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Simulated Annealing for Placement

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Annealing is a physical process used to harden metals, glass, etc. ... SA is a process that attempts to find a global minimum in a specific cost function. ... – PowerPoint PPT presentation

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Title: Simulated Annealing for Placement


1
Simulated Annealing for Placement
  • Adam Miller
  • March 26, 2002

2
Overview
  • When is Simulated Annealing (SA) used?
  • What is SA?
  • How does SA work?
  • Demonstrations of SA

3
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

4
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

5
How does SA work?
  • Begin in an initial state.
  • Evaluate cost function
  • Make a change to the system
  • Random change
  • Deterministic change

6
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

7
How does SA work?
  • Looping the algorithm
  • Same temperature iterations
  • Continual temperature decrease
  • Ending the loop
  • Cost function value
  • Accepted Change Percentage
  • Temperature Minimum

8
Cost Functions
  • Figure of merit based on the state of the system
  • Simplified Calculation
  • Estimation

9
Cost Functions
  • Examples in VLSI placement
  • Wire length
  • Number of crossings or layer changes
  • Area
  • Heat
  • Delay
  • Combinations of the above

10
Random Changes
  • Pros
  • Simplified calculations
  • Wide range
  • Cons
  • Ignored information
  • Greater number of iterations

11
Deterministic Changes
  • Pros
  • Fewer iterations
  • Less information wasted
  • Cons
  • Method for determining best change varies
  • Can take more time per iteration
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