Simulated Annealing Refined Replica Exchange Global Search Algorithm

Abstract

Replica exchange (RE, or called parallel tempering) method can be used as a super simulated annealing. This chapter presents an effective global search algorithm in the use of replica exchange strategy refined by SA. Markov chain Monte Carlo (MCMC) (Andrieu et al., Mach Learn 50(1–2):5–43, 2003; Baldi and Brunak, Bioinformatics: the machine learning approach, 2nd edn. MIT, Cambridge, 2001; Bootsma and Ferguson, Proc Natl Acad Sci U S A 104(18):7588–7593, 2007; Iba, Int J Mod Phys C 12(5):623–656, 2001) algorithms are sampling from probability distributions based on constructing a Markov chain (Ross, Introduction to probability models, 9th edn. Elsevier Science & Technology Books Publisher, 2006) that has the desired distribution as its equilibrium distribution (Wikipedia, the free encyclopedia (en.wikipedia.org/wiki/): Epidemic model, Compartmental models in epidemiology, Mathematical modelling of infectious disease, Markov chain Monte Carlo, Parallel tempering, Metropolis-Hastings algorithm, etc. (and references therein)). The sampling strategy is very critical for a successful MCMC algorithm. However, in practice, the MCMC sampling methods such as Gibbs sampling (Baldi and Brunak, Bioinformatics: the machine learning approach, 2nd edn. MIT, Cambridge, 2001, Chapter 4.5) (from this reference we may know that Gibbs sampling can be rewritten as a Metropolis algorithm), Metropolis-Hastings (MH) algorithm (Baldi and Brunak, Bioinformatics: the machine learning approach, 2nd edn. MIT, Cambridge, 2001, Chapter 4.5), Multiple-try Metropolis (MM) algorithm sometimes just randomly walk (Ross, Introduction to probability models, 9th edn. Elsevier Science & Technology Books Publisher, 2006) and take a long time to explore all the solution space, will often double back and cover ground already covered, and usually own a slow algorithm convergence. In this chapter a more efficient sampling strategy of simulated annealing (Kirkpatrick et al., Science 220(4598):671–680, 1983)-refined RE (Earl and Deem, Phys Chem Chem Phys 7:3910–3916, 2005; Li et al., App Math Comput 212(1):216–228, 2009; Li et al., Parallel Comput 35(5):269–283, 2009; Swendsen and Wang, Phys Rev Lett 57(21):2607–2609, 1986; Thachuk et al., BMC Bioinformatics 8:342–362, 2007) is enclosed into the MCMC simulation.