5 research outputs found
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 metaheur铆sticos h铆bridos, basados en reducci贸n de instancias de problema. 脡stos son enfocados en la resoluci贸n de problemas de optimizaci贸n combinatorial. La motivaci贸n original de la investigaci贸n radic贸 en lograr, a trav茅s de la reducci贸n de instancias de problemas, el uso efectivo de modelos de programaci贸n lineal entera (ILP) sobre problemas que dado su tama帽o no admiten el uso directo con esta t茅cnica exacta. En este contexto se presenta entre otros desarrollos el framework Construct, Merge, Solve & Adapt (CMSA) para resoluci贸n de problemas de optimizaci贸n combinatorial en general, el cual posteriormente fue adaptado para mejorar el desempe帽o de otras metaheur铆sticas 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)