Transcript Document 7872206

Evolutionary Computational
Intelligence
Lecture 8: Memetic
Algorithms
Ferrante Neri
University of Jyväskylä
The Optimization Problem
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All the problems can be formulated as an
Optimization Problem that is the search of
the maximum (or the minimum) of a given
objective function
Deterministic Methods can fail because
they could converge to local optimum
Evolutionary Algorithms can fail because
they could converge to a sub-optimal solution
“Dialects” Developing in Artificial
Intelligence
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Fogel Owens (USA, 1965)
Evolutionary Programming
Holland Genetic Algorithms (USA, 1973)
Genetic Algorithm
Rechenberg Schwefel (Germany, 1973)
Evolution Strategies
90s Evolutionary Algorithms (EA)
Historical Info about MAs
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The term Memetic Algorithm (MA) is coined
by Moscato (1989)
….but as always the same idea was also
given under the name of
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Hybrid GAs
Baldwinian GAs
Lamarckian GAs
Others…
The Metaphor
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The Meme, the “Selfish Gene” (Dawkin,
1976).
The Meme is a unit of “cultural
transmission” in the same way that genes
are the units of biological transmission.
In EAs, genes are encoding of candidate
solutions, in MAs the memes are also
“strategies” of how to improve the solutions.
Memetic Algorithms
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The combination of Evolutionary
Algorithms with Local Search Operators
that work within the EA loop has been
termed “Memetic Algorithms”
Term also applies to EAs that use instance
specific knowledge in operators
Memetic Algorithms have been shown to be
orders of magnitude faster and more accurate
than EAs on some problems, and are the
“state of the art” on many problems
Michalewicz’s view on EAs
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Local Searchers
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Local Searcher (LS): a deterministic method
able to find the nearest local optimum
Local Searchers can be classified according
to:
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Order
Pivot Rule
Depth
Neighborhood
Local Searchers’ Classification
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Order zero if it uses just the function (direct
search), order one if it uses the first
derivative, order two if it uses the second
derivative
Steepest Ascent Pivot Rule: the LS
explores all the Neighborhood (e.g HookeJeeves Method). Greedy Pivot Rule: the LS
chooses the first better search direction
found (e.g. Nelder-Mead Method)
Local Searchers’ Classification
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The depth of the Local Search defines the
termination condition for the outer loop (stop
criterion)
The neighborhood generating function n(i)
defines a set of points that can be reached
by the application of some move operator to
the point i
General Scheme of EAs
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Pseudo-Code for typical EA
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How to Combine EA and LS
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Intelligent Initialization
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The initial population is not given at pseudorandom but it is given according to a heuristic
rule.
Examples: quasi-random generator,
orthogonal arrays
It increases the average fitness but it
decreases the diversity
Intelligent Variation Operators
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Intelligent Crossover: finds the best
combination between parents in order to
generate the most performing offspring (e.g.
heuristic selection of the cut point)
Intelligent Mutation: tries several possible
mutated individuals in order to obtain the
most “lucky” mutation (e.g. bit to flip)
Properly Said Memetic Algorithms:
Local Search acting on Offspring
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Can be viewed as a sort of “lifetime learning”
The LS are applied to the offspring in order to
have more performing individuals
A LS can be viewed also like a special mutation
operator and it is often (but not only!) used to
speed-up the “endgame” of an EA by making the
search in the vicinity
In fact the EAs are efficient in finding solutions
near the optimum but not in finalizing the search
How to apply a Local Searcher?
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Krasnogor (2002) shows that there are theoretical advantages
to using a local search with a move operator (LS to the
offspring ) that is different to the move operators used by
mutation and crossover but…..
How many iterations of the local search are done ?
Is local search applied to the whole population?
– or just the best ?
– or just the worst ?
– or to a certain part of the population according to some
rules?
Basically the right choice depends on the problem!
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Two Models of Lifetime Adaptation
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Lamarckian
 traits
acquired by an individual during its lifetime
can be transmitted to its offspring (refreshing of
the genotype)
 e.g. replace individual with fitter neighbour
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Baldwinian
 traits
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acquired by individual cannot be transmitted
to its offspring (suggests new direction search)
 e.g. individual receives fitness (but not genotype)
of fitter neighbour
Efficiency and Robustness of the
Memetic Algorithms
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Usually the fitness landscapes are
multimodal and very complex, or the decision
space is very big
We would like to implement an algorithm
which
is able to converge, every time it is run, to
the optimal solution in a short time
(avoiding premature convergence and
stagnation)
Adaptivity and Self-Adaptivity
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In order to enhance the efficiency and the
robustness of a MA an adaptive or selfadaptive scheme can be used
Adaptive: the memes are controlled during
the evolution by means of some rules
depending on the state of the population
Self-Adaptive: the adaptive rules are
encoded in the genotype of each individual
Multi-Meme systems
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A Meme Algorithm uses one LS (usually
complex)
A Multi-Meme Algorithm (M-MA) employs a
set (a list) of LSs (usually simple)
If a M-MA is implemented the problem of how
and when to run the LSs arises and some
rules are therefore needed
Adaptivity + Multi-Meme
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In order to properly select from the list the
LS to use for the different stages of the
evolution an adaptive strategy can be
used
If the “necessities” of the evolutionary
process are efficiently encoded it is
possible to use different LSs in different
moments and on different individuals (or set
of individuals)
The use of several Local Searchers
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Local Searchers with different features
explore the search space from different
perspectives
Different Local Searchers should
“compete” and “cooperate” (Ong 2004)
working to solve the classical problem, in
EAs, of the balancing between “exploration”
and “exploitation”
An Example: Adaptivity + Multi-Meme
on the population diversity
The state of the convergence of the algorithm can be
measured on the basis of the coefficient:
 f best  f avg
  min 1,
fbest
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if the convergence is going to approach but it is still quite far
the Nelder-Mead is applied since it is greedy and
explorative in order to jump out from the nearest basin of
attraction
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If the convergence is very near the Hooke-Jeeves is run
since it is a LS with steepest ascent pivot rule and can then
finalize the work in the hopefully found global optimum
Thank
You for Your
Attention
Questions?
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