多阶段随机优化的界及其在发电与输电扩展规划中的应用
Bounds for multi-horizon stochastic optimization with application to power generation and transmission expansion planning
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中文总结 AI 辅助
本文针对多阶段随机优化问题最优值界的计算难题，提出基于场景树分解的界估计技术，通过不同分解与重组策略实现高效求解，在发电与输电扩展规划问题中验证了方法的效率。
中文摘要 AI 辅助
本文研究了用于推导多阶段随机优化问题最优值界的计算高效方法，特别关注其在发电与输电扩展规划中的应用。多阶段随机规划联合捕捉了跨多个时间尺度（例如战略（长期）和运营（短期））的不确定性下的序贯决策。由于其固有的复杂性，尤其是当不确定性跨越多个时间阶段时，直接求解这些问题会变得计算上不可行。为解决这一问题，本文基于场景树的分解，开发并分析了多种新颖的界估计技术。我们系统研究了仅分解运营场景树、仅分解战略场景树，或同时分解两种场景树的三种方式，并设计了两种重组方法以获得有效界。每种方法都形成了一个单调的不等式链，从下方近似原问题的最优值。其中一种方法在运营和同时分解中产生了显著更少的待重组子组数量，从而带来了可观的计算节省。针对一个多阶段混合整数发电与输电扩展规划问题的数值结果，通过不同的分解与重组策略展示了所提方法的效率。
英文摘要
This paper investigates computationally efficient methods for deriving bounds on the optimal value of multi-horizon stochastic optimization problems, with a particular focus on applications in power generation and transmission expansion planning. Multi-horizon stochastic programs capture sequential decision-making under uncertainty across multiple time scales---e.g., strategic (long-term) and operational (short-term)---jointly. Due to their inherent complexity, especially when uncertainties span several time horizons, solving these problems directly becomes computationally prohibitive. To address this, the paper develops and analyzes various novel bounding techniques, based on the dissection of scenario trees. We investigate systematically dissecting (i) only the operational, (ii) only the strategic, or (iii) both scenario trees simultaneously, and we devise two ways to recombine them to obtain valid bounds. Each method leads to a monotonic chain of inequalities that approximate the optimal value of the original problem from below. One of these methods results in a significantly smaller number of subgroups to recombine in the operational and simultaneous dissections, leading to substantial computational savings. Numerical results on a multi-horizon mixed-integer generation and transmission expansion planning problem show the efficiency of the proposed approach through different dissection and recombination strategies.
