  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.
