Transformation of binary data

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I have a function that I try to optimize using Particle Swarm Optimization. Objective function gets a binary string. So these binary strings are candidate solutions of the subject function. I can measure the dissimilarity between two solution, but I need to move one solution towards another by a factor, meaning I need a vector. Is there any methods to do that?

Example:

a = 0011001 
b = 0011010

I want to move a towards b by the factor of 0.4. So I need to find another string that is similarity between a is 0.6 and similarity between b is 0.4.

I hope I could explain myself clear.