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Genetic Algorithms (GAs) Classical Monte Carlo (CMC) Application of GAs to atomic clusters Method overview Results and discussion
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Genetic algorithm - Monte Carlo hybrid method for finding stable geometries of atomic clusters
Application to carbon clusters
Nazım Dugan, Şakir ErkoçMETU, Physics Department
Outline
Genetic Algorithms (GAs)
Classical Monte Carlo (CMC)
Application of GAs to atomic clusters
Method overview
Results and discussion
Genetic Algorithms (GAs)Classical Monte Carlo (CMC)Application of GAs to atomic clustersMethod overviewResults and discussion
Genetic Algorithms (GAs)Classical Monte Carlo (CMC)Application of GAs to atomic clustersMethod overviewResults and discussion
GA Overview
Atomic systems >> 3N degrees of freedom (with empirical potentials)
Minimum potential energy >> maximum stability
Find global minimum on the Potential energy hypersurface
Fitness criteria >> Total potential energy of the system
Encoding :
111010001010100101000101
CTGA....
Genetic Algorithms (GAs)Classical Monte Carlo (CMC)Application of GAs to atomic clustersMethod overviewResults and discussion
Genetic Operations
MutationNatural selectionReproductionCrossover
100110010010100110101100 ........
101110010010100100101100 ........
0011001001
00011001000
1001
1001
001
10011001001
11010001001
10011001101
Genetic Algorithms (GAs)Classical Monte Carlo (CMC)Application of GAs to atomic clustersMethod overviewResults and discussion
-33 eV
-28 eV -32 eV -31 eV -26 eV
Genetic Operations
MutationNatural selectionReproductionCrossover
111010001010100101000101
Genetic Algorithms (GAs)Classical Monte Carlo (CMC)Application of GAs to atomic clustersMethod overviewResults and discussion
Genetic Operations
MutationNatural selectionReproductionCrossover
Genetic Algorithms (GAs)Classical Monte Carlo (CMC)Application of GAs to atomic clustersMethod overviewResults and discussion
100110010010100110101100 001110100011010000101001
100110010010010000101001
Genetic Operations
MutationNatural selectionReproductionCrossover
Genetic Algorithms (GAs)Classical Monte Carlo (CMC)Application of GAs to atomic clustersMethod overviewResults and discussion
We have to decide on
Population sizetoo low >> not enough diversity !!!too high >> not necessary !!!
Mutation ratetoo low >> lose diversity !!!too high >> mutants !!!
Reproduction typeasexualsexual >> how to combine individuals
Natural selection typenot big deal (select better with higher probability)elitism
Genetic Algorithms (GAs)Classical Monte Carlo (CMC)Application of GAs to atomic clustersMethod overviewResults and discussion
Genetic Algorithms (GAs)Classical Monte Carlo (CMC)Application of GAs to atomic clustersMethod overviewResults and discussion
random walkof atoms
if (ΔE < 0)accept if (ΔE > 0)
check convergence
if rand(0-1) < exp(- ΔE / kT)accept
LOOP
LOOP
2 4 6 8 10
-20
20
40
60
80
Genetic Algorithms (GAs)Classical Monte Carlo (CMC)Application of GAs to atomic clustersMethod overviewResults and discussion
Genetic Algorithms (GAs)Classical Monte Carlo (CMC)Application of GAs to atomic clustersMethod overviewResults and discussion
search over all phase space >> local optimization between GA steps >> search over local minima
geometric mutation operations
RotationAtom permutation
Geometric crossover(Deaven - Ho)
Genetic Algorithms (GAs)Classical Monte Carlo (CMC)Application of GAs to atomic clustersMethod overviewResults and discussion
Genetic Algorithms (GAs)Classical Monte Carlo (CMC)Application of GAs to atomic clustersMethod overviewResults and discussion
Generate N clusters randomly
MC local optimization
Natural selection
-29.6342 eV-28.9163 eV -33.3887 eV -28.8877
Genetic Algorithms (GAs)Classical Monte Carlo (CMC)Application of GAs to atomic clustersMethod overviewResults and discussion
Reproduction
Mutation (Rotation)
Mutation (Shrink)
MC local optimization (1st step)
Genetic Algorithms (GAs)Classical Monte Carlo (CMC)Application of GAs to atomic clustersMethod overviewResults and discussion
C20 animation
Genetic Algorithms (GAs)Classical Monte Carlo (CMC)Application of GAs to atomic clustersMethod overviewResults and discussion
Parallelization
Distribute individuals to available nodes
MC local optimization takes much more time >> all nodes do MC
GA operations takes no time >> master node gathers individuals and do GA
~100 % efficiency !!!
Genetic Algorithms (GAs)Classical Monte Carlo (CMC)Application of GAs to atomic clustersMethod overviewResults and discussion
Genetic Algorithms (GAs)Classical Monte Carlo (CMC)Application of GAs to atomic clustersMethod overviewResults and discussion
n = 11 n = 16
n = 20shrink 0.5
n = 38Shrink 0.85
Carbon clusters (Tersoff - Brenner potential energy function)
n = 12 n = 14
n = 22shrink 0.5
n = 32Shrink 0.8
n = 19
References
R.L. Johnston, Dalton Trans., 4193(2003)
B. Hartke, Chem. Phys. Lett. 240, 560(1995)
S.K. Gregurik, M.K. Alexander, B. Hartke, J. Chem Phys. 104, 2684(1996)
S. Hobday, R. Smith, J. Chem. Soc., Faraday Trans. 93, 3919(1997)
M. Iwamatsu, J. Chem Phys. 112, 10976(2000)
J. Zhao, R. Xie, J. Comp. Theoretical Nanoscience 1, 117(2004)
D.M. Deaven, K.M. Ho, Phys. Rev. Lett. 75, 288(1995)
Thank you