Large-Scale and Big Data Optimization

在当今的数字世界中，随着数据量的不断增加，需要解决前所未有的优化问题。机器学习、通信和社交网络、物流系统是许多突出的应用领域中的一些，在这些领域中，优化问题出现了数万或数百万个变量。许多优化模型和算法虽然在适度的维度上表现出很高的效率，但对于这种规模的实例来说，很难扩展，并且不能提供令人满意的解决方案。我的研究的主要和长期目标是为能够在超大规模环境下工作的新型优化算法的设计做出贡献。我计划调查精确方法和启发式方法，并验证在通信、物流和社交网络中的一些特定应用上的发现。 对于精确的方法，目标是整合基于来自几个学科的理论和经验证据的知识，并探索“什么、为什么、如何和做”范式，重点是(I)建模方面，(Ii)数学模型的组合，以及(Iii)并行技术，以便利用结合多核处理器、多线程编程和GPU加速器的异类环境进行超大规模优化。虽然这些环境只在大型机上可用，但现在它们可用于行业易于访问的计算机。 对于启发式方法，重点将放在元启发式方法上，这是一类广泛的求解方法，已成功地应用于许多优化问题。然而，它们似乎已经达到了解决非常大的组合问题的极限，例如在交叉对接或网络优化中出现的问题。这是因为元启发式算法是用自组织方法来探索解空间的，其效率和计算时间高度依赖于局部最优解的拓扑结构，除了一些非常特殊的问题外，局部最优解的拓扑结构是很难预见的。我们计划用机器学习指导的知情探索来取代对解决方案空间的临时探索。将与直接机器学习算法在以下实际问题上进行比较：(I)供应链管理，特别是与交叉对接，以及(Ii)网络优化和(Iii)社交网络中的机制设计。机器学习算法所需的数据将由Cleard和Ciena为前两个应用程序提供，而第三个应用程序需要确定一个组织/工业合作伙伴。 我的研究成果将为行业(如Cleard和Ciena)提供高效和自动化的交叉对接/网络管理的信息技术管理工具，不仅可以提高竞争力，还可以减少能源消耗，从而减少碳足迹。

In today's digital world, with ever increasing amounts of data comes the need to solve optimization problems of unprecedented sizes. Machine learning, communication and social networks, logistics systems are some of the many prominent application domains where optimization problems arise with tens of thousands or millions of variables. Many optimization models and algorithms, while exhibiting great efficiency in modest dimensions, have great difficulties to scale for instances of this size and do not offer satisfactory solution. The primary and long-term objective of my research is to contribute to the design of novel optimization algorithms capable of working in very large-scale setting. I plan to investigate both exact and heuristic methods, and validate the findings on some particular applications in communication, logistics and social networks. For exact methods, the objective is to integrate knowledge based on both theoretical and empirical evidence from several disciplines, and explore the "what, why, how, and do" paradigm with an emphasis on (i) modelling aspects, (ii) combination of mathematical models, and (iii) parallelization techniques in order to take advantage of the heterogeneous environments combining multi-core processors, multi-threaded programming and GPU accelerators for very large scale optimization. While those environment were only available on mainframe computers, they are now available to computers that are easily accessible to the industry. For heuristic methods, focus will be on meta-heuristics, a wide class of solution methods that have been successfully applied to many optimization problems. However, they seem to have reached their limits to solve very large combinatorial problems such as those arising in cross-docking or network optimization. This is because meta-heuristics explore the solution space with ad-hoc methods, whose efficiency and computing time highly depend on the topology of the local optima which, except for some very particular problems, are very difficult to foresee. We plan to replace the ad-hoc exploration of the solution space with an informed exploration guided by machine learning. Comparison will be made with direct machine learning algorithms on practical problems arising in: (i) supply chain management and in particular with cross-docking, and (ii) network optimization and (iii) mechanism design in social networks. Data required by machine learning algorithms will be provided by ClearD and Ciena for the first two applications, and an organization/industrial partner needs to be identified for the third one. The results of my research will provide the industry (like ClearD and Ciena) information technology management tools for efficient and automated cross-docking/network management, not only to improve competitiveness but also to reduce energy consumption and therefore carbon footprint.