论文标题
可能的事件受约束优化和数据添加的解决方案范式
Probable Event Constrained Optimization and A Data-embedded Solution Paradigm
论文作者
论文摘要
本文解决了不确定性下的一类新的优化问题，称为可能的事件约束优化（PECO），该问题通过一组可能的事件约束（PEC）优化了决策变量和受试者的目标函数。这种新类型的约束确保了最佳解决方案对于所有不确定事件的最佳解决方案都是可行的，其关节概率大于用户定义的阈值。 PEC可以用作常规机会约束的替代方案，而后者不能保证解决方案对高概率不确定事件的可行性。鉴于不确定性下的现有优化问题的解决方案方法不适合解决PECO问题，我们开发了一种新型的数据包含的解决方案范式，该解决方案范式使用不确定参数的历史测量/数据作为输入样本。该解决方案范式在概念上很简单，使我们能够制定有效的数据还原方案，从而减轻计算负担，同时保持高精度。
This paper solves a new class of optimization problems under uncertainty, called Probable Event Constrained Optimization (PECO), which optimizes an objective function of decision variables and subjects to a set of Probable Event Constraints (PEC). This new type of constraint guarantees that optimal solutions are feasible for all uncertain events whose joint probabilities are greater than a user-defined threshold. The PEC can be used as an alternative to the conventional chance constraint, while the latter cannot guarantee the solution's feasibility to high-probability uncertain events. Given that the existing solution methods of optimization problems under uncertainty are not suitable for solving PECO problems, we develop a novel data-embedded solution paradigm that uses historical measurements/data of the uncertain parameters as input samples. This solution paradigm is conceptually simple and allows us to develop effective data-reduction schemes which reduce computational burden while preserving high accuracy.
