We consider combinatorial optimization problems with uncertainty in the cost vector. Recently, a novel approach was developed to deal with such uncertainties: instead of a single one robust solution, obtained by solving a min max problem, the authors consider a set of solutions obtained by solving a min max min problem. In this new approach, the set of solutions is computed once and we can choose the best one in real time each time a cost vector occurs yielding better solutions compared to the min max approach. In this paper, we apply the new approach to the absolute and relative regret cases. Algorithms to solve the min max min robust (relative) regret problems are presented with computational experiments.

我们考虑具有成本向量不确定性的组合优化问题。最近，开发了一种新颖的方法来处理此类不确定性：作者考虑了通过解决min max min问题而获得的一组解决方案，而不是通过解决min max问题而获得的单个稳健解决方案。在这种新方法中，解决方案集仅计算一次，并且每次成本向量出现时，与最小最大方法相比，我们可以实时选择最佳解决方案。在本文中，我们将新方法应用于绝对和相对遗憾案例。通过计算实验，提出了解决最小最大最小鲁棒（相对）后悔问题的算法。