Simulated Annealing for Placement

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Simulated Annealing for Placement

• Adam Miller
• March 26, 2002

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Overview

• When is Simulated Annealing (SA) used?
• What is SA?
• How does SA work?
• Demonstrations of SA

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What is Annealing?

• Annealing is a physical process used to harden
  metals, glass, etc.
• Starts at a high temperature and cools slowly.
• Molecular arrangement
• Lowest energy state

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What is Simulated Annealing?

• SA is a process that attempts to find a global
  minimum in a specific cost function.
• Parallels annealing in several ways
• Cost Function
• Temperature

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How does SA work?

• Begin in an initial state.
• Evaluate cost function
• Make a change to the system
• Random change
• Deterministic change

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How does SA work?

• Reevaluate the cost function
• If cost is lower, accept unconditionally
• If cost is higher, accept based on probability,
  based on
• Temperature
• Cost

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How does SA work?

• Looping the algorithm
• Same temperature iterations
• Continual temperature decrease
• Ending the loop
• Cost function value
• Accepted Change Percentage
• Temperature Minimum

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Cost Functions

• Figure of merit based on the state of the system
• Simplified Calculation
• Estimation

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Cost Functions

• Examples in VLSI placement
• Wire length
• Number of crossings or layer changes
• Area
• Heat
• Delay
• Combinations of the above

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Random Changes

• Pros
• Simplified calculations
• Wide range
• Cons
• Ignored information
• Greater number of iterations

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Deterministic Changes

• Pros
• Fewer iterations
• Less information wasted
• Cons
• Method for determining best change varies
• Can take more time per iteration