On the complexity of overcoming gaps with isotropic mutations and elitist selection

We consider the (1+λ) evolution strategy, an evolutionary algorithm for minimization in Rn , using isotropic mutations. Thus, for instance, Gaussian mutations adapted by the 1/5-rule or by σ-self-adaptation are covered. Lower bounds on the (expected) runtime (defined as the number of function evaluations) to overcome a gap in the search space are proved (where the search faces a gap of size ∆ if the distance between the current search point and the set of all better points is at least ∆), showing when the runtime is potentially polynomial and when the runtime is necessarily superpolynomial or even necessarily exponential in n, the dimensionality of the search space.

• Type: Conference
• Year: 2005
• Where: CEC
• Authors: Jens Jägersküpper
• Keywords: Artificial Intelligence, CEC 2005, Gaussian Mutations, Isotropic Mutations, Search Space