A Distribution Evolutionary Algorithm for the Graph Coloring Problem

TL;DR

This paper introduces DEA-PPM, a novel distribution evolutionary algorithm that efficiently solves the graph coloring problem by combining a population-based probability model with exploration and refinement strategies.

Contribution

It proposes a new distribution evolutionary algorithm with a distribution population, orthogonal exploration, and iterative vertex removal for improved graph coloring solutions.

Findings

DEA-PPM achieves competitive results with small populations.

The algorithm effectively balances exploration and exploitation.

Numerical experiments outperform existing metaheuristics.

Abstract

Graph coloring is a challenging combinatorial optimization problem with a wide range of applications. In this paper, a distribution evolutionary algorithm based on a population of probability model (DEA-PPM) is developed to address it efficiently. Unlike existing estimation of distribution algorithms where a probability model is updated by generated solutions, DEA-PPM employs a distribution population based on a novel probability model, and an orthogonal exploration strategy is introduced to search the distribution space with the assistance of an refinement strategy. By sampling the distribution population, efficient search in the solution space is realized based on a tabu search process. Meanwhile, DEA-PPM introduces an iterative vertex removal strategy to improve the efficiency of $k$-coloring, and an inherited initialization strategy is implemented to address the chromatic problem well. The cooperative evolution of the distribution population and the solution population leads to a good balance between exploration and exploitation. Numerical results demonstrate that the DEA-PPM of small population size is competitive to the state-of-the-art metaheuristics.utes to its competitiveness to the state-of-the-art metaheuristics.