标题： 基于选址规划的鲁棒性双目标方法 显示英文标题

标题： A biobjective approach to robustness based on location planning

摘要： 寻找优化问题的鲁棒解在实践中是一个重要的问题，并且已经提出了各种定义解鲁棒性的概念。 可恢复鲁棒性的思想要求一旦实际场景变得已知，解就可以恢复为可行解。 文献中的通常方法是在名义情况下或最坏情况下最小化恢复解的目标函数值。 由于恢复本身也是昂贵的，因此存在恢复成本与所获得的解值之间的权衡；我们在双目标框架下研究这两种情况下的恢复成本和解值。 为此，我们假设恢复成本可以用度量来描述。 我们证明这会导致一个选址规划问题，将到目前为止一直被视为独立的两个研究领域结合起来。 我们展示如何通过最小化固定最坏情况下的目标函数值的恢复成本来计算该双目标问题的弱帕累托最优解，并提出针对有限不确定性集的线性问题和拟凸问题的方法。 此外，我们推导出一些情况，在这些情况下，不确定性集的大小可以减小而不改变帕累托最优解集。 显示英文摘要

摘要： Finding robust solutions of an optimization problem is an important issue in practice, and various concepts on how to define the robustness of a solution have been suggested. The idea of recoverable robustness requires that a solution can be recovered to a feasible one as soon as the realized scenario becomes known. The usual approach in the literature is to minimize the objective function value of the recovered solution in the nominal or in the worst case. As the recovery itself is also costly, there is a trade-off between the recovery costs and the solution value obtained; we study both, the recovery costs and the solution value in the worst case in a biobjective setting. To this end, we assume that the recovery costs can be described by a metric. We demonstrate that this leads to a location planning problem, bringing together two fields of research which have been considered separate so far. We show how weakly Pareto efficient solutions to this biobjective problem can be computed by minimizing the recovery costs for a fixed worst-case objective function value and present approaches for the case of linear and quasiconvex problems for finite uncertainty sets. We furthermore derive cases in which the size of the uncertainty set can be reduced without changing the set of Pareto efficient solutions.