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，其中出现了数万或数百万个变量的优化问题。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，但在这种规模的实例上扩展有很大的困难，并且不能提供令人满意的解决方案。我研究的主要和长期目标是为能够在非常大规模的环境中工作的新型优化算法的设计做出贡献。我计划研究精确方法和启发式方法，并在通信，物流和社交网络的一些特定应用中验证研究结果。

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.