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Pythagoras: A New Agent-based Simulation System
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
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