# 2Minimum Common String Partition Problem

This chapter deals with a combinatorial optimization (CO) problem from computational biology known as the *unbalanced minimum common string partition* (UMCSP) problem. The UMCSP problem includes the *minimum common string partition* (MCSP) problem as a special case. First, an ILP model for the UMCSP problem is described. Second, a greedy heuristic initially introduced for the MCSP problem is adapted for application to the UMCSP problem. Third, the application of a general hybrid metaheuristic labeled construct, merge, solve and adapt (CMSA) to the UMCSP problem is described. The CMSA algorithm is based on the following principles. At each iteration, the incumbent sub-instance is modified by adding solution components found in probabilistically constructed solutions to the problem tackled. Moreover, the incumbent sub-instance is solved to optimality (if possible) by means of an ILP solver such as CPLEX. Finally, seemingly useless solution components are removed from the incumbent sub-instance based on an ageing mechanism. The results obtained indicate that the CMSA algorithm outperforms the greedy approach. Moreover, they show that the CMSA algorithm is competitive with CPLEX for small and medium problems, whereas it outperforms CPLEX for larger problems. Note that this chapter is based on [BLU 13].

## 2.1. The MCSP problem

Given that the special case – that is, the MCSP problem – is easier to describe than the UMCSP, we will first describe the ...

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