Explaining Adaptation in Genetic Algorithms With Uniform Crossover: The Hyperclimbing Hypothesis

The hyperclimbing hypothesis is a hypothetical explanation for adaptation in genetic algorithms with uniform crossover (UGAs). Hyperclimbing is an intuitive, general-purpose, non-local search heuristic applicable to discrete product spaces with rugged or stochastic cost functions. The strength of this heuristic lie in its insusceptibility to local optima when the cost function is deterministic, and its tolerance for noise when the cost function is stochastic. Hyperclimbing works by decimating a search space, i.e. by iteratively fixing the values of small numbers of variables. The hyperclimbing hypothesis holds that UGAs work by implementing efficient hyperclimbing. Proof of concept for this hypothesis comes from the use of a novel analytic technique involving the exploitation of algorithmic symmetry. We have also obtained experimental results that show that a simple tweak inspired by the hyperclimbing hypothesis dramatically improves the performance of a UGA on large, random instances of MAX-3SAT and the Sherrington Kirkpatrick Spin Glasses problem.Comment: 22 pages, 5 figure

Theme Preservation and the Evolution of Representation ABSTRACT

In his thesis Toussaint calls for a “general project to develop theories on adaptation processes that account for the adaptation of representations”. The theory developed in this paper is a contribution to this project. We first define the simple concept of a genotypic theme and define what it means for mutation operators to be theme preserving and theme altering. We use the idea of theme preservation to develop the concept of subrepresentation. Then we develop a theory that illuminates the behavior of a mutation-only fitness proportional evolutionary algorithm in which mutation preserves genotypic themes with high probability. Our theory shows that such evolutionary algorithms implicitly implement what we call subrepresentation evolving multithreaded evolution, i.e. such EAs conduct second-order search over a predetermined set of representations and exploit promising representations for first order evolutionary search. We illuminate subrepresentaiton evolving multithreaded evolution by comparing and contrasting it with the behavior of island model EAs. Our theory is immediately useful in understanding the significance of the low probability with which theme altering type 2 mutations are applied to genotypes of the evolutionary systems in Toussaint’s thesis