GRASP for Linear Integer Programming

In this paper we introduce a GRASP for the solution of general linear integer programs (IP). The strategy is based on the separation of the set of variables into the integer subset and the continuous subset. The procedure starts by solving the linear programming (LP) relaxation of the problem. Values for the integer variables are then chosen, through a randomised greedy construction heuristic based on rounding around the LP relaxation. The continuous variables can then be determined in function of them, by solving a linear program where all the integer variables are fixed. Afterwards, local search improvements are made on this solution; these improvements still correspond to changes made exclusively on the integer variables, after which the continuous variables are recomputed through LP solutions. When the linear program leads to a feasible solution, the evaluation of the choice of the IP variables is determined directly by the objective function. If the choice of the IP variables induces an infeasible solution, the evaluation is measured by the sum of infeasibilities, which can be determined by simple algebraic manipulations.