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.

本文考虑了 2SP 打包问题的快速算法组合的选择。2SP 问题在于将矩形放置在给定宽度的条带上以获得最小条带长度。2SP封装在很多行业都有应用，但是相关算法的适用性受限于它们的运行时间。在解决组合优化问题时，更长的运行时间会增加获得更高质量解决方案的机会。这意味着运行时间与解决方案质量的权衡对于解决带材包装等问题很重要。考虑到一些有限的运行时间，需要一种方法来提供可能的最佳解决方案。但是，通常不存在在所有可能条件下都优于所有其他方法的单一算法。因此，算法组合可以在有限的运行时间内可靠地提供高质量的解决方案。我们提出了一种基于一组训练实例的算法性能来选择算法组合的方法。投资组合涵盖了具有在给定运行时间中可以获得的最佳解决方案的实例，受所选算法的最小计算成本的影响。在对设计和文献数据集进行的广泛实验中评估投资组合。我们证明了我们的方法能够将解决方案质量从训练数据集传递到测试数据集。换句话说，我们的算法选择方法可以从训练实例中学习。我们还将我们的投资组合选择方法的性能与其他一些更直接的投资组合选择方法进行了比较。