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NAVY Research GroupDepartment of Computer Science
Faculty of Electrical Engineering and Computer Science VŠB-TUO17. listopadu 15
708 33 Ostrava-PorubaCzech Republic
Evolutionary Algorithms as a Complex Dynamical Systems
Ivan Zelinka
MBCS CIPT, www.bcs.org/http://www.springer.com/series/10624
Department of Computer ScienceFaculty of Electrical Engineering and Computer Science, VŠB-TUO
17. listopadu 15 , 708 33 Ostrava-PorubaCzech Republic
www.ivanzelinka.eu
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Topics
• Evolutionary algorithms and mutual relations between its dynamics, complex networks and its control.
• Complex systems and behavior
• EA and feedback loop control system
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Objectives
What do you can expect from this tutorial:• An introduction into complex behavior, such as:
– Chaotic– Stochastic– Catastrophe
• Sketch why EAs can be considered as a complex systems • Relations between EA dynamics and complex networks• EA as a feedback loop cybernetic system
What do you cannot expect from this tutorial:• To be expert on any of above mentioned fields
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Tutorial structure
The tutorial structure is:• Complex system overview• Complex system behavior (chaos, randomness,
determinism)• Evolutionary algorithms (EA) dynamics
– Dynamics of EAs– Dynamics of EA strategies
• Complex networks• EA and complex networks (CN)
– CN as a part of Eas strategies– EAs dynamics as a complex network
• Control EAs dynamics
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Evolutionary and genetic dynamics, processes and laws
Fitness
Population dynamic
Hereditability
Hereditability
DNA coding (Schrodinger,
Watson and Creek)
Feature
Fitness
MEndelDar win
Tur ing Bar iccel i Moder n comput er evol ucionist s: Hol l and, Schwef el , Rechenber g, Fogel , Baeck, Pr ice, Koza, O'Nei l l , Ryan, ...
Gregor Johann Mendel July 20, 1822
–January 6, 1884.
Gregor Charles Darwin 12 February 1809 –19 April 1882.
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Initial population setting
Control parameters definition of the selected evolutionary algorithm
Fitness evaluation of each individual
(parent)
Parent selection based on their
fitness
Offspring creation
Mutation of a new offsprings
Fitness evaluation
Best individual selection from
parents and offsprings
New empty population
occupation by selected individuals
Old population is replaced by new
one
Evolutionary loop
Evolution – the central dogma
From the above mentioned main ideas of Darwin and Mendel theory of evolution, ECT uses some building blocks, see the diagram.
The evolutionary principles are transferred into computational methods in a simplified form that will be outlined now.
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Complex networks and EAsTwo ways of use
• CN as a controlling structure of EA dynamics
• EAs dynamics as a social interactions creating complex network
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Complex networks inside EAsCN as a controlling structure of EA dynamics
• CN and internal dynamics of PSO
– Star
– Ring
– Wheel
– Pyramid
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Evolution as a complex networkHow to convert
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Evolution as a complex network
An example of activated leaders with moment when evolution has found global extreme. In such a moment the best individual is repeatedly selected (see line after 230 migrations) and become to be extremely attractive node of all.
20 Ivan Zelinka, Donald Davendra and Vaclav Snasel
F ig. 18. and it s histogram of the vert ices
connect ions (note that winning vertex has
with almost 900 connect ions).
F ig. 19. An example of ” rich become to
be richer” , see also Figure 20 and 21
0 50 100 150 200 250 3000
20
40
60
80
100
Migration No.
Indiv
idu
alN
o.
F ig. 20. An example of act ivated leaders
with moment when evolut ion has found
global ext reme. In such a moment the best
individual is repeatedly selected (see line
after 230 migrat ions) and become to be
ext remely at t ract ive node of all.
F ig. 21. An example of act ivated leaders
with moment when evolut ion has found
global ext reme.
rather than randomly remoted algorithms. We think that this is quite
logical and close to the idea of prefered linking in the complex networks
modelling social behavior (citat ion networks, etc)
6. Evaluat ion and vizualizat ion: Evaluat ion has been done so that histogram
has been vizualized for each evolut ionary process (e.g. Figure 16), and ac-
t ivated vert ices e.g. Figure 25. To vizualize all experiments we have joined
all those figures (i.e. with act ivated vert ices) into one figure to vizualize
behavior of EAs from CNS point of view. As an example one can see Fig-
ures 30, 31,32, 36,37. Most of this figures show two phases; phase of ” free”
compet it ion, when each vertex (individual) has a chance to win and phase
of ” winner take all” , i.e. when no bet ter solut ion are generated (we are in
global extreme or EAs has got into stagnat ion) and st ill the same vertex
is selected like a winner. This ” e↵ect ” has been observable especially for
20 Ivan Zelinka, Donald Davendra and Vaclav Snasel
F ig. 18. and it s histogram of the vert ices
connect ions (note that winning vertex has
with almost 900 connect ions).
0 50 100 150 200 250 3000
20
40
60
80
Migration No.
Ind
ivid
ual
No
.
F ig. 19. An example of ” rich become to
be richer” , see also Figure 20 and 21
F ig. 20. An example of act ivated leaders
with moment when evolut ion has found
global ext reme. In such a moment the best
individual is repeatedly selected (see line
after 230 migrat ions) and become to be
ext remely at t ract ive node of all.
F ig. 21. An example of act ivated leaders
with moment when evolut ion has found
global ext reme.
rather than randomly remoted algorithms. We think that this is quite
logical and close to the idea of prefered linking in the complex networks
modelling social behavior (citat ion networks, etc)
6. Evaluat ion and vizualizat ion: Evaluat ion has been done so that histogram
has been vizualized for each evolut ionary process (e.g. Figure 16), and ac-
t ivated vert ices e.g. Figure 25. To vizualize all experiments we have joined
all those figures (i.e. with act ivated vert ices) into one figure to vizualize
behavior of EAs from CNS point of view. As an example one can see Fig-
ures 30, 31,32, 36,37. Most of this figures show two phases; phase of ” free”
compet it ion, when each vertex (individual) has a chance to win and phase
of ” winner take all” , i.e. when no bet ter solut ion are generated (we are in
global ext reme or EAs has got into stagnat ion) and st ill the same vertex
is selected like a winner. This ” e↵ect ” has been observable especially for
An example of ”rich become to be richer”
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Evolution as a complex network
KCoreComponents
FindGraphPartition
PageRankCentrality
CommunityGraphPlot
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Evolution as a complex networkNetwork attributes interpretation
• Adjacency graph
• Graph partition
• Degree centrality
• Community
• …
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Adjacency graph
• Meaning: Graph with vertices and oriented edges.
• Interpretation: Visualization of evolutionary dynamics in the form of so called graph. Each vertex represent one individual in the population and each edge (oriented of course) represent successful offspring creation (i.e. fitness improvement of active parent in this philosophy) between parents connected by that edge.
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Graph partition
• Meaning: Graph partition finds a partition of vertices such that the number of edges having endpoints in different parts is minimized. For a weighted graph, graph partition finds a partition such that the sum of edge weights for edges having endpoints in different parts is minimized.
• Interpretation: Individuals in population are separated into ”groups” according to their interactions with another individuals, based on their success in active individual fitness improvements. ”Endpoints” can be understood like successful participation of selected individuals in active individual fitness. On Figure 2 is partition visualized by colors. This analysis gives view on population structure and shows the set of individuals that got or donate oriented edges (support from / to) the same group of individuals. Based on number of connections or weights (if multiple edges are understood like integer weights) of edge, it can be analyzed what part of population was the most important in the evolutionary dynamics for given case.
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Degree centrality
• Meaning: Degree centrality of g gives a list of vertex degrees for the vertices in the underlying simple graph of g. Degree centrality will give high centralities to vertices that have high vertex degrees. The vertex degree for a vertex v is the number of edges incident to v. For a directed graph, the in-degree is the number of incoming edges and the out-degree is the number of outgoing edges. For an undirected graph, in-degree and out-degree coincide.
• Interpretation: Degree centrality shows how many in-coming (support from individuals) or out-coming (support to individuals) edges vertex individual under study has. This quantity can be related to progress of the evolutionary search and used to made conclusion of what set of individuals has maximally contribute to that. On Figure 4 are individuals sized according to that degree.
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Community
• Meaning: Community graph plot attempts to draw the vertices grouped into communities.
• Interpretation: Community graph plot showing the individuals grouped into communities. Communities (with border are individuals that communicate amongst themselves (higher density of edges in community, multi edges are not visualized here, rather than between communities) and community are then joined by connections that are ”one-way” and shows flow
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Evolution as a complex network
• M. Soleimani-Pouri et al. dealt with solving of the
maximum clique problem in social networks, In: Soleimani-pouri M, Rezvanian A, Meybodi MR (2014) An Ant Based Particle
Swarm Optimization Algorithm for Maximum Clique Problem in Social
Networks, Springer International Publishing, pp 455–462.,
where ant based particle swarm algorithm is used.
• Q. Wu and J-K. Hao made a review on algorithms for maximum clique problem , In: Wua Q, Hao JK (2014) A review
on algorithms for maximum clique problems. European Journal of Operational Research.
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Evolution as a complex network
• M. Gong et al. described complex network clustering by multiobjective discrete particle swarm optimization based on decomposition , In: Gong M, CaiQ, Chen X, Ma L (2014) Complex network clustering by multiobjectivediscrete particle swarm optimization based on decomposition. IEEE Transactions on Evolutionary Computation 18:82–97 .
• In: Li Y, Liu J, Liu C (2014) A comparative analysis of evolutionary and memetic algorithms for community detection from signed social networks. Soft Computing 18:329–348 , a comparative analysis of evolutionary and memetic algorithms for community detection from signed social networks is described etc.
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Evolution as a complex network
• Since 1999, D. Ashlock et al. described graph-based genetic algorithm using a combinatorial graph to limit choice of crossover partner , In: Ashlock D, Smucker M,
Walker J (1999) Graph based genetic algorithms. In: Evolutionary Computation, IEEE, pp 1362–1368.
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Evolution as a complex network
• In 2007, S. Mabu et al. described a graph-based evolutionary algorithm and graph-based evolutionary algorithm with reinforcement learning , In: Mabu S,
Hirasawa K, Hu J (2007) A graph-based evolutionary algorithm: Genetic network programming (gnp) and its extension using reinforcement
learning. Evolutionary Computation 15:369–398 . These algorithms deal with dynamic environment by using the higher expression ability of graph structure and inherently equipped functions in it.
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Evolution as a complex network
• In the years 2010 and 2011, I. Zelinka et al. described the method for visualizing the dynamics of EA by the CNs and investigated the analogy between the individuals in the population and nodes of the CN and the relationships between individuals in the EA and edges between the nodes in CN, In: – Zelinka I, Davendra DD, Snasel V, Senkerik R, Jasek R (2010) Preliminary investigation on
relations between complex networks and evolutionary algorithms dynamics. In: Computer Information Systems and Industrial Management Applications (CISIM) 31.
– Zelinka I, Davendra DD, Senkerik R, Jasek R (2011) Do evolutionary algorithm dynamics create complex network structures? In: Complex Systems, Vol. 20, Issue 2.
– Zelinka, Ivan, Snasel, Vaclav, Abraham, Ajith (Eds.) , Handbook of Optimization, Springer, 2013
– Zelinka I. et. al, Evolutionary algorithms dynamics and its hidden complex network structures. CEC 2014, p. 3246 – 3251, Beijing, China
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Evolution as a complex network
• In 2014, D. D. Davendra et al. analyzed the development of the CN in the discrete self-organizing migrating algorithm in Davendra D, Zelinka I, Senkerik R, Pluhacek M (2014) Complex network analysis of discrete self-organising migrating algorithm. In: Nostradamus 2014: Prediction, Modeling and Analysis of Complex Systems, pp 161–174.
• As we will show in the next sections, our approach extends the ideas already mentioned in the previous slide. The way how we construct the CN reflects the behavior of individuals during the generations of the DE.
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ExamplesDE driven by CN centralities
Skanderova L., Fabian T., Differential Evolution Dynamic Analysis by Complex Network, submitted for publication.
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ExamplesDE driven by CN centralities
Skanderova L., Fabian T., Differential Evolution Dynamic Analysis by Complex Network, submitted for publication.
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ExamplesDE driven by CN centralities
Skanderova L., Fabian T., Differential Evolution Dynamic Analysis by Complex Network, submitted for publication.
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ExamplesDE driven by CN centralities
Skanderova L., Fabian T., Differential Evolution Dynamic Analysis by Complex Network, submitted for publication.
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ExamplesDE driven by CN centralities
Skanderova L., Fabian T., Differential Evolution Dynamic Analysis by Complex Network, submitted for publication.
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ExamplesABC driven by CN centralities
Davendra D., Metlicka M., Ensemble Centralities based Adaptive Artificial Bee Algorithm , CEC 2015, Sendai, Japan
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ExamplesABC driven by CN centralities
Davendra D., Metlicka M., Ensemble Centralities based Adaptive Artificial Bee Algorithm , CEC 2015, Sendai, Japan
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ExamplesABC driven by CN centralities
Davendra D., Metlicka M., Ensemble Centralities based Adaptive Artificial Bee Algorithm , CEC 2015, Sendai, Japan
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ExamplesABC driven by CN centralities
Davendra D., Metlicka M., Ensemble Centralities based Adaptive Artificial Bee Algorithm , CEC 2015, Sendai, Japan
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ExamplesABC driven by CN centralities
Davendra D., Metlicka M., Ensemble Centralities based Adaptive Artificial Bee Algorithm , CEC 2015, Sendai, Japan
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Complex system overview
• Is evolutionary dynamics complex?
• What is it complex system?
• Can be complex system controlled?
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Complex system overview
Growth
Models
Cel
lula
r A
uto
mat
a
Emergence
Hierarchical ModelsFractals
ChaosComplex systems
Adaptive behavior
Computation
Coadap
tation Recursion
Stra
nge
att
ract
ors
Phase transition
Self organ
ization
Inco
mputab
ilityArtificial life, artificial intelligence, swarm intelligence, adaptation in natural processes ...
Complex networks, economical systems, social networks and systems, nervous system, cells and living things, including human beings, modern energy or telecommunication infrastructures, ...
Systems exhibiting deterministic chaos dynamics: economy, climate, physics, biology, astrophysics, numerical calculations, ...
Complexity of fractals in visualization, systems with chaotic behavior, static structures in physics and modeling of dynamic processes of growth, hierarchical models and information processing and communication,...
Numerical simulation, Kolmogorov algorithm complexity, P and NP problems, incomputability and physical limits of computation,...
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Complex system overview
• One of many possible definition of a complex system is like:
• A complex system is a system composed of interconnected parts that as a whole exhibit one or more properties (behavior among the possible properties) not obvious from the properties of the individual parts. This characteristic of every system is called emergence.
• A systems complexity may be of one of two forms: disorganized complexity and organized complexity. In essence, disorganized complexity is a matter of a very large number of parts, and organized complexity is a matter of the subject system (quite possibly with only a limited number of parts) exhibiting emergent properties.
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Complex system overview
Today a lot of various informal descriptions of complex systems have been put forward, and these may give some insight into their, very often interesting, properties. As mentioned in the special edition of Science journal(Vol. 284. No. 5411, 1999)) about complex systems highlighted several of these:
• A complex system is a highly structured system, which shows structure with variations.
• A complex system is one whose evolution is very sensitive to initial conditions or to small perturbations, one in which the number of independent interacting components is large, or one in which there are multiple pathways by which the system can evolve. This is very typical for deterministic chaos system.
• A complex system is one that by design or function or both is difficult to understand and verify.
• A complex system is one in which there are multiple interactions between many different components Complex systems are systems in process that constantly evolve and unfold over time.
• ...
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Complex system overview
A complex adaptive system has some or all of the following attributes*:• The number of parts (and types of parts) in the system and the
number of relations between the parts is non-trivial – however, there is no general rule to separate "trivial" from "non-trivial";
• The system has memory or includes feedback;• The system can adapt itself according to its history or feedback;• The relations between the system and its environment are non-
trivial or non-linear;• The system can be influenced by, or can adapt itself to, its
environment; and• The system is highly sensitive to initial conditions. • ...
* Johnson, Neil F. (2007). Two's Company, Three is Complexity: A simple guide to the science of all sciences. Oxford: Oneworld. ISBN 978-1-85168-488-5.
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Complex system overview
Examples of complex systems include natural as well as artificial:
• ant colonies• human economies• social structures• climate• nervous systems• cells and living things• including human beings• modern energy or telecommunication infrastructures
and much more. Many systems of research and technology interest to humans are complex systems. Complex systems are studied by many areas of natural science, mathematics, physics, biology and social science. Fields that specialize in the interdisciplinary study of complex systems include systems theory, complexity theory, systems ecology and mainly cybernetics.
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Complex system behavior
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Complex system behavior
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Complex networks to CML
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Dynamic of CML is then
understand like changes in
connections between
vertices
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Complex networks to CML
Figure 30 Example 6: Dynamics of the complex network with edges deactivation by real number
coefficient. Different colors including white one represent different vertices (sites) activation.
Figure 31 Example 7: Dynamics of the complex network with edges deactivation by real number
coefficient. Different colors including white one represent different vertices (sites) activation.
Figure 32 Example 8: Zoom of the network with 20 vertices in 500 iterations.
CONCLUSION
In this paper we have proposed method how to visualize and simulate (model) complex network
dynamics by means of the CML systems. CML modeling is well known in the domain of so-
called spatiotemporal deterministic chaos. For analysis and control of the CML systems has been
developed numerous techniques, based on classical mathematics as well as on the heuristic
methods. Based on this fact we have used and tested method, how to visualize CN dynamics as a
CML system. As a summarization and conclusion can be state this:
The main model of complex network, used for simulations here, has been based on
randomly initialized network with different number of vertices.
Edges between vertices have been also initialized randomly, however, roulette method
from genetic algorithms, have been used to add the new edge to the vertex, and/or
increase or decrease importance of existing edge. Roulette method has been used in order
to prefer richer vertices (i.e. vertices with more incoming edges) and thus support in this
way the main idea of complex networks with small world phenomenon.
Two different dynamics of CN has been used. The first one was based on fact that a
simple small CN has been initialized and then, after each iteration, a new vertex has been
added and selected edges adjusted. This is visualized in Figure 20. The second one has
been based on preliminary fact, that we already have developed network, with constant
number of vertices and dynamic itself depends only on the edge weights evolution.
All substantial and typical results are visualized via Figure 17 - Figure 32 and it can be
stated that our technique of CNCML is usable and complex behavior of CN can be
visualized in this way. It is also obvious, that methods of analysis and control of CMLs
can be also used for CNCML, because conversion classical CN to the CNCML basically
create specific, more complex version, of the CML and there are no restriction of use of
Dynamics of the complex network with edges deactivation by real number coefficient. Different colors including white one represent different vertices (sites) activation.
Zoom of the network with 20 vertices in 500 iterations.
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• Deterministic?
• Stochastic?
• Chaotic?
• Emergent?
What kind of behavior can we expect?
77 navy.cs.vsb.cz
Chaos - behavior
Wright A., Agapie A.: Cyclic and Chaotic Behavior in Genetic Algorithms. In: Proc. of Genetic and Evolutionary Computation Conference (GECCO),San Francisco, July 7-11 (2001)
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Chaos - hamiltonian systems
• The study of Hamiltonian systems has its roots in the 19th century when it was introduced by Irish mathematician William Hamilton.
• For mechanical systems, typical feature of Hamiltonian systems is that no dissipation of energy occurs in them, so that mechanical Hamiltonian system is also the so-called conservative one.
• In general dynamical system theory the term “conservative” means that certain scalar function, having typical properties of energy, is preserved along system trajectories.
• The creation of chaos theory for Hamiltonian systems was contributed to by scientists such as Boltzman (who established the foundations of ergodic theory and discovered the contradiction between the reversibility of a system and irreversibility of its behavior) and Poincare.
• Hamiltonian systems included application in many areas of physics, such as plasma physics, quantum mechanics and others.
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Chaos - dissipative systems
• Dissipative dynamic systems are systems where energy
escapes into the surroundings and state space volume is
reduced.
• Typical examples include weight on spring (dissipation
being caused by friction between the body and air and
energy losses inside the material), motion of a wheel,
electronic resonance circuits.
• Since the topics of dissipative dynamic systems are the
subject of a whole presentation, demonstration of a
exact real system will be given here.
• Well-known classical example of a dynamic system is
defined by the Lorenz system.
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Chaos - universal features
• Deterministic chaos possesses many features that are common to chaotic
behavior irrespective of the physical system which is the cause of this
behavior.
• This common nature is expressed by the term universality so as to stress
the universal nature of the phenomena.
• The quantity and properties of the features as well as the complexity of links
between them are so extensive that they could make up a topic for a
separate publication.
• These include, in particular, Feigenbaum’s constants α and δ , the U-
sequence, Lyapunov exponents, self-similarity and processes by which a
system usually passes from deterministic behavior to chaotic behavior:
intermittence, period doubling, metastable chaos and crises.
• Another property which is, curiously, not included in the pantheon of
universalities will be mentioned at the beginning: the deterministic nature
and non-predictability of deterministic chaos.
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Chaos - universal featuresDeterminism and Unpredictability of the Behavior of Deterministic Chaos - Sensitivity
to Initial Conditions
• The deterministic structure of systems which generate chaos and their unpredictability constitute another typical feature of the universal properties of deterministic chaos.
• It is actually irrelevant what type the chaotic system is (chemical, biological, electronic, economic, ...): it holds invariably that their mathematical models are fully deterministic (there is no room for randomness as such in them) and are unpredictable in their behavior.
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Selected examplesAstronomy - the Three-Body Problem
α Centauri A a B … 23AU, 80 yearsα Centauri C 13000 AU
Artistic vision system of 3 stellar HD 188753 A, in the constellation Cygnus. In this
triple star system orbiting planets like Jupiter around the brightest star in about 3.3
day! .
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Selected examplesElectronic System - Chua’s Circuit
• Electronic circuits are among the most popular systems used to demonstrate deterministic chaos.
• Their popularity comes from the fact that electronic circuits are easy to set up and provide fast response to impulse.
• Typical representatives of electronic circuits with deterministic chaos include Chua’s circuit, whose hardware design and behavior are shown in next slide.
• Chua’s circuit can be described mathematically, which can be used to simulate the behavior of the circuit.
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Selected examplesElectronic System - Chua’s Circuit
• The core of Chua’s circuit is a nonlinear resistor, sometimes called Chua’s diode.
• Chua’s attractor visualized by the program Mathematica (left) and on the oscilloscope connected to its hardware implementation.
• In
the nonlinear resistor g(x) is represented by
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Selected examplesSpatiotemporal Chaos
• This is a spatiotemporally coupled system with the development of n equations that affect each other via a coupling constant, usually denoted ε.
• CML can be regarded as a field of kind of “oscillators” which affect each other.
• Mathematical description of a CML using an iteration equation for its activity consists in where the function which is denoted f(...) represents the iteration equation.
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Selected examplesHidden attractors
• An oscillation in a dynamical system can be easily localized numerically if initial conditions from its open neighborhood lead to long-time behavior that approaches the oscillation.
• Such oscillation (or a set of oscillations) is called an attractor, and its attracting set is called the basin of attraction.
• Thus, from a computational point of view in applied problems of nonlinear analysis of dynamical models, it is essential to regard attractors as self-excited attractors or hidden attractors depending on the simplicity of finding its basin of attraction in the phase space.
GA Leonov, NV Kuznetzov, Hidden attractors in dynamical systems. From hidden oscillations in Hilbert-Kolmogorov, Aizerman, and Kalman problems to hidden chaotic attractor in Chua circuits
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Selected examplesHidden attractors
Remember, chaos has been observed inside EAs
Are hidden attractors in EAs dynamic too?
What happen if HA is met?
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Selected examplesChaos - Links
• Lorenz attractor: http://www.youtube.com/watch?v=iu4RdmBVdps
• Chaos document:http://www.youtube.com/watch?v=EF5Wvi_Iiy4
• Double Pendulum Chaos:http://www.youtube.com/watch?v=QXf95_EKS6E
• Fractals – Hunting The Hidden Dimension –document about fractal geometry and chaos: https://www.youtube.com/watch?v=s65DSz78jW4
• The Strange New Science of Chaos: https://www.youtube.com/watch?v=fUsePzlOmxw
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Control EAs dynamics
Caenorhabditis elegans
• In its Neural Network:
– Neurons: ~ 300
– Synapses: ~ 3000
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Control EAs dynamics
The worm Caenorhabditis elegans has 297 nerve cells. The neurons switch one another on or off, and, making 2345 connections among themselves. They form a network that stretches through the nematode’s millimeter-long body.How many neurons would you have to commandeer to control the network with complete precision?The answer is: 49
-- Adrian Cho, Science, 13 May 2011, vol. 332, p 777
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Control EAs dynamics
“…very few individuals (approximately 5%) within honeybee swarms can guide the group to a new nest site.”
I.D. Couzin et al., Nature, 3 Feb 2005, vol. 433, p 513
These 5% of bees can be considered as “controlling” or “controlled” agents
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Control EAs dynamics
• How many controllers to use?
• Where to put them (which nodes to “pin”)?
• Objective: To achieve cost-effective control (e.g. synchronization) with good performance
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Complex system behavior Control
• Off line control
• Realtime control
• Mathematica example
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EA as CN
• Zelinka I, Davendra DD, Snasel V, Senkerik R, Jasek R (2010) Preliminary investigation on relations between complex networks and evolutionary algorithms dynamics. In: Computer Information Systems and Industrial Management Applications (CISIM) 31.
• Zelinka I, Davendra DD, Senkerik R, Jasek R (2011) Do evolutionary algorithm dynamics create complex network structures? In: Complex Systems, Vol. 20, Issue 2.
• Zelinka, Ivan, Snasel, Vaclav, Abraham, Ajith (Eds.) , Handbook of Optimization, Springer, 2013
• Zelinka I. et. al, Evolutionary algorithms dynamics and its hidden complex network structures. CEC 2014, p. 3246 – 3251, Beijing, China
• Davendra D, Zelinka I, Senkerik R, Pluhacek M (2014) Complex network analysis of discrete self-organising migrating algorithm. In: Nostradamus 2014: Prediction, Modeling and Analysis of Complex Systems, pp 161–174.
• Skanderova L., Fabian T., Differential Evolution Dynamic Analysis by Complex Network, submitted for publication.
• Davendra D., Metlicka M., Ensemble Centralities based Adaptive Artificial Bee Algorithm , CEC 2015, Sendai, Japan
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CN in Eas
• Soleimani-pouri M, Rezvanian A, Meybodi MR (2014) An Ant Based Particle Swarm Optimization Algorithm for Maximum Clique Problem in Social Networks, Springer International Publishing, pp 455–462.
• Wua Q, Hao JK (2014) A review on algorithms for maximum clique problems. European Journal of Operational Research.
• Gong M, Cai Q, Chen X, Ma L (2014) Complex network clustering by multiobjectivediscrete particle swarm optimization based on decomposition. IEEE Transactions on Evolutionary Computation 18:82–97 .
• Li Y, Liu J, Liu C (2014) A comparative analysis of evolutionary and memetic algorithms for community detection from signed social networks. Soft Computing 18:329–348
• Ashlock D, Smucker M, Walker J (1999) Graph based genetic algorithms. In: Evolutionary Computation, IEEE, pp 1362–1368.
• Mabu S, Hirasawa K, Hu J (2007) A graph-based evolutionary algorithm: Genetic network programming (gnp) and its extension using reinforcement learning. Evolutionary Computation 15:369–398 .
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Conclusions
• EA behavior can be visualized as a complex network – CN
• EAs can exhibit different classes of behavior• Chaos can be also observed inside EA• CN can be evaluated by classical mathematical tools
developed for CN• CN can be converted to CML• CML can be controlled…• … then EAs dynamics can be controlled too• EA is feedback loop control system
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