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.
The paper @cite_34 presents the basic and adaptive versions of the DE algorithm with parallel architecture (master-slave). With this architecture, the computational load is divided and the overall performance is improved. An explosion and mirror mutation operators were also included into DE. The explosion is a mechanism that reinitializes the population when the stagnation has occurred, and, thus, it is responsible for preventing premature convergence. The second mechanism, the mirror mutation, was designed to perform a local search by using mirror angles within the sequence.
@cite_34
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As one of the popular evolutionary algorithms, differential evolution (DE) shows outstanding convergence rate on continuous optimization problems. But prematurity probably still occurs in classical DE when using relatively small population, which is discussed in this paper. Considering that large population may significantly raise the computational effort, we propose a modified DE using smaller population (DESP) by introducing extra disturbance to its mutation operation. In addition, an adaptive adjustment scheme is designed to control the disturbance intensity according to the improvement during the evolution. To test the performance of DESP, two groups of experiments are conducted. The results show that DESP outperforms DE in terms of convergence rate and accuracy. This paper proposes a new differential evolution (DE) algorithm for unconstrained continuous optimisation problems, termed @math μJADE, that uses a small or micro' ( @math μ) population. The main contribution of the proposed DE is a new mutation operator, current-by-rand-to-pbest.' With a population size less than 10, @math μJADE is able to solve some classical multimodal benchmark problems of 30 and 100 dimensions as reliably as some state-of-the-art DE algorithms using conventionally sized populations. The algorithm also compares favourably to other small population DE variants and classical DE. In differential evolution (DE), there are many adaptive algorithms proposed for parameters adaptation. However, they mainly aim at tuning the amplification factor F and crossover probability CR. When the population diversity is at a low level or the population becomes stagnant, the population is not able to improve any more. To enhance the performance of DE algorithms, in this paper, we propose a method of population adaptation. The proposed method can identify the moment when the population diversity is poor or the population stagnates by measuring the Euclidean distances between individuals of a population. When the moment is identified, the population will be regenerated to increase diversity or to eliminate the stagnation issue. The population adaptation is incorporated into the jDE algorithm and is tested on a set of 25 scalable CEC05 benchmark functions. The results show that the population adaptation can significantly improve the performance of the jDE algorithm. Even if the population size of jDE is small, the jDE algorithm with population adaptation also has a superior performance in comparisons with several other peer algorithms for high-dimension function optimization. Differential evolution (DE) has attracted much attention recently as an effective approach for solving numerical optimization problems. However, the performance of DE is sensitive to the choice of the mutation strategy and associated control parameters. Thus, to obtain optimal performance, time-consuming parameter tuning is necessary. Different mutation strategies with different parameter settings can be appropriate during different stages of the evolution. In this paper, we propose to employ an ensemble of mutation strategies and control parameters with the DE (EPSDE). In EPSDE, a pool of distinct mutation strategies along with a pool of values for each control parameter coexists throughout the evolution process and competes to produce offspring. The performance of EPSDE is evaluated on a set of bound-constrained problems and is compared with conventional DE and several state-of-the-art parameter adaptive DE variants.