Testing Solution Algorithms for Bilevel Programming Transportation Models in a Mixed Economic System

由于私人行为者一般追求自己的利益，而公共部门机构一贯按照他们所认为的集体公共利益行事，因此发展模型以预测公共政策对个人和私人组织行动的影响的努力变得复杂。例如，政府发展运输系统将对个人和公司的移动和设施位置产生影响，这反过来又将影响运输系统的绩效并对其产生新的需求。在过去的十年中，区域科学家和经济学家已经开始发展双层数学模型，代表和模拟公共和私人决策之间的相互作用。这些模型的测试都是小例子，因为在使用大型数据集（例如代表现实世界问题的数据集）时，还没有开发出有效的程序（算法）来确定最佳解决方案。该项目将开发和测试新的算法，以解决公私混合交通系统的大型双层规划模型。这项研究将分三步进行。首先，将完善连接公共和私营部门决策的大规模双层交通规划模型。其次，将开发并测试一套解决方案算法，使该模型能够在拥有韩国大型交通网络数据的超级计算机上使用。最后，分析了模型和求解算法作为公共政策制定手段的有效性。这个项目将带来理论和方法上的好处。通过确定双层规划模型在多大程度上有助于解释和预测公共和私人的相互作用，以及通过评估它们如何有助于公共政策的形成，将取得理论进展。当使用超级计算机时，将通过开发一种或多种有效的双层模型解算法来取得方法上的进步。对这些模型的速度和成本的更好评估也将会出现。因此，这项研究将扩大我们对公共和私营部门行为者如何在现代住区中相互关联的理解，并将增加我们对如何使用数学建模程序来解决复杂社会问题的认识。

Attempts to develop models to predict the impacts of public policies on the actions of individuals and private organizations have been complicated by the fact that private actors generally pursue their own interests, while public-sector agencies operate consistently with what they perceive to be the collective public interest. Governmental development of a transportation system, for example, will have impacts on movements and facility locations of individuals and corporations, which in turn will affect performance on the transport system and create new demands on it. In the last decade, regional scientists and economists have begun development of bi-level mathematical models that represent and simulate the interaction between public and private decisions. Tests of these models have been small examples, because efficient procedures (algorithms) have not been developed to determine optimal solutions when large data sets (such as those that would represent real-world problems) are used. This project will develop and test new algorithms to solve large bi-level programming models for mixed public-private transportation systems. The research will proceed in three steps. First, a large-scale bi-level transportation planning model linking public- and private-sector decisions will be refined. Second, a set of solution algorithms will be developed and tested to enable the model's use on a supercomputer with data on a large Korean transportation network. Finally, the validity of the model and the solution algorithm as a means of establishing public policies will be analyzed. Theoretical and methodological benefits will result from this project. Theoretical advances will be made by determining the extent to which bi-level programming models help explain and predict public and private interactions and by assessing how they can assist in the formation of public policy. Methodological advances will be made through development of one or more efficient solution algorithms for bi-level models when using supercomputers. Better assessments of the speed and costs of such models also will be available. This research therefore will expand our understandings of how public- and private- sector actors relate in modern settlements, and it will increase our knowledge of how mathematical modelling procedures can be used to address complex social problems.