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Purpose – In this work, the authors show the performance of the proposed diploid scheme (a representation where each individual contains two genotypes) with respect to two dynamic optimization problems, while addressing drawbacks the authors have identified in previous works which compare diploid evolutionary algorithms (EAs) to standard EAs. The paper aims to discuss this issue. Design/methodology/approach – In the proposed diploid representation of EA, each individual possesses two copies of the genotype. In order to convert this pair of genotypes to a single phenotype, each genotype is individually evaluated in relation to the fitness function and the best genotype is presented as the phenotype. In order to provide a fair and objective comparison, the authors make sure to compare populations which contain the same amount of genetic information, where the only difference is the arrangement and interpretation of the information. The two representations are compared using two shifting fitness functions which change at regular intervals to displace the global optimum to a new position. Findings – For small fitness landscapes the haploid (standard) and diploid algorithms perform comparably and are able to find the global optimum very quickly. However, as the search space increases, rediscovering the global optimum becomes more difficult and the diploid algorithm outperforms the haploid algorithm with respect to how fast it relocates the new optimum. Since both algorithms use the same amount of genetic information, it is only fair to conclude it is the unique arrangement of the diploid algorithm that allows it to explore the search space better. Originality/value – The diploid representation presented here is novel in that instead of adopting a dominance scheme for each allele (value) in the vector of values that is the genotype, dominance is adopted across the entire genotype in relation to its homologue. As a result, this representation can be extended across any alphabet, for any optimization function.

Purpose – The purpose of this paper is to present a study of the effect of different types of annealing schedules for a ribonucleic acid (RNA) secondary structure prediction algorithm based on simulated annealing (SA). Design/methodology/approach – An RNA folding algorithm was implemented that assembles the final structure from potential substructures (helixes). Structures are encoded as a permutation of helixes. An SA searches this space of permutations. Parameters and annealing schedules were studied and fine-tuned to optimize algorithm performance. Findings – In comparing with mfold, the SA algorithm shows comparable results (in terms of F-measure) even with a less sophisticated thermodynamic model. In terms of average specificity, the SA algorithm has provided surpassing results. Research limitations/implications – Most of the underlying thermodynamic models are too simplistic and incomplete to accurately model the free energy for larger structures. This is the largest limitation of free energy-based RNA folding algorithms in general. Practical implications – The algorithm offers a different approach that can be used in practice to fold RNA sequences quickly. Originality/value – The algorithm is one of only two SA-based RNA folding algorithms. The authors use a very different encoding, based on permutation of candidate helixes. The in depth study of annealing schedules and other parameters makes the algorithm a strong contender. Another benefit is that new thermodynamic models can be incorporated with relative ease (which is not the case for algorithms based on dynamic programming).

Background RNA visualization software tools have traditionally presented a static visualization of RNA molecules with limited ability for users to interact with the resulting image once it is complete. Only a few tools allowed for dynamic structures. One such tool is jViz.RNA. Currently, jViz.RNA employs a unique method for the creation of the RNA molecule layout by mapping the RNA nucleotides into vertexes in a graph, which we call the detailed graph, and then utilizes a Newtonian mechanics inspired system of forces to calculate a layout for the RNA molecule. The work presented here focuses on improvements to jViz.RNA that allow the drawing of RNA secondary structures according to common drawing conventions, as well as dramatic run-time performance improvements. This is done first by presenting an alternative method for mapping the RNA molecule into a graph, which we call the compressed graph, and then employing advanced numerical integration methods for the compressed graph representation. Results Comparing the compressed graph and detailed graph implementations, we find that the compressed graph produces results more consistent with RNA drawing conventions. However, we also find that employing the compressed graph method requires a more sophisticated initial layout to produce visualizations that would require minimal user interference. Comparing the two numerical integration methods demonstrates the higher stability of the Backward Euler method, and its resulting ability to handle much larger time steps, a high priority feature for any software which entails user interaction. Conclusion The work in this manuscript presents the preferred use of compressed graphs to detailed ones, as well as the advantages of employing the Backward Euler method over the Forward Euler method. These improvements produce more stable as well as visually aesthetic representations of the RNA secondary structures. The results presented demonstrate that both the compressed graph representation, as well as the Backward Euler integrator, greatly enhance the run-time performance and usability. The newest iteration of jViz.RNA is available at https://jviz.cs.sfu.ca/download/download.html. Electronic supplementary material The online version of this article (doi:10.1186/s12859-017-1682-0) contains supplementary material, which is available to authorized users.

This paper presents two in-depth studies on RnaPredict, an evolutionary algorithm for RNA secondary structure prediction. The first study is an analysis of the performance of two thermodynamic models, Individual Nearest Neighbor (INN) and Individual Nearest Neighbor Hydrogen Bond (INN-HB). The correlation between the free energy of predicted structures and the sensitivity is analyzed for 19 RNA sequences. Although some variance is shown, there is a clear trend between a lower free energy and an increase in true positive base pairs. With increasing sequence length, this correlation generally decreases. In the second experiment, the accuracy of the predicted structures for these 19 sequences are compared against the accuracy of the structures generated by the mfold dynamic programming algorithm (DPA) and also to known structures. RnaPredict is shown to outperform the minimum free energy structures produced by mfold and has comparable performance when compared to suboptimal structures produced by mfold.

Motivation: Ribonucleic acid is vital in numerous stages of protein synthesis; it also possesses important functional and structural roles within the cell. The function of an RNA molecule within a particular organic system is principally determined by its structure. The current physical methods available for structure determination are time-consuming and expensive. Hence, computational methods for structure prediction are sought after. The energies involved by the formation of secondary structure elements are significantly greater than those of tertiary elements. Therefore, RNA structure prediction focuses on secondary structure. Results: We present P-RnaPredict, a parallel evolutionary algorithm for RNA secondary structure prediction. The speedup provided by parallelization is investigated with five sequences, and a dramatic improvement in speedup is demonstrated, especially with longer sequences. An evaluation of the performance of P-RnaPredict in terms of prediction accuracy is made through comparison with 10 individual known structures from 3 RNA classes (5S rRNA, Group I intron 16S rRNA and 16S rRNA) and the mfold dynamic programming algorithm. P-RnaPredict is able to predict structures with higher true positive base pair counts and lower false positives than mfold on certain sequences. Availability: P-RnaPredict is available for non-commercial usage. Interested parties should contact Kay C. Wiese (wiese@cs.sfu.ca). Contact: wiese@cs.sfu.ca

In this paper we introduce pEvoSAT, a permutation based Genetic Algorithm (GA), designed to solve the boolean satisfiability (SAT) problem when it is presented in the conjunctive normal form (CNF). The use of permutation based representation allows the algorithm to take advantage of domain specific knowledge such as unit propagation, and pruning. In this paper, we explore and characterize the behavior of our algorithm. This paper also presents the comparison of pEvoSAT to GASAT, a leading implementation of GAs for the solving of CNF instances.

Recently, there is a resurgence of interest in the RNA secondary structure prediction problem due to the discovery of many new families of non-coding RNAs with a variety of functions. This paper describes and presents a novel algorithm for RNA secondary structure prediction based on an ensemble-based approach. An evaluation of the performance in terms of sensitivity and specificity is made. Experiments were performed on eleven structures from four RNA classes (RNaseP, Group I intron 16S rRNA, Group I intron 23S rRNA and 16S rRNA). Three RNA secondary structure similarity metrics (base pair distance, tree edit distance, and thermodynamic energy distance) and their effects on the clustering algorithm were explored. The significant contribution of this paper is in the examining of the various results from employing different dissimilarity metrics. Overall, the base pair distance dissimilarity metric shows better results with the other two distance metrics (tree edit distance and thermodynamic energy distance). The results presented in this paper demonstrate that SARNA-Ensemble-Predict can give comparable performance to a state-of-the-art algorithm Sfold in terms of sensitivity.

Pseudoknots are RNA tertiary structures which perform essential biological functions. This paper presents SARNA-Predict-pk, an algorithm for pseudoknotted RNA secondary structure prediction based on Simulated Annealing (SA). The research presented here extends previous work of SARNA-Predict and incorporates a new thermodynamic model into the algorithm, effectively enabling it to predict pseudo-knotted RNA structures. An evaluation of the performance of SARNA-Predict-pk in terms of prediction accuracy is made via comparison with several state-of-the-art prediction algorithms. We measured the sensitivity and specificity using five prediction algorithms. Three of these are dynamic programming algorithms: Pseudoknot (pknotsRE), NUPACK, and pknotsRG-mfe. The other two are heuristic algorithms: SARNA-Predict-pk and HotKnots algorithms. An evaluation for the performance of SARNA-Predict-pk in terms of prediction accuracy was verified with native structures. Experiments on ten individual known structures from six RNA classes (tRNA, viral RNA, anti-genomic HDV, telomerase RNA, tmRNA, and RNaseP) were performed. The results presented in this paper demonstrate that SARNA-Predict-pk can out-perform other state-of-the-art algorithms in terms of prediction accuracy.

Covariance models are a powerful description of non-coding RNA (ncRNA) families that can be used to search nucleotide databases for new members of these ncRNA families. Currently, estimation of the parameters of a covariance model (state transition and emission scores) is based only on the observed frequencies of mutations, insertions, and deletions in known ncRNA sequences. For families with very few known members, this can result in rather uninformative models where the consensus sequence has a good score and most deviations from consensus have a fairly uniform poor score. It is proposed here to combine the traditional observed-frequency information with known information about free energy changes in RNA helix formation and loop length changes. More thermodynamically probable deviations from the consensus sequence will then be favored in database search. The thermodynamic information may be incorporated into the models as informative priors that depend on neighboring consensus nucleotides and on loop lengths.

Two extensive analyzes on RnaPredict, an evolutionary algorithm for RNA folding, are presented here. The first study evaluates the performance of Individual Neares Neighbor (INN) and Individual Nearest Neighbor-Hydrogen Bond (INN-HB), two stacking-energy thermodynamic models; the criteria for comparison is the correlation between the prediction accuracy and the free energy of predicted structures for 9 RNA sequences. Despite some variance, a trend between lower free energies and increases in true positive base pairs is apparent. In general, this correlation decreases as the sequence length increases. The second study compares the performance of RnaPredict against the mfold dynamic programming algorithm (DPA) on the same sequences in terms of specificity and sensitivity. The results indicate that RnaPredict has comparable performance to mfold on sub-optimal structures, and outperforms mfold's minimum free energy structures.

This paper presents an extension to P-RnaPredict, a parallel evolutionary algorithm (EA) for RNA folding. The impact of three pseudorandom number generators (PRNGs) on the EA's performance is evaluated. The generators tested included the C standard library PRNG RAND, a parallelized multiplicative congruential generator (MCG), and a parallelized Mersenne Twister (MT). P-RnaPredict was implemented using the message passing interface (MPI) and tested on a 128 node Beowulf cluster. The PRNG comparison testing was performed with four known structures that are 118, 122, 543, and 556 nucleotides in length. PRNGs effects were investigated and predicted structures compared to known structures

This paper presents a comparison of two types of algorithms for RNA secondary structure prediction: an implementation of Nussinov's dynamic programming algorithm (DPA), and P-RnaPredict, a parallel evolutionary algorithm (EA). The research presented here builds on previous work and examines the results from tests of three RNA sequences that are 118, 543, and 784 nucleotides in length. A variety of EA parameter settings were employed based on previous experimentation. Predicted structures were compared to those generated by the Nussinov DPA and to known structures to determine relative accuracy. Results indicate that the EA demonstrated high prediction accuracy and outperformed the Nussinov DPA on all tested sequences

This paper presents a fully parallel version of RnaPredict, a genetic algorithm (GA) for RNA secondary structure prediction. The research presented here builds on previous work and examines the impact of three different pseudorandom number generators (PRNGs) on the GA's performance. The three generators tested are the C standard library PRNG RAND, a parallelized multiplicative congruential generator (MCG), and a parallelized Mersenne Twister (MT). A fully parallel version of RnaPredict using the Message Passing Interface (MPI) was implemented on a 128-node Beowulf cluster. The PRNG comparison tests were performed with known structures whose sequences are 118, 122, 468, 543, and 556 nucleotides in length. The effects of the PRNGs are investigated and the predicted structures are compared to known structures. Results indicate that P-RnaPredict demonstrated good prediction accuracy, particularly so for shorter sequences.

This paper presents a parallel version of RnaPredict, a genetic algorithm (GA) for RNA secondary structure prediction. The research presented here builds on previous work and examines the impact of three different pseudorandom number generators (PRNGs) on the GA's performance. The three generators tested are the C standard library PRNG RAND, a parallelized multiplicative congruential generator (MCG), and a parallelized Mersenne Twister (MT). A fully parallel version of RnaPredict using the Message Passing Interface (MPI) was implemented. The PRNG comparison tests were performed with known structures that are 118, 122, 543, and 556 nucleotides in length. The effects of the PRNGs are investigated and the predicted structures are compared to known structures.

This work builds on previous research from an EA used to predict secondary structure of RNA molecules. The EA has the goal of predicting which canonical base pairs will form hydrogen bonds and helices. The addition of stacking energies, through INN and INN-HB, to our thermodynamic model has enhanced our predictions. We test three RNA sequences of lengths 118, 543, and 784 nucleotides using a variety of previously successful operators and parameter settings. The accuracy of the predicted structures are compared against those generated by the Nussinov DPA and also to known structures. The EA showed high accuracy of prediction especially on short sequences. On all tested sequences, the EA outperforms the Nussinov DPA.

This work presents a coarse-grained distributed genetic algorithm (GA) for RNA secondary structure prediction. This research builds on previous work and contains two new thermodynamic models, INN and INN-HB, which add stacking-energies using base pair adjacencies. Comparison tests were performed against the original serial GA on known structures that are 122, 543, and 784 nucleotides in length on a wide variety of parameter settings. The effects of the new models are investigated, the predicted structures are compared to known structures and the GA is compared against a serial GA with identical models. Both algorithms perform well and are able to predict structures with high accuracy for short sequences.

This paper presents a new coarse-grained distributed genetic algorithm (GA) for the prediction of the secondary structure of RNA molecules, based largely on a serial permutation-based GA. The benefits of the distributed GA over our existing serial GA are analyzed and demonstrated. We also analyze the impact of the keep-best reproduction (KBR) and roulette wheel selection (STDS) GA replacement techniques. Finally, we verify the increase in convergence speed of our distributed GA. Tests was performed on 241 and 785 nucleotide sequences. Overall, the distributed GA is found to improve upon the serial GA performances, with a much more pronounced impact on the STDS selection strategy. There is also a notable acceleration in convergence speed.

This paper presents new results with a permutation-based genetic algorithm (GA) to predict the secondary structure of RNA molecules. More specifically, the proposed algorithm predicts which canonical base pairs forms hydrogen bonds and builds helices, also known as stems. We discuss a GA where a permutation is used to encode the secondary structure of RNA molecules. We have tested RNA sequences of lengths 76, 210, 681, and 785 nucleotides over a wide variety of operators and parameter settings and focus on discussing in depth the results with two crossover operators asymmetric edge recombinations (ASERC) and symmetric edge recombination (SYMERC) that have not been analyzed in this domain previously. We demonstrate that the keep-best reproduction (KBR) operator has similar benefits as in the travelling salesman problem (TSP) domain. We also compare the results of the permutation-based GA with a binary GA, demonstrating the benefits of the newly proposed representation.

RNA is an important molecule as it serves a key role in the translation from the genetic information encoded in DNA in protein synthesis. Computational techniques for RNA folding suffer from combinatorial explosion. In this paper, a genetic algorithm (GA) will be used to attempt to solve the secondary structure prediction of RNA molecules.

The basic function of a biomolecule is determined by its 3 dimensional shape, otherwise known as the tertiary structure. However, existing empirical methods to determine this shape are too costly and lengthy to be practical. RNA is of interest as a biomolecule because it is central in several stages of protein synthesis. Also, its secondary structure dominates its tertiary structure. In our model, RNA secondary structure develops as a consequence of bonds which form between specific pairs of nucleotides known as the canonical base pairs. Searching a sequence of nucleotides for all possible base pairs is rapid and straightforward; the challenge comes from attempting to predict which specific canonical base pairs will form bonds in the real structure. Various algorithms have been used for RNA structure prediction such as dynamic programming, and comparative methods [1] and stochastic methods such as genetic algorithms (GA).

This paper presents a Genetic Algorithm (GA) to predict the secondary structure of RNA molecules, where the secondary structure is encoded as a permutation. More specifically, the proposed algorithm predicts which specific canonical base pairs will form hydrogen bonds and build helices, also known as stems. Since RNA is involved in both transcription and translation and also has catalytic and structural roles in the cell, determining the structure of RNA is of fundamental importance in helping to determine RNA function. We introduce a GA where a permutation is used to encode the secondary structure of RNA molecules. We discuss results on RNA sequences of lengths 76, 210, 681, and 785 nucleotides and present several improvements to our algorithm. We show that the Keep-Best Reproduction operator has similar benefits as in the traveling salesman problem domain. In addition, a comparison of several crossover operators is provided. We also compare the results of the permutation-based GA with a binary GA, demonstrating the benefits of the newly proposed representation.

This paper presents a genetic algorithm (GA) to predict the secondary structure of RNA molecules, where the secondary structure is encoded as a permutation. More specifically the proposed algorithm predicts which specific canonical base pairs will form hydrogen bonds and build helices, also known as stem loops. Since RNA is involved in both transcription and translation and also has catalytic and structural roles in the cell, knowing its structure is of fundamental importance since it will determine the function of the RNA molecule. We discuss results on RNA sequences of lengths 76, 681, and 785 nucleotides and present several improvements to our algorithm. We show that the Keep-Best Reproduction operator has similar benefits as in the TSP domain. In addition, a comparison of several crossover operators is provided, demonstrating that CX, an operator that is marginal in the TSP domain, performs very well in the RNA folding domain.

Pseudoknots are RNA tertiary structures which perform essential biological functions. This paper discusses SARNA-Predict-pk, a RNA pseudoknotted secondary structure prediction algorithm based on Simulated Annealing (SA). The research presented here extends previous work of SARNA-Predict and further examines the effect of the new algorithm to include prediction of RNA secondary structure with pseudoknots. An evaluation of the performance of SARNA-Predict-pk in terms of prediction accuracy is made via comparison with several state-of-the-art prediction algorithms using 20 individual known structures from seven RNA classes. We measured the sensitivity and specificity of nine prediction algorithms. Three of these are dynamic programming algorithms: Pseudoknot (pknotsRE), NUPACK, and pknotsRG-mfe. One is using the statistical clustering approach: Sfold and the other five are heuristic algorithms: SARNA-Predict-pk, ILM, STAR, IPknot and HotKnots algorithms. The results presented in this paper demonstrate that SARNA-Predict-pk can out-perform other state-of-the-art algorithms in terms of prediction accuracy. This supports the use of the proposed method on pseudoknotted RNA secondary structure prediction of other known structures.

Genetic Algorithms (GAs) have traditionally been designed to work on bitstrings. More recently interest has shifted to the application of GAs to constraint optimization and combinatorial optimization problems. Important for an effective and efficient search is the use of a suitable crossover operator. This paper analyses the performance of six existing crossover operators in the traveling salesman domain. While the edge recombination operator was reported to be the most suitable operator in the TSP domain, our results suggest that this is only true for symmetric TSPs. The problem with edge recombination is that it inverts edges found in the parents. This has no negative effect for the symmetric TSP but can have a substantial effect if the TSP is asymmetric. We propose an edge based crossover operator for the asymmetric TSP and demonstrate its superiority over the traditional edge recombination. Another interesting finding is that order crossover (OX) which has an average performance for symmetric problems, performs very well on asymmetric problems.

This paper presents a comparison of two genetic algorithms (GAs) that use different selection strategies. The first GA uses the standard selection strategy of roulette wheel selection and generational replacement (STDS), while the second GA uses an intermediate selection strategy in addition to STDS. Our previous research has shown that this intermediate selection strategy, which we call “Keep-Best Reproduction (KBR)”, found solutions of lower cost for a variety of travelling salesman problems. In this paper, we study the effects of crossover and mutation probabilities on STDS as well as on KBR. We study the effect of recombination alone, mutation alone and both together. We compare the performance of the different selection strategies and discuss the environment that each selection strategy needs to flourish in. Overall, KBR is found to be the selection strategy of choice. We also present empirical evidence that suggests that KBR is more robust than STDS with regard to operator probabilities.