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.
Evolutionary algorithms have been quite successful in solving PFO. An ecology inspired algorithm for PFO is presented in @cite_8 . A key concept of this algorithm is the definition of habitats. These habitats, or clusters, are determined by using a hierarchical clustering algorithm. For example, in a multimodal optimization problem, each peak can become a promising habitat for some populations. Two categories of ecological relationships can be defined, according to the defined habitats, intra-habitats' relationships that occur between populations inside each habitat, and inter-habitats' relationships that occur between habitats. The intra-habitats' relationships are responsible for intensifying the search, and the inter-habitats' relationships are responsible for diversifying the search.
@cite_8
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The ecological principle of competitive exclusion asserts that two species cannot indefinitely occupy the same niche [Sj. Attempts have been made to state this principle as a mathematical theorem. A standard example is due to Volterra [14]. (See Example 2.1 below.) He constructed a model of two species competing for a single resource and showed that one of the species must go extinct. Although the concept of niche is rather vague, it is generally agreed that Volterra’s model is an example of two species competing for the same niche and is therefore an illustration of the principle of competitive exclusion. The generalizations of Volterra’s model have dealt largely with the introduction of more realistic assumptions about the interactions between species. These assumptions have led to some interesting mathematical problems, many of them unsolved. The purpose of this paper is to state these problems precisely, to give proofs of the known results, and to indicate the unanswered questions. The basic object of study is an idealized ecological community consisting of a certain number of species living together in an isolated geographical area. We shall assume that the community interactions are independent of both space and time and that each species is distributed uniformly over the region. The basic variables are the population densities of each of the species. The One of the most critical issues that remains to be fully addressed in existing multimodal evolutionary algorithms is the difficulty in pre-specifying parameters used for estimating how far apart optima are. These parameters are typically represented as some sorts of niching parameters in existing EAs. Without prior knowledge of a problem, it is almost impossible to determine appropriate values for such niching parameters. This paper proposes a PSO for multimodal optimization that removes the need of these niching parameters. Our results show that the proposed algorithm, Fitness Euclidean-distance Ratio based PSO (FER-PSO) is able to reliably locate multiple global optima on the search landscape over some widely used multimodal optimization test functions, given that the population size is sufficiently large. Evolutionary algorithms (EAs) are often well-suited for optimization problems involving several, often conflicting objectives. Since 1985, various evolutionary approaches to multiobjective optimization have been developed that are capable of searching for multiple solutions concurrently in a single run. However, the few comparative studies of different methods presented up to now remain mostly qualitative and are often restricted to a few approaches. In this paper, four multiobjective EAs are compared quantitatively where an extended 0 1 knapsack problem is taken as a basis. Furthermore, we introduce a new evolutionary approach to multicriteria optimization, the strength Pareto EA (SPEA), that combines several features of previous multiobjective EAs in a unique manner. It is characterized by (a) storing nondominated solutions externally in a second, continuously updated population, (b) evaluating an individual's fitness dependent on the number of external nondominated points that dominate it, (c) preserving population diversity using the Pareto dominance relationship, and (d) incorporating a clustering procedure in order to reduce the nondominated set without destroying its characteristics. The proof-of-principle results obtained on two artificial problems as well as a larger problem, the synthesis of a digital hardware-software multiprocessor system, suggest that SPEA can be very effective in sampling from along the entire Pareto-optimal front and distributing the generated solutions over the tradeoff surface. Moreover, SPEA clearly outperforms the other four multiobjective EAs on the 0 1 knapsack problem. This paper applies an ecology-inspired algorithm (ECO) to solve a complex problem from bioinformatics. The ecological-inspired algorithm represents a new perspective to develop cooperative evolutionary algorithms. Different algorithms are applied to compose the computational ecosystem, both homogeneously and heterogeneously. The aim is to search low energy conformations for the Protein Structure Prediction problem, concerning the 2D-AB off-lattice model. From the results, the heterogeneous configuration obtained the best conformations for almost all cases, possibly due to the use of different intensification and diversification strategies provided by different search algorithms.