In recent years, stochastic programming has gained increasing attention as a tool to support the scheduling of generating units in the face of uncertain information. One approach that has a long‐standing history in stochastic programming is the Benders decomposition (BD). However, BD is known to suffer from a series of shortcomings, for example, oscillation and tailing‐off effect. To reduce these drawbacks, regularization techniques are appealing options. However, even if regularized, BD may still struggle to converge due to the growing computational burden of its master problem (MP) over the iterations — this is especially noticeable in mixed‐integer programming models. Thus, to tackle this growing MP, we propose decomposing it using dual decomposition. We test our methodology on a testbed comprised of 108 cases from a system with 46 buses. Our results show that our methodology is effective both in terms of running times as well as the optimality gap.

中文翻译：

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拉格朗日松弛，弯曲变形和水平束方法在随机热液机组组合问题中的结合

近年来，作为面对不确定信息支持发电机组调度的工具，随机规划越来越受到关注。Benders分解（BD）是在随机编程中具有悠久历史的一种方法。但是，已知BD具有一系列缺点，例如，振荡和拖尾效应。为了减少这些缺点，正则化技术是有吸引力的选择。但是，即使进行了正则化，由于其主问题（MP）在迭代过程中的计算负担越来越大，BD仍可能难以收敛-这在混合整数编程模型中尤其明显。因此，为了解决这个不断增长的MP，我们建议使用对偶分解对其进行分解。我们在包含46个总线的系统的108个案例的测试平台上测试了我们的方法。