Genatic Algorithm Solving 8queen

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Genatic Algorithm Solving 8-queen

• Presented by
• Huda Younies Al_azzeh

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Genetic algorithms

• A genetic algorithm starts with a randomly
  generated population of individuals, with each
  individual ordinarily represented as a string of
  symbols.
• Each (potential) individual in the population is
  rated according to a fitness function which
  measures how good an individual is with respect
  to the underlying problem.
• For example, in the 8-queens problem
• an individual represents a configuration of
  queens and is a string of digits from 1, 2, ,
  8 of length 8 so that the first digit details
  the location of the first queen in the first
  column, the second digit details the location of
  the second queen in the second column, and so on
• the fitness of an individual is the number of
  pairs of non-attacking queens in the
  configuration.

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Genetic algorithms (2)

• Having generated an initial population at random,
  we iteratively generate a new population from the
  old one until some appropriate terminating
  condition is met, e.g., an individual in the
  population is fit enough or the number of
  iterations has hit some bound.
• Each iteration consists of the following process
  repeated P where P is the current population
• randomly select two individuals X and Y from the
  current population P so that fitter individuals
  are more likely to be selected
• from X and Y, reproduce a child Z
• with a small probability mutate the child Z by
  randomly replacing one symbol in the string with
  a randomly chosen symbol
• add the child Z to the new population newP.
• So, after this iteration the new population newP
  has exactly the same size as the current
  population P. The current population P is now
  replaced with the new population newP and the
  next iteration begins.
• Reproduction and mutation are done as follows.

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Genetic algorithms (3)

• Reproduction of the child Z from two individuals
  X and Y is achieved through crossover.
• The crossover of X and Y yields a child Z as
  follows
• a random bit position in the strings X and Y is
  chosen so that both strings are partitioned into
  a prefix and a suffix
• the suffix of Y is then concatenated onto the
  prefix of X, and the suffix of X is concatenated
  onto the prefix of Y to get two children
• the fittest of the two children so obtained is
  taken to be the child Z.

The 8-queens problem.
X
The individual Y and the corresponding 8-queens
configuration.
The second child and the corresponding 8-queens
configuration fitness 19.
The first child is taken to be child Z.
Randomly generate a bit position.
The two interim children.
Crossover prefixes and suffixes.
The individual X and the corresponding 8-queens
configuration.
The first child and the corresponding 8-queens
configuration fitness 20.
Y
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The genetic algorithm

• Genetic-algorithm
• P ? randomly generated initial population
• repeat
• newP ? ?
• for i 1 to P do
• X ? randomly chosen individual of P with
• probability proportional to fitness
• Y ? randomly chosen individual of P with
• probability proportional to fitness
• Z ? reproduced from X and Y
• if small random probability then mutate Z
• newP ? Z
• until some individual is fit enough or a certain
  number of iterations have been done
• return the fittest individual