Parallel Simulated Annealing SE 295 Parallel Programming Practice Project

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Parallel Simulated AnnealingSE 295 Parallel
Programming PracticeProject

• Karthik Raman
• Supercomputer Education Research Centre

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Simulated Annealing Recap

• Heuristic for hard combinatorial optimisation
  problems or continuous optimisation
• Borrowed idea from condensed matter physics
  annealing of metals
• Perturb configuration of system
• Accept all moves that reduce cost
• Accept those that increase cost with low
  probability (Metropolis Criterion)

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Key Annealing Parameters

• T0 initial temperature
• ? Temperature Factor
• Length of run
• Stopping conditions
• Often decided by trial-and-error

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Exploration of Cooling Schedule Parameters
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TSPLIB

• Public database of TSP problems by Reinelt
• Wide variety of problems
• Symmetric TSP Euclidean Space
• Optimal tours known for many cases

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Multiple Independent Runs

• Processes start with same T0, ?, different
  initial configurations and different random
  number seeds
• Proceed for a fixed number of iterations and
  then 'interact'
• Strategies for redistribution?

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Redistribution of Solutions

• Genetic Crossover (Hiroyasu et al, 2002)
• Elitist strategy
• Why redistribute?

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Experiments with Redistribution

• T00.7 ?0.9
• T0 for second phase?
• Iterations in Phase I?
• Effect of redistribution on different datasets?

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berlin52
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pr1002
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pr299
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rl1304
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u574
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vm1084
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Comparison with existing algorithms

• DIMACS Challenge on TSP
• Optimal tours with program rankings available
• pr1002 rank 95 (total 134)
• rl1304 rank 95 (total 134)
• vm1084 rank 88 (total 100)

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Conclusions

• Redistribution improves quality of optimum
• Desirable especially for large datasets
• Effective utilisation of multiple processes
  (more useful work)

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Continuous optimisation

• Similar ideas as in combinatorial optimisation
• Similar parameters T0, ?, T0'
• Several test functions commonly used
• Rosenbrock
• Goldstein-Price

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Rosenbrock test function 2D
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Goldstein-Price Test function 2D
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Conclusions

• Redistribution requires more function evaluations
  
• Redistribution improves quality of optimum even
  in continuous optimisation
• Possibility of determining iterations in Phase I
  through exploratory experiments
• Other strategies for distribution e.g. Genetic
  crossover
• Improving execution time and optimum quality by
  fine-tuning cooling parameters

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References

• Press W H, Flannery B P, Teukolsky S A and
  Vetterling W T (1993), Numerical Recipes in C
  The Art of Scientific Computing, Cambridge
  University Press pp.444455.
• Karlsson P (2002) Simulated Annealing applied
  to the travelling salesman problem Technical
  Report, Uppsala University (Sweden).
• Hiroyasu T, Miki M and Ogura M (2000) Parallel
  Simulated Annealing using Genetic Crossover
  Proceedings of IASTED International Conference
  Parallel and Distributed Computing Systems
  pp.139144.
• Lee F-H A (1995) Parallel Simulated Annealing on
  a Message-Passing Multi-computer PhD Thesis,
  Utah State University.
• TSPLIB http//www.iwr.uni-heidelberg.de/groups/co
  mopt/ software/TSPLIB95/
• Siarry P, Berthiau G, Durbin F and Haussy J C E A
  (1997) Enhanced Simulated Annealing for Globally
  Minimizing Functions of Many Continuous
  Variables ACM Transactions on Mathematical
  Software 23209228
• DIMACS TSP Challenge Instance Comparison Page.
  http//www.research.att.com/dsj/chtsp/testform1.
  html