论文标题
一阶段和两阶段可靠优化的最佳方案减少
Optimal Scenario Reduction for One- and Two-Stage Robust Optimization
论文作者
论文摘要
强大的优化通常遵循最坏的观点，其中单个场景可能决定给定解决方案的客观值。因此，减少不确定性集的大小而不会过多地更改产生的客观价值，这是一项艰巨的任务。另一方面，许多方案的强大优化问题往往很难解决，特别是对于两个阶段问题。因此，降低的不确定性集可能是在合理时间内找到解决方案的核心。我们提出了减少方案方法，以保证由此产生的强大解决方案的性能。一个和两阶段可靠优化的方案减少问题是构成的优化问题，仅取决于不确定性集，而不取决于基础决策问题。实验结果表明，降低的不确定性集的客观值与原始客观值密切相关，从而比使用通用物质聚类方法（如K-均值）相比提供了更好的解决方案。
Robust optimization typically follows a worst-case perspective, where a single scenario may determine the objective value of a given solution. Accordingly, it is a challenging task to reduce the size of an uncertainty set without changing the resulting objective value too much. On the other hand, robust optimization problems with many scenarios tend to be hard to solve, in particular for two-stage problems. Hence, a reduced uncertainty set may be central to find solutions in reasonable time. We propose scenario reduction methods that give guarantees on the performance of the resulting robust solution. Scenario reduction problems for one- and two-stage robust optimization are framed as optimization problems that only depend on the uncertainty set and not on the underlying decision making problem. Experimental results indicate that objective values for the reduced uncertainty sets are closely correlated to original objective values, resulting in better solutions than when using general-purpose clustering methods such as K-means.
