The existing BBO has poor population diversity which is generated by a mutation operator because it replaces some of the selected SIVs of an island with random SIVs. In SBBO algorithm, the mutation operator is modified by introducing a spiral search phase in mutation along with random search.

Spiral Search

In this phase of mutation operator, some of the SIVs for the new island are searched in a spiral trajectory, as defined by Fermat's spiral function, around the best island so far as shown in Figure 1 for a two and three-dimensional spaces with radius r and angle θ. In the figure, red and blue spirals correspond to negative and positive $r$ respectively for any given positive value of θ.

This method uses the similar movement of species in mutation operator around the best island so far and is defined mathematically by following Equation.

where,Ri(t) is the absolute distance between the best island and $i^{th}$ island at $t^{th}$ iteration and $l$ is randomly generated by following equation.

Random Search

The population diversity in BBO can be increased by random search by generating the new SIVs using the randomly selected islands. The mathematical model for random search is given in the following Equation.

Improved Mutation Operator

Algorithm:

• Input: A population P having n islands

• Output: Modified population P

• Steps:

  • for i=1 to n

    • if rand()<0.5

      • Update Island_i with spiral search equation

    • else

      • Update the island with random search equation