Solving Challenging Large Scale QAPs

TL;DR

This paper presents a parallel branch-and-bound approach utilizing advanced lower bounding techniques to solve large-scale quadratic assignment problems (QAPs), achieving first-time solutions for certain instances with over 50 dimensions.

Contribution

The authors develop and implement a scalable parallel branch-and-bound method with novel lower bounding procedures for large QAPs, demonstrating successful solutions for previously unsolved instances.

Findings

Successfully solved tai30a and sko42 QAP instances for the first time.

Implemented a parallel framework utilizing over 100,000 cores.

Demonstrated effectiveness of Lagrangian DNN relaxation and Newton-bracketing in bounding.

Abstract

We report our progress on the project for solving larger scale quadratic assignment problems (QAPs). Our main approach to solve large scale NP-hard combinatorial optimization problems such as QAPs is a parallel branch-and-bound method efficiently implemented on a powerful computer system using the Ubiquity Generator (UG) framework that can utilize more than 100,000 cores. Lower bounding procedures incorporated in the branch-and-bound method play a crucial role in solving the problems. For a strong lower bounding procedure, we employ the Lagrangian doubly nonnegative (DNN) relaxation and the Newton-bracketing method developed by the authors' group. In this report, we describe some basic tools used in the project including the lower bounding procedure and branching rules, and present some preliminary numerical results. Our next target problem is QAPs with dimension at least 50, as we have succeeded to solve tai30a and sko42 from QAPLIB for the first time.