C. Di Chio et al. (Eds.): EvoApplications 2011, Part I, LNCS 6624, pp. 32–42, 2011.
© Springer-Verlag Berlin Heidelberg 2011
A Study on the Mutation Rates of a Genetic Algorithm
Interacting with a Sandpile
Carlos M. Fernandes
1,2
, Juan L.J. Laredo
1
, Antonio M. Mora
1
, Agostinho C. Rosa
2
,
and Juan J. Merelo
1
1
Department of Architecture and Computer Technology, University of Granada, Spain
2
LaSEEB-ISR-IST, Technical Univ. of Lisbon (IST)
{cfernandes,acrosa}@laseeb.org
{juanlu.jimenez,amorag77,jjmerelo}@gmail.com
Abstract. This paper investigates the mutation rates of a Genetic Algorithm
(GA) with the sandpile mutation. This operator, which was specifically de-
signed for non-stationary (or dynamic) optimization problems, relies on a Self-
Organized Criticality system called sandpile to self-adapt the mutation intensity
during the run. The behaviour of the operator depends on the state of the sand-
pile and on the fitness values of the population. Therefore, it has been argued
that the mutation distribution may depend on to the severity and frequency of
changes and on the type of stationary function that is chosen as a base-function
for the dynamic problems. An experimental setup is proposed for investigating
these issues. The results show that, at least under the proposed framework, a
GA with the sandpile mutation self-adapts the mutation rates to the dynamics of
the problem and to the characteristics of the base-function.
1 Introduction
Self-Organized Criticality (SOC) [5] describes a property of complex systems that
consists of a critical state formed by self-organization at the border of order and
chaos. While order means that the system is working in a predictable regime where
small disturbances have only local impact, chaos is an unpredictable state sensitive to
initial conditions or small disturbances. One of the characteristics of SOC is that small
disturbances can lead to the so-called avalanches, i.e., events that are spread spatially
or temporally through the system. Such events occur independently of the initial state
and the same perturbation may lead to small or large avalanches, showing a power-
law proportion between their size and quantity. This means that large (catastrophic)
events may hit the system from time to time and reconfigure it. When combined with
a Genetic Algorithm (GA), SOC can introduce large amounts of genetic novelty into
the population, periodically, and in an unsupervised and non-deterministic manner.
The present work investigates a recently proposed mutation scheme for a GA based
on a SCO model called the sandpile [5] and studies the distribution of its mutation
rates when varying two parameters that regulate the dynamics of non-stationary fit-
ness functions. The sandpile mutation [3, 4] was specifically designed for dynamic
optimization and differs from previous proposals that integrate SOC in Evolutionary