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In addition, full exploration of the space can be limited by an initial population that poorly covers parameter space. It is important to avoid setting the rate too high because this will swamp out the directed nature of the GA search that is provided by selection and crossover. It would be useful to have the GA detect when the population is starting to converge and increase the mutation rate accordingly. This is sometimes done indirectly using niching or sharing operators, which are discussed below.

Adding constraints to general optimization methods is an active area of research, but today there are no ideal ways to apply them to GAS. The standard trick is to add a penalty term to the fitness function that acts whenever the constraint is not satisfied. For the spline fit potential just discussed, we could add the penalty 'function shown in Figure 6 . Its value is zero for distances greater than the penalty function cutoff, but quickly climbs to positive infinity for shorter distances. For distances less than that where the Genetic Algorithms Tutorial 21 h $ 5 "True Potential" I -Spline Fit Function Figure 6 An illustration of the problems that can arise when parts of parameter space are nonphysical.

In the second definition, the mutation rate specifies the fraction of individuals that have a mutation. Some individuals are chosen to be mutated, and one bit in each of these flips. No bits in the other individuals are examined. The mutation operator provides the rationale for using Gray codes. When almost any bit is flipped in a Gray-coded binary number, the value of the number will change by the smallest possible integer amount. Therefore, mutation has the effect of local search in parameter space.

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Activation by Charcoal by Bancroft W. D.

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