A Shrinking Boundary Algorithm for Discrete System Models

Abstract

Improved mathematical optimization procedures are steadily finding wider use in engineering system studies, but the difficulties associated with the solution of discrete decision variable models remain formidable. An algorithm is described which will solve a certain class of problems formulated as linear integer programs. The procedure employs parallel shifts of selected boundary planes. This is accomplished by incrementing the appropriate slack variables which are constrained to be integers when the restraint conditions are formulated as diophantine equations. A hierarchy of variables is established to direct the boundary shifts. Feasibility and sensitivity tests truncate the search.