This paper presents a two-level protein folding optimization on a three-dimensional AB off-lattice model. The first level is responsible for forming conformations with a good hydrophobic core or a set of compact hydrophobic amino acid positions. These conformations are forwarded to the second level, where an accurate search is performed with the aim of locating conformations with the best energy value. The optimization process switches between these two levels until the stopping condition is satisfied. An auxiliary fitness function was designed for the first level, while the original fitness function is used in the second level. The auxiliary fitness function includes expression about the quality of the hydrophobic core. This expression is crucial for leading the search process to the promising solutions that have a good hydrophobic core and, consequently, improves the efficiency of the whole optimization process. Our differential evolution algorithm was used for demonstrating the efficiency of the two-level optimization. It was analyzed on well-known amino acid sequences that are used frequently in the literature. The obtained experimental results show that the employed two-level optimization improves the efficiency of our algorithm significantly, and that the proposed algorithm is superior to other state-of-the-art algorithms.
Abstract Protein structure prediction (PSP) plays an important role in the field of computational molecular biology. Although powerful optimization algorithms have been proven effective to tackle the PSP, researchers are faced with the challenge of time consuming simulations. This paper introduces a new modification of differential evolution (DE) which makes use of the computationally cheap surrogate models and gene expression programming (GEP) in order to address the aforementioned issue. The incorporated GEP is used to generate a diversified set of configurations, while radial basis function (RBF) surrogate model helps DE to find the best set of configurations. In addition to this, covariance matrix adaptation evolution strategy (CMAES) is also adopted to explore the search space more efficiently. The introduced algorithm, called SGDE, is tested on real-world proteins from the Protein data bank (PDB) using both a simplified and an all-atom model. The experiments show that SGDE performs better than the state-of-the-art algorithms on the PSP problems in both terms of the convergence rate and accuracy. In the case of run time complexity, SGDE significantly outperforms the other competitive algorithms for the adopted all-atom model.