José Luis Soncco-Álvarez

Memetic and Opposition-Based Learning Genetic Algorithms for Sorting Unsigned Genomes by Translocations

A standard genetic algorithm (\(\mathcal{G\!A}_{{ \mathrm{S}}}\)) for sorting unsigned genomes by translocations is improved in two different manners: firstly, a memetic algorithm (\(\mathcal{G\!A}_{{ \mathrm{M}}}\)) is provided, which embeds a new stage of local search, based on the concept of mutation applied in only one gene; secondly, an opposition-based learning (\(\mathcal{G\!A}_{{ \mathrm{OBL}}}\)) mechanism is provided that explores the concept of internal opposition applied to a chromosome. Both approaches include a convergence control mechanism of the population using the Shannon entropy. For the experiments, both biological and synthetic genomes were used. The results showed that \(\mathcal{G\!A}_{{ \mathrm{M}}}\)outperforms both \(\mathcal{G\!A}_{{ \mathrm{S}}}\)and \(\mathcal{G\!A}_{{ \mathrm{OBL}}}\)as confirmed through statistical tests.

Memetic algorithm for sorting unsigned permutations by reversals

Sorting by reversals unsigned permutations is a problem exhaustively studied in the fields of combinatorics of permutations and bioinformatics with crucial applications in the analysis of evolutionary distance between organisms. This problem was shown to be NP-hard, which gave rise to the development of a series of approximation and heuristic algorithms. Among these approaches, evolutionary algorithms were also proposed, from which to the best of our knowledge a parallel version of the first proposed genetic algorithm computes the highest quality results. These solutions were not optimized for the case when the population reaches a degenerate state, that is when individuals of the population remain very similar, and the procedure still continues consuming computational resources, but without improving the individuals. In this paper, a memetic algorithm is proposed for sorting unsigned permutations by reversals, using the local search as a way to improve the fitness function image of the individuals. Also, the entropy of the population is controlled, such that, when a degenerate state is reached the population is restarted. Several experiments were performed using permutations generated from biological data as well as hundreds of randomly generated permutations of different size, from which some ones were chosen and used as benchmark permutations. Experiments have shown that the proposed memetic algorithm uses more adequately the computational resources and gives competitive results in comparison with the parallel genetic algorithm and outperforms the results of the standard genetic algorithm.

Parallelization of genetic algorithms for sorting permutations by reversals over biological data

Reversals are operations of great biological significance for the analysis of the evolutionary distance between organisms. Genome rearrangement through reversals, consists in finding the shortest sequence of reversals to transform one genome represented as a signed or unsigned permutation into another. When genes are non oriented and correspondingly permutations are unsigned, sorting by reversals came arise as a challenging problem in combinatorics of permutations. In fact, this problem is known to be NP-hard, but the question whether it is NP-complete remains open for more than twenty years. When permutations are signed and correspondingly genes are oriented, the problem is known to be in P. A parallelization of a standard GA Genetic Algorithm is proposed for the problem of sorting unsigned permutations. This GA was previously reported in the literature as the most competitive regarding precision for which as control mechanism an 1.5-approximation algorithm was used. For the parallelization, the MPI Library of the C language was used and experiments were performed for calculating the execution time and precision. By increasing the number of individuals, experiment showed improvement in relation to previous approaches. Additionally, a virtualization of the GA using a MicroBlaze processor from Xilinx was performed on OVP for which the average number of executed instructions was of approximately 1.40 Giga instruction per second. In this extended version of this works originally presented in NaBIC 2013 biological data was generated and it was shown how the parallelization can be applied for their analysis. Specifically, the evolutionary distances between different pairs of organism were computed based on the set of non common genes in their mitochondrial DNA genome and the reversal distance between the sequences of common genes.

Computing translocation distance by a genetic algorithm

Translocation is a useful operation on strings with challenging questions in combinatorics of permutations and interesting applications in analysis of sequences. A translocation operation essentially is the interchange of prefixes and suffixes among two substrings of a string. For the case of genomes represented as strings, symbols that represent genes and chromosomes are modeled as substrings of the genomes; thus, translocation is an operation that models the interaction between chromosomes inside a genome. The translocation distance between two genomes is defined as the minimum number of translocations to convert one genome into another and has been proved to be a meaningful manner of modeling the evolutive distance between organisms. The particular case of unsigned genomes, those in which the orientation of the genes are not considered, is particularly difficult, while the signed case, in which the orientation of genes is considered, has been proved to be polynomially decidable. This paper presents an innovative Genetic Algorithm (GA) approach to solve the unsigned translocation distance problem. A distinguishing feature of the proposed GA is that it uses as fitness function the translocation distance for randomly generated signed versions of the input (that is an unsigned genome). Experiments over randomly generated strings (synthetic genomes) showed that the proposed GA approach computes answers that are better than those computed by an L5+ε-approximation algorithm, the latter also implemented as part of this work.

Parallelization and virtualization of genetic algorithms for sorting permutations by reversals

Reversals are operations of great biological significance for the analysis of the evolutionary distance between organisms. Genome rearrangement through reversals, consists in finding the shortest sequence of reversals to transform one genome represented as a signed or unsigned permutation into another. When genes are non oriented and correspondingly permutations are unsigned, sorting by reversals came arise as a challenging problem in combinatorics of permutations. In fact, this problem is known to be NP-hard, but the question whether it is NP-complete remains open for more than twenty years. When permutations are signed and correspondingly genes are oriented, the problem is known to be in P. A parallelization of a standard GA (Genetic Algorithm) is proposed for the problem of sorting unsigned permutations. This GA was previously reported in the literature as the most competitive regarding precision for which as control mechanism an 1.5-approximation algorithm was used. For the parallelization, the MPI Library of the C language was used and experiments were performed for calculating the execution time and precision. By increasing the number of individuals, experiment showed improvement in relation to previous approaches. Additionally, a virtualization of the GA using a MicroBlaze processor from Xilinx was performed on OVP for which the average number of executed instructions was of approximately 1.40 Giga instruction per second.

Opposition-Based Memetic Algorithm and Hybrid Approach for Sorting Permutations by Reversals

Sorting unsigned permutations by reversals is a difficult problem; indeed, it was proved to be NP-hard by Caprara (1997). Because of its high complexity, many approximation algorithms to compute the minimal reversal distance were proposed until reaching the nowadays best-known theoretical ratio of 1.375. In this article, two memetic algorithms to compute the reversal distance are proposed. The first one uses the technique of opposition-based learning leading to an opposition-based memetic algorithm; the second one improves the previous algorithm by applying the heuristic of two breakpoint elimination leading to a hybrid approach. Several experiments were performed with one-hundred randomly generated permutations, single benchmark permutations, and biological permutations. Results of the experiments showed that the proposed OBMA and Hybrid-OBMA algorithms achieve the best results for practical cases, that is, for permutations of length up to 120. Also, Hybrid-OBMA showed to improve the results of OBMA for permutations greater than or equal to 60. The applicability of our proposed algorithms was checked processing permutations based on biological data, in which case OBMA gave the best average results for all instances.

Parallel genetic algorithms with sharing of individuals for sorting unsigned genomes by reversals

Rearrangement by reversals is a suitable global operation when treating genomes with a single chromosome. Sorting unsigned genomes by reversals is an NP-hard optimization problem. Several approximation algorithms were proposed, among them, in previous work, a competitive genetic algorithm and its standard parallel version, that provides a substantial speedup, were introduced. In this paper, two approaches using island models to parallelize such algorithm are presented. The first approach uses the unidirectional ring communication topology to exchange individuals between neighboring islands and, the second uses a complete graph scheme for the distribution of individuals among islands. Both approaches were proposed with the objective of improving precision (that is, for reducing the number of reversals) and decreasing the runtime regarding the sequential GA. Experiments were performed with randomly generated synthetic genomes and the results show that the parallel approach using the ring communication topology outperforms the previously proposed GA and its parallel version in terms of accuracy, providing solutions with less reversals and, that the parallel approach using the complete graph topology does not provide significant improvements. Both the new parallel GA approaches get competitive speedups regarding the speedup achieved by the standard parallel version of the genetic algorithm.

Variable neighborhood search for the large phylogeny problem using gene order data

Computing evolutionary distances using gene order data is a complex combinatory problem; nevertheless, for specific metrics exact polynomial algorithms were proposed, having in many cases non trivial approaches. This scenario can become harder if we want to reconstruct phylogenies based on gene order data: first it is necessary to explore the search space of possible tree structures which is well-known to be exponential; second, it is necessary a method for evaluating the cost of these trees, i.e. to find a labeling of the internal nodes that leads to the most parsimonious cost of a tree under a given evolutionary distance. The latter problem was shown to be NP-hard even for 3 genomes (median problem) under many evolutionary distances. In this paper we propose a variable neighborhood search approach for solving the large phylogeny problem for data based on gene orders. Also, a greedy approach is proposed for the small phylogeny problem aiming to reduce the running time of the Kovac et al. dynamic programming approach. Our proposed algorithms were implemented as the software called HELPHY. Experiments showed that the running time is improved for finding trees with good scores (reversal distance) for the Campanulaceae dataset, and a new tree structure was found having the best known score (double cut and join distance) for the case of Hemiascomycetes dataset.

Parallel memetic genetic algorithms for sorting unsigned genomes by translocations

The rearrangement of genomes is an important tool for studying the evolution of genomes and specifically for the construction of phylogenies. A translocation splits and combines the strings of genes of a pair of chromosomes inside a genome and is considered a suitable operation for rearrangement of genomes with multiple chromosomes. The translocation distance between two genomes is the minimum number of translocations necessary to convert one of them into the other. Computing the translocation distance between two unsigned genomes, that is the case in which the direction of the genes between the chromosomes is not considered, is known to be an MV-hard optimization problem. Among several approximation algorithms that were proposed for solving this problem, the authors introduced in a previous work a genetic algorithm approach improved with opposition based learning and memetic mechanisms. In this paper, two parallel treatments of the sequential memetic approach are introduced for solving the translocation distance problem for unsigned genomes. The first approach, computes in parallel the fitness over all individuals of a population. This method intends speeding-up the sequential memetic algorithm. The second approach, processes in parallel multiple populations and was proposed for improving precision providing solutions with a less number of translocations than the sequential memetic algorithm. Several experiments were performed with randomly generated synthetic and biologically based genomes. Results show that the parallel approaches outperform the sequential memetic algorithm.