An algorithm is presented for solving all-integer linear programming problems which successively searches hyperplanes parallel to the optimal hyperplane containing the solution to the associated linear programming problem with the integer restrictions suppressed. These hyperplanes are searched for integer solution points using a dynamic programming formulation. Numerical examples of this technique and some computational results are also presented.

An approximate but fairly rapid method for solving integer linear programming problems is presented, which utilizes, in part, some of the philosophy of “direct search” methods. The method is divided into phases which can be applied in order and has the desirable characteristic that a best feasible solution is always available. Numerical results are presented for a number of test problems. Some possible extensions and improvements are also presented.

Mathematical problems in which some explicitly stated function of ma:~y independent variables is to be minimized or maximized andin which the variables may also be subjected to various explicitly stated constraints (usually called the general problem ot' mathematical programming), continue to be difficult te solve in practice.The prescott work is an extension of previous ideas on unconstrained optimization by "search" techniques, to the more difficult problem of constrained optimization.The essence of the method herei~ presented is to use linear programming in certain situations where constraints limit search techniques to find a fruitful direction in which to continue the search.Computational experience, while limited, has indicated that the procedure is reasonably efhcier~t.