A Unified Markov Chain Approach to Analysing Randomised Search Heuristics
This provides theoretical tools for analyzing randomized search heuristics, which is incremental as it builds on existing Markov chain methods.
The paper tackles the analysis of convergence, convergence rate, and expected hitting time in randomized search heuristics by proposing a unified Markov chain approach, establishing conditions for convergence and deriving bounds for these metrics, with computational studies to investigate them.
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.