Evolutionary Computational Intelligence

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Evolutionary Computational Intelligence

• Lecture 8 Memetic Algorithms

Ferrante Neri University of Jyväskylä
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The Optimization Problem

• 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

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Dialects Developing in Artificial Intelligence

• Fogel Owens (USA, 1965)
  Evolutionary Programming
• Holland Genetic Algorithms (USA, 1973)
  Genetic Algorithm
• Rechenberg Schwefel (Germany, 1973)
  Evolution Strategies
• 90s Evolutionary Algorithms (EA)

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Historical Info about MAs

• The term Memetic Algorithm (MA) is coined by
  Moscato (1989)
• .but as always the same idea was also given
  under the name of
• Hybrid GAs
• Baldwinian GAs
• Lamarckian GAs
• Others

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The Metaphor

• 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.

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Memetic Algorithms

• 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

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Michalewiczs view on EAs
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Local Searchers

• Local Searcher (LS) a deterministic method able
  to find the nearest local optimum
• Local Searchers can be classified according to
• Order
• Pivot Rule
• Depth
• Neighborhood

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Local Searchers Classification

• 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 Hooke-Jeeves Method).
  Greedy Pivot Rule the LS chooses the first
  better search direction found (e.g. Nelder-Mead
  Method)

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Local Searchers Classification

• 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

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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

• The initial population is not given at
  pseudo-random 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

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Intelligent Variation Operators

• 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)

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Properly Said Memetic Algorithms Local Search
acting on Offspring

• 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

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How to apply a Local Searcher?

• 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

• 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
• Baldwinian
• traits acquired by individual cannot be
  transmitted to its offspring (suggests new
  direction search)
• e.g. individual receives fitness (but not
  genotype) of fitter neighbour

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Efficiency and Robustness of the Memetic
Algorithms

• 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)

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Adaptivity and Self-Adaptivity

• In order to enhance the efficiency and the
  robustness of a MA an adaptive or self-adaptive
  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

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Multi-Meme systems

• 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

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Adaptivity Multi-Meme

• 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)

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The use of several Local Searchers

• 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

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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
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 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
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• Thank You for Your Attention
• Questions?