An objective hyperplane search procedure for solving the general all-integer linear programming problem

We describe an objective hyperplane search method for solving a class of integer linear programming (ILP) problems. We formulate the search as a bounded knapsack problem and develop requisite theory for formulating knapsack problems with composite constraints and composite objective functions that facilitate convergence to an ILP solution. A heuristic solution algorithm was developed and used to solve a variety of test problems found in the literature. The method obtains optimal or near-optimal solutions in acceptable ranges of computational effort.