1,595 research outputs found
Fitness landscape of the cellular automata majority problem: View from the Olympus
In this paper we study cellular automata (CAs) that perform the computational
Majority task. This task is a good example of what the phenomenon of emergence
in complex systems is. We take an interest in the reasons that make this
particular fitness landscape a difficult one. The first goal is to study the
landscape as such, and thus it is ideally independent from the actual
heuristics used to search the space. However, a second goal is to understand
the features a good search technique for this particular problem space should
possess. We statistically quantify in various ways the degree of difficulty of
searching this landscape. Due to neutrality, investigations based on sampling
techniques on the whole landscape are difficult to conduct. So, we go exploring
the landscape from the top. Although it has been proved that no CA can perform
the task perfectly, several efficient CAs for this task have been found.
Exploiting similarities between these CAs and symmetries in the landscape, we
define the Olympus landscape which is regarded as the ''heavenly home'' of the
best local optima known (blok). Then we measure several properties of this
subspace. Although it is easier to find relevant CAs in this subspace than in
the overall landscape, there are structural reasons that prevent a searcher
from finding overfitted CAs in the Olympus. Finally, we study dynamics and
performance of genetic algorithms on the Olympus in order to confirm our
analysis and to find efficient CAs for the Majority problem with low
computational cost
On the Neutrality of Flowshop Scheduling Fitness Landscapes
Solving efficiently complex problems using metaheuristics, and in particular
local searches, requires incorporating knowledge about the problem to solve. In
this paper, the permutation flowshop problem is studied. It is well known that
in such problems, several solutions may have the same fitness value. As this
neutrality property is an important one, it should be taken into account during
the design of optimization methods. Then in the context of the permutation
flowshop, a deep landscape analysis focused on the neutrality property is
driven and propositions on the way to use this neutrality to guide efficiently
the search are given.Comment: Learning and Intelligent OptimizatioN Conference (LION 5), Rome :
Italy (2011
NILS: a Neutrality-based Iterated Local Search and its application to Flowshop Scheduling
This paper presents a new methodology that exploits specific characteristics
from the fitness landscape. In particular, we are interested in the property of
neutrality, that deals with the fact that the same fitness value is assigned to
numerous solutions from the search space. Many combinatorial optimization
problems share this property, that is generally very inhibiting for local
search algorithms. A neutrality-based iterated local search, that allows
neutral walks to move on the plateaus, is proposed and experimented on a
permutation flowshop scheduling problem with the aim of minimizing the
makespan. Our experiments show that the proposed approach is able to find
improving solutions compared with a classical iterated local search. Moreover,
the tradeoff between the exploitation of neutrality and the exploration of new
parts of the search space is deeply analyzed
Robust Multi-Cellular Developmental Design
This paper introduces a continuous model for Multi-cellular Developmental
Design. The cells are fixed on a 2D grid and exchange "chemicals" with their
neighbors during the growth process. The quantity of chemicals that a cell
produces, as well as the differentiation value of the cell in the phenotype,
are controlled by a Neural Network (the genotype) that takes as inputs the
chemicals produced by the neighboring cells at the previous time step. In the
proposed model, the number of iterations of the growth process is not
pre-determined, but emerges during evolution: only organisms for which the
growth process stabilizes give a phenotype (the stable state), others are
declared nonviable. The optimization of the controller is done using the NEAT
algorithm, that optimizes both the topology and the weights of the Neural
Networks. Though each cell only receives local information from its neighbors,
the experimental results of the proposed approach on the 'flags' problems (the
phenotype must match a given 2D pattern) are almost as good as those of a
direct regression approach using the same model with global information.
Moreover, the resulting multi-cellular organisms exhibit almost perfect
self-healing characteristics
Boolean Dynamics with Random Couplings
This paper reviews a class of generic dissipative dynamical systems called
N-K models. In these models, the dynamics of N elements, defined as Boolean
variables, develop step by step, clocked by a discrete time variable. Each of
the N Boolean elements at a given time is given a value which depends upon K
elements in the previous time step.
We review the work of many authors on the behavior of the models, looking
particularly at the structure and lengths of their cycles, the sizes of their
basins of attraction, and the flow of information through the systems. In the
limit of infinite N, there is a phase transition between a chaotic and an
ordered phase, with a critical phase in between.
We argue that the behavior of this system depends significantly on the
topology of the network connections. If the elements are placed upon a lattice
with dimension d, the system shows correlations related to the standard
percolation or directed percolation phase transition on such a lattice. On the
other hand, a very different behavior is seen in the Kauffman net in which all
spins are equally likely to be coupled to a given spin. In this situation,
coupling loops are mostly suppressed, and the behavior of the system is much
more like that of a mean field theory.
We also describe possible applications of the models to, for example, genetic
networks, cell differentiation, evolution, democracy in social systems and
neural networks.Comment: 69 pages, 16 figures, Submitted to Springer Applied Mathematical
Sciences Serie
A characterisation of S-box fitness landscapes in cryptography
Substitution Boxes (S-boxes) are nonlinear objects often used in the design
of cryptographic algorithms. The design of high quality S-boxes is an
interesting problem that attracts a lot of attention. Many attempts have been
made in recent years to use heuristics to design S-boxes, but the results were
often far from the previously known best obtained ones. Unfortunately, most of
the effort went into exploring different algorithms and fitness functions while
little attention has been given to the understanding why this problem is so
difficult for heuristics. In this paper, we conduct a fitness landscape
analysis to better understand why this problem can be difficult. Among other,
we find that almost each initial starting point has its own local optimum, even
though the networks are highly interconnected
Evolutionary games on graphs
Game theory is one of the key paradigms behind many scientific disciplines
from biology to behavioral sciences to economics. In its evolutionary form and
especially when the interacting agents are linked in a specific social network
the underlying solution concepts and methods are very similar to those applied
in non-equilibrium statistical physics. This review gives a tutorial-type
overview of the field for physicists. The first three sections introduce the
necessary background in classical and evolutionary game theory from the basic
definitions to the most important results. The fourth section surveys the
topological complications implied by non-mean-field-type social network
structures in general. The last three sections discuss in detail the dynamic
behavior of three prominent classes of models: the Prisoner's Dilemma, the
Rock-Scissors-Paper game, and Competing Associations. The major theme of the
review is in what sense and how the graph structure of interactions can modify
and enrich the picture of long term behavioral patterns emerging in
evolutionary games.Comment: Review, final version, 133 pages, 65 figure
Biology of Applied Digital Ecosystems
A primary motivation for our research in Digital Ecosystems is the desire to
exploit the self-organising properties of biological ecosystems. Ecosystems are
thought to be robust, scalable architectures that can automatically solve
complex, dynamic problems. However, the biological processes that contribute to
these properties have not been made explicit in Digital Ecosystems research.
Here, we discuss how biological properties contribute to the self-organising
features of biological ecosystems, including population dynamics, evolution, a
complex dynamic environment, and spatial distributions for generating local
interactions. The potential for exploiting these properties in artificial
systems is then considered. We suggest that several key features of biological
ecosystems have not been fully explored in existing digital ecosystems, and
discuss how mimicking these features may assist in developing robust, scalable
self-organising architectures. An example architecture, the Digital Ecosystem,
is considered in detail. The Digital Ecosystem is then measured experimentally
through simulations, with measures originating from theoretical ecology, to
confirm its likeness to a biological ecosystem. Including the responsiveness to
requests for applications from the user base, as a measure of the 'ecological
succession' (development).Comment: 9 pages, 4 figure, conferenc
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