Pythagoras is a multi-sided agent-based model (ABM) created to support the growth and refinement of the U.S. Marine Corps Warfighting Laboratory's's Project Albert. Anything with a behavior can be represented as an agent. The interaction of the agents and their behaviors can lead to unexpected or emerging group behaviors, which is the primary strength of this type of modeling approach. As Pythagoras has grown in capability, it has been applied to a wide variety of tactical, operational and campaign-level topics in conventional and irregular warfare.
Pythagoras offers a unique set of capabilities in the area of agent-based simulations:
Irregular Warfare Pythagoras is best employed to study situations that are not well represented in traditional, legacy simulations. An illustrative example is an Improvised explosive attack on a vehicle convoy. Figure 1 shows a convoy of blue vehicle agents traveling down a road in an urban setting. There are three improvised explosive device agents emplaced along the roadside, and a triggering agent alongside the building. The convoy agents are told to follow one another, except for the leader agent at the head of the column, whose behavior is to drive along the road.
Figure 2 shows the situation after two of the vehicles have passed the corner of the building, 13 time steps after Figure 1. The triggering agent's behavior is to watch for blue vehicles. Upon seeing two vehicles, the triggering agent orders the IEDs to change their behavior from completely passive (do nothing) to aggressive (attack!). The IEDs explode, killing two convoy vehicles, which become transparent, and damaging two others, which change their color. The IEDs did not attack the convoy until ordered to do so by the triggering agent. This simple scenario was constructed by one analyst in about two hours, and illustrates both the ease of use and the applicability of Pythagoras to many combat and non-combat analysis situations. This scenario was used to examine alternatives for convoy protection, such as IED
Agent-based simulations create software entities that are capable of responding to their perceived or actual situations based upon sets of decision rules. The interactions among different agents can create autonomous and emergent (i.e., unplanned and unforeseen) behavior. Pythagoras introduces new capabilities to modeling and simulation, such as “soft” decision rules, dynamic affiliation, behavior-change triggers, and non-lethal weapons effects.
Soft decision rules may create agent behaviors that emerge as unique within any class of agents that were originally defined as identical (except for incidental variables such as agent location). The soft decision rules can have a narrow range, indicating a well disciplined, homogenous group whose decision rules are similar or identical, or they can have a wide range, providing for significant variation among individuals. Soft decision rules can be used with all of an agent's attributes, as well as leadership style and effectiveness, marksmanship, engagement desire, group affiliation preferences and other characteristics of the agent.
Dynamic affiliation allows agents to change sides as a function of events and actions that occur as the simulation plays out. One agent can change another agent's affiliation using influence techniques, such as propaganda, through one-time actions that happen to the agent, or affiliation changes may simply evolve across multiple actions.
Behavior-change triggers allow agents to change their behavior as a function of events or actions. Agents can change from aggressive to passive behaviors as their attributes change or due to some action taken by a friend or enemy. Behavior changes can be induced by individual events, group events, or can be ordered by leader agents. There is no limit to the number of behaviors that can be defined by the user. These alternate behaviors can be chained together to create complex behavior trees. Non-lethal weapons not only cause suppression, they may also change the affiliation or attributes of an agent. Suppression causes an agent to cease activity for a period of time. The changed attributes or affiliations may cause a behavior change trigger to occur or may cause other agents to interact with the changed agent in a different way. Pythagoras retains many legacy simulation capabilities. It includes direct and indirect fire weapons, sensors, communication devices and terrain. Agents can represent people, weapon systems, or other objects. Both traditional combat and new, non-combat scenarios can be represented.
Pythagoras is continuously being improved with new features and capabilities. It has recently added generic resources, generic attributes, communication devices, and expanded its recording of various measures of effectiveness for post-run analysis.
The diverse set of applications modeled with Pythagoras attest to its versatility and utility. Pythagoras has been used to study improvements to squad echelon night vision equipment in a peacekeeping scenario. It has been used to study tactics, techniques and procedures in response to a weapon of mass destruction attack on a military installation. Students at the Naval Academy have used it to study historical battles as diverse as The Battle of Ia Drang (one of the first US Army battles in Viet Nam), The Battle of Midway, and Chancellorsville. It was used to study tactics for using air-delivered ordnance to clear shallow water obstacles and mines. It is currently being used to support two different studies (one by Northrop Grumman and the other by students at the Naval Postgraduate School) of population dynamics in areas of the world where an insurgency is possible and the Marines are sent in to provide disaster relief after an earthquake.
Pythagoras runs on a PC or any other platform that supports Java 1.5 and JAXB 2.0. It is particularly suitable for data farming — executing large numbers of repetitions of parametric runs to identify areas of unexpected behaviors and nonlinear results in a coevolving landscape.
Its heritage traces back to Project Albert, an international project dedicated to research in the human aspects of warfare, such as intangibles, co-evolving goals and non-linear relationships.
Pythagoras originally began as a method by which the existing US Marine Corps-provided Archimedes model could be enhanced, modified, or controlled to enable it to run large problem sets on multiple platforms and be analyzed via data farming techniques on the Gilgamesh platform located at the Maui High Performance Computing Center (MHPCC).