(530b) Collaborative CyberInfrastructure Site for Mixed-Integer Nonlinear Programming

In this presentation we describe a joint collaboration between Carnegie Mellon University and the IBM T. J. Watson Research Center researchers who have developed a Collaborative CyberInfrastructure for Mixed-Integer Nonlinear Programming (MINLP): http://www.minlp.org, that has been funded by the National Science Foundation under Grant OCI-0750826: ?OpenCyberInfrastructure for Mixed-integer Nonlinear Programming: Collaboration and Deployment via Virtual Environments.

Optimization is one of the strategic technologies for cyberinfrastructure computational tools. Many of the challenging application models 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 predict the performance of physical, chemical, biological, financial or social systems. These optimization problems correspond to Mixed-Integer Nonlinear Programs (MINLP), which in logic form can be represented as Generlaized Disjunctive Programming (GDP) problems in terms of Boolean and continuous variables and algebraic equations, disjunctions and logic propositions. While MINLP optimization can be applied to a very wide class of problems, it represents one of the most challenging optimization problems. On the combinatorial side, MINLP are known to be "NP hard". On the side of nonlinearities, many MINLP models are nonconvex, which means that in the continuous space they may give rise to many local solutions.

The major goal of this site is to create a library of optimization problems in different application areas in which one or several alternative models are presented with the derivation of their mathematical formulations. The emphasis of this project is on the formulation of models, since this is an area that is particularly critical in MINLP since often alternative formulations can have vastly different computational performance. The goal is also to illustrate good and bad practices of modeling in MINLP problems. Each model has one or several instances that can serve to test various algorithms. While we are emphasizing MINLP models, MILP and NLP models can also be submitted, particularly if they are relevant to problems that also have MINLP formulations.

The cyberinfrastructure site is aimed at the optimization community that is increasingly interested in the solution and application of large-scale MINLP problems. This community involves academics and people from industry, and is highly multidisciplinary. It involves operations researchers, industrial, chemical and mechanical engineers, economists, chemists and biologists. This community, however, is largely disconnected, especially between algorithm developers and application domain researchers.

The site provides a mechanism for researchers and users to contribute towards the creation of the library of optimization problems, and to provide a forum of discussion for algorithm developers and application users where alternative formulations, as well as performance and comparison of algorithms can be discussed.

The site, which was launched in October 2009, contains information on tutorials, bibliography and resources on MINLP. The library currently contains 22 problems that were submitted in areas such as engineering, operations management, physics and finance. We describe some of these problems and discuss some of their main features. Finally, we summarize the talk by highlighting some of the lessons leaned in putting together the MINLP Cyberinfrastructure site.