Evolutionary Computational Intelligence

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Evolutionary Computational Intelligence

• Lecture 3
• Genetic Algorithms

Ferrante Neri University of Jyväskylä
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GA Quick Overview

• Developed USA in the 1970s
• Early names J. Holland, K. DeJong, D. Goldberg
• Typically applied to
• discrete optimization
• Attributed features
• not too fast
• good heuristic for combinatorial problems
• Special Features
• Traditionally emphasizes combining information
  from good parents (crossover)
• many variants, e.g., reproduction models,
  operators

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Genetic algorithms

• Hollands original GA is now known as the simple
  genetic algorithm (SGA)
• Other GAs use different
• Representations
• Mutations
• Crossovers
• Selection mechanisms

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GAs in EAs
Representation Binary strings
Recombination N-point or uniform
Mutation Bitwise bit-flipping with fixed probability
Parent selection Fitness-Proportionate
Survivor selection All children replace parents
Speciality Emphasis on crossover
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Representation

• A chromosome is encoded as a binary number
• Due to the inner discretization of the binary
  encoding GA can turn out more efficient in
  discrete optimization

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Representation in the population

• Thus a population of couple (L,b) can be seen as
  a matrix of binary numbers
• Each line is a chromosome

1 0 1 0 0 1 1 0
1 1 0 1 0 1 1 1
0 1 1 0 1 1 0 0
1 0 0 1 1 0 0 0
0 0 1 1 1 0 0 1
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Parent Selection Mechanisms

• The individuals that are undergoing recombination
  are selected by means of a Selection Mechanism
• Classical selection mechanisms are
• Fitness Proportionate
• Ranking
• Tournament

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Fitness Proportionate Selection

• It is the first one used in SGA
• It is given a probability to be chosen to each
  solution
• Such probability is proportionate to the fitness
  value taken by each single solution
• The sum of the probabilities is clearly one
• A random number between 0 and 1 is sampled and in
  a roulette stile the individual is selected

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Ranking Selection 1/2

• Individuals are sorted accoding to their fitness
  value and a probability is assigned according to
  their position in the list (rank)
• Then, the a probability is assigned to each
  solution by means of
• Linear Ranking
• Exponential Ranking

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Ranking Selection 2/2

• Linear if 1.0 lt s ? 2.0 and µ is the total
  number of ranks, the probability for the
  individual ranked i is
• Exponential if c is a normalize constant factor
  which allows the sum of all the probabilities
  being equal to 1, the probability of the
  individual ranked i is

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Tournament Selection

• Pick up a couple of solutions (at random) and
  compare their fitness, the better individual is
  in the mating pool
• It can work also with groups of individuals
  picking up a subset of them
• It does not require a sorting or a knowledge of
  the fitness distribution over the individuals of
  the population

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Selection Pressure

• Its the property of the selection component in
  following the promising search directions
• In other words, a parent selection mechanism
  which selects the best individuals many times has
  a high selection pressure
• In linear ranking ruled by s

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Crossover

• The selected parents undergo recombination
• In a SGA, the recombination is the crossover
• Crossover is an operator which combines two
  parents in order to produce one, two or more
  offspring
• The analogy of biological crossover in binary
  encoding is very straightforward

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1-point crossover

• Its the original crossover employed by Holland
• It selects a random cut-point and switch head
  and tail of two chromosomes

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n-point crossover

• Choose n random crossover points
• Split along those points
• Glue parts, alternating between parents
• Generalisation of 1 point (still some positional
  bias)

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Uniform crossover

• Usually it is performed by means of a randomly
  generated mask
• This mask says which genes must be flipped for
  generating the first child
• Make an inverse copy of the gene for the second
  child

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Mutation

• It is usually applied to the newly generated
  offspring before calculating its fitness value
• Alter each gene independently with a probability
  pm
• pm is called the mutation rate
• Typically between 1/pop_size and 1/
  chromosome_length

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Crossover OR mutation?

• Decade long debate which one is better /
  necessary / main-background
• Answer (at least, rather wide agreement)
• it depends on the problem, but
• in general, it is good to have both
• both have another role
• mutation-only-EA is possible, crossover-only-EA
  seems not to work

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Survivor Selection

• In this course the main feature of a GA is that
  the algorithm must be generational (also called
  age-based)
• In other words, the parents must be replaced by
  the newly generated offspring
• Some implementation employ elitism a restricted
  number of parents, the best, are copied for the
  subsequent generation

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Generation

• The loop made up of parent selection,
  recombination (crossover) mutation, survivor
  selection is called generation

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Other representations

• Gray coding of integers (still binary
  chromosomes)
• The distance between two subsequent decimal
  numbers is one bit (unlike binary coding).
• Integers
• Floating point variables

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Integer representations

• Some problems naturally have integer variables,
  e.g. TSP, scheduling problems
• Crossover and mutation are similar as in the case
  of binary encoding
• N-point crossover can be applied

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Perturbating mutation

• It picks up a small subset of genes
• Adds (subtracts) a small quantity to the selected
  genes
• It must be assured that this operation does not
  generate a perturbed individual outside the
  decision space

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Swap mutation

• Pick two alleles at random and swap their
  positions
• Preserves most of adjacency information (4 links
  broken), disrupts order more

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Insert Mutation

• Pick two allele values at random
• Move the second to follow the first, shifting
  the rest along to accommodate
• Note that this preserves most of the order and
  the adjacency information

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Inversion mutation for permutations

• Pick two alleles at random and then invert the
  substring between them.
• Preserves most adjacency information (only breaks
  two links) but disruptive of order information

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Scramble mutation for permutations

• Pick a subset of genes at random
• Randomly rearrange the alleles in those positions
• (note subset does not have to be contiguous)

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Crossovers for integer representation

• It exists a plenty of crossovers designed for
  several applications
• Order 1 crossover
• Partially mapped crossover
• Cycle crossover
• Edge crossover

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Real Encoded Representation

• The original EA with real encoding was Evolution
  Strategies
• Nevertheless in 80s several real encoded GAs
  were designed
• Details will be shown at the next lecture..