Fourer*, Robert (AMPL Optimization Inc.)

Robert Fourer

Dr. Robert Fourer
AMPL Optimization Inc.
Evanston, IL 60201

Phone: (847) 846-8486


Model-Based Optimization: Principles and Trends

As optimization methods have been applied more broadly and effectively, a key factor in their success has been the adoption of a model-based approach. A researcher or analyst focuses on modeling the problem of interest, while the computation of a solution is left to general-purpose, off-the-shelf solvers; independent modeling languages and systems manage the difficulties of translating between the human modeler’s ideas and the computer software’s needs. This tutorial introduces model-based optimization with examples from the AMPL modeling language and various popular solvers, concluding with a survey of current software.

Interests: Optimization, operations research, related fields
Appropriate audience: Advanced undergraduate, graduate students

Assigning People in Practice

Chances are you've been stuck at least once with a problem of assigning people to offices, projects, tables, etc. The venerable idea of an “optimal assignment problem” can be useful in these circumstances, if applied with care. This presentation describes a variety of real assignment applications along with rules for success that they suggest. Many of the principles also apply to optimization modeling in other contexts.

Interests: Optimization, operations research
Appropriate audience: Advanced undergraduate, graduate students

The Ascendance of the Dual Simplex Method: A Geometric View

First described in the 1950s, the dual simplex evolved in the 1990s to become the method most often used in solving linear programs. Factors in the ascendance of the dual simplex method include the development of an efficient variant of the steepest-edge criterion, and an improved understanding of the consequences of bounded variables. The ways that these come together to engineer a highly effective algorithm are still not widely appreciated, however. Following an introduction to the origins of computationally practical simplex methods, this talk employs a geometric approach to the dual simplex method to provide a unified and straightforward description of the factors that work in its favor.

Interests: Optimization, numerical computing
Appropriate audience: First-year graduate students and above

New Programming Tools and Interfaces for Deploying Optimization Models

Though fundamentally declarative in design, optimization modeling languages are invariably implemented within larger modeling systems that provide a variety of programming options. Although programming is not used to describe models, it facilitates the integration of models into broader algorithmic schemes and business applications. This presentation surveys ways in which a programming interface can be useful for model development and deployment, beginning with scripting features built into modeling systems, continuing with APIs for controlling modeling systems from programs in general-purpose languages, and concluding with some new ideas for tight integration and solver callbacks. Examples use the AMPL modeling language and system along with the popular data science languages Python and R.

Interests: Optimization applications
Appropriate audience: Second-year graduate students and above

Identifying Good Near-Optimal Formulations for Hard Mixed-Integer Programs

When an exact mixed-integer programming formulation resists attempts at solution, sometimes much better results can be achieved by “cheating” a bit on the formulation. Typically, a judicious choice of reformulation, restriction, or decomposition serves to make the problem easier, in a way not guaranteed to preserve the solution's optimality but highly unlikely to make much of a difference given the model and data of interest. This tutorial illustrates such an approach through a series of case studies. All rely on trial and error, a flexible modeling language, and a good general-purpose solver, and each is seen to be founded on one or two simple ideas that have the potential to be more broadly applied.

Interests: Optimization applications
Appropriate audience: Second-year graduate students and above

Education & Background

  • Ph.D., Operations Research, Stanford University
  • B.S., Mathematics, Massachusetts Institute of Technology

Robert Fourer is co-founder and President of AMPL Optimization Inc. Since 1979 he has also been on the faculty of Industrial Engineering and Management Sciences at Northwestern University, where he is now Professor Emeritus.

Dr. Fourer is an authority on the design and implementation of computer software to support large-scale optimization.  In collaboration with colleagues in Computing Science Research at Bell Laboratories, he initiated the design and development of AMPL, which has become one of the most widely used software systems for modeling and analyzing optimization problems, with users in hundreds of universities, research institutes, and corporations worldwide; he is also author of a popular book on AMPL.  Additionally, he has been a key contributor to the NEOS Server project and other efforts to make optimization services available over the Internet, and has supported development of open-source software for operations research through his service on the board of the COIN-OR Foundation.

In recognition of the broad impact of optimization modeling languages in Operations Research and associated fields, Dr. Fourer shared the INFORMS Impact Prize in 2012.  He has also been a recipient of the Fellow Award of INFORMS, the Medallion Award of the Institute of Industrial Engineers, and a Guggenheim Foundation Fellowship, and was a member of teams that received the INFORMS Computing Society Award, for AMPL, and the Mathematical Optimization Society’s Beale-Orchard-Hays Prize, for NEOS.