Solving the Quadratic Assignment Problem using Deep Reinforcement Learning

TL;DR

This paper introduces a deep reinforcement learning approach with a novel double pointer network to solve the NP-hard Quadratic Assignment Problem, achieving near-optimal solutions without instance-specific retraining.

Contribution

It presents a new deep RL method with a double pointer network for QAP, capable of solving large instances efficiently and accurately.

Findings

Solutions are on average within 7.5% of a high-quality baseline.

The method outperforms the baseline on 1.2% of instances.

No instance-specific retraining is required for out-of-sample solutions.

Abstract

The Quadratic Assignment Problem (QAP) is an NP-hard problem which has proven particularly challenging to solve: unlike other combinatorial problems like the traveling salesman problem (TSP), which can be solved to optimality for instances with hundreds or even thousands of locations using advanced integer programming techniques, no methods are known to exactly solve QAP instances of size greater than 30. Solving the QAP is nevertheless important because of its many critical applications, such as electronic wiring design and facility layout selection. We propose a method to solve the original Koopmans-Beckman formulation of the QAP using deep reinforcement learning. Our approach relies on a novel double pointer network, which alternates between selecting a location in which to place the next facility and a facility to place in the previous location. We train our model using A2C on a large dataset of synthetic instances, producing solutions with no instance-specific retraining necessary. Out of sample, our solutions are on average within 7.5% of a high-quality local search baseline, and even outperform it on 1.2% of instances.