Interfacing Optimization and Applications

建模语言在实践中被大量使用，因此为优化方面的协作研究提供了重要的工具。这个项目将通过扩大优化工具和环境在应用领域的使用来促进这种交互。由于对应用程序的规模和复杂性的要求越来越高，数学程序员在建模框架内开发算法和工具以推进应用程序和优化方面的最新技术变得至关重要。研究的重点将是在目标项目中提供优化技术的明确示例，并将在实际环境中解决大规模优化的计算和理论方面的问题。该提案的新工具、环境和算法将支持在模型开发期间使用应用程序和优化专家的直接输入进行建模的交互式方法。该提案将在四个应用领域展示这种相互作用，即视频点播系统的架构设计，断层治疗背景下的癌症治疗计划，数据挖掘的数学规划方法以及经济学中出现的互补性问题的解决方案。一个关键的需求是应用程序中优化结果的可视化；为此，将提供建模语言和MATLAB之间的链接。此链接的另一个好处是为MATLAB编程环境提供了复杂的数学编程能力。为了解决领域专家确定的重要问题和方面，所产生的优化问题非常大，需要大量的计算资源。几个新工具将在元计算机上生成这些优化问题的公式和解决方案，所有这些工具都将利用Condor预先存在的“现成”工作站池。该研究的一个关键组成部分将推导出在提议的框架内工作的新算法，并利用元竞争资源。其中包括几个新的大规模互补问题求解器和一个容错并行混合整数规划求解器。这项工作的一个基本目标是教育其他学科的研究人员，主要是高级本科生和研究生，了解这些工具的效用、使用和功能。本提案中详细介绍的几个应用程序合作是在基于本项目主题的课程的第一次教学期间与同事和学生互动的直接结果。

Modeling languages are heavily used in practice and therefore supply a critical vehicle for collaborative research in optimization. This project will faciliate this interaction by broadening the usage of optimization tools and environments in application areas. Due to the increasing demands in the size and complexity of applications, it has become vitally important for mathematical programmers to develop algorithms and tools within a modeling framework in order to advance the state-of-the-art in both applications and optimization. The thrust of the research will be in providing explicit examples of optimization technology, within targeted projects, and will address computational and tlieoretical aspects of large scale optimization in a practical setting.The new tools, environments, and algorithms of this proposal will enable an interactive approach to modeling with direct input from application and optimization experts during model development. The proposal will demonstrate such interactions within four application areas, namely the architectural design of video on-demand systems, cancer treatment plans in the context of tomotherapy, mathematical programming approaches to data mining, and the solution of complementarity problems arising in economics. A pivotal need is for visualization of optimization results within the application; a link between modeling languages and MATLAB will be provided for this purpose. An additional benefit of this link is the provision of a sophisticated mathematical programming capability to the MATLAB programniing environment.To address important issues and facets identified by domain experts, the resulting optimization problems are very large and require vast amounts of computing resources. Several new tools to enable the formulation and solution of such optimization problems on a metacomputer will be generated, all utilizing a pool of pre-existing, "off-the-shelf" workstations via Condor. A key component of the research will derive new algorithms that work within the proposed framework and exploit the metacomptiting resources. These include several new solvers for large scale complementarity problems and a fault tolerant parallel mixed integer programming solver.A fundamental goal of this effort is to educate researchers in other disciplines, primarily senior level undergraduates and graduate students, on the utility, use and power of these tools. Several of the application collaborations detailed in this proposal are direct consequences of interactions with colleagues and students during the first teaching of a course based on the topics of this project.