On the concept of density control and its application to a hybrid optimization framework: Investigation into cutting problems

Abstract

The Generate-and-Solve ( GS) methodology is a hybrid approach that combines a metaheuristic component with an exact solver. GS has been recently introduced in the literature in order to solve cutting and packing problems, showing promising results. The GS framework includes a metaheuristic engine ( e.g., a genetic algorithm) that works as a generator of reduced instances of the original optimization problem, which are, in turn, formulated as mathematical programming problems and solved by an integer programming solver. In this paper, we present an extended version of GS, focusing primarily on the concept of a new Density Control Operator ( DCO). The role of this operator is to adaptively control the dimension of the reduced instances in such a way as to allow a much steadier progress towards a better solution, thereby avoiding premature convergence. In order to assess the potentials of this novel version of the GS methodology, we conducted computational experiments on a set of difficult benchmark instances of the constrained non-guillotine cutting problem. The results achieved are quantitatively and qualitatively discussed in terms of effectiveness and efficiency, showing that the proposed variant of the GS hybridization framework is highly suitable when effectiveness is a major requirement.