In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is used to model the imprecise probabilities. In one of the interpretations, a possibility distribution (a membership function of a fuzzy set) in the set of coefficient realizations induces a necessity measure, which in turn defines a family of probability distributions in this set. The distributionally robust approach is then used to transform the imprecise constraints into deterministic counterparts. Namely, the uncertain left-had side of each constraint is replaced with the expected value with respect to the worst probability distribution that can occur. It is shown how to represent the resulting problem by using linear or second order cone constraints. This leads to problems which are computationally tractable for a wide class of optimization models, in particular for linear programming.
翻译:本文将讨论一组具有不确定线性限制的优化问题。 假设限制系数是随机矢量,其概率分布仅部分为已知的随机矢量。 概率理论用于模拟不精确概率。 在一种解释中, 一套系数实现中可能的分布( 模糊组合的会籍功能) 引出一种必要性的测量, 从而在这套系数中定义了概率分布的组合。 然后, 使用分布稳健的方法将不精确的制约转化为确定性对应物。 也就是说, 每种制约的不确定性左侧被替换为最坏概率分布的预期值。 显示如何通过使用线性或第二顺序锥体限制来代表由此产生的问题。 这导致问题, 这些问题可以计算为广泛的优化模型, 特别是线性编程模式 。