Decomposition-Based Optimization: A New Solver Paradigm

该奖项的研究目标是（1）开发基于分解的高级方法，用于解决大规模优化问题，（2）将这些方法与当前最先进的技术相结合，以及（3）通过建模语言和对标准API的扩展，使用户可以访问这些方法（应用程序接口）提供的最先进的优化软件。虽然分解技术已被证明在某些应用中非常有效，但由于缺乏集成其他先进技术的数学理论，这些方法尚未在商业求解器中采用;实现困难;与模型结构自动检测相关的挑战;以及缺乏对表达分解策略的建模语言的支持。本研究的目的是克服这些挑战，并开发实用的方法和先进的方法的实施，沿着与支持建模的从业人员。本研究的影响将是在允许从业人员有机会获得强大的方法来优化大规模系统，其不断增加的复杂性是在实践中驱动的数据和存储的可用性增加。除其他外，分解方法是优化大规模系统的方法，这些系统由相对较少的系统级约束连接的较小的子系统组成。这种系统的一个典型例子是由地理上分布的仓库组成的物流系统，每个仓库都有一个相关的运输车队。当放松系统级约束时，底层优化问题分解，从而产生更有效的解决方法。分解可以提供一种实用的并行化方法，从而提供一种利用多核/多处理器架构的商品化的手段。所有方法都将以开源方式实施，并通过COIN-OR开源库（http：//www.example.com）分发，以确保广泛传播。www.coin-or.org

The research objectives of this award are (1) to develop advanced methodologies based on decomposition for the solution of large-scale optimization problems, (2) to integrate these methodologies with current state-of-the-art techniques, and (3) to make these methodologies accessible to users through modeling languages and extensions to the standard APIs (Application Program Interfaces) provided by current state-of-the-art optimization software. Although decomposition techniques have proven very effective in certain applications, these methods have not been adopted in commercial solvers due to lack of a mathematical theory integrating other advanced techniques; difficulties in implementation; challenges associated with automatic detection of model structure; and lack of support in modeling languages for expressing decomposition strategies. This research aims to overcome these challenges and to develop practical methodologies and implementations of advanced methods, along with support for modeling by practitioners.The impact of this research will be in allowing practitioners to have access to powerful methods of optimizing large-scale systems, whose ever-increasing complexity is being driven in practice by the increased availability of data and storage. Among other things, decomposition methods are the methods of choice for the optimization of large-scale systems consisting of smaller subsystems linked by relatively few system-level constraints. One typical example of such a system is a logistics system consisting of geographically distributed warehouses, each with an associated fleet of delivery vehicles. When the system-level constraints are relaxed, the underlying optimization problem decomposes, leading to more efficient solution methods. Decomposition may provide a practical approach to parallelization and thus a means of capitalizing on the commoditization of multi-core/multi-processor architectures. All methodologies will be implemented in open source and distributed through the COIN-OR open source repository (http://www.coin-or.org), ensuring wide dissemination.