On solving two-stage distributionally robust disjunctive programs with a general ambiguity set
On solving two-stage distributionally robust disjunctive programs with a general ambiguity set
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DOI：
10.1016/j.ejor.2019.05.033
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发表时间：
2019-12
期刊：
影响因子：
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通讯作者：
M. Bansal;Sanjay Mehrotra
中科院分区：
文献类型：
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作者：
M. Bansal;Sanjay Mehrotra
我们引入了两阶段的分布鲁棒析取程序（TSDR-DP）与析取约束在这两个阶段和一个一般的模糊集的概率分布。TSDR-DP包含了各种类型的两阶段分布鲁棒规划，其中第二阶段问题是非凸规划（如混合二元规划，半连续规划，非凸二次规划，可分离非线性规划等）。TSDR-DP是一个风险规避程度可由决策者选择的优化模型。它推广了两阶段随机析取规划（风险中性）和两阶段鲁棒析取规划（最保守）。据我们所知，上述特殊情况下的TSDR-DP尚未研究到现在。在本文中，我们开发的分解算法，利用Balas的线性规划等价的确定性析取规划或L形方法中的顺序凸化方法，解决TSDR-DP。我们提出的充分条件下，我们的算法是收敛的。这些算法推广了Bansal等人的分布鲁棒整数L形算法。(SIAM J. on Optimization 28：2360-2388，2018）用于TSDR混合二进制程序，TSDR-DP的子类。此外，我们制定了一个半连续规划（SCP）作为一个析取程序，并使用我们的结果TSDR-DP解决一般的两阶段分布鲁棒SCP（TSDR-SCP）和TSDR-SCP具有半连续流入集在第二阶段。
We introduce two-stage distributionally robust disjunctive programs (TSDR-DPs) with disjunctive constraints in both stages and a general ambiguity set for the probability distributions. The TSDR-DPs subsume various classes of two-stage distributionally robust programs where the second stage problems are non-convex programs (such as mixed binary programs, semi-continuous program, nonconvex quadratic programs, separable non-linear programs, etc.). TSDR-DP is an optimization model in which the degree of risk aversion can be chosen by decision makers. It generalizes two-stage stochastic disjunctive program (risk-neutral) and two-stage robust disjunctive program (most-conservative). To our knowledge, the foregoing special cases of TSDR-DPs have not been studied until now. In this paper, we develop decomposition algorithms, which utilize Balas’ linear programming equivalent for deterministic disjunctive programs or his sequential convexification approach within L-shaped method, to solve TSDR-DPs. We present sufficient conditions under which our algorithms are finitely convergent. These algorithms generalize the distributionally robust integer L-shaped algorithm of Bansal et al. (SIAM J. on Optimization 28: 2360-2388, 2018) for TSDR mixed binary programs, a subclass of TSDR-DPs. Furthermore, we formulate a semi-continuous program (SCP) as a disjunctive program and use our results for TSDR-DPs to solve general two-stage distributionally robust SCPs (TSDR-SCPs) and TSDR-SCP having semi-continuous inflow set in the second stage.