Genetic Algorithms and Genetic Programming for Multiscale Modeling

249 Pages·2007·2.35 MB·English

by  Kumara Sastry

Genetic Algorithms and Genetic Programming for
Multiscale Modeling: Applications in Materials
Science and Chemistry and Advances in Scalability
Kumara Sastry
IlliGAL Report No. 2007019
September 2007
Illinois Genetic Algorithms Laboratory
University of Illinois at Urbana-Champaign
117 Transportation Building
104 S. Mathews Avenue Urbana, IL 61801
Office: [phone]
Fax: [phone]

(cid:2)c 2007 by Kumara Narasimha Sastry. All rights reserved.

GENETIC ALGORITHMS AND GENETIC PROGRAMMING FOR MULTISCALE
MODELING: APPLICATIONS IN MATERIALS SCIENCE AND CHEMISTRY AND
ADVANCES IN SCALABILITY
BY
KUMARA NARASIMHA SASTRY
MENGR., Birla Institute of Technology & Science, 1998
M.S., University of Illinois at Urbana-Champaign, 2001
DISSERTATION
Submitted in partial fulfillment of the requirements
for the degree of Doctor of Philosophy in Systems and Entrepreneurial Engineering
in the Graduate College of the
University of Illinois at Urbana-Champaign, 2007
Urbana, Illinois

Abstract
Effective and efficient multiscale modeling is essential to advance both the science and synthesis
in a wide array of fields such as physics, chemistry, materials science, biology, biotechnology and
pharmacology. This study investigates the efficacy and potential of using genetic algorithms for
multiscalematerialsmodelingandaddressessomeofthechallengesinvolvedindesigningcompetent
algorithms that solve hard problems quickly, reliably and accurately. In particular, this thesis
demonstrates the use of genetic algorithms (GAs) and genetic programming (GP) in multiscale
modeling with the help of two non-trivial case studies in materials science and chemistry.
The first case study explores the utility of genetic programming (GP) in multi-timescaling
alloy kinetics simulations. In essence, GP is used to bridge molecular dynamics and kinetic Monte
Carlo methods to span orders-of-magnitude in simulation time. Specifically, GP is used to regress
symbolically an inline barrier function from a limited set of molecular dynamics simulations to
enable kinetic Monte Carlo that simulate seconds of real time. Results on a non-trivial example of
vacancy-assisted migration on a surface of a face-centered cubic (fcc) Copper-Cobalt (CuxCo1−x)
alloy show that GP predicts all barriers with 0.1% error from calculations for less than 3% of active
configurations, independent of type of potentials used to obtain the learning set of barriers via
molecular dynamics. The resulting method enables 2–9 orders-of-magnitude increase in real-time
dynamics simulations taking 4–7 orders-of-magnitude less CPU time.
The second case study presents the application of multiobjective genetic algorithms (MOGAs)
in multiscaling quantum chemistry simulations. Specifically, MOGAs are used to bridge high-
level quantum chemistry and semiempirical methods to provide accurate representation of complex
molecular excited-state and ground-state behavior. Results on ethylene and benzene—two com-
mon building-blocks in organic chemistry—indicate that MOGAs produce high-quality semiempir-
ical methods that (1) are stable to small perturbations, (2) yield accurate configuration energies on
iii
untestedandcriticalexcitedstates, and(3)yieldab initio qualityexcited-statedynamics. Thepro-
posedmethodenablessimulationsofmorecomplexsystemstorealisticmulti-picosecondtimescales,
well beyond previous attempts or expectation of human experts, and 2–3 orders-of-magnitude re-
duction in computational cost.
While the two applications use simple evolutionary operators, in order to tackle more complex
systems, their scalability and limitations have to be investigated. The second part of the thesis
addresses some of the challenges involved with a successful design of genetic algorithms and ge-
netic programming for multiscale modeling. The first issue addressed is the scalability of genetic
programming, where facetwise models are built to assess the population size required by GP to
ensureadequatesupplyofrawbuildingblocksandalsotoensureaccuratedecision-makingbetween
competing building blocks.
This study also presents a design of competent genetic programming, where traditional fixed
recombination operators are replaced by building and sampling probabilistic models of promising
candidate programs. The proposed scalable GP, called extended compact GP (eCGP), combines
the ideas from extended compact genetic algorithm (eCGA) and probabilistic incremental program
evolution (PIPE) and adaptively identifies, propagates and exchanges important subsolutions of a
search problem. Results show that eCGP scales cubically with problem size on both GP-easy and
GP-hard problems.
Finally, facetwise models are developed to explore limitations of scalability of MOGAs, where
the scalability of multiobjective algorithms in reliably maintaining Pareto-optimal solutions is ad-
dressed. The results show that even when the building blocks are accurately identified, massive
multimodality of the search problems can easily overwhelm the nicher (diversity preserving oper-
ator) and lead to exponential scale-up. Facetwise models are developed, which incorporate the
combined effects of model accuracy, decision making, and sub-structure supply, as well as the effect
of niching on the population sizing, to predict a limit on the growth rate of a maximum number
of sub-structures that can compete in the two objectives to circumvent the failure of the niching
method. The results show that if the number of competing building blocks between multiple objec-
tives is less than the proposed limit, multiobjective GAs scale-up polynomially with the problem
size on boundedly-difficult problems.
iv