Open Cyberinfrastructure for Mixed-integer Nonlinear Programming: Collaboration and Deployment via Virtual Environments

优化是网络基础设施计算工具的战略技术之一，因为这一领域涉及在许多可能的备选方案中选择“最佳”设计或计划。实践中的大多数具有挑战性的应用问题(如工程设计和制造、新陈代谢网络分析、证券投资)都需要使用离散变量(主要是0-1变量)来表示逻辑选择，以及处理非线性，以便准确地模拟物理、化学、生物、金融或社会系统的性能。这种优化领域被称为混合整数非线性规划(MINLP)。MINLP是解决确定性优化模型的最通用工具之一，现在有一个重要的优化社区，对大规模MINLP问题的解决和应用越来越感兴趣。这个社区是高度多学科的，涉及运筹学研究人员、工业、化学和机械工程师、经济学家、化学家和生物学家。然而，困难在于MINLP是最具挑战性的优化问题之一，特别是在处理非凸函数时，因为这可能会产生局部解。因此，在合理的计算时间内找到大规模MINLP模型的全局最优解仍然是一个很大程度上尚未解决的问题。该建议的主要目的是解决在合理的计算时间内，在一个独特的虚拟协作环境中解决实际大规模MINLP优化问题的挑战，该环境可以将算法开发者和应用研究人员聚集在一起。为了应对这些挑战，本提案的主要目标是：(A)为虚拟协作创造一个网络基础设施环境，以开发和收集工具，挑战测试问题，并传播开放源码软件；(B)开发基本算法、预测严格下限的公式，以及用于解决大规模非凸MINLP问题的开放源码软件；(C)测试在现实世界应用中出现的具有挑战性问题的测试软件，主要是工程应用，但也包括生物和金融应用。这一提议的一个主要成果将是开发新的算法和开源软件，用于解决非凸MINLP优化问题，使其达到完全全局最优或接近最优。这项研究还将包括开发各种真实世界的应用问题，这些问题将被记录为替代配方的案例研究。案例研究将与IBM和一些流程行业联合开发。拟议的项目将由来自卡内基梅隆大学和IBM沃森研究中心的多学科研究人员团队进行。从更广泛的角度来看，这项建议将导致一个强大的虚拟协作框架的开发，这将有助于推动MINLP优化的最先进水平，并成为研究人员和行业从业者的独特资源。这个虚拟框架将用于开发和传播开源软件，并从各种不同的应用领域收集具有挑战性的测试问题。另一个重要特点是教育部分，因为将包括关于MINLP建模和编码的教育模块。这项研究的主要成果将通过在信息通报、会议和定期期刊出版物上举行的特别会议来传播。我们还打算参与外展活动，通过这个项目中出现的真实世界的测试题来提高人们对数学的兴趣。最后，CMU和IBM一直非常积极地在研究领域积极招募代表性不足的少数族裔。对于这个项目，调查人员将积极寻求包括来自少数族裔和代表性不足群体的优秀本科生和研究生参与我们的工作。

Optimization is one of the strategic technologies for cyberinfrastructure computational tools since this area deals with the selection of the "best" design or plan among many possible alternatives. Most of the challenging application problems in practice (e.g. engineering design and manufacturing, analysis of metabolic networks, portfolio investment) require the use of discrete variables (mostly 0-1 variables) to represent logic choices, as well as the handling of nonlinearities in order to accurately model the performance of physical, chemical, biological, financial or social systems. This optimization area is known as Mixed-Integer Nonlinear Programming (MINLP). MINLP is one of the most general tools for addressing deterministic optimization models, and there is now a significant optimization community that is increasingly interested in the solution and application of large-scale MINLP problems. This community is highly multidisciplinary involving operations researchers, industrial, chemical and mechanical engineers, economists, chemists and biologists. The difficulty, however, is that MINLP represents one of the most challenging optimization problems, particularly when dealing with non-convex functions, since this may give rise to local solutions. Therefore, finding the global optimum solution of large-scale MINLP models in reasonable computational times, remains a largely unsolved problem.The major objective of this proposal, which is a joint research effort between researchers at Carnegie Mellon and IBM Watson Research Center, is to address the challenge of solving practical large-scale MINLP optimization problems in reasonable computational times, and within a unique virtual collaborative environment that can bring together algorithm developers and application researchers. In order to address these challenges, the major goals of this proposal, are (a) Create a cyberinfrastructure environment for virtual collaboration for developing and collecting tools, and challenging test problems, and for disseminating open-source software; (b) Develop basic algorithms, formulations for predicting tight lower bounds, and open-source software for solving large-scale nonconvex MINLP problems; (c) Test software with challenge problems arising in real-world applications, mostly in engineering but also in biology and finance. A major outcome of this proposal will be the development of novel algorithms and open-source software for solving nonconvex MINLP optimization problems to either full global optimality or near-optimality. The research will also include the development of a variety of real-world application problems that will be documented as case studies with alternative formulations. The case studies will be developed jointly with IBM and a number of process industries. The proposed project will be conducted by a multidisciplinary team of researchers from Carnegie Mellon and IBMWatson Research Center.From a broader viewpoint, this proposal will lead to the development of a powerful virtual collaborative framework that will help to advance the state-of-the-art of MINLP optimization, and be a unique resource for researchers and industrial practitioners. This virtual framework will be used to develop and disseminate open-source software, and collect challenging test problems from a variety of different application areas. Another important feature will be the educational component, since education modules on MINLP modeling and codes will be included. The major results of this research will be disseminated through special sessions at INFORMS, conferences, and regular journal publications. We also intend to be involved in outreach activities to promote interest in mathematics through real-world test problems that arise in this project. Finally, CMU and IBM have been very active in aggressively recruiting under-represented minorities in research. For this project, investigators will actively seek to include outstanding undergraduate and graduate students to participate in our work from minorities and under-represented groups.