Solving the Quadratic Assignment Problem on heterogeneous environment (CPUs and GPUs) with the application of Level 2 Reformulation and Linearization Technique

TL;DR

This paper introduces a modified level 2 RLT algorithm for the Quadratic Assignment Problem that leverages heterogeneous CPU-GPU systems, achieving significant speedups and memory reductions, and solving two previously unsolved instances.

Contribution

A novel CPU-GPU based level 2 RLT algorithm for QAP that outperforms existing methods in speed and memory usage, solving new instances for the first time.

Findings

Up to 140 times faster than level 3 RLT methods

97% less memory usage compared to previous approaches

Successfully solved two large QAP instances for the first time

Abstract

The Quadratic Assignment Problem, QAP, is a classic combinatorial optimization problem, classified as NP-hard and widely studied. This problem consists in assigning N facilities to N locations obeying the relation of 1 to 1, aiming to minimize costs of the displacement between the facilities. The application of Reformulation and Linearization Technique, RLT, to the QAP leads to a tight linear relaxation but large and difficult to solve. Previous works based on level 3 RLT needed about 700GB of working memory to process one large instances (N = 30 facilities). We present a modified version of the algorithm proposed by Adams et al. which executes on heterogeneous systems (CPUs and GPUs), based on level 2 RLT. For some instances, our algorithm is up to 140 times faster and occupy 97% less memory than the level 3 RLT version. The proposed algorithm was able to solve by first time two instances: tai35b and tai40b.