Large Scale Optimization for Nonlinear Mixed Integer Programs and Applications

尽管在解决方法和计算机硬件方面取得了进展，但一些真实的生活优化问题仍然具有挑战性。从医疗保健调度和路由，电信网络设计，能源规划，环保意识的物流和供应链网络所产生的问题是这样的重要和复杂的问题的例子。 虽然非线性混合规划（NMIP）提供了丰富的模型，但其解决方案仍然是一个很大的挑战。 我们提出了一种新的解决方法来解决NMIP优化问题相结合的四个主要方法：边界点，分解，分支定界，线性化/近似方法。问题首先被分解成容易解决的问题，每个问题都可以有效地解决。这些小问题的解决方案，然后结合起来，以提供一个整体解决方案的原始问题。 该提案是一项重大研究计划的一部分，旨在解决从实际应用中获得灵感的困难数学规划问题。它将使研究生能够在建模和解决复杂的现实生活中的问题，这将对一些行业产生直接影响的培训。

Some real life optimization problems remain challenging despite the advances in solution approaches and computer hardware. Problems arising from healthcare scheduling and routing, telecommunications network design, energy planning, environmentally-conscious logistics and supply chain networks are examples of such important and complex problems. While Nonlinear Mixed Integer Programming (NMIP) provides a wealth of models, its solution remains a big challenge. We propose a novel solution approach to tackle NMIP optimization problems by combining four major approaches: interior-point, decomposition, branch-and-bound, and linearization/approximation methods. The problems are first fragmented into easy-to-solve problems that can be each solved efficiently. The solutions from these smaller problems are then combined to provide an overall solution to the original problem. The proposal is part of a major research program to solve hard mathematical programming problems that are inspired from practical applications. It will enable the training of graduate students in the modeling and solution of complex real-life problems that will have a direct impact on a number of industries.