Automatically Generated Algorithms for the Vertex Coloring Problem

• Published in: PloS one Vol. 8; no. 3; p. e58551
• Main Authors: Contreras Bolton, Carlos, Gatica, Gustavo, Parada, Víctor
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 13.03.2013; Public Library of Science (PLoS)
• Subjects: Algorithms; Artificial intelligence; Automation; Calibration; Color; Coloring; Combinatorial analysis; Competition; Computation; Computer applications; Computer Graphics; Computer Science; Engineering; Evolutionary algorithms; Feasibility Studies; Genetic algorithms; Graph coloring; Graph theory; Heuristic; Hybridization; Integer programming; Mathematics; Mechanical properties; Methods; Optimization; Problem solving; Problems; Social and Behavioral Sciences; Chile; New York; United States > US
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0058551

The vertex coloring problem is a classical problem in combinatorial optimization that consists of assigning a color to each vertex of a graph such that no adjacent vertices share the same color, minimizing the number of colors used. Despite the various practical applications that exist for this problem, its NP-hardness still represents a computational challenge. Some of the best computational results obtained for this problem are consequences of hybridizing the various known heuristics. Automatically revising the space constituted by combining these techniques to find the most adequate combination has received less attention. In this paper, we propose exploring the heuristics space for the vertex coloring problem using evolutionary algorithms. We automatically generate three new algorithms by combining elementary heuristics. To evaluate the new algorithms, a computational experiment was performed that allowed comparing them numerically with existing heuristics. The obtained algorithms present an average 29.97% relative error, while four other heuristics selected from the literature present a 59.73% error, considering 29 of the more difficult instances in the DIMACS benchmark.