The graph coloring problem (GCP) is a widely studied combinatorial optimization problem due to its numerous applications in many areas, including time tabling, frequency assignment, and register allocation. The need for more efficient algorithms has led to the development of several GC solvers. In this paper, the authors introduce a team of Finite Learning Automata, combined with the random wal...

The Graph Coloring Problem (GCP) is a classical NP-complete problem for which several approximate solution algorithms have been proposed: Brelaz algorithm, simulated annealing (SA), ant colony optimization (ACO). This paper reports empirical results on the GCP over a collection of graphs of some approximate solution algorithms. Among them, we test a recently proposed Gravitational Swarm Intelli...

We present an automated algorithm selection method based on machine learning for the graph coloring problem (GCP). For this purpose, we identify 78 features for this problem and evaluate the performance of six state-of-the-art (meta)heuristics for the GCP. We use the obtained data to train several classification algorithms that are applied to predict on a new instance the algorithm with the hig...

We introduce a new nature inspired algorithm to solve the Graph Coloring Problem (GCP): the Gravitational Swarm. The Swarm is composed of agents that act individually, but that can solve complex computational problems when viewed as a whole. We formulate the agent’s behavior to solve the GCP. Agents move as particles in the gravitatory field defined by some target objects corresponding to graph...

In this paper, we combine a novel Sequential Graph Coloring Heuristic Algorithm (SGCHA) with a non-systematic method based on a cultural algorithm to solve the graph coloring problem (GCP). The GCP involves finding the minimum number of colors for coloring the graph vertices such that adjacent vertices have distinct colors. In our solving approach, we first use an estimator which is implemented...

Graph Coloring Problem (GCP) bears an enormous significance to the researchers in the field of soft computing. In this paper, we demonstrate a Quantum-Inspired Evolutionary Algorithm (QEA) to solve GCP. We use two dimensional arrays of Q-bits called Q-bit individual to produce binary individual. Q-gate operation is applied as a variation operator on Q-bit individuals. In traditional evolutionar...

The Graph k-Colorability Problem (GCP) is a well known NP-hard problem which consist in finding the k minimum number of colors to paint the vertices of a graph in such a way that any two vertices joined by an edge have always different colors. Many years ago, Simulated Annealing (SA) was used for graph coloring task obtaining good results; however SA is not a complete algorithm and it not alway...

Huge color class redundancy makes the graph coloring problem (GCP) very challenging for genetic algorithms (GAs), and designing effective crossover operators is notoriously difficult. Thus, despite the predominance of population based methods, crossover plays a very minor role in most state-of-the-art approaches to solving the GCP. Two main encoding methods have been adopted for heuristic and G...

The paper investigates the influence of versatile crossover and mutation operators on the efficiency of evolutionary search in solving two important classes of hard optimization problems. Chromosome representations of set partitions and permutations defined in the paper are not problem–oriented and are described together with their versatile variation operators. The proposed representations are...

In this chapter a new formulation of the robust graph coloring problem (RGCP) is proposed. In opposition to classical GCP defined for the given graph G(V,E) not only elements of E but also Ē can be subject of color conflicts in edge vertices. Conflicts in Ē are assigned penalties 0<P(e)<1. In addition to satisfying constraints related to the number of colors and/or a threshold of the acceptable...