Lévy flights as an underlying mechanism for global optimization algorithms

In this chapter we propose and advocate the use of the so called Lévy flights as a driving mechanism for a class of stochastic optimization computations. This proposal, for some reason overlooked until now, is - in the author's opinion - very relevant to our need for an algorithm which is capable of generating trial steps of very different length in the search space. The required balance between short and long steps can be easily and fully controlled. A simple example of the approximated Lévy distribution, implemented in FORTRAN 77, is given. We also discuss the physical grounds of presented methods.