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步，但一些现实生活中的优化问题仍然具有挑战性。医疗保健计划和路线、电信网络设计、能源规划、注重环保的物流和供应链网络所产生的问题就是这些重要而复杂的问题的例子。 虽然非线性混合整数规划(NMIP)提供了丰富的模型，但其求解仍然是一个巨大的挑战。结合内点法、分解法、分枝定界法和线性化/逼近法，提出了一种新的求解NMIP优化问题的方法。这些问题首先被分割成容易解决的问题，每个问题都可以有效地解决。然后，将这些较小问题的解决方案组合在一起，为原始问题提供整体解决方案。 该提案是一项重大研究计划的一部分，该计划旨在解决受实际应用启发的数学规划难题。它将使研究生能够在建模和解决复杂的现实问题方面进行培训，这些问题将对许多行业产生直接影响。

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.