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.

This work deals with the so-called minimum capacitated dominating set (CAPMDS) problem, which is an NP-Hard combinatorial optimization problem in graphs. In this paper we describe the application of a recently introduced hybrid algorithm known as Construct, Merge, Solve & Adapt (CMSA) to this problem. Moreover, we evaluate the performance of a standalone ILP solver. The results show that both CMSA and the ILP solver outperform current stateof-the-art algorithms from the literature. Moreover, in contrast to the ILP solver, the performance of CMSA does not degrade for the largest problem instances. The experimental evaluation is based on a benchmark dataset containing two different graph topologies and considering graphs with variable and uniform node capacities.

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