Cellular Automata and AgentBased Simulation

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Cellular Automata andAgent-Based Simulation
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Discrete-Time Simulation

• Discrete-Time simulation
• Simulation time advances discretely in uniform
  time steps j 1, 2, 3,
• s(j) state at simulation time j
• i(j) input at simulation time j
• Next state
• Function of the current state and current input
• s(j1) F(s(j), i(j)) where F is the next state
  function
• Example Up/Down Counter
• s an n-bit integer N2n
• i control input (0count down 1count up)
• s(j1) s(j)-1 mod N if i(j)0
• s(j1) s(j)1 mod N if i(j)1

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Cellular Automata

• Discrete-time operation
• State space is discretized into cells in a
  k-dimension rectangular grid
• Neighborhood of a cell refers to those cells
  adjacent to that cell (including diagonals)
• Example in 2D cellular automata, each cell has 8
  neighbors
• Next state of cell a function of current state of
  cell and current state of neighbors (locality)
• Example vehicle traffic where cell represents a
  road segment

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Example Game of Life (GOL)

• Cell state
• 0 dead
• 1 alive
• Next state rules
• Survive a live cell remains alive if it has 2 or
  3 neighbors in the 1 state
• Deaths a live cell becomes dead if it has 0 or 1
  neighbors (loneliness) or if it has 4 or more
  neighbors (overcrowding)
• Birth a dead cell becomes alive if it has
  exactly 3 neighbors that are alive otherwise it
  remains dead

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Examples
Stable patterns
Oscillating pattern
Cycle of pattern that moves

• Source Zeigler, Praehofer, Kim, Theory of
  Modeling and Simulation, Academic Press, p.43.

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Another Example
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Observations

• Cellular automata System consists of many
  autonomous agents (cells)
• Behavior of each agent defined by simple rules
• Each agent only utilizes local information
• System-wide behaviors can emerge from the
  collection of autonomous agents, e.g.,
• Dynamic behavior dies out
• Periodic behavior
• Chaotic outcome highly sensitive to small
  disturbances, e.g., small changes in initial
  conditions have a large affect (e.g., Butterfly
  effect)
• Self-organizing random unordered configurations
  evolve to states of less entropy (outcome highly
  insensitive to large disturbances)
• Unpredictable (not periodic) behavior, but
  showing regular patterns
• Many systems of practical interest exhibit these
  kinds characteristics (biological systems, e.g.,
  ant foraging or flocks of birds, schools of fish,
  spread of disease, economic systems, )

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Agents

• Agent-based simulations are often used to study
  these types of systems
• No standard definition of agents is universally
  accepted
• Agent characteristics
• A discrete, identifiable individual with a set of
  characteristics and rules governing its behavior
• Resides in an environment where it interacts with
  other agents
• Goal-directed
• Autonomous and self-directed
• Has the ability to learn and adapt its behaviors
  over time based on experience, e.g., rule that
  modify its rules of behavior

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Other Definitions

• An agent is any entity that can be viewed as
  perceiving its environment through sensors and
  acting upon its environment through effectors
  Russel and Norvig, 1995
• Intelligent agents continuously perform three
  functions Hayes-Roth, 1995
• perception of dynamic conditions in the
  environment
• action to affect conditions in the environment
• reasoning to interpret perceptions, solve
  problems, draw inferences, and determine actions
• Intelligent agents are software entities that
  carry out some set of operations on behalf of a
  user or another program with some degree of
  independence or autonomy, and in so doing, employ
  some knowledge or representation of the users
  goals or desires IBM White paper, 1995
• Autonomous agents are computational systems that
  inhabit some complex dynamic environment, sense
  and act autonomously in this environment, and by
  doing so, realize a set of goals or tasks for
  which they are designed Maes, 1995

Source Margaret Loper, Feb 2007
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Definitions continued

• Software agents are programs that engage in
  dialogs and negotiate and coordinate transfer of
  information Coen, 1995
• Autonomous agents are systems capable of
  autonomous, purposeful action in the real world
  Brustolini, 1991
• a hardware or (more usually) software-based
  computer system that enjoys the following
  properties Wooldridge and Jennings, 1995
• Autonomy agents operate without the direct
  intervention of humans or others, and have some
  kind of control over their actions and internal
  state
• Social ability agents interact with other agents
  (and possibly humans) via some kind of
  agent-communication language
• Reactivity agents perceive their environment,
  (which may be the physical world, a user via a
  graphical user interface, a collection of other
  agents, the INTERNET, or perhaps all of these
  combined), and respond in a timely fashion to
  changes that occur in it
• Pro-activeness agents do not simply act in
  response to their environment, they are able to
  exhibit goal-directed behavior by taking the
  initiative.

Source Margaret Loper, Feb 2007
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Agent Properties
Source Margaret Loper, Feb 2007
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Applications
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Example Power Market

• Examine impact of deregulation on market structure

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Agent-Based Model Development

• Identify agents, define agent behavior
• Identify agent relationships, interactions
• Develop agent-based models on framework
• Collect data
• Validate agent behavior models
• Run model, collect and analyze results
• Close ties to process-oriented simulations if one
  views each process as an agent

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Agent-Based Modeling

• Typically used when
• System naturally represented as autonomous agents
• Decisions and behaviors can be defined discretely
  (with boundaries)
• Important that agents adapt and change behaviors
• Important that agents learn and engage in dynamic
  strategic behaviors
• Agents have a dynamic relationship with other
  agents, and agent relationships form and dissolve
• Scaling up is important

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References

• Brustoloni, J., "Autonomous Agents
  Characterization and Requirements," Carnegie
  Mellon Technical Report CMU-CS-91-204,
  Pittsburgh Carnegie Mellon University, 1991.
• Coen, M., The SodaBot Agent, http//www.ai.mit.e
  du/people/sodabot/slideshow/total/P001.html.
• Franklin, S. and A. Graesser, Is it an Agent, or
  just a Program? A Taxonomy for Autonomous
  Agents, Proceedings of the Third International
  Workshop on Agent Theories, Architectures, and
  Languages, Springer-Verlag, 1996,
  http//www.cs.memphis.edu/franklin/AgentProg.html
  .
• Hayes-Roth, B., "An Architecture for Adaptive
  Intelligent Systems," Artificial Intelligence
  Special Issue on Agents and Interactivity, 72,
  329-365, 1995.
• Honavar, V., Intelligent Agents and Multi Agent
  Systems, A Tutorial presented at IEEE CEC 99,
  Washington, D.C., July 1999.
• IBM, The IBM Agent, http//activist.gpl.ibm.com
  81/WhitePaper/ptc2.htm.
• Maes, P. Agents That Reduce Work and Information
  Overload. Software Agents. Cambridge, MA MIT
  Press. 1997.
• Russell, S. and Norvig, P. Artificial
  Intelligence A Modern Approach. New York
  Prentice-Hall 1995.
• Wooldridge, M. and N. Jennings, "Agent Theories,
  Architectures, and Languages a Survey," in
  Wooldridge and Jennings Eds., Intelligent Agents,
  Berlin Springer-Verlag, 1-22, 1995.