Multi-objective Strip Packing

Good algorithms exist for solving the 2D rectangular strip packing problem when the objective is to minimize the amount of wasted material. However, in some applications other criteria are also important. We describe new heuristics for strip packing that optimize not only for wastage, but also for the efficient use of the cutting equipment, by minimizing the number of independent cuts required by a packing. We describe and evaluate two algorithms for multi-objective strip packing using these heuristics: a fast deterministic algorithm that gives good results very quickly; and a multi-objective evolutionary algorithm that gives excellent results across a range of benchmark problems, yet still runs in reasonable (and easily controllable) time. We show that both algorithms return a set of packings offering a range of trade-offs between the two objectives, and also that by using heuristics that consider cuts, the evolutionary algorithm derives packings with wastage levels that are better than any previously-published algorithm that optimizes for wastage alone.