Framework of algorithm portfolios for strip packing problem

Abstract

In this paper selection of fast algorithm portfolios for 2SP packing problem is considered. The 2SP problem consists in placing rectangles on a strip of the given width for minimum strip length. The 2SP packing has application in many industries, but suitability of the related algorithms is limited by their runtimes. While solving combinatorial optimization problems, longer runtimes increase chances of obtaining higher quality solutions. This means that runtime vs solution quality trade-off is important in solving problems such as strip packing. Given some limited runtime, a method is needed to provide the best solution possible. However, a single algorithm outperforming all other methods under all possible conditions usually does not exist. Therefore, algorithm portfolios can reliably provide high quality solutions in the limited runtime. We propose a method choosing algorithm portfolios on the basis of the algorithm performance on a set of training instances. A portfolio covers the instances with the best solutions which could be obtained in the given runtime, subject to the minimum computational cost of the selected algorithms. The portfolios are evaluated in extensive experiments carried out on designed and literature datasets. We demonstrate that our method is capable of carrying over solution quality from the training datasets to the testing datasets. In other words, our algorithm selection method can learn from the training instances. We also compare performance of our portfolio selection method with some other more straightforward approaches to the portfolio selection.