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Genetic Algorithm


Introduction to Artificial Intelligence

            Genetic Algorithms

        Practical Issues: Selection
‘Roulette’ Problems
 The basic ‘roulette’ selection, in which each
 individual is assigned a probability of selection
 according to their fitness in proportion to total
 fitness, suffers from a number of problems
   suppose the fitness varies from e.g. -10 to +10
      we could add 10 (or 11), but suppose we don’t know the
      lower bound of fitness
   as the solution is nearly reached, all fitnesses will be
   roughly the same, so have roughly equal chance,
      four individuals with x= 29, 29, 30, 30 when maximising x2
      over [0 31] have fitness proportions 0.242, 0.242, 0.258,
Fitness Scaling
 A frequently used solution is to ‘scale’ the
 fitness function in some way
 Fitness scaling alters (transforms) the fitness in
 some way, such that
   the fitness of an average individual is still average
   below average individuals have low fitness
   above average individuals have high fitness
 There are two main methods used
   linear scaling
   sigma scaling
Linear Scaling
 For the population, find
    the average (mean) fitness
    the minimum (min) fitness
 Scale by the equation
                           f  f min 
             f scale  0.9
                          f               0.1
                           mean  f min 


                        fmin        fmean fmax
Sigma Scaling
 For the population, find
    the average (mean) fitness
    the standard deviation (std) of fitness
 Scale by the equation
                    f  f m ean           
    f scale    max
                    2f           1.0, 0.1
                        std               
 Has a very similar effect to linear scaling, except
 when there are outliers
 If selection of the next generation is left to
 chance, then there is always a possibility that
 the best individual in the population does not
   the GA may ‘wander off’ from a good solution
 In ‘elitist’ strategies, the best individual always
 survives to the next generation
   there are minor variations possible
      the best individual survives to the next generation
      and is then is the pool for crossover, mutation, etc.
      the best individual survives to the next generation
      and is ‘protected’ from any genetic operators
Overlapping Populations
 As a further refinement, it is also possible to
 not replace the entire population at each
   straight overlapping
      a proportion of the population
        – e.g. 50%
      survives unchanged, the other 50% undergo operators
   elitist overlapping
      temporarily allow the population size to grow by adding in
      new individuals (all the old ones remain)
      the old and the new then ‘fight’ for survival

 In practice, any variation that you can think of!
Other Selection Mechanisms
 Proportional selection
   calculate the fitness proportions as before
   multiply the fitness proportion by the population size
   round this to the nearest integer
   that many of the individual survive
 Tournament selection
   to select a new population of size N, from N
   repeat N times
      pick two individuals at random from the population
      the one with the highest fitness survives
   supposedly mirrors natural competition more closely

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