Análise Gráfica Comparativa dos Resultados da Matheurística Proposta para o Problema do Safe Set

Abstract

This work presents a complementary graphical analysis of the results obtained in the Undergraduate Thesis on the Safe Set Problem. The objective is to comparatively analyze the performance of the different configurations of the proposed matheuristic, emphasizing the behavior of the heuristics across different groups of instances through comparative graphs, both on an instance-by-instance basis and on grouped instances. Pseudo-random instances from the literature, varying in graph size and density, were used. The graphical analysis indicates that the configurations based on the matheuristic known as Large Neighbourhood Search achieved significant improvements over the initial solutions, especially for strategies employing a larger number of constructive iterations. The graphs allowed for a visual assessment of the behavior of the different algorithm configurations, highlighting trends related to the density and size of the instances.