@article{FriedrichKoetzingKrejcaetal.2016,
  author    = {Friedrich, Tobias and K{\"o}tzing, Timo and Krejca, Martin Stefan and Sutton, Andrew M.},
  title     = {Robustness of Ant Colony Optimization to Noise},
  series = {Evolutionary computation},
  volume    = {24},
  journal   = {Evolutionary computation},
  publisher = {MIT Press},
  address   = {Cambridge},
  issn      = {1063-6560},
  doi       = {10.1162/EVCO_a_00178},
  pages     = {237 -- 254},
  year      = {2016},
  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 (mu + 1) EA outperforms any ACO algorithm, with smaller mu being better; however, in the case of large noise, the (mu + 1) EA fails, even for high values of mu (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. is small enough, dependent on the variance s2 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.},
  language  = {en}
}
@article{DoerrNeumannSutton2016,
  author    = {Doerr, Benjamin and Neumann, Frank and Sutton, Andrew M.},
  title     = {Time Complexity Analysis of Evolutionary Algorithms on Random Satisfiable k-CNF Formulas},
  series = {Algorithmica : an international journal in computer science},
  volume    = {78},
  journal   = {Algorithmica : an international journal in computer science},
  publisher = {Springer},
  address   = {New York},
  issn      = {0178-4617},
  doi       = {10.1007/s00453-016-0190-3},
  pages     = {561 -- 586},
  year      = {2016},
  abstract  = {We contribute to the theoretical understanding of randomized search heuristics by investigating their optimization behavior on satisfiable random k-satisfiability instances both in the planted solution model and the uniform model conditional on satisfiability. Denoting the number of variables by n, our main technical result is that the simple () evolutionary algorithm with high probability finds a satisfying assignment in time when the clause-variable density is at least logarithmic. For low density instances, evolutionary algorithms seem to be less effective, and all we can show is a subexponential upper bound on the runtime for densities below . We complement these mathematical results with numerical experiments on a broader density spectrum. They indicate that, indeed, the () EA is less efficient on lower densities. Our experiments also suggest that the implicit constants hidden in our main runtime guarantee are low. Our main result extends and considerably improves the result obtained by Sutton and Neumann (Lect Notes Comput Sci 8672:942-951, 2014) in terms of runtime, minimum density, and clause length. These improvements are made possible by establishing a close fitness-distance correlation in certain parts of the search space. This approach might be of independent interest and could be useful for other average-case analyses of randomized search heuristics. While the notion of a fitness-distance correlation has been around for a long time, to the best of our knowledge, this is the first time that fitness-distance correlation is explicitly used to rigorously prove a performance statement for an evolutionary algorithm.},
  language  = {en}
}