  We introduce the quadratic balanced optimization problem (QBOP) which can be
used to model equitable distribution of resources with pairwise interaction.
QBOP is strongly NP-hard even if the family of feasible solutions has a very
simple structure. Several general purpose exact and heuristic algorithms are
presented. Results of extensive computational experiments are reported using
randomly generated quadratic knapsack problems as the test bed. These results
illustrate the efficacy of our exact and heuristic algorithms. We also show
that when the cost matrix is specially structured, QBOP can be solved as a
sequence of linear balanced optimization problems. As a consequence, we have
several polynomially solvable cases of QBOP.
