23 research outputs found
First-Hitting Times Under Additive Drift
For the last ten years, almost every theoretical result concerning the
expected run time of a randomized search heuristic used drift theory, making it
the arguably most important tool in this domain. Its success is due to its ease
of use and its powerful result: drift theory allows the user to derive bounds
on the expected first-hitting time of a random process by bounding expected
local changes of the process -- the drift. This is usually far easier than
bounding the expected first-hitting time directly.
Due to the widespread use of drift theory, it is of utmost importance to have
the best drift theorems possible. We improve the fundamental additive,
multiplicative, and variable drift theorems by stating them in a form as
general as possible and providing examples of why the restrictions we keep are
still necessary. Our additive drift theorem for upper bounds only requires the
process to be nonnegative, that is, we remove unnecessary restrictions like a
finite, discrete, or bounded search space. As corollaries, the same is true for
our upper bounds in the case of variable and multiplicative drift
A Unifying View on Recombination Spaces and Abstract Convex Evolutionary Search
This is the author accepted manuscript. The final version is available from Springer via the DOI in this record.Proceedings of EvoCOP 2019 - 19th European Conference on Evolutionary Computation, 24-26 April 2019, Leipzig, GermanyPrevious work proposed to unify an algebraic theory of fitness landscapes and a geometric framework of evolutionary algorithms (EAs). One of the main goals behind this unification is to develop an analytical method that verifies if a problem's landscape belongs to certain abstract convex landscapes classes, where certain recombination-based EAs (without mutation) have polynomial runtime performance. This paper advances such unification by showing that: (a) crossovers can be formally classified according to geometric or algebraic axiomatic properties; and (b) the population behaviour induced by certain crossovers in recombination-based EAs can be formalised in the geometric and algebraic theories. These results make a significant contribution to the basis of an integrated geometric-algebraic framework with which analyse recombination spaces and recombination-based EAs