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[ Introduction | Agenda | Hotels & Directions ] |
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On the occasion of Alexander Meeraus's 60th birthday it is appropriate to consider again some of the themes in computational economics that Alex has created or promoted via the GAMS software. For many years I have consciously and unconsciously passed along to my students pieces of Alex's wisdom without ever cataloging these ideas. This paper is an opportunity to review some of those ideas and the contributions they have made and are making to the development of computational economics.
This question may seem odd when we are all celebrating the 15th anniversary of GAMS, a successful modeling system with thousands of users worldwide. Nevertheless, this same question was recently raised to me by an important customer with several convincing arguments. Organizations, markets, technology and customer requirements are rapidly changing over time. These changes presentchallenges to all of us who are active in developing modeling technology. During my presentation I will address these challenges and elaborate on some of the more technical ones.
GAMS has proved to be a very significant addition to the Agricultural Economists tool box. This paper first reviews the impacts it has had. After that the presentation addresses emerging forces that will shape the way GAMS will be used in the future. Finally I will cover developments that could be pursued to maintain and or expand future GAMS applicability.
GAMS has always made it possible to switch solvers with a single option statement. This has made model use less risky and more reliable. In addition, new and improved solvers are easily made available to old users.
We will talk about the interactions between GAMS and solvers, mainly from an NLP perspective, and discuss current work on topics such as quality assurance, model status reporting, new GAMS-functions, user-defined functions, and emerging needs for extra information from new types of solvers.
Within the history of modeling languages, we can observe three major phases that shift the emphasis from computational issues to modeling issues and finally the application or the real problems. The dominant constraints in the first phase were the computational limits of our algorithms. The second phase has the model in focus. We believe that we are entering a third phase which has the application as its focus and the optimization model is just one of many analytic tools that help making better decisions.
In this talk we discuss the three phases, focusing on future directions of modeling languages and environments. We provided some background information to support and explain some of the early design decisions, which we believe are still valid today and guide us into the future.
There is a long tradition of work implementing CGE models in GAMS, including two modeling "systems": Hercules (Drud and Pyatt) and MPSGE (Rutherford). Work with CGE models in "native" GAMS started in the mid-1980s with the "Cameroun Model" by Shanta Devarajan, which was based on the CGE model code in Fortran in the book by Dervis, de Melo, and Robinson. The ERS/USDA model of the U.S. built on the Cameroun model, generalizing the code. Both the Cameroun and ERS/USDA models are in the GAMS library.
Since then, there have been a number of "standard", flexible, single-country models, most recently from IFPRI by Hans Lofgren, Rebecca Harris, and Sherman Robinson. There are also many examples of GAMS/CGE models using a variety of solution approaches, including setting up the model as a special NLP problem (e.g., Alan Manne, Victor Ginsburgh, Jean Waelbroeck, and Michiel Keyzer). There have been parallel developments in CGE model formulation (including implementation of multi-country and dynamic models), methods of parameter estmation, GAMS solvers, and GAMS language features.
The interaction between model developers, model users, and GAMS and solution software developers has been incredibly productive. The role of Alex Meeraus in fostering this collaboration has been crucial, providing enormous support to the the CGE work program in economics.
The Gamma Knife is a highly specialized treatment unit that provides an advanced stereotactic approach to the treatment of tumors, vascular malformations, and pain disorders within the head. Inside a shielded treatment unit, beams from 201 radioactive sources are focused so that they intersect at the same location in space, resulting in a spherical region of high dose referred to as a shot of radiation. The location and width of the shots can be adjusted using focussing helmets. By properly combining a set of shots, larger treatment volumes can be successfully treated with the Gamma Knife.
The goal of this project is to automate the treatment planning process. For each patient, an optimization seeks to produce a homogeneous dose distribution that conforms closely to the treatment volume, while avoiding overdosing nearby sensitive structures. The variables in the optimization can include the number of shots of radiation along with the size, the location, and the weight assigned to each. Formulation of such problems using a variety of mathematical programming models is described, and the solution of several test and real-patient examples is demonstrated.
This represents joint work with:
David M. Shepard, Department of Radiation Oncology, University of Maryland
We discuss various issues related to an integrated assessment of global climate change, including: