In this paper, an optimization problem with uncertain constraint coefficients is considered. Possibility theory is used to model the uncertainty. Namely, a joint possibility distribution in constraint coefficient realizations, called scenarios, is specified. This possibility distribution induces a necessity measure in scenario set, which in turn describes an ambiguity set of probability distributions in scenario set. The distributionally robust approach is then used to convert the imprecise constraints into deterministic equivalents. Namely, the left-hand side of an imprecise constraint is evaluated by using a risk measure with respect to the worst probability distribution that can occur. In this paper, the Conditional Value at Risk is used as the risk measure, which generalizes the strict robust and expected value approaches, commonly used in literature. A general framework for solving such a class of problems is described. Some cases which can be solved in polynomial time are identified.
翻译:在本文中,考虑了不确定制约系数的优化问题。 使用概率理论来模拟不确定性。 也就是说, 指定了限制系数实现过程中的共同可能性分布, 称之为假设情景。 这种可能性分布在假设情景集中引发了一种必要的措施, 这反过来又描述了假设情景集中概率分布的一套模糊性。 然后, 使用分布稳健的方法将不精确的制约转化为确定性等值。 也就是说, 使用风险措施对可能发生的最差的概率分布进行风险评估, 评估不精确制约的左侧。 在本文中, 将风险中的条件值用作风险措施, 将文献中常用的严格稳健和预期值方法加以概括。 描述了解决这类问题的一般框架。 确定了一些可以在多元时间内解决的案例 。