A Unified Markov Chain Approach to Analysing Randomised Search Heuristics

by   Jun He, et al.

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.


page 1

page 2

page 3

page 4


On the limitations of single-step drift and minorization in Markov chain convergence analysis

Over the last three decades, there has been a considerable effort within...

Asymptotically Stable Drift and Minorization for Markov Chains with Application to Albert and Chib's Algorithm

The use of MCMC algorithms in high dimensional Bayesian problems has bec...

Bioinspired Bipedal Locomotion Control for Humanoid Robotics Based on EACO

To construct a robot that can walk as efficiently and steadily as humans...

Drift Theory in Continuous Search Spaces: Expected Hitting Time of the (1+1)-ES with 1/5 Success Rule

This paper explores the use of the standard approach for proving runtime...

Quantitative convergence rates for reversible Markov chains via strong random times

Let (X_t) be a discrete time Markov chain on a general state space. It i...

Convergence rate bounds for iterative random functions using one-shot coupling

One-shot coupling is a method of bounding the convergence rate between t...

Concentration Bounds for Co-occurrence Matrices of Markov Chains

Co-occurrence statistics for sequential data are common and important da...

Please sign up or login with your details

Forgot password? Click here to reset