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Mathematical Problems in Engineering
Volume 2013, Article ID 398141, 9 pages
Research Article

Solving Two-Dimensional HP Model by Firefly Algorithm and Simplified Energy Function

1School of Information Science and Engineering, Southeast University, Nanjing, Jiangsu 210096, China
2Grover School of Engineering, The City College of New York, New York, NY 10031, USA

Received 18 December 2012; Accepted 9 January 2013

Academic Editor: Saeed Balochian

Copyright © 2013 Yudong Zhang 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.


In order to solve the HP model of the protein folding problem, we investigated traditional energy function and pointed out that its discrete property cannot give direction of the next step to the searching point, causing a challenge to optimization algorithms. Therefore, we introduced the simplified energy function into a turn traditional discrete energy function to continuous one. The simplified energy function totals the distance between all pairs of hydrophobic amino acids. To optimize the simplified energy function, we introduced the latest swarm intelligence algorithm, the firefly algorithm (FA). FA is a hot nature-inspired technique and has been used for solving nonlinear multimodal optimization problems in dynamic environment. We also proposed the code scheme strategy to apply FA to the simplified HP model with the clash test strategy. The experiment took 14 sequences of different chain lengths from 18 to 100 as the dataset and compared the FA with standard genetic algorithm and immune genetic algorithm. Each algorithm ran 20 times. The averaged energy convergence results show that FA achieves the lowest values. It concludes that it is effective to solve 2D HP model by the firefly algorithm and the simplified energy function.