Abstract In 2005, David Pisinger asked the question “where are the hard knapsack problems?”. Noting that the classical benchmark test instances were limited in difficulty due to their selected structure, he proposed a set of new test instances for the 0-1 knapsack problem with characteristics that made them more challenging for dynamic programming and branch-and-bound algorithms. This important work highlighted the influence of diversity in test instances to draw reliable conclusions about algorithm performance. In this paper, we revisit the question in light of recent methodological advances – in the form of Instance Space Analysis – enabling the strengths and weaknesses of algorithms to be visualised and assessed across the broadest possible space of test instances. We show where the hard instances lie, and objectively assess algorithm performance across the instance space to articulate the strengths and weaknesses of algorithms. Furthermore, we propose a method to fill the instance space with diverse and challenging new test instances with controllable properties to support greater insights into algorithm selection, and drive future algorithmic innovations.

中文翻译：

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重温硬背包问题在哪里？通过实例空间分析

摘要 2005 年，David Pisinger 提出了“硬背包问题在哪里？”的问题。注意到经典基准测试实例由于其选择的结构而在难度上受到限制，他为 0-1 背包问题提出了一组新的测试实例，其特征使它们对动态规划和分支定界算法更具挑战性。这项重要的工作强调了测试实例多样性的影响，以得出关于算法性能的可靠结论。在本文中，我们根据最近的方法论进步（以实例空间分析的形式）重新审视这个问题，使算法的优势和劣势能够在尽可能广泛的测试实例空间中进行可视化和评估。我们展示了困难实例所在的位置，并客观地评估整个实例空间的算法性能，以阐明算法的优缺点。此外，我们提出了一种方法，用具有可控属性的多样化和具有挑战性的新测试实例填充实例空间，以支持对算法选择的更深入了解，并推动未来的算法创新。