Heuristics for multiobjective multiple sequence alignment.

BACKGROUND: Aligning multiple sequences arises in many tasks in Bioinformatics. However, the alignments produced by the current software packages are highly dependent on the parameters setting, such as the relative importance of opening gaps with respect to the increase of similarity. Choosing only one parameter setting may provide an undesirable bias in further steps of the analysis and give too simplistic interpretations. In this work, we reformulate multiple sequence alignment from a multiobjective point of view. The goal is to generate several sequence alignments that represent a trade-off between maximizing the substitution score and minimizing the number of indels/gaps in the sum-of-pairs score function. This trade-off gives to the practitioner further information about the similarity of the sequences, from which she could analyse and choose the most plausible alignment. METHODS: We introduce several heuristic approaches, based on local search procedures, that compute a set of sequence alignments, which are representative of the trade-off between the two objectives (substitution score and indels). Several algorithm design options are discussed and analysed, with particular emphasis on the influence of the starting alignment and neighborhood search definitions on the overall performance. A perturbation technique is proposed to improve the local search, which provides a wide range of high-quality alignments. RESULTS AND CONCLUSIONS: The proposed approach is tested experimentally on a wide range of instances. We performed several experiments with sequences obtained from the benchmark database BAliBASE 3.0. To evaluate the quality of the results, we calculate the hypervolume indicator of the set of score vectors returned by the algorithms. The results obtained allow us to identify reasonably good choices of parameters for our approach. Further, we compared our method in terms of correctly aligned pairs ratio and columns correctly aligned ratio with respect to reference alignments. Experimental results show that our approaches can obtain better results than TCoffee and Clustal Omega in terms of the first ratio.

Greedy Hypervolume Subset Selection in Low Dimensions.

Given a nondominated point set [Formula: see text] of size [Formula: see text] and a suitable reference point [Formula: see text], the Hypervolume Subset Selection Problem (HSSP) consists of finding a subset of size [Formula: see text] that maximizes the hypervolume indicator. It arises in connection with multiobjective selection and archiving strategies, as well as Pareto-front approximation postprocessing for visualization and/or interaction with a decision maker. Efficient algorithms to solve the HSSP are available only for the 2-dimensional case, achieving a time complexity of [Formula: see text]. In contrast, the best upper bound available for [Formula: see text] is [Formula: see text]. Since the hypervolume indicator is a monotone submodular function, the HSSP can be approximated to a factor of [Formula: see text] using a greedy strategy. In this article, greedy [Formula: see text]-time algorithms for the HSSP in 2 and 3 dimensions are proposed, matching the complexity of current exact algorithms for the 2-dimensional case, and considerably improving upon recent complexity results for this approximation problem.

Hypervolume Subset Selection in Two Dimensions: Formulations and Algorithms.

The hypervolume subset selection problem consists of finding a subset, with a given cardinality k, of a set of nondominated points that maximizes the hypervolume indicator. This problem arises in selection procedures of evolutionary algorithms for multiobjective optimization, for which practically efficient algorithms are required. In this article, two new formulations are provided for the two-dimensional variant of this problem. The first is a (linear) integer programming formulation that can be solved by solving its linear programming relaxation. The second formulation is a k-link shortest path formulation on a special digraph with the Monge property that can be solved by dynamic programming in [Formula: see text] time. This improves upon the result of [Formula: see text] in Bader ( 2009 ), and slightly improves upon the result of [Formula: see text] in Bringmann et al. ( 2014b ), which was developed independently from this work using different techniques. Numerical results are shown for several values of n and k.

MOSAL: software tools for multiobjective sequence alignment.

: Multiobjective sequence alignment brings the advantage of providing a set of alignments that represent the trade-off between performing insertion/deletions and matching symbols from both sequences. Each of these alignments provide a potential explanation of the relationship between the sequences. We introduce MOSAL, a software tool that provides an open-source implementation and an on-line application for multiobjective pairwise sequence alignment.

Improvements on bicriteria pairwise sequence alignment: algorithms and applications.

MOTIVATION: In this article, we consider the bicriteria pairwise sequence alignment problem and propose extensions of dynamic programming algorithms for several problem variants with a novel pruning technique that efficiently reduces the number of states to be processed. Moreover, we present a method for the construction of phylogenetic trees based on this bicriteria framework. Two exemplary cases are discussed. RESULTS: Numerical results on a real dataset show that this approach is very fast in practice. The pruning technique saves up to 90% in memory usage and 80% in CPU time. Based on this method, phylogenetic trees are constructed from real-life data. In addition of providing complementary information, some of these trees match those obtained by the Maximum Likelihood method. AVAILABILITY AND IMPLEMENTATION: Source code is freely available for download at URL http://eden.dei.uc.pt/paquete/MOSAL, implemented in C and supported on Linux, MAC OS and MS Windows.

On local search for bi-objective knapsack problems.

In this article, a local search approach is proposed for three variants of the bi-objective binary knapsack problem, with the aim of maximizing the total profit and minimizing the total weight. First, an experimental study on a given structural property of connectedness of the efficient set is conducted. Based on this property, a local search algorithm is proposed and its performance is compared to exact algorithms in terms of runtime and quality metrics. The experimental results indicate that this simple local search algorithm is able to find a representative set of optimal solutions in most of the cases, and in much less time than exact algorithms.