  The convergence, convergence rate and expected hitting time play fundamental
roles in the analysis of randomised search heuristics. This paper presents a
unified Markov chain approach to studying them. Using the approach, the
sufficient and necessary conditions of convergence in distribution are
established. Then the average convergence rate is introduced to randomised
search heuristics and its lower and upper bounds are derived. Finally, novel
average drift analysis and backward drift analysis are proposed for bounding
the expected hitting time. A computational study is also conducted to
investigate the convergence, convergence rate and expected hitting time. The
theoretical study belongs to a prior and general study while the computational
study belongs to a posterior and case study.
