Abstract
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.
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We would like to thank SCIP developers team and IBM for the SCIP and Cplex academic licenses. We also thank the anonymous reviewers, whose works and contributions helped us to improve the quality of the paper.
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Appendix: Detailed experiments results
Appendix: Detailed experiments results
Tables 5, 6, 7, 8, 9, and 10 show the results for each instance. Column frac presents the percentage of variables whose values in the optimal solution of the linear relaxation were fractional. Column root refers to the value of the optimal solution of the linear relaxation at the root node, whilst columns lb and ub represent the final lower an upper bound found by the exact algorithm, respectively. Columns \(H_1\), \(H_2\), \(H_3\), and \(H_4\) show the value of the solution found by RA, BCPA, ILPBN-VNS, and ILPBS-VNS, respectively. Instances are named r-XX-YY-ZZ-N. where XX indicates \(|\varSigma |\), YY refers to \(|S^c|=|S^f|\), ZZ to |t|, and N is used to express different test cases with similar structures. The best solutions found by heuristics are highlighted in boldface. We also highlight the root lower bound and the final upper bound found by the exact approach when they are optimum. The symbol \(*\) are used to indicate that the information was not available after the time limit. We use the symbol − instead of the value of the solution found by a heuristic, when it could not be find due to the time limit.
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Torres, J.P.T., Hoshino, E.A. LP-based heuristics for the distinguishing string and substring selection problems. Ann Oper Res 316, 1205–1234 (2022). https://doi.org/10.1007/s10479-021-04138-5
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DOI: https://doi.org/10.1007/s10479-021-04138-5