Robust combinatorial optimization problems under budgeted interdiction uncertainty
研究在预算干扰不确定性下，如何找到对参数变化表现良好的组合优化解，发现对抗问题可线性求解，但鲁棒问题为NP难且不可近似，实验表明某些模型仍可扩展。
Abstract In robust combinatorial optimization, we would like to find a solution that performs well under all realizations of an uncertainty set of possible parameter values. How we model this uncertainty set has a decisive influence on the complexity of the corresponding robust problem. For this reason, budgeted uncertainty sets are often studied, as they enable us to decompose the robust problem into easier subproblems. We propose a variant of discrete budgeted uncertainty for cardinality-based constraints or objectives, where a weight vector is applied to the budget constraint. We show that while the adversarial problem can be solved in linear time, the robust problem becomes NP-hard and not approximable. We discuss different possibilities to model the robust problem and show experimentally that despite the hardness result, some models scale relatively well in the problem size.