动态设施选址问题的数据驱动型自适应鲁棒优化方法研究

Dynamic facility location problem has been recognized as a fundamental issue in the fields of both combinatorial optimization and supply chain & logistics management. It also has been challenging to solve due to the ever-changing and limited information of key elements. To this end, based on our previous research, we propose a project addressing the data-driven adaptive robust optimization for dynamic facility location problem with limited information. First, we develop a deterministic model by analyzing several adjustment policies, which aims to lay a foundation for modeling the robust optimization. Then, we present a support vector cluster method incorporating a piece-wise linear kernel learning algorithm to construct the adjustable uncertainty set, which is able to be adapted to the dynamic environment, and keep the robust model computational tractable, even though taking full use of available data. To further simplify the robust model, we develop a robust counterpart based on the duality theory. An exact algorithm is proposed then and an online iteration state learning method is developed to accelerate the convergence rate. Last, we apply the model and algorithm proposed in practice by using historical and ongoing cases. We expect that the research can extend the fundamental methods in the fields of both facility location problem and robust optimization, as well as provide theoretical support for decision-makers improving the response ability under uncertainty and dynamics.

动态设施选址是组合优化及供应链与物流管理领域的代表性问题。关键因素的动态性及其信息的有限性对提高选址方案的可行性以及决策者快速响应环境变化的能力提出了挑战。为此，申请者基于前期研究，提出动态设施选址问题的数据驱动型自适应鲁棒优化方法研究项目。首先，研究动态设施选址确定型优化模型，并提出基于分段线性核学习支持向量聚类的可调节不确定集合构建方法，以充分利用当前有限信息提高不确定集合的准确性；基于此，构建自适应鲁棒优化模型，保证方案最优性与鲁棒性的最佳平衡，且具有较高的计算易处理性；然后，基于对偶理论研究优化模型的鲁棒对等式，以降低模型求解的复杂程度；为提高模型求解精度及效率，在精确算法研究的基础上，提出基于迭代过程在线学习的近似求解算法；为验证研究成果有效性，基于历史及现行案例对其应用。本研究期望能拓展设施选址问题及鲁棒优化领域基础理论，并为决策者提高动态环境下的响应能力提供理论和方法支持。

网络规划问题在诸多领域的战略决策中起着重要作用，如重大突发事件应急响应、物联通讯网络构建、物流与供应链网络设计等，其核心是设施选址问题。本项目针对有限动态不确定信息下的设施选址问题展开了深入研究。研究成果主要包括：完全信息下基于随机规划的大规模网络设计优化模型及求解算法、有限信息下基于鲁棒优化的大规模网络设计模型及求解算法、基于在线学习的大规模即时急救服务网络动态部署优化方法、基于拉格朗日原始-对偶在线学习的服务网络资源动态分配方法、考虑内生不确定性和主动干预决策的网络设计可靠性优化等。上述研究综合运用随机规划、鲁棒优化、马尔科夫决策过程、排队论等优化方法，并创新性地提出了数据驱动的在线学习优化算法，显著提高了在有限动态不确定信息下网络选址决策的可行性和可靠性。围绕上述内容，项目组共完成学术论文14篇，其中已在Omega、IEEE Transactions on Engineering Management、International Journal of Production Research、Transportation Research Part E: Logistics and Transportation Review等领域权威期刊发表8篇。项目研究成果可为诸多领域不确定环境下的网络设计优化问题提供理论和方法指导，有助于进一步丰富和完善数据驱动的优化决策方法和应用场景。