Multiple-Try Simulated Annealing Algorithm for Global Optimization

Wei Shao,Guangbao Guo

doi:10.1155/2018/9248318

Abstract

Simulated annealing is a widely used algorithm for the computation of global optimization problems in computational chemistry and industrial engineering. However, global optimum values cannot always be reached by simulated annealing without a logarithmic cooling schedule. In this study, we propose a new stochastic optimization algorithm, i.e., simulated annealing based on the multiple-try Metropolis method, which combines simulated annealing and the multiple-try Metropolis algorithm. The proposed algorithm functions with a rapidly decreasing schedule, while guaranteeing global optimum values. Simulated and real data experiments including a mixture normal model and nonlinear Bayesian model indicate that the proposed algorithm can significantly outperform other approximated algorithms, including simulated annealing and the quasi-Newton method.

Highlights

Since the 21st century, the modern computers have greatly expanded the scientific horizon by facilitating the studies on complicated systems, such as computer engineering, stochastic process, and modern bioinformatics
The MTMSA algorithm is a combination of the simulated annealing (SA) algorithm and multiple-try Metropolis (MTM) algorithm [16]
The main purpose of this example is to demonstrate that the MTMSA algorithm could compute the optimization problem in the case of multiple local maxima and outperform its counterparts in terms of accuracy and efficiency

Summary

Introduction

Since the 21st century, the modern computers have greatly expanded the scientific horizon by facilitating the studies on complicated systems, such as computer engineering, stochastic process, and modern bioinformatics. A large volume of high dimensional data can be obtained, but their efficient computation and analysis present a significant challenge. With the development of modern computers, Markov chain Monte Carlo (MCMC) methods have enjoyed a enormous upsurge in interest over the last few years [1, 2]. During the past two decades, various advanced MCMC methods have been developed to successfully compute different types of problems (e.g., Bayesian analysis, high dimensional integral, and combinational optimization). As an extension of MCMC methods, the simulated annealing (SA) algorithm [1,2,3] has become increasingly popular since it was first introduced by Kirkpatrick et al (1983). As Monte Carlo methods are not sensitive to the dimension of data sets, the SA algorithm plays an important role in molecular physics, computational chemistry, and computer science. It has been successfully applied to many complex optimization problems

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