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Placement by Thermodynamic

Simulated AnnealingCSE624 Heuristic Optimization

Mahmud Rasih ÇELENLİOĞLU

October 2013

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Outline

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• Placement Problem

• Contribution of Paper

•

Proposed Method

• Results

• Conclusion

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Integrated Circuit Placement Problem

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The placement quality affects both the area and

speed of circuits.

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Contribution of the Paper

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• In combinatorial optimization problems, SA issuccessfull.

• However, SA requires costly experimental studies infine tuning the most suitable annealing schedule.

• A new schedule is derived from thermodynamiclaws.

• Temperature in this method is free to evolve and itsvalue is continuously updated from the variation ofstate functions as the internal energy and entropy.

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Parameters & Functions

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• T0 = -avg(abs( Δ C))/ ln(P) & Tend = 0.0025

ΔC: cost variationLn(P): high probability of acceptance

• How to find temperature T?

Derived from 1. & 2. thermodynamic laws Rule 1: Conservation of total energy Rule 2: Efficiency is always lower than %100

•

Cost Evaluation Function Bounding Box

• What is stopping condition?

T < Tend && T is stabilized

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Bounding Box

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span of BB in direction X & Y

average channel capacity in track X, Y

(constant)compensates underestimated area of multiterminal nets

(depends on the # of terminals of net n)(n <= 3 then q=1, n = 50 then q=2.79 )

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Probability of Accepting New Solution

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• In physics, the Boltzmann factor is a weighting factor that determines the relative probability of a particle to be in a state in a multi-state system in thermodynamic equilibrium (there are no netflows of matter or energy) at temperature T

• ΔC = C B - C A

accept if cost is decreased

Boltzman Factor

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Thermodynamic Simulated Annealing

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• It provides an alternative method to performcooling close to equilibrium without experimentaladjustments

• TSA is a reversible process that is intermediate statesare also equilibrium states

• Temperature is free to evolve (not controlled) butcan be measured from thermodynamic laws

cost variation

entropy variation

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Thermodynamic Simulated Annealing

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• In information theory, Shannon entropy quantifiesthe expected value of the information contained ina message (ΔI = -ln(P) )

• Δ I = -ln(P) is converted to Δ S = ln(P)

set of transformations accepteduntil kth iteration set of movements tried withincrement in cost until kth iteration

run-time/quality trade off

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• Negative values appear in initial stages whenC i > C 0. To prevent this;

Thermodynamic Simulated Annealing

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increment in costno change in entropy

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--swap 2 blocks or move--block to an empty position--Bounding Box

--Boltzmann Factor

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• Range limiter: Maximum distance that a block canbe moved is linearly shortened with temperature

• It is calculated once the 80% of the acceptancerate is reached

Performance Improvement

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Results

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Results

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Results

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Conclusion

• TSA provides a different cooling schedule derivedfrom thermodynamic laws

• Temperature drop is not controlled externally butcomputed from current state

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Thank You

&

Questions ?