. In the compute vs compute (CVC) mode, each ed platfom is contolled by its own contolle distinct fom the fuzzy RM used by the blue platfoms. In the second mode, the human vs compute (HVC) mode, a human playe contols a ed platfom though an inteactive gaphical use inteface (GUI). Thee can be multiple ed platfoms. At each time step, the human playe can contol any of the ed platfoms, but only one of them pe time step. Those ed platfoms not unde human contol un unde thei own logic as in the CVC mode. Thee diffeent GUIs can be easily accessed fom the SG softwae. These GUIs ae the scenaio builde, the map builde, and the human contol playe inteface (HCPI). Figue 4 displays the scenaio builde GUI that allows the constuction of blue and ed agents with geneal chaacteistics. Though this GUI both blue and ed agents can be given vaious assets such as diffeent types of adas, ESM, EA systems, etc. This GUI allows the ceation of a teain map that is discussed below. The scenaio ceated can be placed in a database fo futhe data mining and coevolutionay analysis. Effects due to weathe, system losses, atmospheic attenuation, multipath, clutte, etc., can be included in the calculation, although they can not be cuently called fom the GUI. Fig. 4 Scenaio Builde tool Figue 5 displays the map builde GUI that can be called fom the scenaio geneato GUI. The map builde allows the constuction of vaious maps on which the ed and blue agents can inteact as the scenaios ae played out. The map defines a battlespace that can include vaious envionments such as oceans, foest, desets, cities, and jungles. Maps ceated by the map builde can be saved in a database fo euse. Fig. 5 Map Builde tool

16 Fuzzy Logic Resouce Management and Coevolutionay Game-based Optimization 13 Once the above tools have been used to ceate blue and ed platfoms, thei assets, and the battlespace map, a battle can be initiated in eithe CVC o HVC modes. In both modes, the esults ae ecoded in the database fo late data mining to impove the RM s adaptive esponse. Section 6.2 discusses an example of output fom the SG unning in CVC mode. Figue 6 displays the human contol playe inteface that is used in the HVC mode. It includes a digital simulation of a ada s PPI display simila to those used in eal ada systems. Taget ange and beaing can be detemined fom the PPI display o the digital eadout at the lowe ight. When the blue taget is in ange, the human playe can fie a missile. A pobabilistic model detemines the effectiveness of the missile. Finally, each ed platfom has a limited numbe of missiles so the playe must be cautious in using them. Fig. 6 The human contol inteface that allows a human EA expet to contol a ed platfom The simulated PPI display is designed to imitate the popeties of a eal PPI display. In this way, decisions made by the EA expet playing the game that ae subsequently automatically stoed in the database fo late data mining will eflect tuth. The display can also show the effects of natually occuing noise, ada system noise, multipath, clutte, jamming, and false tagets, and can simulate the phospho decay of a eal ada PPI display. 5.4 Citeion fo Reoptimization The citeion fo eoptimization is fomulated based upon a detemination that a paticula paamete set has become ineffective. In the EA community, failue to delay, disupt, o deny infomation can be the basis fo labeling a paamete set ineffective. Outight loss of platfoms is anothe simple measue of ineffectiveness that can be used. Kinded to how humans change and eplace stategies, the RM uses the eoptimization citeion as a point of ebuilding and econstucting stategies. When the eoptimization citeion is tiggeed, a GA is called to eoptimize the oot concepts of the decision and stategy tees. One simple appoach to detemining this citeion is to analyze oot concept membeship functions values ove time when blue loses to ed. If it is detemined that blue s failue elated to cetain oot concept membeship functions not tiggeing an action by the RM, these membeship functions could be made moe sensitive.

17 14 Smith and Rhyne Afte many coevolutionay geneations, it is possible that both the blue and ed goups will have evolved to the point that they ae vey effective in dealing with each othe but no longe effective in dealing with agents fom past geneations. Fo a eal system unning the RM, this could be a deadly defect, as it is not uncommon to encounte opposing systems manufactued at many diffeent times. 5.5 Stopping Citeion fo Coevolution Just as with a genetic algoithm, in a coevolutionay game-based optimization, a stopping citeion must be defined. Upon completion of the game, seveal iteations of a paticula scenaio can be played. A citeion fo eoptimization detemines when the RM will eoptimize its paametes. This optimization is kinded to the scenaio-based optimization discussed in Refs. 6 and 20, howeve the scenaios optimized ove ae ecodings of the pevious games since the last optimization. Since the eoptimization citeion detemines how many scenaios the optimization is taking into account, this citeion is nontivial. 5.6 Automatic Constuction of a Fitness Function fo Coevolution When eoptimizing it is necessay to incopoate knowledge of an agent s histoy, specifically those events that led to eoptimization. A method of doing this is to constuct fitness functions that contain a histoy of the agent and upon maximization esult in agents that will not epoduce past mistakes. This subsection develops an algoithm fo the automatic constuction of such functions, efeed to as symbolically ecusive fitness functions. This fist step in poducing a symbolically ecusive fitness function involves multiplying the fitness function used in the pevious coevolutionay geneation fo blue optimization by a poduct of Heaviside step functions fo the cuent coevolutionay geneation. The fitness function fo the fist coevolutionay geneation is fomed by multiplying the Heaviside step functions by the fitness function used duing the initial genetic algoithm-based data mining pocess, efeed to as the zeoth ode fitness function. The poduct of Heaviside step functions includes one Heaviside step function as a facto fo each offending oot concept evaluated at each time step since the last eoptimization. The agument of each Heaviside step function is the diffeence between the offending oot concept membeship function evaluated appopiately at each time step and a theshold. The esulting poduct fitness function is efeed to as a symbolically ecusive fitness function. The idea is that unless the GA optimization poduces a oot concept membeship function which fo this set of input data, exceeds the appopiate theshold, the symbolically ecusive fitness function will etun a value of zeo. Using the symbolically ecusive fitness function the GA can be used to ensue that the membeship function value fo a paticula oot concept will be above a cetain theshold. This tigges an appopiate action by the RM the next time ed exhibits the behavio that led to blue s loss and subsequent eoptimization. A simila pocedue is used when eoptimizing ed. By evaluating the fitness ove the cuent coevolutionay geneations as well as pevious coevolutionay geneations, the esulting paamete sets will be effective fo the cuent ed stategy, as well as the pevious ed stategies. This allows the RM to adapt to cuent stategies without being vulneable to pevious stategies that could be used by olde ed agents. 5.7 A Simple Example of Coevolutionay Optimization Using the Fuzzy Concept Close This subsection povides a simple example of coevolutionay data mining using the fuzzy oot concept close. CVC and HVC coevolution ae consideed as well as a compaison between the techniques.

18 Fuzzy Logic Resouce Management and Coevolutionay Game-based Optimization 15 Fo both HVC and CVC modes, a loss by blue esults in immediate eoptimization of blue s paamete set. A loss by a computeized ed agent esults in eoptimization of the ed agent s paamete set. The stopping citeion fo eoptimization fo both modes is a maximum numbe of coevolutionay geneations. A coevolutionay geneation efes to a single battle followed by eoptimization of ed o blue. A blue loss occus if one of blue s agents is disabled due to the successful delivey of a ed missile. A pobabilistic model detemines the effectiveness of the fied missile. A blue win occus if the blue agent goup is able to delay ed a cetain numbe of time steps t. Finally, a ed loss occus if blue wins. In HVC mode, the human playe acting as a ed agent can locate blue agents using the PPI displa y descibed in Section 5.3. When a blue agent is located on the sceen, the use clicks on the taget egion and pesses the fie button located in the lowe ight-hand cone to launch a missile. One simple class of expeiments that has been conducted consists of one blue agent vs one ed agent. It was typically found that all thee paametes in blue s vesion of close showed little change fo the last 33% of the coevolutionay geneations. The human opponent opeating the ed agent tended to fixate on the same stategies. This suggested that in HVC optimization the human playe quickly eached the limits of his o he expetise, esulting in the RM s paametes eaching a constant value. Thus the optimization of blue conveged apidly. In CVC mode, thee is no human playe contolling a ed agent. The ed agents ae contolled by thei own logic that includes a stategy tee. Each blue agent is contolled by a copy of the RM, as in HVC mode. The blue agent s decision tee has the oot concept close on it. The ed agent has a stategy tee with his peception of close. It is assumed that ed has vey good intelligence about blue, hence the mathematical fom that ed is using fo close is the same as the one blue uses. Red is uncetain about the value of blue s paametes fo close and, as such, how they slightly diffe fom those of blue. Both blue and ed can change duing the coevolutionay pocess. Red s paametes fo his vesion of close detemine the admissible egion of phase space that ed attempts to occupy so as not to invoke an action by blue. Assuming a given initial position and velocity fo ed, these paametes in tun detemine ed s value of acceleation, hence ed s tajectoy. In a simple expeiment with one blue agent vs one ed agent opeating in CVC mode, convegence was not nealy as fast as in HVC mode. The compute-contolled ed agent is typically capable of exhibiting many moe stategies than the human-contolled ed agent in HVC mode. Thus the coevolutionay pocess ends up exploing the combined ed-blue paamete space longe, esulting in a geate likelihood of a global maximum being found fo the fitness function, esulting in an RM that is moe obust than in the HVC case. The moe obust RM obtained though use of the CVC optimization can be undestood intuitively as follows. If ed can exhibit moe stategies by using CVC mode than in HVC mode, then the blue RM is foced to be moe adaptive to compete. Thee is a isk duing coevolution that with both ed and blue coevolving, they will become vey specialized in dealing with each othe. Fo example, without taking pope pecautions, blue agents of the 1000 th coevolutionay geneation might be effective against ed agents of that geneation, but ineffective against agents of geneations 100 though 999. Fotunately, the stuctue of the symbolically ecusive fitness function pevents this, because its fom etains the past histoy of the agents, focing the blue agents of the 1000 th geneation to be effective against ed agents of the peceding o cuent geneation.

19 16 Smith and Rhyne 6. EXAMPLES OF MULTIPLATFORM RESPONSE This section examines a specific example of the fuzzy RM s ability to optimally allocate electonic attack esouces. Input equiements and output chaacteistics ae consideed and illustated though the actual output of the cuent implementation of the RM. Many examples like those included in this section demonstate that the infomation data-mined using the GA is extemely valuable. 6.1 Input Scenaios and Output of the Fuzzy RM The fuzzy RM uses as input the position and numbe of ally platfoms (ships, planes, etc.), as well as emitte ange, beaing, elevation, and the emitte ID, with the associated uncetainty fo the ID. The effect of the data is to stimulate the vaious fuzzy logic concepts, esulting in diffeent actions by the algoithm. The emitte ID is used to detemine the technique o techniques (fo ID s with uncetainty) that the ally platfom o platfoms can execute against the emitte. Figue 7 shows a battlefoce of thee ships and also an incoming aicaft with counte tageting (CTAR) ada. The type of the theat emitte is not well known, i.e., the aicaft s ID is not known with 100% cetainty. The ship initially closest to the aiplane, the caie, is disabled and cannot paticipate in joint EA. With the theat s classification not being well known, and because a foe of some type is indicated, the RM diects the two ships with functioning EA systems to engage in joint EA against the incoming foe, subsequently defending the disabled ship. Midway though the battle, a helicopte was detected by the ships sensos. It was detemined to be a foe with uncetain ada ID. The fuzzy RM detemined joint EA was called fo and diected the two ships with functioning EA systems to use two beams and simultaneously conduct joint EA against the incoming aiplane and helicopte. Fig. 7 Input scenaio fo aiplane theat with uncetain ada ID, late aiving helicopte theat with uncetain ada ID to the ight.

20 Fuzzy Logic Resouce Management and Coevolutionay Game-based Optimization 17 Fig. 8 RM output fo the fist pat of the scenaio whee two platfoms ae attacking the theat with the thid platfom disabled Fig. 9 RM output fo the second pat of the scenaio whee both platfoms split thei beams to attack the late aiving enemy helicopte Figue 8 displays the output of the algoithm duing the fist pat of the scenaio depicted in Fig. 7, when only the aiplane has been detected. A pola plot with oigin at the centoid of the battlegoup is used to display the positions of the thee ships (diamonds), and the incoming emitte (tiangle maked with designation foe type ). Communications and electonic attack techniques used by each ship ae listed to the side. The aows unning fom the ships to the foe-type emitte indicate electonic attack. The aows indicate that the RM has diected the two ships with functioning EA systems to attack the aiplane since it has been detemined to be a foe with uncetain ada ID. The caie continues to monito the battlespace. Figue 9 displays the output of the RM duing the final stage of the scenaio duing which the second foe, the helicopte, was detected by the sensos. Since the helicopte was a foe with uncetain ada ID, the fuzzy RM decided it should be attacked. The RM diected the two ships with functioning EA systems to use two beams and simultaneously attack both foes. A copy of the RM uns on each of the blue platfoms. A pola plot of the kind depicted in Figs. 8 and 9 is displayed each second of the RM s opeation. The RM makes its decisions as a function of battlespace geomety, blue assets, and intelligence epots elated to ed assets. At any given time, thee is no commanding platfom. This is a valuable aspect since if a blue platfom is lost though any mechanism, the goup is not delayed as command is tansfeed to anothe platfom. The RM has been tested fo many diffeent militay scenaios [6,21-22,24-27]. It has been detemined to be vey effective by compaing its decisions to the judgment of human expets. 6.2 A Battle Ceated Using the Scenaio Geneato The softwae descibed in Section 5.3 is extemely useful fo evaluating the RM and detemining the value of infomation data-mined in the second data mining step. The natual output of the scenaio geneato is a compute-geneated movie. This subsection includes fames fom such a movie fo the scenaio descibed below. It illustates the opeation of the RM while the SG uns in the CVC mode. The scenaio geneato also ceates a coesponding database eflecting the RM s decisions fo late analysis and subsequent data mining to impove the RM s adaptive esponse.

21 18 Smith and Rhyne The following ae the events leading up to the fictitious battle. A blue plane is downed and a blue platfom goup is sent in to escue it. The blue goup consists of fou ESM-/EA-equipped ships as follows: one caie, one cuise, and two destoyes. Thee is also a blue escue helicopte and an ESM- /EA-equipped blue suppot plane. The blue goup will encounte a theat mix consisting of thee ed fighte planes (each with multiole adas) and two ed land-based seach and acquisition adas (LSAR). Due to the geopolitical divesity of the egion, IDs ae only given with 50% cetainty. The RM handles uncetainty in ID vey well. Figues 10 though 13 display the simulation ceated by the scenaio builde and map builde fo time steps 1, 3, 7, and 11. Dake egions indicate deset and lighte egions wate. The paticula time step that the pictue coesponds to is given at the bottom in the left-hand cone. Each platfom is indicated by an asteisk labeled with the platfom s type. The platfom s activity at each time step is displayed next to its type. A blue platfom s jamming pocess is depicted as a line emeging fom the blue platfom and ending on the ed platfom. Figue 11 depicts the fist instance of jamming. Fig. 10 The fist time step of the blue RM s opeations; the six blue platfoms monito fo ed activity Fig. 11 The thid time step of the blue RM s opeations, blue sensos have detected the pesence of ed ada activity. The RM has diected the blue suppot plane to engage in EA against two ed platfoms. Figue 10 depicts the initial state of both the ed and blue platfom goups duing the fist time step of the RM s un. A copy of the RM unning on each blue platfom detemines its behavio. An algoithm diffeent fom the blue RM contols the ed platfoms. The events of the battle ae saved in a database fo data mining opeations and coevolutionay analysis. Duing the fist time step, the southen ed land-based seach and acquisition ada acquies the blue escue helicopte. The southen LSAR communicates this infomation to the est of the ed goup. The blue helicopte is subsequently acquied by the emaining ed platfoms.

22 Fuzzy Logic Resouce Management and Coevolutionay Game-based Optimization 19 Figue 11 depicts the events of time step 3. The nothen LSAR has acquied pio to this time step the blue suppot plane and destoye 1. The blue goup detemines, based on senso data, that CTAR systems ae active. The fuzzy RM unning on the entie blue goup diects the suppot plane to engage in EA against ed fighte 1 and the nothen ed multiole attack plane. In doing so, the suppot plane potects not only itself, but also the helicopte. The suppot plane attacks fighte 1 and the multiole attack plane, not the nothen LSAR ada. The fuzzy RM diected the suppot plane to attack the moe theatening emittes. This elates to a concept known as lethality used by the fuzzy RM to detemine a queue of platfoms to attack at each time step, and the fact that the suppot plane has only two EA beams and limited powe. Figue 12 shows that by time step seven the RM unning on each membe of the blue goup has diected them to engage in simultaneous EA against all nothen ed theats. Duing time steps eight and nine (not pictued), the RM detemines that simultaneous EA against all nothen and southen theats is equied. Coopeative EA against all theats is initiated in time step nine. Fo a eal-time system, a decision inteval is much smalle than the display inteval between the time steps indicated at the lowe left in Figs. 10 though 13. Figue 13 indicates that at time step 11 all nothen and southen theats ae unde EA attack by the blue foce. Thus, the fuzzy RM has endeed the battlespace secue fo the blue goup by time step 11. Fig. 12 By the seventh time step, the RM unning on all the blue platfoms has diected them to engage in simultaneous EA against all nothen ed theats. Fig. 13 By the eleventh time step, the blue RM has secued the battlespace fo the blue platfom goup. 7. MEASURES OF EFFECTIVENESS, COMBINATORIAL EA, AND A GAME-THEORETIC APPROACH TO RULE INVERSION This section discusses two appoaches to the evaluation of algoithms like the RM. The fist involves showing lage quantities of output, pefeably in a gaphic o movie fomat to expets. The second is to constuct a measue of effectiveness (MOE) fo automatic evaluation of the RM. Also discussed ae methods of using this MOE to automatically detemine paametes essential to EA techniques though