Size of neighborhood more important than temperature for stochastic local search

We investigate stochastic local search by Markov chain analysis in a high and a low dimensional discrete space. In the n-dimensional space Bⁿ a function called Jump is considered. The analysis shows that an algorithm using a large neighborhood and never accepting worse points performs much better than any local search algorithm accepting worse points with a certain probability. We also investigate functions in the space Bⁿ with many local optima. We compare stochastic local search using large neighborhoods with a local search using optimal temperature schedules which depend on the state of the Markov process