用于随机车辆路径问题的分解整数L形方法
The disaggregated integer L-shaped method for the stochastic vehicle routing problem
AI总结：
本文提出分解整数L形方法求解随机车辆路径问题，利用单调追索性质构造新型最优性割和下界泛函，并给出问题特定的追索下界以加速求解，实验取得最先进结果。
摘要：
本文提出了一种新的整数L形方法，用于求解两阶段随机整数规划问题，其中第一阶段解可以分解为互不相交的组件，且每个组件具有单调的追索函数。在最小化问题中，单调性性质规定，一个组件的追索成本必须始终高于或等于其任何子组件的追索成本。该方法利用了在该性质下有效的新型最优性割和新的下界泛函。随机车辆路径问题特别适合用这种方法求解，因为其解可以分解为一组路径。我们考虑具有随机需求的变体，其中追索策略包括：每当车辆没有足够容量来容纳新实现的需求时，就执行一次返回仓库的行程。本文表明，该策略可能导致非单调的追索函数，但当客户需求由几个常用的概率分布族建模时，单调性成立。我们还提出了针对该问题的新的追索下界，这些下界加强了下界泛函，并显著加快了求解过程。在文献实例上的计算实验表明，新方法取得了最先进的结果。
英文摘要：
This paper proposes a new integer L-shaped method for solving two-stage stochastic integer programs whose first-stage solutions can decompose into disjoint components, each one having a monotonic recourse function. In a minimization problem, the monotonicity property stipulates that the recourse cost of a component must always be higher or equal to that of any of its subcomponents. The method exploits new types of optimality cuts and lower bounding functionals that are valid under this property. The stochastic vehicle routing problem is particularly well suited to be solved by this approach, as its solutions can be decomposed into a set of routes. We consider the variant with stochastic demands in which the recourse policy consists of performing a return trip to the depot whenever a vehicle does not have sufficient capacity to accommodate a newly realized customer demand. This work shows that this policy can lead to a non-monotonic recourse function, but that the monotonicity holds when the customer demands are modeled by several commonly used families of probability distributions. We also present new problem-specific lower bounds on the recourse that strengthen the lower bounding functionals and significantly speed up the resolution process. Computational experiments on instances from the literature show that the new approach achieves state-of-the-art results.
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