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In collaboration with with Dr. Magnus
Rattray of Manchester University and Dr. Adam
PrügelBennett of Southhampton University, I have developed a
formalism for describing genetic algorithm evolution. This is based on
the dynamics of cumulants of a phenotypic trait in a population, and
uses maximum entropy inference and statistical mechanics techniques.
This has been shown to predict the dynamics of a finitesized
population very accurately on a number of problems. Recent
introductions can be found in references 2 and 12 below. The former
was a tutorial at the EvoNet Summer School on Theoretical Aspects of
Evolutionary Computing; the latter was an invited lecture at the
Russian Academy of Sciences.
The important question is: can this method be
used to predict effective learning parameters, such as the mutation
and crossover rates, and to test the effectiveness of different
representations and approaches.
 1

Magnus Rattray and Jonathan L. Shapiro.
Cumulative dynamics of a population under multiplicative selection,
mutation, and drift.
Theoretical Population Biology, 60:17  32, 2001.
(Available as an
eprint)
 2

J. L. Shapiro.
Statistical mechanics theory of genetic algorithms.
In L. Kallel, B. Naudts, and A. Rogers, editors, Theoretical
Aspects of Evolutionary Computing, pages 87  108. Springer, 2001.
(full paper)
 3

Jonathan Shapiro.
Genetic algorithms in machine learning.
In G. Paliouras, V. Karkaletsis, and C. D. Spyropoulos, editors, Machine Learning and Its Applications, volume LNAI 2049, pages 146  169.
Springer, 2001.
 4

J. L. Shapiro.
Does datamodel coevolution improve generalization performance of
evolving learner?
Lecture Notes in Computer Science, 1498:540  549, 1998.
(
abstract, full
paper)
 5

M. Rattray and J. L. Shapiro.
Noisy fitness evaluations in genetic algorithms and the dynamics of
learning.
In R. K. Belew and M. D. Vose, editors, Foundations of Genetic
Algorithms 4, pages 117  139. Morgan Kaufmann, 1997.
(
full paper ).
 6

A. PrügelBennett and J. L. Shapiro.
The dynamics of a genetic algorithm for simple Ising systems.
Physica D, 104:75114, 1997.
( abstract ,
full paper ).
 7

J. L. Shapiro and A. PrügelBennett.
Genetic algorithms dynamics in twowell potentials with basins and
barriers.
In R. K. Belew and M. D. Vose, editors, Foundations of Genetic
Algorithms 4, pages 102  116. Morgan Kaufmann, 1997.
 8

Jonathan Shapiro, Adam PrügelBennett, and Magnus Rattray.
A statistical mechanics analysis of genetic algorithms for search and
learning.
In S. W. Ellacott, J. C. Mason, and I. J. Anderson, editors, Mathematics of Neural Networks: Models, Algorithms and Applications, pages
318  323, 1997.
 9

David Corne and Jonathan L. Shapiro, editors.
Evolutionary Computing, volume 1305 of Lecture Notes in
Computer Science.
Springer, 1997.
 10

M. Rattray and J. Shapiro.
The dynamics of genetic algorithms for a simple learning problem.
Journal of Physics: A, 29:7451  7473, 1996.
( full paper ).
 11

Jonathan Shapiro, Magnus Rattray, and Adam PrügelBennett.
Maximum entropy analysis of genetic algorithms.
In K. M. Hanson and R. N. Silver, editors, Maximum Entropy and
Bayesian Methods, pages 303  310, 1996.
 12

J. L. Shapiro, M. Rattray, and A. PrügelBennett.
The Statistical Mechanics Theory of Genetic Algorithm Dynamics,
Plenary Lecture at the First International Conference on Evolutionary
Computation and Its Applications, Moscow, 1996.
(
full paper ).
 13

Jonathan L. Shapiro and Adam PrügelBennett.
Maximum entropy analysis of genetic algorithm operators.
Lecture Notes in Computer Science, 993:1424, 1995.
( abstract ,
full paper ).
 14

A. PrügelBennett and J. L. Shapiro.
An analysis of genetic algorithms using statistical mechanics.
Physical Review Letters, 72(9):1305  1309, 1994.
( abstract, full paper ).
 15

Jonathan Shapiro, Adam PrügelBennett, and Magnus Rattray.
A statistical mechanical formulation of the dynamics of genetic
algorithms'.
Lecture Notes in Computer Science, 865:17  27, 1994.
( abstract,
full paper ).
The following paper is by Magnus Rattray, who was doing a Ph.D. under my
supervision at the time it was written.
 L. M. Rattray, "The Dynamics of a Genetic Algorithm under
Stabilizing Selection", Complex Systems 9 p213234, 1995.
( abstract ,
full paper ).
Jonathan Shapiro
20040127