An Integer Programming Formulation of the Minimum Common String Partition problem

We consider the problem of finding a minimum common partition of two strings (MCSP). The problem has its application in genome comparison. MCSP problem is proved to be NP-hard. In this paper, we develop an Integer Programming (IP) formulation for the problem and implement it. The experimental results are compared with the previous state-of-the-art algorithms and are found to be promising.Comment: arXiv admin note: text overlap with arXiv:1401.453

Computational Performance Evaluation of Two Integer Linear Programming Models for the Minimum Common String Partition Problem

In the minimum common string partition (MCSP) problem two related input strings are given. "Related" refers to the property that both strings consist of the same set of letters appearing the same number of times in each of the two strings. The MCSP seeks a minimum cardinality partitioning of one string into non-overlapping substrings that is also a valid partitioning for the second string. This problem has applications in bioinformatics e.g. in analyzing related DNA or protein sequences. For strings with lengths less than about 1000 letters, a previously published integer linear programming (ILP) formulation yields, when solved with a state-of-the-art solver such as CPLEX, satisfactory results. In this work, we propose a new, alternative ILP model that is compared to the former one. While a polyhedral study shows the linear programming relaxations of the two models to be equally strong, a comprehensive experimental comparison using real-world as well as artificially created benchmark instances indicates substantial computational advantages of the new formulation.Comment: arXiv admin note: text overlap with arXiv:1405.5646 This paper version replaces the one submitted on January 10, 2015, due to detected error in the calculation of the variables involved in the ILP model

Construct, Merge, Solve & Adapt A new general algorithm for combinatorial optimization

[EN]This paper describes a general hybrid metaheuristic for combinatorial optimization labelled Construct,Merge, Solve & Adapt. The proposed algorithm is a specific instantiation of a framework known from theliterature as Generate-And-Solve, which is based on the following general idea. First, generate a reducedsub-instance of the original problem instance, in a way such that a solution to the sub-instance is also asolution to the original problem instance. Second, apply an exact solver to the reduced sub-instance inorder to obtain a (possibly) high quality solution to the original problem instance. And third, make use ofthe results of the exact solver as feedback for the next algorithm iteration. The minimum common stringpartition problem and the minimum covering arborescence problem are chosen as test cases in order todemonstrate the application of the proposed algorithm. The obtained results show that the algorithm iscompetitive with the exact solver for small to medium size problem instances, while it significantlyoutperforms the exact solver for larger problem instancesC. Blum was supported by project TIN2012-37930-02 of the Spanish Government. In addition, support is acknowledged from IKERBASQUE (Basque Foundation for Science). J.A. Lozano was partially supported by the IT609-13 program (Basque Government) and project TIN2013-41272P (Spanish Ministry of Science and Innovation)Peer reviewe

Development of hybrid metaheuristics based on instance reduction for combinatorial optimization problems

113 p.La tesis presentada describe el desarrollo de algoritmos metaheurísticos híbridos, basados en reducción de instancias de problema. Éstos son enfocados en la resolución de problemas de optimización combinatorial. La motivación original de la investigación radicó en lograr, a través de la reducción de instancias de problemas, el uso efectivo de modelos de programación lineal entera (ILP) sobre problemas que dado su tamaño no admiten el uso directo con esta técnica exacta. En este contexto se presenta entre otros desarrollos el framework Construct, Merge, Solve & Adapt (CMSA) para resolución de problemas de optimización combinatorial en general, el cual posteriormente fue adaptado para mejorar el desempeño de otras metaheurísticas sin el uso de modelos ILP. Los algoritmos presentados mostraron resultados que compiten o superan el estado del arte sobre los problemas Minimum Common String Partition (MCSP), Minimum Covering Arborescence (MCA) y Weighted Independent Domination (WID)