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Authors: Czibula, Gabriela | Crişan, Gloria-Cerasela | Pintea, Camelia-M. | Czibula, Istvan-Gergely

Article Type: Research Article

Abstract: The Matrix Bandwidth Minimization Problem (MBMP) seeks for a simultaneous reordering of the rows and the columns of a square matrix such that the nonzero entries are collected within a band of small width close to the main diagonal. The MBMP is a NP-complete problem, with applications in many scientific domains, linear systems, artificial intelligence, and real-life situations in industry, logistics, information recovery. The complex problems are hard to solve, that is why any attempt to improve their solutions is beneficent. Genetic algorithms and ant-based systems are Soft Computing methods used in this paper in order to solve some MBMP …instances. Our approach is based on a learning agent-based model involving a local search procedure. The algorithm is compared with the classical Cuthill-McKee algorithm, and with a hybrid genetic algorithm, using several instances from Matrix Market collection. Computational experiments confirm a good performance of the proposed algorithms for the considered set of MBMP instances. On Soft Computing basis, we also propose a new theoretical Reinforcement Learning model for solving the MBMP. Show more

Keywords: natorial optimization, matrix bandwidth minimization problem, soft computing, reinforcement learning

Citation: Informatica, vol. 24, no. 2, pp. 169-180, 2013