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An estimation of distribution algorithm for minimizing the total flowtime in permutation flowshop scheduling problems Bassem Jarboui , Mansour Eddaly , Patrick Siarry. Reactive power and voltage control based on general quantum genetic algorithms John G. This promising research area is now of much interest for biomedical practitioners, and a few papers have even applied EDAs to this domain. One of these early works uses Bayesian networks as the paradigm for modeling the interactions among genes, while an UMDA approach explores the search space to find the candidate interactions [ 55 ].
The subsequent literature evaluation of the most reliable interactions unveils that many of them have been previously reported in the literature. The objective of protein structure prediction is to predict the native structure of a protein from its sequence.
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In protein design, the goal is to create new proteins that satisfy some given structural or functional constraints. Frequently, both problems are addressed using function optimization. As the possible solution space is usually huge, complex and contains many local optima, heuristic optimization methods are needed.
The efficiency of the optimization algorithm plays a crucial role in the process. In this section, we review applications of EDAs to different variants of protein structure prediction and protein design problems. We start by reviewing some important concepts related to protein models and energy functions in optimization. Then, we propose an initial general classification of EDA applications to protein problems according to how sophisticated and detailed the protein models used are.
Subsequently, we give a more detailed classification based on the specificities of the protein problems. Protein structure prediction and protein design are usually addressed by minimizing an energy function in the candidate solution space. Two essential issues in the application of EDAs and other optimization algorithms to these problems are the type of protein representation employed and the energy function of choice. There are many factors that influence the stability of proteins and have to be taken into account to evaluate candidate structures.
The native state is thought to be at the global free energy minimum of the protein.
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Electrostatic interactions, including hydrogen bonds, van der Waals interactions, intrinsic propensities of the amino acids to take up certain structures, hydrophobic interactions and conformational entropy contribute to free energy. Determining to what extent the function can represent all of these factors, as well as how to weight each one are difficult questions that have to be solved before applying the optimization method.
Simplified protein models omit some of these factors and are a first problem-solving approximation. For example, the approximate fold of a protein is influenced by the sequence of hydrophobic and hydrophilic residues, irrespective of what the actual amino acids in that sequence are [ 56 ]. Therefore, a first approximation could simply be constructed by a binary patterning of hydrophobic and hydrophilic residues to match the periodicity of secondary structural elements.
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Simplification can be further developed to consider proteins represented using this binary patterning and to approximate the protein structure prediction problem as two- and three-dimensional lattices. In this case, the energy function measures only hydrophobic and hydrophilic interactions. Optimal protein structure Figure 3-ProteinStructure. Depending on how sophisticated and detailed the protein model used is, EDAs can be divided into two groups: EDAs applying a simplified model [ 57 - 60 ] and EDAs using more detailed atomic-based models [ 61 - 63 ].
A more thorough classification is related to the type of problems addressed:. In [ 58 - 60 ], EDAs are used to solve bi-dimensional and three-dimensional simplified protein folding problems. The hydrophobic-polar HP [ 65 ], and functional protein models [ 66 ] are optimized using EDAs based on probabilistic models of different complexity i.
The results achieved outperform other evolutionary algorithms. Due to the particular topology of this instance, other evolutionary algorithms consistently fail to find the optimal solution [ 58 ]. Side chain placement problems are dealt with using UMDA with discrete representation in [ 62 , 63 ]. The approach is based on the use of rotamer libraries that can represent the side chain configurations using their rotamer angles. For these problems, EDAs have achieved very good results in situations where other methods fail [ 63 ].
Results are better when EDAs are combined with local optimization methods as in [ 63 ], where variable neighborhood search [ 68 ] is applied to the best solutions found by UMDA. Belda et al. The results of the population based incremental learning algorithm PBIL [ 9 ] and the Bayesian optimization algorithm BOA [ 18 ] are compared with two different types of genetic algorithms. Results showed that some of the ligands designed using the computational methods had better docking energies than peptides designed using a purely chemical knowledge-based approach [ 61 ].
Combining probabilistic models able to represent probabilistic dependencies with information about residue interactions in the protein contact graph is shown to improve the search efficiency for the evaluated problems. In [ 59 ], EDAs that use loopy probabilistic models are combined with inference-based optimization algorithms to deal with the same problems.
For several protein instances, this approach manage to improve the results obtained with tree-based EDAs. The alphabet reduction problem is addressed in [ 57 ] using the extended compact genetic algorithm EcGA [ 69 ]. The problem is to reduce the letter amino acid AA alphabet into a lower cardinality alphabet. A genetics-based machine learning technique uses the reduced alphabet to induce rules for protein structure prediction features. The results showed that it is possible to reduce the size of the alphabet used for prediction from twenty to just three letters resulting in more compact rules.
Results of using EDAs and the HP model to simulate the protein folding process are presented in [ 64 ]. Some of the features exhibited by the EDA model that mimics the behaviour of the protein folding process are investigated. The features considered include the correlation between the EDA success rate and the contact order of the protein models, and the relationship between the generation convergence of EDAs for the HP model and the contact order of the optimal solution. Other issues analyzed are the differences in the rate of formation of native contacts during EDA evolution, and how these differences are associated with the contact separation of the protein instance.
Throughout this paper, we reviewed the state-of-the-art of EDA applications in bioinformatics. As soon as researchers realized the need to apply a randomized, population-based, heuristic search, EDAs emerged as a natural alternative to commonly used genetic algorithms. Since the possible solution space is huge for most of the addressed problems, researchers have made use of efficient EDA implementations. A group of interesting papers demonstrate the efficiency and the competitive accuracy of this novel search paradigm in a set of challenging NP-hard genomic and proteomic bioinformatic tasks.
As the number of EDA application papers in bioinformatics is modest and the number and variety of problems is constantly growing, there is room for new EDA applications in the field.
An interesting opportunity for future research is the adaptation and application of multivariate EDA models that can efficiently deal with the huge dimensionality of current bioinformatic problems. Going further than simple univariate models, bio-experts could explicitly inspect the probabilistic relationships among problem variables for each generation of the evolutionary process.
This would create opportunities for improved accuracy. These probabilistic relationships induced from the evolutionary model are an attractive way of proposing novel biological hypotheses to be further tested by bio-experts. RA was in charge of the writing and coordination process. All authors read and approved the final manuscript. National Center for Biotechnology Information , U. Journal List BioData Min v. BioData Min. Published online Sep Author information Article notes Copyright and License information Disclaimer.
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Corresponding author. Received Jan 18; Accepted Sep This article has been cited by other articles in PMC. Abstract Evolutionary search algorithms have become an essential asset in the algorithmic toolbox for solving high-dimensional optimization problems in across a broad range of bioinformatics problems. Introduction As a consequence of increased computational power in the last decades, evolutionary search algorithms emerged as important heuristic optimization techniques in the early eighties. Estimation of distribution algorithms Estimation of distribution algorithms [ 1 - 5 ] are evolutionary algorithms that work with a multiset or population sets of candidate solutions points.
Open in a separate window. Figure 1. Table 1 EDA pseudocode. Characteristics of EDAs Essentially EDAs assume that it is possible to build a model of the promising areas of the search space, and use this model to guide the search for the optimum. A taxonomy of EDAs Since several EDAs have been proposed with a variety of models and learning algorithms, the selection of the best EDA to deal with a given optimization problem is not always straightforward.