GPU tabu search: A study on using GPU to solve massive instances of the maximum diversity problem

Abstract

The maximum diversity problem (MDP), a widely studied combinatorial optimization problem due to its broad applications, has seen numerous heuristic methods proposed. However, none of these approaches have addressed the challenges posed by massive instances. Currently, state-of-the-art heuristics are not well-suited for massive instances due to two primary reasons. Firstly, they rely on a matrix-based representation, which proves highly inefficient for sparse instances commonly encountered in massive scenarios. Secondly, as the problem size increases, their local search operators experience a slowdown. This work introduces a GPU-based tabu search algorithm designed to tackle such massive instances. To address the limitations of the state-of-the-art heuristics, our GPU tabu search employs more efficient data structures for sparse instances and leverages GPU parallel capabilities to expedite the local search process. We tested our approach on established small and medium instances, ranging from 2,000 to 5,000 vertices, as well as massive instances with up to 45,000 vertices. In these tests, our approach was compared with a state-of-the-art algorithm. Experimental results demonstrate an up to 30x speedup with of our proposal and its effectiveness on massive instances.