Explaining optimization in genetic algorithms with uniform crossover

Abstract

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.