This work aims to evaluate and propose matheuristics for the Distinguishing String Selection Problem (DSSP) and the Distinguishing Substring Selection Problems (DSSSP). Heuristics based on mathematical programming have already been proposed for String Selection problems in the literature and we are interested in adopting and testing different approaches for those problems. We proposed two matheuristics for both the DSSP and DSSSP by combining the Variable Neighbourhood Search (VNS) metaheuristic and mathematical programming. We compare the linear relaxation, lower bounds found through the branch-and-bound technique, and the matheuristics in three different groups of instances. Computational experiments show that the Basic Core Problem Algorithm (BCPA) finds overall better results for the DSSP. However, it was unable to provide any solutions for some hard DSSSP instances in a reasonable time limit. The two matheuristics based on the VNS have their own niche related to the different groups of instances. They found good solutions for the DSSSP while the BCPA failed. All the obtained data are available in our repository.

这项工作旨在评估和提出区分字符串选择问题 (DSSP) 和区分子字符串选择问题 (DSSSP) 的数学方法。文献中已经针对字符串选择问题提出了基于数学规划的启发式方法，我们有兴趣采用和测试这些问题的不同方法。我们通过结合可变邻域搜索 (VNS) 元启发式和数学编程，为 DSSP 和 DSSSP 提出了两种数学算法。我们比较了三组不同实例中的线性松弛、通过分支定界技术找到的下界和数学。计算实验表明，基本核心问题算法 (BCPA) 为 DSSP 找到了总体上更好的结果。然而，它无法在合理的时间限制内为某些硬 DSSSP 实例提供任何解决方案。这两种基于 VNS 的数学有自己的领域，与不同的实例组相关。当 BCPA 失败时，他们为 DSSSP 找到了很好的解决方案。所有获得的数据都可以在我们的存储库中找到。