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

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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.