Year: 2021
Type: preprint
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.
Source: arXiv (Cornell University)
DOI: 10.12752/8130
Authors: Fujii, Koichi, Ito, Naoki, Kim, Sunyoung, Kojima, Masakazu, Shinano, Yuji, Toh, Kim-Chuan
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3124680217