JuMP: A modeling language for mathematical optimization

Monday, October 18, 2021

The JuMP logo.

As an author of the paper JuMP: A Modeling Language for Mathematical Optimization, I am honored to have recently received the Mathematical Optimization Society’s Beale—Orchard-Hays Prize, an academic award given once every three years for work in the area of computational mathematical optimization. The award, in fact, is about the open source software project JuMP, which I started with Iain Dunning and Joey Huchette while we were PhD students at MIT’s Operations Research Center almost nine years ago. The humbling milestone of the Beale—Orchard-Hays Prize seems like a good occasion to reflect on JuMP, how it has matured and grown as an independent community-driven project, and Google’s role in enabling me to serve as JuMP’s BDFL.

JuMP was created—in the classical open source fashion—to scratch an itch. As graduate students, we wanted a software package that would enable us to write down and solve optimization problems, especially constrained optimization problems like linear programming and integer programming problems. We wanted it to be not only easy, but also fast and powerful. At the time, one was faced with trade-offs between ease-of-use, speed, and flexibility. For example, optimization libraries in Python were user-friendly but introduced noticeable performance bottlenecks. Commercial software such as AMPL was efficient but hard to extend. Low-level interfaces in C or C++ introduced complexities that were distracting for teaching and academic research. We weren’t satisfied with these trade-offs, and began experimenting with a new programming language called Julia that promised to provide the best of both worlds.

Our early experiments showed that Julia was indeed capable of impressive performance. While similar libraries based on Python could be slower to construct the data structure describing the optimization problem than to solve it, our prototype of JuMP was competitive with state-of-the-art commercial libraries. This gave us confidence that JuMP could be useful for the community, and we made the initial public release in October 2013.

Since then, it’s been a real ride! The first JuMP developers workshop in 2017 attracted thirteen speakers from four continents; this year’s workshop featured 32 virtual talks. Of the 800+ citations to the award-winning paper, we were surprised to discover that that about 75% of them were from outside the fields of operations research or optimization itself; about 20% are in energy and power systems, another 20% are in control and engineering, and the remaining citations are spread across scientific applications, computer science, machine learning, and other fields. These figures speak to the role of optimization as a fundamental technology that can be applied almost anywhere. One example application using JuMP of which I’m perhaps most proud is a study by Sepulveda et al. on cost-effective ways to decarbonize the power grid. This study is cited both by Bill Gates in his new book, “How to Avoid a Climate Disaster,” and by Google’s methodologies and metrics framework for its goal of operating data centers and campuses entirely on carbon-free energy by 2030.

As JuMP’s core development team grew beyond MIT and its original creators graduated, it was important for JuMP to find a new home for its long-term sustainability. We were lucky to find NumFOCUS, a nonprofit organization supporting open source scientific software (of which Google is a corporate sponsor). As a Google employee, I have continued contributing code for JuMP, traveling to workshops, and serving in leadership roles thanks in no small part to Google’s generous open source policies and support from my team and management chain. Last year, I was granted the honorific of Benevolent Dictator for Life (BDFL). I plan to use this power judiciously and rarely, relying instead on JuMP’s strong culture of consensus-driven development.

As for the future, JuMP’s 1.0 release is near on the horizon, and I look forward to whatever comes next!

By Miles Lubin, Algorithms & Optimization Team, Google Research