Efficient Heuristic Procedures for Integer Linear Programming with an Interior

This paper presents and evaluates some new heuristic procedures for seeking an approximate solution of pure integer linear programming problems having only inequality constraints. The computation time required by these methods (after obtaining the optimal noninteger solution by the simplex method) has generally been only a small fraction of that used by the simplex method for the problems tested (which have 15 to 300 original variables). Furthermore, the solution obtained by the better procedures consistently has been close to optimal and frequently has actually been optimal. Plans for generalizing these methods also are outlined. A companion paper presents an optimal “bound-and-scan” algorithm that may be used in conjunction with these approximate procedures.