@inproceedings(Kotzing:2011:foga,
  title = {Simple max-min ant systems and the optimization of linear 
pseudo-Boolean functions},
  author = {Timo Kotzing and Frank Neumann and Dirk Sudholt and Markus 
Wagner},
  booktitle =	{Foundations of Genetic Algorithms},
  year =	2011,
  editor = 	{Hans-Georg Beyer and W.B. Langdon},
  pages =       {209--218},
  address = 	{Schwarzenberg, Austria},
  month = 	{5-9 Jan},
  organisation = {SigEvo},
  publisher = 	{ACM},
  note =	{},
  keywords =    {},
  ISBN13 =      {978-1-4503-0633-1},
  url =         {},
  size = 	{},
  doi = {doi:10.1145/1967654.1967673},
  abstract = {With
 this paper, we contribute to the understanding of ant colony 
optimisation (ACO) algorithms by formally analysing their runtime 
behaviour. 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 the pheromones.

We provide a general upper bound of O((n<sup>3</sup> log n)rho)
 on the running time 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.},
  notes =	{ACM order number 910114},
)