Soft Computing approaches on the Bandwidth Problem

TL;DR

This paper explores Soft Computing methods, including genetic algorithms, ant-based systems, and reinforcement learning, to address the NP-complete Matrix Bandwidth Minimization Problem, demonstrating promising computational results and proposing a novel theoretical model.

Contribution

It introduces a hybrid Soft Computing approach with learning agents and a new reinforcement learning model for MBMP, advancing solution techniques for this complex problem.

Findings

Proposed algorithms outperform classical methods on benchmark instances.

Soft Computing methods show good computational performance.

Reinforcement Learning model offers a new theoretical perspective.

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 problem.