Two encoding schemes for a multi-objective Cutting Stock Problem

This work presents a multi-objective approach to solve a Constrained Guillotine Two-Dimensional Cutting Stock Problem. The single-objective formulation of the problem has been widely studied in the related literature, so a large number of heuristics, meta-heuristics, and exact algorithms have been proposed in order to optimise the total profit obtainable from the available surface. However, in some industries, where the material is cheap enough or easily recycled, a faster generation of pieces and a minimum usage of the machinery could be more decisive aspects in determining the efficiency of the production process. For this reason, we have focused on a multi-objective formulation of the problem which seeks to maximise the total profit obtainable from the raw material, as well as minimise the number of cuts to achieve the pieces placed on the material. To solve this multi objective problem we have applied Multi-objective Optimisation Evolutionary Algorithms given its great effectiveness with other types of real-world multi-objective problems. For the application of this kind of algorithms it has been necessary to define an encoding scheme which allows to deal with the problem intrinsic features. In this case, we have defined two encoding schemes which are based on a post-fix notation, thus simplifying the representation of guillotine patterns. The first encoding scheme controls the pieces included in the solution in order to generate valid builds. The second one generates a full solution, including all the available pieces, although the final values for the objectives are limited by the available surface. The computational results demonstrate that, in both cases, the multi-objective approach provides solutions with good compromise between the two objectives.