Pythagoras: A New Agent-based Simulation System - Northrop ...

Pythagoras: A New Agent-based Simulation System 


Edmund J. Bitinas, Zoe A. Henscheid, and Lap V. Truong 

Northrop Grumman Mission Systems, Information and Technical Services Division 

Pythagoras is a new agent-based simulation (“distillation”) originally 

developed by Northrop Grumman to support Project Albert, a U.S. Marine 

Corps–sponsored international initiative focusing on human factors in 

military combat and noncombat situations. Pythagoras introduces new 

capabilities to modeling and simulation, such as soft decision rules, 

dynamic sidedness, behavior-change triggers, and nonlethal weapons. Soft 

decision rules create instances of agents from the same agent class whose 

behaviors can be unique to the agent. Dynamic sidedness allows agents to 

change sides as a function of events and actions. Behavior-change triggers 

allow agents to change their behavior as a function of events or actions. 

Nonlethal weapons not only cause suppression, they may also change the 

sidedness (affiliation) of an agent. Pythagoras scenarios include a cavesearch 

scenario in which U.S. Marines look for an elusive agent. In a 

peacekeeping scenario, the Marines use short-range nonlethal weapons 

(such as leaflets or food) to sway the affiliation of villagers, while an enemy 

is broadcasting anti-Marine propaganda with an indirect-fire nonlethal 

weapon (a bullhorn). Pythagoras is written in Java, runs on a PC, and is 

hosted at the Maui High Performance Computing Center, where it is available 

for data farming—executing large numbers of repetitions of parametric 

runs to identify areas of unexpected behaviors and nonlinear results in a 

coevolving landscape. 

Introduction 

Traditional combat modeling and simulation have concentrated on the physical aspects 

of combat. Rates of movement, rates of fire, lethality, the effect of weather, terrain, 

etc., are all phenomena that are measurable to some degree and lend themselves to 

mathematical representations. However, as Figure 1 shows, the combat environment 

involves not only the physical world, but also human factors (features that motivate 

soldiers or deter them from engaging in combat) and leadership (the ability to inspire, 

integrate, and employ soldiers and weapons to attain an objective). The three components 

are tightly coupled. For example, weapons work best when used by well-trained 

troops who are directed by enlightened leaders. 

Six years ago, the U.S. Congress authorized an applied research project to evaluate 

nontraditional combat simulation techniques potentially useful for addressing three 

areas that were largely omitted in existing combat simulations: 

• Nonlinearity: Small changes in input can have disproportionate effects on outcomes. 

• Intangibles: Human factors, leadership, and other intangibles can change outcomes. 

• Coevolving landscape: Adversaries continually anticipate one another’s actions, 

and base their decisions on that anticipation. 

Technology Review Journal • Spring/Summer 2003 45


Figure 1. Combat environment: Physical elements, human factors, and leadership are 

tightly coupled 

With those three research objectives in mind, Project Albert was conceived. Initially 

led by the U.S. Marine Corps Combat Development Command (MCCDC) at Quantico, 

Virginia, the project is currently headed by the Marine Corps Warfighting Laboratory, 

also at Quantico. It quickly expanded into an international effort involving eight other 

countries. The approach was to proceed in parallel along three different but related 

paths. First, Project Albert would harness the power of supercomputing technology to 

enable massive experimentation and analysis on a scale then rarely, if ever, attempted. 

Second, the consortium would develop a set of visualization tools to assist in the 

analysis of the experiments. Third, Project Albert commissioned the development of 

new agent-based simulations (called distillations) that did not start with the traditional 

physical foundations, but instead concentrated on the exploration of human factors and 

leadership in the combat environment. For a description of Project Albert, see the Web 

page [1]. 

Overview of Pythagoras Distillation 

Northrop Grumman was tasked to build a new distillation that used agent-based technology 

in diverse, innovative ways to model human behavior and its effect on combat and 

noncombat situations. Three design criteria were specified for the new distillation: 

• It must be easy enough to use that a military officer with a nontechnical degree 

could learn it in no more than eight hours. 

• It must incorporate fuzzy logic in some way. 

• It must be data farmable (i.e., able to run in batch mode on a parallel-processor 

supercomputer—specifically, at the Maui High Performance Computing Center in 

Maui, Hawaii). 

The resulting prototype distillation, christened Pythagoras, enables a user to create 

various intelligent agents and assign them behaviors based on motivators and detractors. 

46 

Weapons 

Sensors 

Platforms 

Ammunition 

Terrain 

Weather 

• Decision Making 

Intelligence 

Communication 

Inspiration 

Physical 

Elements 

Leadership 

Human 

Factors 

Technology Review Journal • Spring/Summer 2003 

Morale 

Training 

Confidence 

Fatigue 

Fear 

Comradeship


The agents can either act as individuals or be loosely or tightly controlled by one or 

more leader agents. Pythagoras is written in Java, making it platform-independent. It 

can be run in a supercomputer environment as a batch job, enabling tens of thousands of 

repetitions to be run in a short time; or it can be used and run interactively on a PC 

through a graphical user interface (GUI). 

Pythagoras offers a unique set of capabilities in the area of agent-based simulations: 

• Incorporates soft rules to distinguish unique agents 

• Uses desires to motivate agents into moving and shooting 

• Includes the concept of affiliation (established by sidedness, or color value) to 

differentiate agents into members of a unit, friendly agents, neutrals, or enemies 

• Allows for behavior-changing events and actions (called triggers) that may be 

invoked in response to simulation activities 

• Retains traditional weapons, sensors, and terrain 

Each capability is discussed below. 

Soft Rules to Create Individuality 

Each person has a unique interpretation of language. History offers countless examples 

of military orders whose intent was misinterpreted, leading to unexpected and sometimes 

disastrous consequences. In a military context, an order may be given as “Hold 

fire until the enemy gets close.” To a fighter pilot, close may be six miles, but an 

embassy security guard may interpret the same order to mean six feet. And even if 

several people agree on a distance—say, 400 feet—some will evaluate that distance a 

little long and be seen as trigger-happy, whereas others will evaluate it a little short and 

be seen as overcautious. 

Fuzzy logic attempts to capture the complex, dynamic nature of the world and the human 

interpretation of that world, while creating a mathematical underpinning that will allow a 

“crisp”-thinking digital computer to represent and act on it. However, for analysis, we 

determined that a strict interpretation and implementation of fuzzy logic might cloud the 

interpretation of the results of our Pythagoras experiments. Instead, we designed a 

feature for Pythagoras called soft decision rules, which not only assigns each agent its 

own threshold within the fuzzy-logic trade space but also ensures traceability. It avoids 

the “everything is gray” phenomenon that sometimes occurs in direct implementations 

of fuzzy logic. 

Pythagoras allows all decision variables and some human factors to be softened by the 

user. The approach is to reflect variation between individual agents by establishing a 

midpoint for the variable in question and then allowing the user to provide a uniformly 

distributed range around that value. When an agent is instantiated at the beginning of a 

scenario run, it selects its decision-variable values from the distribution at random. By 

controlling the spread, agents can be instantiated as very homogeneous (e.g., welltrained, 

disciplined military troops) or quite heterogeneous (e.g., a crowd of villagers), 

or some value in between. Each decision variable has its own control, so some aspects 

of behavior can be tight, others loose. Figure 2 illustrates three alternative degrees of 

individuality. 



Figure 2. Three alternative degrees of individuality 

In each of the three cases illustrated in Figure 2, the midpoint for the behavior variable 

is 5. That value might, for example, represent the minimum number of enemies from 

which an agent would retreat. The red uniform distribution represents a firm, homogeneous 

behavior variable, for which the range is ±1 around the midpoint of 5. The green 

uniform distribution depicts a softer behavior variable, for which the range is ±2 around 

the midpoint, indicating that the value of the behavior variable could lie in the range of 3 

to 7. The loosest of the three definitions for the behavior variable is described by the 

blue uniform distribution. In that case, the range is ±4 around the midpoint, and values 

for the behavior variable could range from a low of 1 to a high of 9. Individual behavior 

drawn from such a loose distribution would be quite heterogeneous. 

Agent Desires to Move 

In Pythagoras, agents can be assigned movement desires, from the possible selections 

listed in Table 1, to determine their movement paths as a scenario unfolds. During each 

decision cycle, an agent establishes which desires are active (e.g., too far from a leader), 

and, if the sum of the desires to move exceeds a user-determined threshold, the agent 

then uses the strengths of the desires to determine a direction of movement. If multiple 

desires are active, they can be adjudicated at the user’s discretion by one of four 

alternative methods: 

• Through vector algebra, using direction weighted by desire 

• By priority (i.e., the strongest desire) 

• At random, with the relative weight of each desire determining its probability of 

selection 

• By applying vector algebra for only the two strongest desires 

Although the list of existing desires is small, it can be used to represent a variety of 

behaviors. 

48 

Probability 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0 

0 

2 

4 6 

Decision Threshold 

Common decision threshold = 5 

Firm/low individuality range ±1 around the threshold 

Soft/medium individuality range ±2 around the threshold 

Loose/high individuality range ±4 around the threshold 


8 

10 

Firm 

Soft 

Loose


Table 1. Decision variables (desires) used to establish agent movement directions 

Toward (if d> ) or away from (if d< ) closest leader 

Toward (if d> ) or away from (if d< ) closest unit member 

Toward farthest unit member (if d> ) 

Toward next way point (if d> ) 

Toward (if d> ) or away from (if d< ) nearest enemy 

Toward small number of enemy (if number of enemy within deand e> 

Toward objective 

At random 

Continue in same direction 

Stay in place 

) 

Avoid bad terrain (if mobility < or detection > or defense < ) 

Prefer good terrain (if azimuth, mobility > and detection < and defense > ) 

d = Distance 

= Specified value (different for different variables) 

e = Enemy count 

Once the agent chooses a direction of movement based on the active desires, the agent 

reviews the terrain suitability of the selected path. If the terrain is unsuitable because of 

movement, concealment, and/or protection considerations, the agent first looks to the 

right and left of the desired path until suitable terrain is identified. The agent then 

searches farther to the right and left to see if an additional shift of direction will put the 

agent on preferred terrain. For example, the desired path may put the agent in a swamp, 

so the agent will look right and left until a path on grass is found. Then the agent may 

search a few more degrees (the range is user controlled) to see whether a road is 

available in roughly the desired direction. 

Dynamic Sidedness for Two-Dimensional Affiliation 

In Pythagoras, each agent may be assigned a value for each of the three color 

properties—red, green, and blue—that can be used to establish affiliation among the 

agents. One, two, or all three of the properties can be used to establish an affiliation, and 

different agents can use different sets of properties for that purpose. Pythagoras uses 

the terms greenness, blueness, and redness to make the properties generic (and allow 

for visual display of the property in the scenario playback tool). Each of the three 

properties can take a value from 0 to 255 (which corresponds to standard color-monitor 

gun settings used by Java to control image colors). Figure 3 shows an example of both 

blue and green being used to establish affiliation. 

Agents with similar color (as measured by either the difference in absolute value or the 

root sum square of the differences of the active colors) are considered to be members 

of the same unit. Those whose color is close are considered to be friends. Those whose 

colors are far apart are considered to be enemies. Colors between those of enemy and 

friendly agents represent neutrals. That approach allows for multiple affiliations within a 

single scenario, as might be found in a crowd; or it can be used to establish command 

hierarchies, as would be found in a military organization (e.g., slightly different blue 

uniforms could represent different companies). 



Blueness 

0 

0 

255 

Greenness 

Figure 3� Two-color sidedness used to establish two-dimensional affiliation 

Sidedness, or color value, is governed by soft rules at the start of the simulation (agents 

can be initiated with more or less redness, for example) and can be changed over the 

course of the simulation by various events and actions, such as those listed in Table 2� 

Because not all colors are required to establish affiliation, one or two colors could be 

used to represent a different property—for example, fear, hunger, morale, or intelligence� 

Increases and decreases in that property can alter agents’ perception of one 

another� Alternatively, such a change can cause a behavior-change event, described 

below� 

Table 2� Currently implemented side-change events and actions 

50 

255 

• Being shot at 

– One change for each occurrence 

– Paintball weapons 

Arriving at way point 

Arriving at objective 

Detecting no leader from same unit 

All is well 

– Used to restore original conditions 

– Example: 

Temporarily no leader, then leader reacquired 


Unit 

Friendly 

Neutral 

Enemy (anything 

outside the 

outermost circle)

Behavior-Change Triggers 


The final feature of Pythagoras that is used to represent behavior is the behavior-change 

event/action, or trigger. When an agent experiences one of the events/actions listed in 

Table 3, the current behavior template is replaced by a new one, defined by new movement 

and shooting desires, new color-change values, and a new set of behavior-change 

triggers. For example, an agent can be set to walk up and down a street, as if on patrol, 

but when the agent is shot at, his behavior changes to look for protective terrain, such as 

a doorway. 

To enhance behavior-change triggers, the user can decide how they will be applied. 

A trigger can affect either an individual agent or a user-defined group of agents, or it 

may cause an agent to order subordinates to change their behavior (for example, “Sound 

the charge!”). For that purpose, leadership can be defined as either charismatic or 

hierarchical: 

• Under charismatic leadership, agents follow the highest or strongest leader. 

• Under hierarchical leadership, agents follow the lowest ranking leader whom they 

consider to be their leader (troops follow the sergeant, who follows the major, who 

follows the general). Thus, orders can ripple through a group of agents, much as 

they would in a military organization. 

As usual in Pythagoras, the behavior-change threshold values are governed by soft rules, 

so some agents will be more resistant to change. In addition, an agent can be assigned an 

obedience value that determines, at random, whether the agent will accept or reject an 

ordered behavior-change event/action. 

Because the behavior template for an agent includes new triggers, and each template 

is uniquely named, a series of templates can be constructed to represent a complex 

behavior tree or network, with agents moving from one behavior to another as a scenario 

Table 3. Currently implemented behavior-change triggers 

Events/actions that cause agent to change behavior include 

– Being shot at 

– Detecting enemy 

– Detecting friend 

– Arriving at way point or objective 

– Suffering friendly casualties (fewer than x% 

known remaining) 

– Losing leader (no leader within d) 

– Red, green, or blue becoming greater or less than c 

– Absolute time step 

– Relative time step 

Trigger reads new, complete, explicitly named behavior template (including setting 

new triggers) 

Delay before behavior takes effect (future capability), which simulates communication/ 

spinup time 

x = Force strength 

d = Distance 

c = Color value 



unfolds. Because they are separate objects, different agent types can share the behavior 

templates, and there is no practical limit to the number of templates that can be created. 

Weapon Options 

Pythagoras allows agents to carry as many as three different weapons. Weapons can be 

either direct fire (which requires a line of sight) or indirect fire (which does not): 

• Direct-fire weapons have range-dependent probabilities of hit—and of kill, given a 

hit—which may be modified by the target agent’s vulnerability. 

• Indirect-fire weapons have circular-error-probable accuracies and lethal radii, both 

of which may be range-dependant. 

An indirect-fire weapon’s lethal radii can be modeled using either the traditional Carlton 

damage function or a “cookie-cutter” blast. The Carlton damage function describes the 

damage radiating out from a hit point through the following equation: 

where Pk is the probability of kill, distance is the distance of the target from the impact 

point, and radius is the size of the blast radius. The cookie-cutter blast causes an equal 

amount of damage to all objects within the blast radius, regardless of their distance from 

the impact point. Both weapon types have input rates of fire and limited ammunition. 

In Pythagoras, the target may be suppressed for multiple time steps by a hit by a directfire 

weapon or a near miss by an indirect-fire weapon that does not kill the target. 

Suppressed agents do not move, sense, or shoot, but they recover those capabilities after 

a user-input amount of time. At the user’s discretion, kills can be random (stochastic), 

deterministic (fractional damage), or a combination of both. 

Agents can also change each other’s colors, by using military countermeasures or 

nonlethal weapons that can act as paintball guns. An example of a nonlethal weapon 

would be propaganda that alters an agent’s affiliation in some way. Propaganda in the 

form of leaflets can be modeled as a direct-fire weapon aimed at a specific target. On 

the other hand, preaching or any other form of public speech or exhortation can be 

modeled as an indirect-fire weapon, aimed in a general direction and affecting everyone 

within range. 

Agents will automatically shoot at enemies within range, unless they are given a “hold 

fire” command that allows them to shoot only if fired on within a user-specified number 

of time steps. The user can assign agents multiple weapons and set the weapon selection 

criteria to be based on either the highest probability of hit (best chance that the target 

will be suppressed) or the lowest probability of kill (for a nonlethal situation). 

Multiband Sensors 

Sensors are also abstracted. Each agent may have up to three, each of which operates in a 

specific signature band, labeled A, B, or C. The sensors have a range-dependent probability 

of detection, which is modified by intervening terrain and a target agent’s detectability. 

For example, signature band A could be the bandwidth of the naked eye and signature 

band B might describe the bandwidth of an infrared device. A terrain feature, such as 

foliage, would thwart the naked eye’s view, but an infrared device could “see” the 

52 

P=e 

k 

–[( distance × distance)/( radius × radius)] 

, 

Technology Review Journal • Spring/Summer 2003


thermal image of a camouflaged person standing in the foliage. Such foliage could be 

modeled in Pythagoras as having a concealment value of 100% in band A and 0% in 

band B. 

Sensors also have a field of view and, for modeling humans, a probability that the agent 

is looking forward (i.e., in the direction of travel), to the side, or to the rear. Terrain 

features reduce the probability of line of detection differently in each band. 

Representation of Terrain 

All agents exist in a user-defined playbox of up to 1000 × 1000 pixels. On the playbox, 

a user can create terrain features—polygons that have a floor, a ceiling, and factors for 

mobility; concealment in each of the three signature bands; and protection that reduces 

the weapon’s effectiveness. Currently, a pixel can be associated with at most one terrain 

feature. Agents can either move on the terrain or floor or operate at an altitude. 

Sample Scenarios 

Pythagoras has two major advantages: 

• It can be used quickly to assess various sample scenarios. 

• It can be combined with more complex and detailed models to provide insights into 

situations that may not be possible with other simulations. 

Rapid prototyping of scenarios, weapons, sensors, behavior patterns, etc., allows users 

to undertake complex problems in new ways without the burden of months of software 

development. Several sample scenarios are discussed below. 

Village Patrol. We have used Pythagoras to study crowd behavior in an antiterrorist/ 

force protection scenario, represented as a village patrol, developed for the Marine 

Corps to evaluate various night-vision devices in peacekeeping operations. Figure 4 

shows a screen shot of the “play forward” capability of the Pythagoras GUI for that 

scenario. The scene is a village with buildings, parks, and streets, represented in Figure 4 

as large areas of color—e.g., the geometric shapes such as rectangles and trapezoids 

denote buildings. The blue dots represent Marines, the red dots are peaceful villagers, 

and the orange dots are hostile villagers. The hostiles include a terrorist leader, located 

in a religious structure, who can communicate with the hostiles, warning them of the 

presence of the Marines. 

Marine agents patrol the village at night, inspecting the villagers and looking for 

terrorists. The Marines are directed in part by a scout/sniper team that is strategically 

placed to help spot villagers. The villagers and terrorists alike move toward the food 

distribution point at the harbor at the top of the screen. Peaceful villagers, once 

approached by Marines and found to have proper identification and no weapons, are 

directed to the food distribution point. Hostile villagers attempt to avoid the Marines 

and are shackled in place after the Marines find and inspect them. Measures of effectiveness 

(MOEs) include the number of villagers detected and fed, the number of 

hostiles shackled, and the number of hostiles reaching the food distribution point, a 

potentially disastrous event. 

We first used this scenario to establish a night-vision-capability base case by modeling 

the probability of detection for the Pythagoras sensors, applying the results of physics- 



Road 

Figure 4. Antiterrorist/force protection in village patrol scenario 

based models of various night-vision capabilities, e.g., MODTRAN, IICCD, NVTherm/ 

Acquire, IIMRC, and SSCAM. The models considered a variety of climatic conditions 

(e.g., desert or tropical) and ambient light conditions (e.g., cloudy night or quarter 

moon). To gain insight into the benefits of various devices and mixes of devices in a 

fairly traditional peacekeeping scenario, we then repeated the base-case runs, distributing 

various mixes of new night-vision devices among the Marines, and compared the 

resulting MOEs to one another and to the base-case MOEs. 

The scenario itself was built in a few days, and the sensor capabilities were altered by 

changing the eXtensible Markup Language (XML) files in a batch mode or by substituting 

one XML data block for another. We made the entire analysis proceed quickly, so 

that hundreds of cases could be analyzed. 

Battle of Midway. To represent human behaviors of opposing military forces, a U.S. 

Naval Academy midshipman majoring in history has used Pythagoras to study the 

options available to the Japanese Admiralty at the Battle of Midway. Historically, when 

the Japanese learned of the presence of U.S. aircraft carriers, they changed the weapon 

loads on their attack aircraft from bombs (which they planned to use against Midway 

Island) to torpedoes. Alternatively, the Japanese commander could have sent the aircraft 

to attack the U.S. fleet with the already-loaded bombs. Or he could have decided to use 

fighter aircraft as escorts to the bombers, allowing more bombers to penetrate our 

fighter defenses. 

54 

WP1 

WP5 

WP1 

Agent’s name 

WP1 

WP1 

WP1 

WP1 

WP1 

WP2 

WP1 

WP4 

WP2 

WP1 

WP5 

WP1 

WP6 WP3 WP6 WP3 

Body of Water 

WP1 

WP4 

WP1 WP2 

WP1 

WP0 

WP8 

WP1 


WP4 

WP1 

WP3 

WP1 

WP4 

WP1 

WP2 

River 

WP1 

WP1 

WP8


The midshipman first created a base case from the historical record, setting a scale for 

the battle (in terms of miles per pixel), speeds of the combatants (pixels per time step), 

and various sensor and weapon capabilities. He estimated the capabilities using the 

historical record for ships sighted, weapons launched, and ship damage in the base case. 

He then altered the decision made by the Japanese, sending the bombers alone in one 

case and adding some of the available fighter escorts in another. 

He found that the results on the Japanese carrier fleet were the same—all four carriers 

were sunk regardless of the Japanese admiral’s decision. However, the decision to send 

the attack aircraft armed with bombs would have resulted in the loss of one to two U.S. 

carriers, had they gone in alone; or two to three U.S. carriers, had they gone with escorts 

and detected the U.S. carrier that was operating alone. Since the Japanese at the time 

still had carriers operating in the Aleutians and the Coral Sea, and the United States had a 

total of just three carriers in the Pacific, the strategic result could have been dramatically 

different, delaying the U.S. counteroffensive in the Pacific. 

The midshipman was able to build the base case in a few days, calibrate it, and complete 

the model runs in less than one week. 

Clearing Shallow-Water Obstacles. The Marine Corps was searching for a near-term 

solution to the problem of shallow-water obstacles used to disrupt or defeat a Marine 

Corps surface assault. One proposed option was to use bombs—specifically, the 2000-lb 

Joint Direct Attack Munition (JDAM)—to clear shallow-water obstacles and mines. A 

JDAM could use impulse and overpressure to detonate mines close to the explosion. 

More distant mines would be pushed aside by the blast plume, which propagates well in 

water. That capability was tested at Eglin Air Force Base, Florida, in a shallow pond, 

carefully measuring the effects of various sizes of bombs in various depths of water. The 

necessary number of bombs remained to be determined, as well as spacing and delivery 

accuracy. The question posed to Project Albert was, “Could Pythagoras help at all?” 

In answering that question, it was ascertained that, while physics can measure the 

behavior of objects in the physical world, Pythagoras can measure behaviors as well. To 

use Pythagoras, we had to reproduce in Pythagoras’ terms the physical behavior of the 

various components of the system. Mines and obstacle agents were created, as were 

amphibious assault vehicle (AAV) agents. 

The AAV agents’ behavior was modeled such that they maintained specified spacing 

between one other as they moved through a series of way points. That behavior allowed 

the AAVs to form a ragged column and move ashore. Each AAV stopped whenever it 

encountered an obstacle, because the obstacle would suppress the AAV by firing a 

nonlethal weapon at it. However, the mine would fire a lethal weapon at the AAV at the 

range of half its width, representing the effect that resulted when the AAV hit the mine. 

With just one shot per mine, each mine killed at most one AAV. 

To enable the JDAMs’ effects to work properly in Pythagoras, two components were 

required: destruction and movement. To model the destruction and movement effects, a 

bomber agent (B-2) was created to drop the JDAMs on hit-point agents. The placement 

of the hit points represented the various options for weapon delivery and overall 

accuracy, combining target location error and weapon delivery error into a single offset 

from the weapon aim point. The mines and obstacles initially perceived the aim points to 

be neutral, because appropriate sidedness (color) values were used. However, when the 

hit points were actually attacked by an indirect-fire weapon—the JDAM—all mines that 



were close enough to the explosion were detonated using Pythagoras’ cookie-cutter 

blast capability. 

However, because the aim points were modeled with a vulnerability setting of zero, 

they were unharmed by the JDAMs’ effects—so only their color was changed through 

Pythagoras’ paintball weapon capability. The aim points were also assigned a nonzero 

leadership value. When the aim points’ color changed, the mines and obstacles perceived 

the aim points to be their leaders and were assigned a behavior to move away from their 

leader to a distance equal to the blast plume of the bomb. When the JDAM impacts 

were spaced in time, some obstacles were blown forward along the lane that was 

being cleared through the obstacles. They were then blown backward along the same 

lane by a subsequent bomb, creating a seesaw effect. 

We found that, when the AAVs had poor ability to navigate through the lane created by 

the JDAMs, their survivability was even worse than if no JDAMs had been dropped at all, 

because the mines that were blown out of the channel combined with mines that were 

unaffected, resulting in a much denser minefield than was originally there. Although the 

result is intuitive, none of the analysts involved thought of that outcome until it was 

observed in Pythagoras. Thus, the lanes must be marked well enough to avoid navigation 

errors and must be wide enough to allow safe passage. 

Competing for Hearts and Minds. A test scenario demonstrated the use of soft rules. 

A set of villagers was created whose colors varied randomly from shades of red to 

shades of blue. A set of peacekeepers, armed with short-range, nonlethal weapons, was 

sent into the village. The short-range weapons represented leaflets or candy bars. A 

villager receiving a leaflet became more blue and friendly to the peacekeepers. Simultaneously, 

a charismatic enemy organizer in the town hall was using an indirect-fire, widearea-effect 

weapon—a bullhorn. Exposure slowly turned the villagers deeper red. Once 

red enough, the villagers perceived the charismatic enemy organizer to be their leader 

and moved off to the town hall. (One variant gave them rocks to throw at the peacekeepers, 

once they became hostile.) 

The peacekeepers were typically able to placate only a limited number of villagers, the 

rest going to the town hall to become followers of the charismatic organizer. Occasionally, 

however, when all remaining villagers had been pacified, a few peacekeepers would 

head to the town hall to attempt to turn some of the followers back into villagers. 

Eventually, a steady-state condition was created between the number of villagers and the 

number of followers. In one case, the charismatic leader ran out of batteries for his 

bullhorn. Soon the peacekeepers moved up to the town hall and pacified all of the villagers. 

Once the source of their discontent had been eliminated, pacification was easy. 

Summary 

The combination of changing color, changing strength of desire or motivation, behaviorchanging 

events/actions, and group and individual dynamics—all present in the current 

Pythagoras prototype—has already demonstrated that this new capability offers a 

powerful, flexible way to represent human behavior in military modeling and simulation. 

Soft rules allow each agent (or object, in a traditional legacy simulation) to be created 

slightly or greatly different from other agents of the same class. In a combat model, for 

example, some troops would be better marksmen, braver, or more obedient than others. 

56 



Pythagoras’ development continues with additional features, new desires and triggers, 

and other agent capabilities. Its application to various military problems is only now 

being uncovered, but agent-based simulation tools are the future of military modeling 

and simulation. Pythagoras will help to lead the way. 

Summary 

1. U.S. Marine Corps, Project Albert Web site, http://www.projectalbert.org or http:// 

mcwl.quantico.usmc.mil/divisions/albert/index.asp. 

Author Profiles 

Edmund J. Bitinas, an operations research analyst for 

Northrop Grumman Mission Systems’ Information and 

Technical Services Division, Systems Analysis and Engineering, 

has specialized in developing military models and 

simulations for more than 24 years. He designed and developed 

Combat IV and has applied it to more than 50 different 

campaign-level studies and analyses. He has supported the 

Ballistic Missile Defense Organization on Theater Missile 

Defense campaign-level issues, performed campaign studies 

of the Joint Strike Fighter for the Turkish Air Force and 

Singapore Air Force, and supported the U.S. Air Force Air 

Combat Command in the 2001 Quadrennial Defense Review, 

also performing campaign analyses. Mr. Bitinas currently 

supports the U.S. Marine Corps on a variety of analysis tasks. 

He is also the lead analyst for the Marine Corps’ participation 

in the development and testing of the Joint Wargaming 

System. In addition, he is designing software for Project 

Albert. He holds a BS in computer science and an MS in 

operations research from the Illinois Institute of Technology. 

edmund.bitinas@ngc.com 

Zoe A. Henscheid, an operations research analyst for 

Northrop Grumman Mission Systems’ Information and 

Technical Services Division, has supported a variety of 

analysis tasks for the U.S. Marine Corps. She has established 

baseline ammunition requirements for the proposed High 

Mobility Artillery Rocket System, assessed current and 

potential weapon system capabilities across several 

Expeditionary Fire Support missions, and established a 

multiattribute value model used to assess multirole radar 

system alternatives. She holds a BS in industrial engineering 

from the University of Illinois, Champaign-Urbana, and has 

completed graduate courses in industrial engineering. 

zoe.henscheid@ngc.com 



58 

Lap V. Truong, a software engineer for Northrop 

Grumman Mission Systems’ Information and Technical 

Services Division, has specialized in software development 

for more than six years. He supported the development 

of a secure Internet Web site for the Security and 

Exchange Commission’s Electronic Data Gathering 

Analysis and Retrieval System. He holds an MS in computer 

science with a concentration in software engineering 

from George Mason University. He is pursuing an MS 

in technology management at George Mason University. 

lap.truong@ngc.com

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