Probabilistic Methods in Landscape Analysis: phase transitions, interaction structures, and complexity measures

In recent years, the study of the phase transition behavior and typical-case complexity of search and optimization problems have become an active research topic, drawing attention from researchers from computer science, mathematics, and statistical physics. The probabilistic method that has been developed since 1960s plays an important role in this development. We give a brief introduction to the problems, techniques, and results in the phase transition analysis of search and optimization problems, and present an overview on our recent work, illustrating how probabilistic methods can be used in landscape analysis and how the results give us insight into the behavior and complexity of evolutionary algorithms.