Automatically Generated Algorithms for the Vertex Coloring Problem

Abstract

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.

Automatic Combination of Operators in a Genetic Algorithm to Solve the Traveling Salesman Problem

“…To evaluate the performance of each individual, i.e., the quality of a combination of occurrence probabilities of crossover and mutation operators in a GA-TSP, a type of evaluation function employed in genetic programming is used, which, to compare the performance of the trees/programs, uses the average error of a group of training instances [ 22 – 24 ]. The proposed evaluation function minimizes the average relative error of the GA to solve a set of TSP instances.…”