title: Robustness of Ant Colony Optimization to Noise.
abstract: Recently, ant colony optimization (ACO) algorithms have proven to be efficient in uncertain environments, such as noisy or dynamically changing fitness functions. Most of these analyses have focused on combinatorial problems such as path finding. We rigorously analyze an ACO algorithm optimizing linear pseudo-Boolean functions under additive posterior noise. We study noise distributions whose tails decay exponentially fast, including the classical case of additive Gaussian noise. Without noise, the classical [Formula: see text] EA outperforms any ACO algorithm, with smaller [Formula: see text] being better; however, in the case of large noise, the [Formula: see text] EA fails, even for high values of [Formula: see text] (which are known to help against small noise). In this article, we show that ACO is able to deal with arbitrarily large noise in a graceful manner; that is, as long as the evaporation factor [Formula: see text] is small enough, dependent on the variance [Formula: see text] of the noise and the dimension n of the search space, optimization will be successful. We also briefly consider the case of prior noise and prove that ACO can also efficiently optimize linear functions under this noise model.
authors.affiliation: Hasso Plattner Institute, University of Potsdam, Potsdam, Germany friedrich@hpi.de.
authors.forename: Tobias
authors.initials: T
authors.lastname: Friedrich
authors.affiliation: Hasso Plattner Institute, University of Potsdam, Potsdam, Germany timo.koetzing@hpi.de.
authors.forename: Timo
authors.initials: T
authors.lastname: Kötzing
authors.affiliation: Hasso Plattner Institute, University of Potsdam, Potsdam, Germany martin.krejca@hpi.de.
authors.forename: Martin S
authors.initials: MS
authors.lastname: Krejca
authors.affiliation: Hasso Plattner Institute, University of Potsdam, Potsdam, Germany andrew.sutton@hpi.de.
authors.forename: Andrew M
authors.initials: AM
authors.lastname: Sutton
mesh_terms: D000465:Algorithms; D000818:Animals; D001000:Ants / Q000502:physiology*; D008962:Models, Theoretical; D009622:Noise; D010675:Pheromones / Q000502:physiology
chemical_list: D010675:Pheromones
keywords: Ant colony optimization; Noisy Fitness; Run time analysis; Theory