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Solving MIPs via scaling-based augmentation

机译:通过基于缩放的增强来解决MIPS

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摘要

Augmentation methods for mixed-integer (linear) programs are a class of primal solution approaches in which a feasible solution is iteratively augmented to a better solution or proved to be optimal. It is well known that the performance of these methods, i.e., number of iterations needed, can theoretically be improved by scaling methods. We extend these results by an improved and extended convergence analysis, which shows that bit scaling and geometric scaling theoretically perform identically well in the worst case for 0/1 polytopes, as well as show that in some cases, geometric scaling can outperform bit scaling arbitrarily, leading to the first strong separation between these two methods.
机译:混合整数(线性)程序的增强方法是一类原始解决方案方法,其中可行的解决方案迭代地增强到更好的解决方案或被证明是最佳的。 众所周知,通过缩放方法理论上可以改善这些方法的性能,即所需的迭代数量。 我们通过改进和扩展的收敛性分析来扩展这些结果,这表明位缩放和几何缩放在0/1多台面的最坏情况下理论上和几何缩放,以及显示在某些情况下,几何缩放可以任意呈现比特缩放 ,导致这两种方法之间的第一次强烈分离。

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