Multiple sequence alignment is a central problem in Bioinformatics and a challenging one for optimisation algorithms. An established integer programming approach is to apply branch-and-cut to a graph-theoretical model. The models are exponentially large but are represented intensionally, and violated constraints can be located in polynomial time. This report describes a new integer program formulation that generates polynomial-sized models small enough to be passed to generic solvers. It is a hybrid formulation relating the sparse alignment graph with a compact encoding of the alignment matrix via channelling constraints. Alignments obtained with a pseudo-Boolean local search algorithm are competitive with those of state-of-the-art algorithms. Execution times are much longer, but in future work we aim to develop a more efficient specialised algorithm. 1

Abstract. Multiple sequence alignment is a central problem in Bioinformatics. A known integer programming approach is to apply branch-and-cut to exponentially large graph-theoretic models. This paper describes a new integer program formulation that generates models small enough to be passed to generic solvers. The formulation is a hybrid relating the sparse alignment graph with a compact encoding of the alignment matrix via channelling constraints. Alignments obtained with a SAT-based local search algorithm are competitive with those of state-of-the-art algorithms, though execution times are much longer. 1

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We propose a metric for the space of multiple sequence alignments that can be used to compare two alignments to each other. In the case where one of the alignments is a reference alignment, the resulting accuracy measure improves upon previous approaches, and provides a balanced assessment of the fidelity of both matches and gaps. Furthermore, in the case where a reference alignment is not available, we provide empirical evidence that the distance from an alignment produced by one program to predicted alignments from other programs can be used as a control for multiple alignment experiments. In particular, we show that low accuracy alignments can be effectively identified and discarded. We also show that in the case of pairwise sequence alignment, it is possible to find an alignment that maximizes the expected value of our accuracy measure. Unlike previous approaches based on expected accuracy alignment that tend to maximize sensitivity at the expense of specificity, our method is able to identify unalignable sequence, thereby increasing overall accuracy. In addition, the algorithm allows for control of the sensitivity/specificity tradeoff via the adjustment of a single parameter. These results are confirmed with simulation studies that show that unalignable regions can be distinguished from homologous, conserved sequences. Finally, we propose an extension of the pairwise alignment method to multiple alignment. Our method, which we call AMAP, outperforms existing protein sequence multiple alignment programs on benchmark datasets. A webserver and software downloads are available at