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Advances in Bioinformatics
Volume 2016, Article ID 7357123, 16 pages
Research Article

Multiphase Simulated Annealing Based on Boltzmann and Bose-Einstein Distribution Applied to Protein Folding Problem

1Instituto Tecnológico de Ciudad Madero, Tecnológico Nacional de México, Avenida Sor Juana Inés de la Cruz s/n, Colonia los Mangos, 89440 Ciudad Madero, TAMPS, Mexico
2Universidad Autónoma de Coahuila, Ciudad Universitaria, 25280 Arteaga, COAH, Mexico
3UPEMOR, Boulevard Cuauhnáhuac 566, Jiutepec, 62550 Mor México, CP, Mexico

Received 24 November 2015; Revised 5 April 2016; Accepted 19 April 2016

Academic Editor: F. Fdez-Riverola

Copyright © 2016 Juan Frausto-Solis et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new hybrid Multiphase Simulated Annealing Algorithm using Boltzmann and Bose-Einstein distributions (MPSABBE) is proposed. MPSABBE was designed for solving the Protein Folding Problem (PFP) instances. This new approach has four phases: (i) Multiquenching Phase (MQP), (ii) Boltzmann Annealing Phase (BAP), (iii) Bose-Einstein Annealing Phase (BEAP), and (iv) Dynamical Equilibrium Phase (DEP). BAP and BEAP are simulated annealing searching procedures based on Boltzmann and Bose-Einstein distributions, respectively. DEP is also a simulated annealing search procedure, which is applied at the final temperature of the fourth phase, which can be seen as a second Bose-Einstein phase. MQP is a search process that ranges from extremely high to high temperatures, applying a very fast cooling process, and is not very restrictive to accept new solutions. However, BAP and BEAP range from high to low and from low to very low temperatures, respectively. They are more restrictive for accepting new solutions. DEP uses a particular heuristic to detect the stochastic equilibrium by applying a least squares method during its execution. MPSABBE parameters are tuned with an analytical method, which considers the maximal and minimal deterioration of problem instances. MPSABBE was tested with several instances of PFP, showing that the use of both distributions is better than using only the Boltzmann distribution on the classical SA.