This paper develops an exact solution algorithm for the Multiple Sequence Alignment (MSA) problem. In the first step, we design a dynamic programming model and use it to construct a novel Multi-valued Decision Diagrams (MDD) representation of all pairwise sequence alignments (PSA). PSA MDDs are then synchronized using side constraints to model the MSA problem as a Mixed-Integer Program (MIP), for the first time, in polynomial space complexity. Two bound-based filtering procedures are developed to reduce the size of the MDDs, and the resulting MIP is solved using logic-based Benders decomposition. For a more effective algorithm, we develop a two-phase solution approach. In the first phase we use optimistic filtering to quickly obtain a near-optimal bound, which we then use for exact filtering in the second phase to prove or obtain an optimal solution. Numerical results on benchmark instances show that our algorithm solves several instances to optimality for the first time, and in case optimality cannot be proven, considerably improves upon a state-of-the-art heuristic MSA solver. Comparison to an existing state-of-the-art exact MSA algorithm shows that our approach is more time efficient and yields significantly smaller optimality gaps.
INFORMS Journal on Computing (accepted)