New Mutation Operator: Parabolic Search Strategy

Parabolic mutation is a new form of mutation which is an approach to providing the best single step information for a single gene mutation.

1. Define a 1D search envelope of size .
2. A single gene is chosen at random from a given chromosome, with value and corresponding chromosome fitness .
3. Create two new chromosomes by copying the original and replacing the selected gene with values of and .
4. Evaluate the new chromosomes and get their fitnesses, and
5. Make a decision based on table I.

    

   Fitness state 1-D Landscape Minimizer Maximizer increasing

   hilltop fit parabola decreasing

   valley fit parabola

   with parabolic fitting [10] as seen in figure 2:

   Let
   
   
   
   
   
   The maximum or minimum is then:
   
   This will find either maximum or minimum values depending on the values of , as shown in figure 2.

6. Replace the gene by the new value and return the chromosome to the population.

 
Figure 2: Parabolic Fit Mutation 

Note that if the space around the original value of the gene, , is strictly increasing or strictly decreasing we have essentially a directed creep mutation. When our values straddle a local minimum, however, we can have very fast convergence to that minimum, depending on the size of .