A projection method for the integer quadratic knapsack problem

This paper presents a new branch and bound algorithm for solving a class of integer quadratic knapsack problems. A previously published algorithm solves the continuous variable subproblems in the branch and bound tree by performing a binary search over the breakpoints of a piecewise linear equation resulting from the Kuhn-Tucker conditions. Here, the paper first presents modifications to a projection method for solving the continuous subproblems. Then it implements the modified projection method in a branch and bound framework and reports computational results indicating that the new branch and bound algorithm is superior to the earlier method.