A dynamic programming branch and bound algorithm for pure integer programming

Several algorithms for linear integer programming have been proposed in which one or more of the conditions are relaxed to produce a solvable problem form. Reimposing these relaxed conditions can lead to a branch and bound process. In this paper an alternative relaxation is proposed in which the integer conditions are maintained but the feasibility conditions are relaxed in a special way. Reimposing feasibility by sequentially setting variables creates the branch and bound process. In special cases, the algorithm reverts to the normal form of dynamic programming.The algorithm is applicable to both linear and non-linear pure integer problems. It has been programmed to solve pure $\text{0}\text{1}$ problems and results of computational experience with some linear problems previously used in the literature are given.