Optimal solutions of combinatorial optimization problems can be sensitive to changes in the cost of one or more elements. Single and set tolerances measure the largest / smallest possible change such that the current solution remains optimal and other solutions become non-optimal for cost changes in one or more elements, respectively. The current definition only applies to subsets of elements. In this paper, we broaden the definition to all elements, for single tolerances, and to all subsets of elements for set tolerances, while proving that key computational and theoretical properties still apply to the new definitions.

翻译：组合优化问题的最优解可能对单个或多个元素的成本变化敏感。单容差和集合容差分别衡量在单个或多个元素成本变化时，当前解保持最优且其他解变得非最优的最大/最小可能变化量。现有定义仅适用于元素子集。本文将定义拓展至所有元素（针对单容差）及所有元素子集（针对集合容差），同时证明关键计算与理论性质在新定义下依然成立。