Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2013, Article ID 398141, 9 pages http://dx.doi.org/10.1155/2013/398141 Research Article Solving Two-Dimensional HP Model by Firefly Algorithm and Simplified Energy Function Yudong Zhang, 1 Lenan Wu, 1 and Shuihua Wang 2 1 School of Information Science and Engineering, Southeast University, Nanjing, Jiangsu 210096, China 2 Grover School of Engineering, he City College of New York, New York, NY 10031, USA Correspondence should be addressed to Lenan Wu; wuln@seu.edu.cn Received 18 December 2012; Accepted 9 January 2013 Academic Editor: Saeed Balochian Copyright © 2013 Yudong Zhang et al. his 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. herefore, we introduced the simpliied energy function into a turn traditional discrete energy function to continuous one. he simpliied energy function totals the distance between all pairs of hydrophobic amino acids. To optimize the simpliied energy function, we introduced the latest swarm intelligence algorithm, the irely 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 simpliied HP model with the clash test strategy. he experiment took 14 sequences of diferent 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. he averaged energy convergence results show that FA achieves the lowest values. It concludes that it is efective to solve 2D HP model by the irely algorithm and the simpliied energy function. 1. Introduction Protein folding is the process by which a protein structure assumes its functional shape or conformation. It is the physical process by which a polypeptide folds into its char- acteristic and functional three-dimensional structure from random coil. Each protein exists as an unfolded polypeptide or random coil when translated from a sequence of mRNA to a linear chain of amino acids [1]. his polypeptide lacks any developed three-dimensional structure. Amino acids interact with each other to produce a well-deined three-dimensional structure, the folded protein, known as the native state. he resulting three-dimensional structure is determined by the amino acid sequence [2, 3]. he protein folding has a challenging search space, since nature identiies the global minimum from more than 10 50 possible conformations for the backbone of a small protein [4]. A successful prediction requires two major components: (1) a set of free energy components for the protein, which are computationally inexpensive enough to be used in the search procedure and suiciently accurate to ensure the uniqueness of the native fold; (2) an eicient optimization procedure which is capable of inding an appropriate minimum for the strongly anisotropic function of hundreds of variables [5, 6]. Scholars tend to use the 2D lattice model (HP model) for protein folding. he HP model was proposed by Lau and Dill [7]. In this model, proteins consist of two diferent kinds of residues, hydrophobic and hydrophilic. he task is to minimize the energy function, which is deined as the counting of every two hydrophobic residues that are nonconsecutive nearest neighbors on the lattice [8]. he recent literatures solving the 2D HP model were reported as follows. Lin and Hsieh [9] proposed an eicient hybrid Taguchi genetic algorithm that combines genetic algorithm, Taguchi method, and particle swarm optimiza- tion, in order to enhance the performance of predicting protein structure. In addition, Lin presented the PSO inspired by a mutation mechanism in a genetic algorithm. In the experiment, Lin demonstrated that their algorithm can be applied successfully to the protein folding problems based on