Irreducible Semi-Autonomous Adaptive Combat (ISAAC):An Arti¯cial-Life Approach to Land Combat

Andrew IlachinskiCenter for Naval Analyses

Alexandria, VA 22302ilachina@cna.org

{ Abstract {

This paper introduces a simple multiagent-based \toy model" of land combat calledISAAC (Irreducible Semi-Autonomous Adaptive Combat) to illustrate how certain as-pects of land combat can be viewed as emergent phenomena resulting from the collec-tive, nonlinear, decentralized interactions among notional combatants. ISAAC takes abottom-up, synthesist approach to the modeling of combat, vice the more traditional top-down, or reductionist approach, and represents a ¯rst step toward developing a complexsystems theoretic analyst's toolbox for identifying, exploring, and possibly exploitingemergent collective patterns of behavior on the battle¯eld. This model was developed aspart of a recently completed project, sponsored by the Marine Corps Combat Develop-ment Command (MCCDC), that assessed the general applicability of \complex systemstheory" to land warfare.

Nunquam ponenda est pluralitatis sine necessitate.(\Though shalt not seek an explanation based on more complex mechanisms, until you are satis¯ed that simpler

mechanisms will not do!")th{ William of Ockham, 14 century

Background

In 1914, F. W. Lanchester introduced a set of coupled ordinary di®erential equations { now commonlycalled the Lanchester Equations (LEs) { as models of attrition in modern warfare [1]. Similar ideaswere proposed around that time by Chase [2] and Osipov [3]. These equations have since servedas the fundamental mathematical models upon which most modern theories of combat attrition arebased.

LEs are very intuitive and therefore easy to apply. For the simplest case of directed ¯re, forexample, they embody the intuitive idea that one side's attrition rate is proportional to the opposingsides size. However, LEs are applicable only under a strict set of assumptions, such as havinghomogeneous forces that are continually engaged in combat, ¯ring rates that are independent ofopposing force levels and are constant in time, and units that are always aware of the position andcondition of all opposing units. LEs also contain a number of signi¯cant shortcomings, includingmodeling combat as a deterministic process, requiring knowledge of \attrition-rate coe±cients" (thevalues of which are, in practice, very di±cult to obtain), inability to account for any suppressivee®ects of weapons, and failure to account for terrain e®ects.

Conceptually, there are two signi¯cant drawbacks to using LEs to model land combat. First, LEsare unable to account for any spatial variation of forces (no link is established, for example, betweenmovement and attrition). Second, they do not incorporate the human factor in combat (i.e., thepsychological and/or decision-making capability of the human combatant).

There have been many extensions to and generalizations of the LEs over the years, all designed tominimize the de¯ciencies inherent in their original formulation (including reformulations as stochasticdi®erential equations and partial di®erential equations). However, most existing models remainessentially Lanchesterian in nature, the driving factor being force-on-force attrition. We believe that

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these models of land warfare are insu±cient for assessing the advanced war¯ghting concepts beingexplored by the Marine Corps. In particular, the Lanchesterian view of combat does not adequatelyrepresent the Marine Corps vision of combat: small, highly trained, well-armed autonomous teamsworking in concert, continually adapting to changing conditions and environments.

To address these shortcomings, we are exploring developments in complex systems theory { par-ticularly the set of multiagent-based simulation tools developed in the arti¯cial life community { asa means of understanding land warfare in a fundamentally di®erent way. Agent-based simulationsof complex adaptive systems are predicated on the idea that the global behavior of a complex sys-tem derives from the low-level interactions among its constituent agents. By relating an individualconstituent of a complex adaptive system to an agent, one can simulate a real system by an arti¯cialworld populated by interacting processes. Agent-based simulations are particularly adept at rep-resenting real-world systems composed of individuals that have a large space of complex decisionsand/or behaviors to choose from.

Complex Systems

In recent years there has been a rapid growth in an interdisciplinary ¯eld popularly known as theScience of Complexity, which studies the behaviors of complex systems [4-6]. A complex system canbe thought of, generically, as a dynamical system composed of many nonlinearly interacting parts.Complexity theory is rooted in the fundamental belief that much of the overall behavior of ostensiblydiverse complex systems (natural ecologies, °uid °ow, the human brain, etc) in fact stems from thesame basic set of underlying principles. This still-developing ¯eld has already introduced promisingnew analytical methodologies and has uncovered many provocative and useful organizing principles.The central thesis of this project (and developed in [7] and [8]) is that land combat can be modeledas a complex adaptive system.

Land Combat as a Complex Adaptive System?

Our work to date has convinced us that military con°icts, particularly land combat, possess almostall of the key features of complex adaptive systems (see table 1): combat forces are composed of alarge number of nonlinearly interacting parts and are organized in a command and control hierarchy;local action, which often appears disordered, induces long-range order (i.e., combat is self-organized);military con°icts, by their nature, proceed far from equilibrium; military forces, in order to survive,must continually adapt to a changing combat environment; there is no master \voice" that dictatesthe actions of each and every combatant (i.e., battle¯eld action e®ectively proceeds according toa decentralized control); and so on. The general approach of this study is to extend these largelyconceptual and general connections between properties of land warfare and properties of complexsystems into a set of practical connections.

References [7] and [8] provide a broad-brush overview of the applicability of nonlinear dynamicsand complex systems theory to land warfare: [7] is a general technical source book of informationon the key ideas, concepts and methodologies of nonlinear dynamics and complex systems theory,

1and contains an extensive glossary of terms ; [8] provides a detailed discussion of how speci¯c \newsciences" ideas can potentially be used to add insight into our conventional understanding of landwarfare.

Two central themes of complexity theory are self-organization and emergence. Self-organizationrefers to the appearance of macroscopic nonequilibrium organized structure due to the collectivenonlinear interactions among a large assemblage of microscopic objects. Emergence refers to theappearance of higher-level properties and behaviors of a system that are not directly deducible fromthe lower-level properties of that system. Emergent properties are properties of the \whole" that

1See WWW URL-address http://www.marine-ns.cots-q.com/second»1/resour»1/glossary/glossary.htm.

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General Property of Description of Relevance to Land Warfare

Complex Systems

Nonlinear interaction Combat forces composed of a large number of nonlinearly interacting parts;

sources include feedback loops in C2 hierarchy, interpretation of (and adap-

tation to) enemy actions, decision-making process, and elements of chance

Nonreductionist The ¯ghting ability of a combat force cannot be understood as a simple

aggregate function of the ¯ghting ability of individual combatants

Emergent Behavior The global patterns of behavior on the combat battle¯eld unfold, or emerge,

out of nested sequences of local interaction rules and doctrine

Hierarchical structure Combat forces are typically organized in a command and control (fractal-

like) hierarchy

Decentralized control There is no master \oracle" dictating the actions of each and every combat-

ant; the course of a battle is ultimately dictated by local decisions made by

each combatant

Self-organization Local action, which often appears \chaotic," induces long-range order

Nonequilibrium order Military con°icts, by their nature, proceed far from equilibrium; understand-

ing how combat unfolds is more important that knowing the \end state"

Adaptation In order to survive, combat forces must continually adapt to a changing envi-

ronment, and continually look for better ways of adapting to the adaptation

pattern of their enemy

Collectivist dynamics There is a continual feedback between the behavior of (low-level) combatants

and the (high-level) command structure

Table 1: Land combat as a complex adaptive system.

are not possessed by any of the individual parts making up that whole: an air molecule is not atornado and a neuron is not conscious.

The fundamental motivation of this study is to develop a multiagent-based software tool toaddress the basic question: \To what extent is land combat a self-organized emergent phenomenon?"As such, its intended use is not as a full system-level model of combat but as an interactive toolbox(or \conceptual playground") in which to explore high-level emergent behaviors arising from variouslow-level (i.e., individual combatant and squad-level) \interaction rules." The idea is not to modelin detail a speci¯c piece of hardware (M16 ri°e, M101 105mm howitzer, etc.), but to provide anunderstanding of the fundamental behavioral tradeo®s involved among a large number of notionalvariables.

ISAAC

We are using complexity theory in this study to develop a multiagent-based simulation of notionalcombat called ISAAC (Irreducible Semi-Autonomous Adaptive Combat); see [9]. ISAAC { whosedynamics is patterned after mobile cellular automata rules { takes a bottom-up, synthesist approachto the modeling of combat, vice the more traditional top-down, or reductionist approach.

Mobile cellular automata have been used before to model predator-prey interactions in naturalecologies [10]. They have also been applied to combat modeling [11], but in a much more limitedfashion than the one ultimately envisioned for ISAAC. More recently, multiagent-based simulationshave been applied successfully to tra±c pattern analysis [12] and social evolution [13]. The ulti-mate goal is for ISAAC to become a fully developed complex systems theoretic analyst's toolboxfor identifying, exploring, and possibly exploiting emergent collective patterns of behavior on thebattle¯eld.

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Models based on di®erential equations homogenize the properties of entire populations and ignorethe spatial component altogether. Partial di®erential equations { by introducing a physical spaceto account for troop movement { fare somewhat better, but still treat the agent population as acontinuum. In contrast, ISAAC consists of a discrete heterogeneous set of spatially distributedindividual agents (i.e., combatants), each of which has its own characteristic properties and rules ofbehavior. These properties can also change (i.e., adapt) as an individual agent evolves in time.

In ISAAC, the \¯nal outcome" of a battle { as de¯ned, say, by measuring the surviving forcestrengths { takes second stage to exploring how two forces might \co-evolve" during combat.

ISAAC Agents

The basic element of ISAAC is an ISAAC Agent (or ISAACA), which represents a primitive combatunit (infantryman, tank, transport vehicle, etc.) that is equipped with the following characteristics:

² Doctrine: a default local-rule set specifying how to act in a generic environment

² Mission: goals directing behavior

² Situational Awareness: sensors generating an internal map of environment

² Adaptability: an internal mechanism to alter behavior and/or rules.

The putative \combat battle¯eld" is represented in ISAAC by a two-dimensional lattice of dis-crete sites. Each site of the lattice may be occupied by one of two kinds of ISAACAs: red or blue.The initial state consists of either user-speci¯ed formations of red and blue ISAACAs positioned atdiagonally opposite corners of the battle¯eld or of a random distribution of red and blue ISAACAsoccupying the central square region (of user-speci¯ed dimension). Red and blue \°ags" are alsotypically (but not always) positioned in diagonally opposite corners: a red °ag in the red ISAACAscorner and a blue °ag in the blue ISAACAs corner. A typical \goal," for both red and blue ISAA-CAs, is to successfully reach the \°ag" positioned in the diagonally opposite corner. ISAAC also hasthe provision of de¯ning a notional terrain. Future versions will include a menu of environmentalobstacles as well.

Each ISAACA exists in one of three states: alive, injured, or killed. Injured ISAACAs can(but are not required to) have di®erent personalities from when they were alive. By default, aninjured ISAACA's ability to shoot an enemy is equal to 1/2 of its ability when alive. Also, if thealive ISAACA chooses its moves from among lattice sites within a distance of two or more from itscurrent position, an injured ISAACA's move range is reduced to the minimum possible range of oneunit.

Each ISAACA has associated with it a set of ranges (sensor range, ¯re range, communicationsrange, etc.), within which it senses and assimilates simple forms of local information (see below),and a personality, which determines the general manner in which it responds to its environment.

ISAAC \Personalities"

Each ISAACA is equipped with a user-speci¯ed personality { or internal value system { de¯ned by aPsix-component personality weight vector, ~! = (! ; ! ; : : : ; ! ), where 0 ·j ! j· 1 and j ! j= 1.1 2 6 i ii

The components of the personality weight vector specify how an individual ISAACA responds todistinct kinds of local information within its sensor and threshold ranges.

The personality weight vector may be state-dependent. That is to say, ~! need not, in general,alive

be equal to ~! . The components of ~! can be also negative, in which case they signify a propensityinjured

for moving away from, rather than toward, a given entity.The default personality rule structure is de¯ned as follows. Since there are two kinds of ISAACAs

(red and blue), and each ISAACA can exist in one of two states (alive and injured), each ISAACA

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can respond to e®ectively four di®erent kinds of information appearing within its sensor range r :sensor

² The number of alive friendly (i.e., like-colored) ISAACAs

² The number of alive enemy (i.e., di®erent colored) ISAACAs

² The number of injured friendly ISAACAs

² The number of injured enemy ISAACAs .

Additionally, each ISAACA can respond to how far it is from both its own (like-colored) \°ag"thand its enemy's \°ag." The i component of ~! represents the relative weight a®orded to moving

thcloser to the i type of information.A personality is de¯ned by assigning a weight to each of the six kinds of information. For

example, one ISAACA might give all its attention to like-colored ISAACAs, and e®ectively ignorethe enemy. An example of a fairly aggressive personality is one whose weight vector is given by~! = (1=20; 5=20; 0; 9=20; 0; 5=20). Such a personality is ¯ve times more \interested" in movingtoward alive enemies than it is in moving toward alive friendlies (e®ectively ignoring injured friendliesaltogether), and is more interested in moving toward injured enemies than it is even in advancingtoward the enemy °ag. An ISAAC that has a personality de¯ned by entirely negative weights { say,~! = (¡1=6;¡1=6;¡1=6;¡1=6;¡1=6;¡1=6) { wants to move away from, rather than toward, everyother ISAACA and both °ags.

An ISAACA's personality weight vector is used to rank each possible move according to a penaltyfunction. The penalty function e®ectively measures the total distance that the ISAACA will be fromother ISAACAs (which includes both friendly and enemy ISAACAs) and from its own and enemy°ags, each weighted according to the appropriate component of the personality weight vector, ~!.An ISAACA moves to the position that incurs the least penalty; i.e., an ISAACA's move is the onethat best satis¯es it's personality-driven desire to \move closer to" other ISAACA's in given statesand either of the two °ags.

Meta-Rules

An ISAACA's default personality may be augmented by a set of meta-rules that tell it how toalter its default personality according to various environmental conditions and contexts. The threesimplest meta-rule classes e®ectively de¯ne the local conditions under which an ISAACA is allowedto advance toward enemy °ag (class 1), cluster with friendly forces (class 2), and engage the enemyin combat (class 3).

For example, a class-1 meta-rule prevents an ISAACA from advancing toward the enemy °agunless it is locally surrounded by some threshold number of friendly ISAACAs. A class-2 meta-rulecan be used to prevent an ISAACA from moving toward friendly ISAACAs once it is surroundedby a threshold number. Finally, a class-4 meta-rule can be used to ¯x the local conditions underwhich an ISAACA is allowed to move toward or away from possibly engaging an enemy ISAACA iscombat. Speci¯cally, an ISAACA is allowed to engage an enemy if and only if the di®erence betweenfriendly and enemy force strengths { locally { exceeds a given threshold.

A global rule set determines combat attrition (see below), communication, reconstitution, and(in future versions) reinforcement. ISAAC also contains both local and global commanders, each ofwhich is equipped with its own unique command-personality and area of responsibility, and obeysan evolving command and control hierarchy of rules [9].

Combat

In its current version, ISAAC adjudicates combat in the simplest possible manner. During thecombat phase of an iteration step for the whole system, each ISAACA X (on either side) is given an

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opportunity to \¯re" at all enemy ISAACAs Y that are within a ¯re range r of X's position. If an¯re

ISAACA is shot by an enemy ISAACA, its current state is degraded either from alive to injured orfrom injured to dead. Once \dead," that ISAACA is permanently removed from further play. Theprobability that a given enemy ISAACA is \shot" is ¯xed by user speci¯ed single-shot probabilitiesfor red-by-blue and blue-by-red.

By default, all enemy ISAACAs within a given ISAACA's ¯re range are targeted for a possiblehit. However, the user has the option of limiting the number of simultaneously engageable enemytargets. If this option is selected, and the number of enemy ISAACAs within an ISAACA's ¯re-range exceeds a user-de¯ned threshold number (say N), then N ISAACAs are randomly chosen fromamong the ISAACAs in this set.

This basic combat \logic" may be enhanced by three additional functions: (1) Defense, whichadds a notional ability to ISAACAs to be able to withstand a greater number of \hits" before havingtheir state degraded, (2) Reconstitution, which adds a provision for previously injured ISAACAs tobe reconstituted to their alive state, and (3) Fratricide, which adds an element of realism to ISAACcombat by making it possible to inadvertently \hit" friendly forces

ISAAC Run Modes

ISAAC is designed to allow the user to explore the evolving patterns of macroscopic behavior thatresult from the collective interactions of individual agents, as well as the feedback that these patternsmight have on the rules governing the individual agents behavior. ISAAC can currently be run inthree di®erent \modes":

² Interactive Mode, in which ISAAC's core engine is run interactively using a ¯xed setof rules. This mode, which allows the user to make 'on-the-°y' changes to the values ofany (or all) parameters de¯ning a given run (including the \decision-making personality" ofindividual ISAACAs), is particularly well suited for quickly and easily playing simple \Whatif?" scenarios. This purely graphical run mode is also useful for interactively \searching" forinteresting emergent behavior. (See Sample # 1 { Sample # 3 below.)

² Data-Collection Mode, in which the user can (1) generate time series of various changingquantities describing the step-by-step evolution of a battle, and (2) keep track of certainmeasures of how well mission objectives are met at a battle's conclusion. Additionally, the usercan generate complete behavioral pro¯les on two dimensional slices of ISAAC's N-dimensionalparameter space. (See Sample # 5 below.)

² Genetic Algorithm \Evolver" Mode, in which a genetic algorithm is used to breed apersonality for one side that is \best" suited for performing some well-de¯ned mission againsta ¯xed personality (and force disposition) for the other. This mode illustrates how programssuch as this can eventually be used to evolve real-world \tactics" and \strategies." (SeeSample # 4 below.)

Sample Behavior

Although the preliminary version of ISAAC can do no more than suggest new ways of thinkingabout some old issues, even at this early juncture, ISAAC already has an impressive repertoire ofemergent behaviors:

² Forward advance² Frontal attack² Local clustering² Penetration

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² Retreat² Attack posturing² Containment² Flanking maneuvers² \Guerrilla-like" assaults² etc...

Moreover, ISAAC frequently displays behaviors that appear to involve some form of \intelligent"division of red and blue forces to deal with local \¯restorms" and skirmishes, particularly those forceswhose personalities have been \evolved" (via a genetic algorithm) to perform a speci¯c mission. Suchbehaviors are not hard-wired but rather an emergent property of a decentralized and nonlinear localdynamics. A small sampling of behaviors is shown below.

Sample # 1: Fluid-like \Collisions"

Figure 1 shows several frames of a simulated engagement that evolves as though it were a clashbetween two viscous °uids. The initial state (not shown) consists of 90 red and 90 blue ISAACAsoccupying random positions within 20-by-20 squares near the lower left and upper right regionsof an 80-by-80 lattice, respectively. The blue force has a personality de¯ned by the weight vector~! = (1=15; 4=15; 1=15; 4=15; 0; 1=3). Each of the red ISAACAs is assigned a random personalityblue

(which is constrained only in giving zero weight to moving toward the red °ag located in the lowerleft corner of the battle¯eld).

Figure 1. Fluid-like \collision" between red and blue ISAACA forces.

Figure 1 shows that the red and blue forces collide head-on but are dispersed and aligned alongtwo narrow columns at time t=50. The two sides continue battling each other in this manner, withneither side gaining an advantage or advancing closer to its enemy's °ag, for a relatively long time(time t=50 to t=110 in the ¯gure). Notice that, at time t=75, several blue ISAACAs have \found"a way to sneak around the bottom of red's column-like formation. This group is able to advancetoward red's °ag unchallenged (see next two frames in ¯gure 1), because it is unseen by the red

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ISAACAs making up red's central column. By time t=125, a cluster of red ISAACAs breaks awayfrom what used to be the central column and advances towards blue's °ag. Meanwhile, blue forcescontinue advancing toward red's °ag at the bottom of the frame.

Sample # 2: Red \Encircles" Blue

Figure 2 shows snapshots of an evolution in which red e®ectively \encircles" blue ISAACAs. Aninteresting question to ask is \How should blue alter its personality (i.e., its \tactics") { during thecourse of the battle { in order to prevent being encircled by red forces?" While ISAAC can be usedto explore the behavioral consequences of matching alternative ¯xed blue personalities against thesame red force, ISAAC does not yet have the °exibility to explore the consequences of a dynamicallychanging personality during a given run.

Figure 2. Red ISAACAs \encircle" blue forces.

Sample # 3: Non-Monotic Behavior

Figure 3 shows snapshots of three separate runs in which red's sensor range is systematically increasedred redin increments of two: r = 5 for the top sequence (SENSOR 2); r = 7 for the middlesensor sensor

redsequence (SENSOR 3); and r = 9 for the bottom sequence (SENSOR 4). Note that blue'ssensorbluesensor range, r , remains ¯xed at r = 5 throughout all three runs.blue;sensorsensor

In each of the runs, there are 100 red and 50 blue ISAACAs. Red is also the more the aggressiveforce: blue will engage in combat if the number of friendly and enemy ISAACAs is locally about even,while red will do so even if outnumbered by four enemy combatants. Both sides are endowed withthe same ¯re range (r = 4), the same single-shot probability (p = 0:005) and can simultaneously¯re

engage the same maximum of 3 enemy targets. Note that the °ags for this sample run are locatednear the middle of the left and right edges of the notional battle¯eld.

The snapshots for SENSOR 2 (top row of ¯gure 3) show that when red's sensor range is equal toblue's, the red force is able to e®ectively \barrel" its way through the blue defenses into blue's °ag.As red advances toward blue's °ag, a number of ISAACAs are \stripped" away from the centralred-°ag:blue-°ag axis as they respond to the presence of nearby blue ISAACAs.

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The snapshots for SENSOR 3 (middle row of ¯gure 3) show that when red's sensor range is twounits greater than blue's, red is not only able to mass almost all of its forces on the blue °ag (alater snapshot would reveal blue's °ag completely enveloped by red forces by time t=100), but todefend its own °ag from all blue forces as well. In this instance, the red force knows enough about,and can respond quickly enough to enemy action such that it is able to march into enemy territorye®ectively unhindered by enemy forces and \scoop up" blue ISAACAs as they are encountered.

What happens when red's sensor range is increased still further? One might intuitively guessthat red can only do at least as well; certainly no worse. However, as the snapshots for SENSOR 4

red(bottom row of ¯gure 3) show, when red's sensor range is increased to r = 9, red does objectivelysensor

worse than it did in any of the preceding runs. \Worse" here means that red is less e®ective in (a)establishing a presence near the blue °ag, and (b) defending blue's advance toward the red °ag.

There is, perhaps, a fundamental lesson to be drawn from this simple example: given that theresources and personalities of both sides remain ¯xed in a con°ict, how \well" side X does overside Y does not necessarily scale monotonically with X's sensor capability. As one side is forcedto assimilate more and more information (with increasing sensor range), there will inevitably comea point where the available resources will be spread too thin and the overall ¯ghting ability willtherefore be curtailed. On the other hand, the deeper lesson here might be that as sensor range isincreased { thereby increasing the amount of \information" that side X is forced to assimilate andrespond to { X's resources and/or tactics (i.e., personality) must also be altered in order to ensureat least the same level of \mission success."

Figure 3. Three sample runs in which red's sensor range is systematically increased in increments ofred red red bluetwo (top: r = 5; middle: r = 7; bottom: r = 9) relative to that of blue (¯xed at r = 5).S S S S

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Sample # 4: GA-Bred \Tactics"

Genetic algorithms (GAs) are a class of heuristic search methods and computational models ofadaptation and evolution based on natural selection.

In nature, the search for bene¯cial adaptations to a continually changing environment (i.e.,evolution) is fostered by the cumulative evolutionary knowledge that each species possesses of itsforebears. This knowledge, which is encoded in the chromosomes of each member of a species, ispassed from one generation to the next by a mating process in which the chromosomes of \parents"produce \o®spring" chromosomes.

GAs mimic and exploit the genetic dynamics underlying natural evolution to search for optimalsolutions of general combinatorial optimization problems. They have been applied to the TravelingSalesman Problem, VLSI circuit layout, gas pipeline control, the parametric design of aircraft,neural net architecture, models of international security, and strategy formulation. An excellentrecent overview of GA is given by Mitchell [14].

Figure 4. GA-bred red personality to perform mission = get as many forces near blue's °ag aspossible while minimizing friendly casualties.

Figure 4 shows an example of a red personality that has been \bred" to perform a speci¯c missionusing a GA. Speci¯cally, the parameters de¯ning the blue side are clamped (except for initial spatialdisposition, which is averaged over during the run), and the GA is used to ¯nd the \best" redpersonality to perform the following mission: get as many red forces near blue's °ag as possiblewhile minimizing red casualties. There are 70 ISAACAs on each side and the blue force is stationedin a semi-circle 25 units away from its °ag in the upper right corner of the battle¯eld.

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Red's \tactic" { which derives solely from the personality found by the GA to be best \suited"2for this mission { is to exploit a few red ISAACAs at the front of the advancing red force, using

them to split apart blue's forces in order to temporarily \weaken" the center region of blue's defense.As soon as this center region is su±ciently weakened, red quickly penetrates through to the blue°ag.

What is most surprising about many of the runs using GA-derived personalities is that the redforce appears to task di®erent ISAACAs with di®erent missions, despite the fact that each redISAACA is endowed with exactly the same personality! Thus, a higher-level tactic { such as usethe two forward positioned ISAACAs to weaken the enemy's center { emerges out of the collectiveinteractions of the same low-level decision rules; i.e., an apparent centralized order induced bydecentralized local dynamics.

Sample # 5: 2D-Slice of N-dim Parameter Space

Figure 5 shows an example of ISAAC's ability to sample a 2D \slice" of what is ostensibly a verylarge N-dimensional parameter space. The scenario is one that probes red's defensive capability. Inthis scenario, both sides start out with 50 ISAACAs each, and red's mission objective is to maximizeblue casualties near the red °ag. The ¯tness function, f , is de¯ned so that red's ¯tness ¼ 1 onlywhen red kills all (or most) of the blue ISAACAs that approach the red °ag.

Red defends its °ag with a personality de¯ned by weight vector ~! = (:1; :4; :1; :4; 0; 0), meaningred

that red ISAACAs \react" to both friendly and enemy ISAACAs, but that they do not \see" either°ag. They are initially positioned near the red °ag in the lower left corner. Blue attacks with apersonality de¯ned by ~! = (10=150; 40=150; 10=150; 40=150; 0; 1=3), so that blue ISAACAs haveblue

a positive weight for advancing toward the red °ag. Blue's sensor and ¯re ranges are r = 4 andsensor

r = 3, respectively, its combat threshold is equal to negative 3 (so that it is fairly aggressive), and¯re

its single-shot probability p = 0:005. Combat ensues for a maximum 125 iteration steps on a size50-by-50 notional battle¯eld.

Figure 5. Two-dimensional \slice" through ISAAC's large N-dimensional parameter space. Thez-axis is a ¯tness measure (0 · f · 1), re°ecting how well the red force performs the mission =

maximize blue casualties.

Figure 5 shows a three-dimensional plot of the ¯tness 0 · f(x; y) · 1 as a function of (x; y),averaged over 50 initial states. Red's sensor range is the x-coordinate of the 2D \slice" (which ranges

2This particular personality was bred using a pool of 75 red personalities and averaging over 25 random initialconditions for each generation. For details see pages 163-201 of [9].

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from 1 to 15) and the combat threshold (see Meta-Rules above) as the y-coordinate (which rangesfrom -25 to 25).

Figure 5 shows that the red force's ability to perform its mission is a strong function of the x andredy parameters chosen for this plot. In particular, red's overall mission ¯tness f ¼ 0 unless r > 1sensor

and its combat threshold is less than about +3. Notice also that while the ¯tness quickly reachesits maximum value for sensor range r = 2, it does not simply increase with increasing sensorsensor

range. The system's phase space clearly has a region of \diminishing returns," beyond which furtherincreases in sensor range simply do not help the overall performance.

For example, if we take a vertical slice of the surface through y = 0 (which de¯nes a red forcethat has a zero combat threshold meta-rule { meaning that an enemy is engaged in combat only ared ISAACA senses that, locally, the numbers of friendly and enemy ISAACAs are equal), we seethat increasing the sensor range to r > 8 e®ectively renders the force incapable of performingsensor

this speci¯c mission at all (i.e., f ¼ 0). The reason behind this, in this very simple scenario, isthat as the sensor range is increased, each red \sees" an increasing number of blue ISAACAs andmust therefore become more and more \aggressive" (i.e. have an increasingly large negative combatthreshold) in order to engage the enemy in combat. For more complex scenarios, where the number(and kinds) of local decisions that are made by each ISAACA may be quite large, plots such asthe one shown in ¯gure 5 are indispensable for gaining useful insights into how all of the di®erentparameters \¯t together" to shape the overall °ow of battle.

Potential Payo®s to Using Multiagent Models such as ISAAC

Most traditional models focus on looking for equilibrium \solutions" among some set of (pre-de¯ned)aggregate variables. The LEs are e®ectively mean-¯eld equations, in which certain variables suchas attrition rate are assumed to represent an entire force and the outcome of a battle is said to be\understood" when the equilibrium state has been explicitly solved for. In contrast, ISAAC focuseson understanding the kinds of emergent patterns that might arise while the overall system is out of(or far from) equilibrium.

The payo® of this multiagent-based approach is a radically new (and decidedly non-Lanchesterian)way of looking at fundamental issues of land combat. Speci¯cally, ISAAC is being designed to helpanalysts:

² Understand how all of the di®erent elements of combat ¯t together in an overall \combatphase space:" Are there regions that are \sensitive" to small perturbations, and, if so, mightthere be a way to exploit this in combat (as in selectively driving an opponent into moresensitive regions of phase space)?

² Assess the value of information: How can I exploit what I know the enemy does not knowabout me?

² Explore tradeo®s between centralized and decentralized command-and-control (C2) struc-tures: Are some C2 topologies more conducive to information °ow and attainment of missionobjectives than others? What do emergent forms of a self-organized C2 topology look like?

² Provide a natural arena in which to explore consequences of various qualitative characteristicsof combat (unit cohesion, morale, leadership, etc.)

² Explore emergent properties and/or other \novel" behaviors arising from low-level rules (evendoctrine if it is well encoded): Are there any universal patterns of combat behavior?

² Provide near-real-time tactical decision aids by providing a \natural selection" (via a geneticalgorithm) of tactics and/or strategies for a given combat scenario

ISAAC provides a natural arena in which to explore the Clausewitzian \fog-of-war," or the e®ects

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of uncertainties and/or inaccuracies of intelligence data and of time-delays in reporting information.More important, from an Information Warfare perspective, ISAAC provides a framework for quan-tifying the \value" of information on a battle¯eld. ISAAC can, in principle, be used to explorethe consequences of given (personality-de¯ned) force and/or weapon mixes. It can also be usedto re-examine traditional measures of combat e®ectiveness and de¯ne requirements for what mightloosely be called nonlinear data collection, which refers to data that capture the continuously evolv-ing relationships among all of the interdependent components of combat (as compared with morestatic measures | such as force attrition | commonly used by conventional models).

The ultimate goal is for ISAAC to become a fully developed complex systems theoretic analyst'stoolbox for identifying, exploring and possibly exploiting emergent collective patterns of behavioron the battle¯eld.

Future Enhancements

The version of ISAAC described in this paper represents but a ¯rst step toward developing an in-herently complex systems theoretic model of land combat, and is motivated by a desire to extendthe largely conceptual links between complex systems theory and land combat, as outlined in table1, to forge a set of practical connections as well. Planned future enhancements include more realis-tic o®ensive and defensive capabilities, an enhanced internal \value-system," added environmentalrealism, and endowing individual ISAACAs with both a memory of, and a facility to learn from,their past actions (using both neural-network and reinforcement learning techniques). A graphical-user-interface to facilitate interactive experimentation is also planned. Reference [6] provides a morethorough discussion of future enhancements.

References

[1] F. W. Lanchester, \Aircraft in warfare," Engineering, Volume 98, 1914, 422-423. (Reprintedon pages 2138-2148, The World of Mathematics, Volume IV, edited by J. Newman, Simon andSchuster, 1956.)

[2] J. V. Chase, \A mathematical investigation of the e®ect of superiority in combats upon the sea,"1902, reprinted in B. A. Fiske, The Navy as a Fighting Machine, Annapolis, MD: U.S. NavalInstitute Press, 1988.

[3] M. Osipov, \The In°uence of the Numerical Strength of Engaged Forces in Their Casualties,"translated by R. L. Helmbold and A. S. Rehm, Naval Research Logistics, Volume 42, No. 3,April 1995, 435-490.

[4] G. A. Cowan, D. Pines and D. Meltzer, editors, Complexity: Metaphors, Models and Reality,Addison-Wesley, 1994.

[5] S. Kau®man, At Home in the Universe: The Search for Laws of Self-Organization and Complex-ity, Oxford University Press, 1995.

[6] C. G. Langton, editor, Arti¯cial Life: An Overview, MIT Press, 1995.

[7] A. Ilachinski, Land Warfare and Complexity, Part I: Mathematical Background and TechnicalSourcebook, Center for Naval Analyses Information Manual CIM-461, July 1996, Unclassi¯ed.

[8] A. Ilachinski, Land Warfare and Complexity, Part II: An Assessment of the Applicability ofNonlinear Dynamics and Complex Systems Theory to the Study of Land Warfare, Center forNaval Analyses Research Memorandum CRM-68, July 1996, Unclassi¯ed.

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[9] A. Ilachinski, Irreducible Semi-Autonomous Adaptive Combat (ISAAC): An Arti¯cial-Life Ap-proach to Land Warfare, Center for Naval Analyses Research Memorandum CRM 97-61, June1997, Unclassi¯ed.

[10] N. Boccara, O. Roblin and M. Roger, \Automata network predator-prey model with pursuit andevasion," Physical Review E, Volume 50, No. 6, December 1994, 4531-4541.

[11] A. E. R. Woodcock, L. Cobb and J.T. Dockery, \Cellular Automata: A New Method for Battle-¯eld Simulation," Signal, January, 1988, 41-50.

[12] C. Barrett, \Simulation Science as it Relates to Data/Information Fusion and C2 Systems,"Brie¯ng Slides, Los Alamos, 1997.

[13] J. M. Epstein and R. Axtell, Growing Arti¯cial Societies: Social Science From the Bottom Up,MIT Press, 1996.

[14] M. Mitchell, An Introduction to Genetic Algorithms, MIT Press, 1996.

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