Metaheuristics: Computer Decision-Making pp 545-573 | Cite as

# GRASP for Linear Integer Programming

## Abstract

In this paper, we introduce a GRASP for the solution of general linear integer problems. The strategy is based on the separation of the set of variables into the integer subset and the continuous subset. The integer variables are fixed by GRASP and replaced in the original linear problem. If the original problem had continuous variables, it becomes a pure continuous problem, which can be solved by a linear program solver to determine the objective value corresponding to the fixed variables. If the original problem was a pure integer problem, simple algebraic manipulations can be used to determine the objective value that corresponds to the fixed variables. When we assign values to integer variables that lead to an impossible linear problem, the evaluation of the corresponding solution is given by the sum of infeasibilities, together with an infeasibility flag. We report results obtained for some standard benchmark problems, and compare them to those obtained by branch-and-bound and to those obtained by an evolutionary solver.

## Keywords

GRASP Linear integer programming.## Preview

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