多阶段自适应线性最优化的线性与分段线性混合决策策略
Hybrid Strategies using Linear and Piecewise-Linear Decision Rules for Multistage Adaptive Linear Optimization
摘要：
决策规则提供了一个丰富和易于处理的框架，解决某些类别的多级自适应最优化问题。最近的文献已经显示出使用线性和非线性决策规则的希望，在这些规则中，等待和观望决策被表示为函数，其参数是待优化的决策变量，潜在的不确定参数。尽管取得了越来越大的成功，但当使用非线性决策规则（在某些情况下为线性决策规则）时，解决现实世界的随机最优化问题在计算上可能会变得非常困难。因此，决策规则，提供了一个有竞争力的解决方案的质量和计算时间之间的权衡变得更有吸引力。鉴于现有的研究一直使用同质的决策规则，本文的主要贡献是混合决策规则的计算探索。我们首先经验验证，在早期阶段具有更高的不确定性分辨率或更多的线性件比在后期阶段的解决方案质量更显着。然后，我们对非递增（即，早期阶段的较高不确定性分辨率）和非递减（即，在后期阶段的更高的不确定性分辨率）混合决策规则，以说明解决方案质量和计算成本之间的权衡。我们还演示了一个线性决策规则优于分段线性决策规则的情况下，在模拟器环境中，这支持需要评估的决策规则的质量从一个前瞻性模型在模拟器中，而不仅仅是使用前瞻性模型的目标函数值。
英文摘要：
Decision rules offer a rich and tractable framework for solving certain classes of multistage adaptive optimization problems. Recent literature has shown the promise of using linear and nonlinear decision rules in which wait-and-see decisions are represented as functions, whose parameters are decision variables to be optimized, of the underlying uncertain parameters. Despite this growing success, solving real-world stochastic optimization problems can become computationally prohibitive when using nonlinear decision rules, and in some cases, linear ones. Consequently, decision rules that offer a competitive trade-off between solution quality and computational time become more attractive. Whereas the extant research has always used homogeneous decision rules, the major contribution of this paper is a computational exploration of hybrid decision rules. We first verify empirically that having higher uncertainty resolution or more linear pieces in early stages is more significant than having it in late stages in terms of solution quality. Then we conduct a comprehensive computational study for non-increasing (i.e., higher uncertainty resolution in early stages) and non-decreasing (i.e., higher uncertainty resolution in late stages) hybrid decision rules to illustrate the trade-off between solution quality and computational cost. We also demonstrate a case where a linear decision rule is superior to a piecewise-linear decision rule within a simulator environment, which supports the need to assess the quality of decision rules obtained from a look-ahead model within a simulator rather than just using the look-ahead model's objective function value.
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