The objective of this project is to develop a method by which managers of large animal feeding operations can increase their herd size by increasing the efficiency of manure management while operating within acceptable environmental tolerances. To achieve this, we have developed a farmscale mathematical optimization model to aid farmer decisions on crop/rotation planning and nutrient application. This […]

Applied Algebra: Solving for Chocolate

Applying algebra in engineering and computer science has a number of advantages and can help solve a great host of problems, from helping Netflix give you better recommendations for what to watch tonight to keeping an airplane in the air. Expanding the use of algebra is a relatively new movement with promising implications. Read the […]


Laura Albert McLay is an affiliate of the optimization group at WID and an Associate Professor of Industrial and Systems Engineering. Her background is in operations research–the discipline of applying advanced analytical methods to make better decisions. She recently gave a SILO Seminar at WID titled A Modified Logistic Regression Markov Chain Model for Forecasting the College Football Playoff illustrating […]

Combinatorial Screening

A problem often encountered by biologists centers around defining appropriate protein and drug (factor) concentrations in a mixture of signaling factors to realize a desired biological outcome. For example, this outcome may be realized in the production of a particular cell-type to be used either as a tool for discovery or a therapeutic. Current high-throughput […]

Computer Architecture

Connect to this wiki page as a companion for the synthesis lecture Optimization and Mathematical Modeling in Computer Architecture, which explores using Mixed Integer Linear Programming (MILP) to solve challenging problems in the field. The book gives in depth case studies of four optimization problems in computer architecture. This companion page provides a brief overview and […]

Domino Art

This Domino Artwork case study describes the optimization model that underlies the NEOS Domino solver, which constructs pictures from target images using complete sets of double-nine dominoes. Complete sets of double-nine dominoes include one domino for each distinct pair of dot values from 0 to 9. The NEOS Domino solver is an implementation of the […]

Economics and Game Theory

Making optimal use of scarce resources is the central theme of economics; constrained optimization lies at the heart of many economic applications. Roger Myerson (Game Theory: Analysis of Conflict, Harvard University Press, 1991) defines game theory as “the study of mathematical models of conflict and cooperation between intelligent rational decision-makers”; optimization theory plays an important […]

Fields of Fuel

The Fields of Fuel game is a multidisciplinary collaboration that integrates researchers from the school of education, department of Computer Sciences, the Great Lakes Bioenergy Research Center (GLBRC), and the Wisconsin Institute for Discovery (WID). These partners are producing together a multiplayer, web-based simulation game designed to educate players about the economic and environmental tradeoffs […]


Fishwerks was developed with input from the U.S. Fish and Wildlife Service to potentially change the way decisions are made about barrier removal in fish habitat. In the past, limited information forced agencies to prioritize barrier removals in simplistic and, in many cases, inefficient ways. Because of such limitations, cumulative passability could not be fully […]


There is an arms race to perform increasingly sophisticated data analysis on ever more varied types of data (text, audio, video, OCR, sensor data, etc.). Current data processing systems typically assume that the data have rigid, precise semantics, which these new data sources do not possess. On the other hand, many of the state-of-the-art approaches […]


Jellyfish is an algorithm for solving data-processing problems with matrix-valued decision variables regularized to have low rank. Particular examples of problems solvable by Jellyfish include matrix completion problems and least-squares problems regularized by the nuclear norm or γ2-norm. Jellyfish implements a projected incremental gradient method with a biased, random ordering of the increments. This biased […]

Mixed-Integer Quadratic Optimization: Algorithms and Complexity

Mixed-integer quadratic programming (MIQP) is the simplest yet arguably the most important class of mixed-integer nonlinear programming (MINLP) that contains two major sources of difficulties: discrete decision variables and nonlinearity in the objective function. Not only many important applications can be naturally modeled as MIQPs, but a variety of more general MINLPs can be reformulated […]

Active learning methods automatically adapt data collection by selecting the most informative samples in order to accelerate machine learning. Because of this, real-world testing and comparing active learning algorithms requires collecting new datasets (adaptively), rather than simply applying algorithms to benchmark datasets, as is the norm in (passive) machine learning research. To facilitate the development, […]

Optimal Power Flow

The Optimal Power Flow (OPF) model represents the problem of determining the best operating levels for electric power plants in order to meet demands given throughout a transmission network, usually with the objective of minimizing operating cost. As electrical power flows according to nonlinear, nonconvex functions of the system’s physical characteristics, this can be a […]


License The version that is downloadable from here (i.e. the file in this directory) is free, but is limited to problems with no more than 300 variables and 2,000 nonzeros. The file LICENSE details how to set up a temporary license that removes the size restriction for a year. A new license string will […]

Structural properties and strong relaxations for mixed integer polynomial optimization

Research in nonconvex nonlinear programming (NLP) and mixed-integer nonlinear programming (MINLP) has witnessed a significant growth at the theoretical, algorithmic and software levels over the last few years. While these new classes of algorithms have already had a remarkable impact across science, engineering, and economics, there exist a variety of important applications that these methods […]

Supply Chain

Supply Chain Management became a popular term in the mid-1990s but, even today, no clear definition of the term has emerged. Instead, for most academics and practitioners, supply chain management is a broad term that covers many functions, including but not limited to manufacturing, warehousing, and transportation, as well as supplier relationship management, inventory management, […]

WEI Smartscape™ Decision Support System

The SmartScape™ DSS (SDSS) software allows users to build and evaluate land-use change scenarios. The SDSS integrates a variety of open-source tools (ExtJS, OpenLayers, GeoExt, Geoserver, Play! Framework) to build a user-friendly web application. Users use a browser-based client to select different places on the landscape using a simple query tool, and enact transformations on […]