A Bound-and-Scan Algorithm for Pure Integer Linear Programming with General Variables

Abstract

A new algorithm for solving the pure-integer linear programming problem with general integer variables is presented and evaluated. Roughly speaking, this algorithm proceeds by obtaining tight bounds or conditional bounds on the relevant values of the respective variables, and then identifying a sequence of constantly improving feasible solutions by scanning the relevant solutions. Encouraging computational experience is reported that suggests that this algorithm should compare favorably in efficiency with existing algorithms. Plans for investigating ways of further increasing the efficiency of the algorithm and of extending it to more general problems also are outlined.