Integer Linear Programming for Sequence Problems: A general approach to reduce the problem size

Sequence problems belong to the most challenging interdisciplinary topics of the actuality. They are ubiquitous in science and daily life and occur, for example, in form of DNA sequences encoding all information of an organism, as a text (natural or formal) or in form of a computer program. Therefore, sequence problems occur in many variations in computational biology (drug development), coding theory, data compression, quantitative and computational linguistics (e.g. machine translation). In recent years appeared some proposals to formulate sequence problems like the closest string problem (CSP) and the farthest string problem (FSP) as an Integer Linear Programming Problem (ILPP). In the present talk we present a general novel approach to reduce the size of the ILPP by grouping isomorphous columns of the string matrix together. The approach is of practical use, since the solution of sequence problems is very time consuming, in particular when the sequences are long.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

An exact mathematical programming approach to multiple RNA sequence-structure alignment

One of the main tasks in computational biology is the computation of alignments of genomic sequences to reveal their commonalities. In case of DNA or protein sequences, sequence information alone is usually sufficient to compute reliable alignments. RNA molecules, however, build spatial conformations—the secondary structure—that are more conserved than the actual sequence. Hence, computing reliable alignments of RNA molecules has to take into account the secondary structure. We present a novel framework for the computation of exact multiple sequence-structure alignments: We give a graph- theoretic representation of the sequence-structure alignment problem and phrase it as an integer linear program. We identify a class of constraints that make the problem easier to solve and relax the original integer linear program in a Lagrangian manner. Experiments on a recently published benchmark show that our algorithms has a comparable performance than more costly dynamic programming algorithms, and outperforms all other approaches in terms of solution quality with an increasing number of input sequences

Computational Performance Evaluation of Two Integer Linear Programming Models for the Minimum Common String Partition Problem

In the minimum common string partition (MCSP) problem two related input strings are given. "Related" refers to the property that both strings consist of the same set of letters appearing the same number of times in each of the two strings. The MCSP seeks a minimum cardinality partitioning of one string into non-overlapping substrings that is also a valid partitioning for the second string. This problem has applications in bioinformatics e.g. in analyzing related DNA or protein sequences. For strings with lengths less than about 1000 letters, a previously published integer linear programming (ILP) formulation yields, when solved with a state-of-the-art solver such as CPLEX, satisfactory results. In this work, we propose a new, alternative ILP model that is compared to the former one. While a polyhedral study shows the linear programming relaxations of the two models to be equally strong, a comprehensive experimental comparison using real-world as well as artificially created benchmark instances indicates substantial computational advantages of the new formulation.Comment: arXiv admin note: text overlap with arXiv:1405.5646 This paper version replaces the one submitted on January 10, 2015, due to detected error in the calculation of the variables involved in the ILP model

Repeated sequences in linear genetic programming genomes

Biological chromosomes are replete with repetitive sequences, micro satellites, SSR tracts, ALU, etc. in their DNA base sequences. We started looking for similar phenomena in evolutionary computation. First studies find copious repeated sequences, which can be hierarchically decomposed into shorter sequences, in programs evolved using both homologous and two point crossover but not with headless chicken crossover or other mutations. In bloated programs the small number of effective or expressed instructions appear in both repeated and nonrepeated code. Hinting that building-blocks or code reuse may evolve in unplanned ways. Mackey-Glass chaotic time series prediction and eukaryotic protein localisation (both previously used as artificial intelligence machine learning benchmarks) demonstrate evolution of Shannon information (entropy) and lead to models capable of lossy Kolmogorov compression. Our findings with diverse benchmarks and GP systems suggest this emergent phenomenon may be widespread in genetic systems

Generalized Buneman pruning for inferring the most parsimonious multi-state phylogeny

Accurate reconstruction of phylogenies remains a key challenge in evolutionary biology. Most biologically plausible formulations of the problem are formally NP-hard, with no known efficient solution. The standard in practice are fast heuristic methods that are empirically known to work very well in general, but can yield results arbitrarily far from optimal. Practical exact methods, which yield exponential worst-case running times but generally much better times in practice, provide an important alternative. We report progress in this direction by introducing a provably optimal method for the weighted multi-state maximum parsimony phylogeny problem. The method is based on generalizing the notion of the Buneman graph, a construction key to efficient exact methods for binary sequences, so as to apply to sequences with arbitrary finite numbers of states with arbitrary state transition weights. We implement an integer linear programming (ILP) method for the multi-state problem using this generalized Buneman graph and demonstrate that the resulting method is able to solve data sets that are intractable by prior exact methods in run times comparable with popular heuristics. Our work provides the first method for provably optimal maximum parsimony phylogeny inference that is practical for multi-state data sets of more than a few characters.Comment: 15 page