Exact Multiple Sequence Alignment by Synchronized Decision Diagrams

Abstract

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 multivalued decision diagram (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 with an existing state-of-the-art exact MSA algorithm shows that our approach is more time efficient and yields significantly smaller optimality gaps.

Accelerating Multiple Sequence Alignments Using Parallel Computing

“…Mojbak et al [51] proposed an exact-MSA approach using forward dynamic programming. Also, in the comprehensive exploration of exact solutions, Hosseininasab et al [52] proposed a framework employing a dynamic programming approach to construct a multivalued decision diagram, representing all PSAs. The synchronization of PSAs with the proposed decision diagram effectively incorporates modeling the MSA problem within polynomial space complexity.…”

Decision Diagrams for Discrete Optimization: A Survey of Recent Advances

“…For example, several works model the sequencing aspect of the problem using a DD (Cire et al 2019, Ploskas et al 2019, Serra et al 2019, Hosseininasab and van Hoeve 2021 since other alternatives would involve big-M constraints that have a loose linear relaxation.…”

On Solving the Minimum Common String Partition Problem by Decision Diagrams

“…By relaxing and restricting DDs, lower and upper bounds for the objective function value of a optimization problem can be obtained [1]. Such DD approaches were already used for various combinatorial problems such as Graph Coloring, Maximal Independent Set, MaxSAT [1,22], and various sequence and string problems such as Repetition-Free Longest Common Subsequence [14], Multiple Sequence Alignment [16], or Constraint-Based Sequential Patter Mining [15]. DDs are also suitable for a hybrid approach with ILP solvers combined using Machine Learning methods [11,21].…”