Fractional Genetic Programming for a More Gradual Evolution

We propose a softening of a genetic program by the so-called fractional instructions. Thanks to their adjustable strengths, a new instruction can be gradually introduced to a program, and the other instructions may gradually adapt to the new member. In this way, a transformation of one candidate into another can be continuos. Such an approach makes it possible to take advantage of properties of real-coded genetic algorithms, but in the realm of genetic programming. We show, that the approach can be successfully applied to a precise generalisation of functions, including those exhibiting periodicity.