Accelerating Ant Colony Optimization for the Vertex Coloring Problem on the GPU

Abstract

Vertex coloring is an assignment of colors to vertex of an undirected graph such that no two vertices sharing the same edge have the same color. The vertex coloring problem is to find the minimum number of colors necessary to color a graph given, which is an NP-hard problem in combinatorial optimization. Ant Colony Optimization (ACO) is a well-known meta-heuristic in which a colony of artificial ants cooperates in exploring good solutions to a combinatorial optimization problem. Several methods applying ACO to the vertex coloring problem have been proposed. The main contribution of this paper is to propose a GPU implementation to accelerate the computation of the ACO algorithm for the vertex coloring problem. In our implementation, we have considered programming issues of the GPU architecture, such as coalescing access of the global memory, bank conflict of the shared memory, etc. The experimental results show that on NVIDIA GeForce GTX 1080, our implementation for 1000 vertices runs in 2.740s, while the CPU implementation on Intel Core i7-4790 runs in 100.866s. Thus, our GPU implementation attains a speed-up factor of 36.81.