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

由于私营部门行为者通常追求自己的利益，而公共部门机构的运作符合它们认为的集体公共利益，因此建立预测公共政策对个人和私营组织行动的影响的模型的努力变得复杂起来。例如，政府对交通系统的发展将对个人和公司的流动和设施位置产生影响，这反过来又会影响交通系统的性能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开发表示和模拟公共和私人决策之间的相互作用的双层数学模型。对这些模型的测试一直是小的例子，因为当使用大数据集(例如那些将代表现实世界问题的数据)时，还没有开发出有效的程序(算法)来确定最优解决方案。该项目将开发和测试新的算法，以解决公共和私人混合交通系统的大型双层规划模型。研究将分三步进行。首先，将完善连接公共部门和私营部门决策的大规模双层交通规划模型。其次，将开发和测试一套求解算法，以使该模型能够在具有韩国大型交通网络数据的超级计算机上使用。最后，对模型和求解算法作为公共政策制定手段的有效性进行了分析。这一项目将带来理论和方法上的好处。将通过确定双层方案拟订模型在多大程度上有助于解释和预测公共和私营部门的相互作用并评估它们如何有助于公共政策的形成，从而取得理论上的进展。当使用超级计算机时，将通过为双层模型开发一个或多个有效的求解算法来取得方法学上的进步。对这类模式的速度和成本也将有更好的评估。因此，这项研究将扩大我们对公共和私营部门行为者在现代住区中的关系的理解，并将增加我们关于如何利用数学建模程序来解决复杂的社会问题的知识。

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.