论文标题
瞬间歧义与设施位置申请的瞬间歧义下的悲观双层线性程序的决策规则方法
Decision Rule Approaches for Pessimistic Bilevel Linear Programs under Moment Ambiguity with Facility Location Applications
论文作者
论文摘要
我们在顺序的两人游戏的背景下研究一个悲观的随机双利计划，在观察到领导者的行动和不确定性的启示之后，领导者在这里做出了二进制的二元决定，而追随者在观察到领导者的行动和启示后做出了持续的等待决定。仅知道均值，协方差和支持的信息。我们将问题提出为分布鲁棒（DR）两个阶段问题。悲观的DR Bilevel程序被证明与通用的两阶段分布相等，在正确条件下，在歧义集的适当条件下，具有随机的目标和随机约束。在连续分布的情况下，使用线性决策规则方法，我们基于（1）0-1半决赛编程（SDP）近似以及（2）精确的0-1共同编程重新启动，基于（1）0-1半决赛编程（SDP）近似bilevel计划上的上限。当歧义集局限于离散分布时，开发了确切的0-1 SDP重新制定，并得出了最坏情况分布的明确结构。为了进一步改善所提出的0-1 SDP的计算，开发了一个切割平面框架。此外，基于混合构成线性编程近似，提出了另一种切皮平面算法。进行了广泛的数值研究，以证明拟议方法在设施位置问题上的有效性。
We study a pessimistic stochastic bilevel program in the context of sequential two-player games, where the leader makes a binary here-and-now decision, and the follower responds a continuous wait-and-see decision after observing the leader's action and revelation of uncertainty. Only the information of the mean, covariance, and support is known. We formulate the problem as a distributionally robust (DR) two-stage problem. The pessimistic DR bilevel program is shown to be equivalent to a generic two-stage distributionally robust stochastic (nonlinear) program with both a random objective and random constraints under proper conditions of ambiguity sets. Under continuous distributions, using linear decision rule approaches, we construct upper bounds on the pessimistic DR bilevel program based on (1) 0-1 semidefinite programming (SDP) approximation and (2) an exact 0-1 copositive programming reformulations. When the ambiguity set is restricted to discrete distributions, an exact 0-1 SDP reformulation is developed, and explicit construction of the worst-case distribution is derived. To further improve the computation of the proposed 0-1 SDPs, a cutting-plane framework is developed. Moreover, based on a mixed-integer linear programming approximation, another cutting-plane algorithm is proposed. Extensive numerical studies are conducted to demonstrate the effectiveness of the proposed approaches on a facility location problem.
