Papers on Genetic Algorithms

In collaboration with with Dr. Magnus Rattray of Manchester University and Dr. Adam Prügel-Bennett 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 finite-sized 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.

Bibliography

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 e-print)

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 data-model co-evolution 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. Prügel-Bennett and J. L. Shapiro.
The dynamics of a genetic algorithm for simple Ising systems.
Physica D, 104:75-114, 1997.
( abstract , full paper ).

7

J. L. Shapiro and A. Prügel-Bennett.
Genetic algorithms dynamics in two-well 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 Prügel-Bennett, 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 Prügel-Bennett.
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. Prügel-Bennett.
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 Prügel-Bennett.
Maximum entropy analysis of genetic algorithm operators.
Lecture Notes in Computer Science, 993:14-24, 1995.
( abstract , full paper ).

14

A. Prügel-Bennett 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 Prügel-Bennett, 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 p213-234, 1995.
  ( abstract , full paper ).