Comparing Extremal and Hysteretic Optimization on the Satisfiability Problem

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?Comparing Extremal and Hysteretic Optimization
on the Satisfiability Problem

• Bruno Gonçalves Stefan Boettcher
• Emory University

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Contents

• Motivation
• Boolean Satisfiability
• Extremal Optimization
• Hysteretic Optimization
• Results
• Discussion

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Motivation
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Boolean Satisfiability and Ising Spin Glasses
Boolean Variable Clauses Broken Clauses Minimum
Nr Broken Clauses

• Ising Spin
• Coupling/Field
• Energy
• Ground state energy

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Extremal Optimization (1)

• Start with random configuration
• Order the variables by fitness
• Change variable of rank i with i chosen with
  (unconditionally)
• Repeat steps 2-4 Nmax times and return the lowest
  cost found

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Extremal Optimization (2)
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Extremal Optimization (3)
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Hysteretic Optimization (1)

• Start with fully magnetized state
• Vary external field from H0 to -?H0 to ?2H0, etc
• Stop when Hn ?n-1H0lt1

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Hysteretic Optimization (2)
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Hysteretic Optimization (3)
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Results

• http//www.ictp.trieste.it/zecchina/SP

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Discussion (1)

• EO is considerably slower but with better results
• EO works best for lower connectivities
• HO is faster but with poorer results
• HO seems to need high connectivities
• Gaussian bond weights

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Discussion (2)
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The End