The evolution of the human society raises more and more difficult endeavors. For some of the real-life problems, the computing time-restriction enhances their complexity. The Matrix Bandwidth Minimization Problem (MBMP) seeks for a simultaneous permutation of the rows and the columns of a square matrix in order to keep its nonzero entries close to the main diagonal. The MBMP is a highly investigated P-complete problem, as it has broad applications in industry, logistics, artificial intelligence or information recovery. This paper describes a new attempt to use the Ant Colony Optimization framework in tackling MBMP. The introduced model is based on the hybridization of the Ant Colony System technique with new local search mechanisms. Computational experiments confirm a good performance of the proposed algorithm for the considered set of MBMP instances.

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 problem.