Mathematical programming strategies for solving the minimum common string partition problem

• We propose an ILP model for the minimum common string partition problem.
• This is the first ILP model for this problem in the literature.
• We could solve 11 out of 45 problem instances from the literature to optimality.
• For the remaining instances we were able to find new best-known solutions.
• We present a heuristic based on the ILP model, applicable to larger instances.

The minimum common string partition problem is an NP-hard combinatorial optimization problem with applications in computational biology. In this work we propose the first integer linear programming model for solving this problem. Moreover, on the basis of the integer linear programming model we develop a deterministic 2-phase heuristic which is applicable to larger problem instances. The results show that provenly optimal solutions can be obtained for problem instances of small and medium size from the literature by solving the proposed integer linear programming model with CPLEX. Furthermore, new best-known solutions are obtained for all considered problem instances from the literature. Concerning the heuristic, we were able to show that it outperforms heuristic competitors from the related literature.