Evolutionary Algorithm for Graph Coloring Problem

TL;DR

This paper presents a novel evolutionary algorithm with binary encoding for the graph coloring problem, dynamically reducing colors during evolution, and demonstrates competitive results on standard benchmarks.

Contribution

Introduces a binary encoding and a dynamic color reduction method in evolutionary algorithms for graph coloring, starting from the theoretical upper bound.

Findings

Achieves results matching expected chromatic numbers on benchmarks

Some datasets exceed expected chromatic numbers

Dynamic color reduction improves solution efficiency

Abstract

The graph coloring problem (GCP) is one of the most studied NP-HARD problems in computer science. Given a graph , the task is to assign a color to all vertices such that no vertices sharing an edge receive the same color and that the number of used colors, is minimal. Different heuristic, meta-heuristic, machine learning and hybrid solution methods have been applied to obtain the solution. To solve this problem we use mutation of evolutionary algorithm. For this purpose we introduce binary encoding for Graph Coloring Problem. This binary encoding help us for mutation, evaluate, immune system and merge color easily and also reduce coloring dynamically. In the traditional evolutionary algorithm (EA) for graph coloring, k-coloring approach is used and the EA is run repeatedly until the lowest possible is reached. In our paper, we start with the theoretical upper bound of chromatic number, that is, maximum out-degree + 1 and in the process of evolution some of the colors are made unused to dynamically reduce the number of color in every generation. We test few standard DIMACS benchmark and compare resent paper. Maximum results are same as expected chromatic color and few data sets are larger than expected chromatic number