  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.
