A Group Theoretic Branch and Bound Algorithm: For the Zero-One Integer Programming (Classic Reprint)

Excerpt from A Group Theoretic Branch and Bound Algorithm

A more precise definition of an optimal correction is given ininduced correction and the resulting LP basic variables constitute a feasible solution to the integer programming problem, then this solution is optimalo Sufficient conditions can be given on when an unconstrained shortest route path can be guaranteed to produce a feasible and thus optimal integer solution. As discussed in the class of problems for which the unconstrained shortest route solution will yield the optimal integer solution can be described qualitatively as steady  state If b is the vector of constants in the integer programming problem, steady state means that the optimal LP solution B-lb is sufficiently large in each component to remain non negative after the correction from the unconstrained shortest route or group problem is obtained.