With this paper, we contribute to the understanding of ant colony optimization (ACO) algorithms by formally analyzing their runtime behavior. We study simple MAX-MIN ant systems on the class of linear pseudo-Boolean functions defined on binary strings of length 'n'. Our investigations point out how the progress according to function values is stored in pheromone. We provide a general upper bound of O((n^3 \log n)/ \rho) for two ACO variants on all linear functions, where (\rho) determines the pheromone update strength. Furthermore, we show improved bounds for two well-known linear pseudo-Boolean functions called OneMax and BinVal and give additional insights using an experimental study.
Cite
@article{arxiv.1007.4707,
title = {Simple Max-Min Ant Systems and the Optimization of Linear Pseudo-Boolean Functions},
author = {Timo Kötzing and Frank Neumann and Dirk Sudholt and Markus Wagner},
journal= {arXiv preprint arXiv:1007.4707},
year = {2010}
}