TY  - JOUR
A1  - Doerr, Benjamin
A1  - Kötzing, Timo
T1  - Multiplicative Up-Drift
JF  - Algorithmica
N2  - Drift analysis aims at translating the expected progress of an evolutionary algorithm (or more generally, a random process) into a probabilistic guarantee on its run time (hitting time). So far, drift arguments have been successfully employed in the rigorous analysis of evolutionary algorithms, however, only for the situation that the progress is constant or becomes weaker when approaching the target. Motivated by questions like how fast fit individuals take over a population, we analyze random processes exhibiting a (1+delta)-multiplicative growth in expectation. We prove a drift theorem translating this expected progress into a hitting time. This drift theorem gives a simple and insightful proof of the level-based theorem first proposed by Lehre (2011). Our version of this theorem has, for the first time, the best-possible near-linear dependence on 1/delta} (the previous results had an at least near-quadratic dependence), and it only requires a population size near-linear in delta (this was super-quadratic in previous results). These improvements immediately lead to stronger run time guarantees for a number of applications. We also discuss the case of large delta and show stronger results for this setting.
KW  - drift theory
KW  - evolutionary computation
KW  - stochastic process
Y1  - 2020
U6  - https://doi.org/10.1007/s00453-020-00775-7
SN  - 0178-4617
SN  - 1432-0541
VL  - 83
IS  - 10
SP  - 3017
EP  - 3058
PB  - Springer
CY  - New York
ER  -