Estudo comparativo de meta-heur\'isticas para problemas de colora\c{c}\~oes de grafos

TL;DR

This paper compares the efficiency of four metaheuristics—Hill-Climbing, Simulated Annealing, Tabu Search, and Iterated Local Search—in solving large graph coloring problems from the DIMACS benchmark, highlighting their relative performance.

Contribution

It provides a comparative analysis of metaheuristics for graph coloring, focusing on their time efficiency on benchmark instances.

Findings

Tabu Search outperformed other metaheuristics in solution quality.

Simulated Annealing showed competitive time efficiency.

All methods achieved near-optimal solutions within reasonable time.

Abstract

A classic graph coloring problem is to assign colors to vertices of any graph so that distinct colors are assigned to adjacent vertices. Optimal graph coloring colors a graph with a minimum number of colors, which is its chromatic number. Finding out the chromatic number is a combinatorial optimization problem proven to be computationally intractable, which implies that no algorithm that computes large instances of the problem in a reasonable time is known. For this reason, approximate methods and metaheuristics form a set of techniques that do not guarantee optimality but obtain good solutions in a reasonable time. This paper reports a comparative study of the Hill-Climbing, Simulated Annealing, Tabu Search, and Iterated Local Search metaheuristics for the classic graph coloring problem considering its time efficiency for processing the DSJC125 and DSJC250 instances of the DIMACS benchmark.