Most research on Strip Packing Problems is focused on the single-objective formulation of the problem. However, in this work we deal with a more general and practical variant of the problem, which not only seeks to optimize the usage of the raw material, but also the production process. For the problem solution, we have applied some of the most-known multi-objective evolutionary algorithms, since they have shown a promising behavior when affording multi-objective real-world problems. For an initial implementation, we proposed a solution codification which is based on a complete representation of the pattern layouts. Such an approach was promising but wasn't suitable to afford large instances. For this reason, we have focused on the design of a codification which can be much more competitive when compared to some tailor-made methods. In this sense, we present a hyperheuristic-based codification as an alternative to combine heuristics in such a way that a heuristic's strengths make up for the drawbacks of another. Results demonstrate the advantage of using multi-objective approaches, hyperheuristic-based representations, and of course, the importance on the selection of appropriate solution codifications.