Mathematical Programming Strategies for Solving the Minimum Common String Partition Problem

TL;DR

This paper introduces the first integer linear programming model and a new heuristic for the NP-hard minimum common string partition problem, achieving optimal solutions for small instances and better solutions than existing heuristics.

Contribution

The paper presents a novel ILP model and a deterministic 2-phase heuristic for the minimum common string partition problem, advancing solution methods for this NP-hard challenge.

Findings

Optimal solutions for small and medium instances using ILP and CPLEX.

New best-known solutions for all tested instances.

The heuristic outperforms existing heuristics in solution quality.

Abstract

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.