Technical Note—An Improved Branch-and-Bound Method for Integer Programming

Two extensions of the successful Beale and Small branch-and-bound mixed-integer algorithm are proposed, utilizing the integer requirements on nonbasic variables to calculate stronger "penalties" when searching down the solution tree and to give a stronger criterion for abandoning unprofitable branches of the tree when backtracking.

Abstract

This note proposes two extensions of the successful Beale and Small branch-and-bound mixed-integer algorithm. The integer requirements on nonbasic variables are utilized to calculate stronger “penalties” when searching down the solution tree and to give a stronger criterion for abandoning unprofitable branches of the tree when backtracking. This stronger criterion is obtained by making use of Gomory cutting-plane constraints. These modifications have produced considerable reductions of the searching effort required for pure integer and predominantly integer problems, and have the further advantage of being very easy to incorporate.