As shown by Tang, Denardo [9] the job Sequencing and tool Switching Problem (SSP) can be decomposed into the following two problems. Firstly, the Tool Loading Problem (TLP) - for a given sequence of jobs, find an optimal sequence of magazine states that minimizes the total number of tool switches. Secondly, the Job Sequencing Problem (JeSP) - find a sequence of jobs minimizing the total number of tool switches. Published in 1988, the well known Keep Tool Needed Soonest (KTNS) algorithm for solving the TLP has time complexity $O(mn)$. Here $m$ is the total number of tools necessary to complete all $n$ sequenced jobs on a single machine. A tool switch is needed since the tools required to complete all jobs cannot fit in the magazine, whose capacity $C < m$. We hereby propose a new Greedy Pipe Construction Algorithm (GPCA) with time complexity $O(Cn)$. Our new algorithm outperforms KTNS algorithm on large-scale datasets by at least an order of magnitude in terms of CPU times.
An Active Learning Algorithm for Ranking from Pairwise Preferences with an Almost Optimal Query Complexity
我们研究了从成对偏好中学习排序的问题，并解决了一个长期存在的开放问题，该问题导致了许多数学的发展，但对于我们的特定问题没有可证明的结果。给定$n$元素的集合$V$，我们希望在给定成对偏好标签的情况下对它们进行线性排序。成对偏好标签是作为对问题“如果偏好，u还是v？$ for two elements $ u，v \in V $. We assume possible non-transitivity paradoxes which may arise naturally due to human mistakes or irrationality. The goal is to linearly order the elements from the most preferred to the least preferred, while disagreeing with as few pairwise preference labels as possible. Our performance is measured by two parameters: The loss and the query complexity (number of pairwise preference labels we obtain). This is a typical learning pro…
