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Showing posts with label optimization. Show all posts
Showing posts with label optimization. Show all posts

A New Library for Network Optimization

Tuesday, February 22, 2022

Networks are all around us from the electrical circuits inside our computers to the multitude of internet servers that route packets of data around the globe. Even the web itself is a network of pages connected to each other by a myriad of blue links.

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A network's structure is referred to as its topology. Network topologies can be physical or logical, centralized or decentralized, and fully or partially connected. Given a network with n nodes, the number of possible topologies grows exponentially with n; even just a dozen nodes admit nearly a trillion trillion possible configurations!

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We are pleased to announce the open source release of network-opt, a C++ library that supports the optimization of network topologies. Using sophisticated techniques for combinatorial search, this algorithm can efficiently construct instances from a family of so-called series-parallel networks that commonly arise in electrical and telecommunications applications. For example, given 15 1-Ω resistors and a target resistance of π Ω, our tool can produce a circuit that achieves six digits of precision:

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For more details, refer to our paper: "Search Strategies for Topological Network Optimization," appearing this month at the Thirty-Sixth AAAI Conference on Artificial Intelligence (AAAI-22).

By Michael D. Moffitt, Core Enterprise Machine Learning

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

The cpu_features library

Wednesday, February 7, 2018

"Write Once, Run Anywhere." That was the promise of Java back in the 1990s. You could write your Java code on one platform, and it would run on any CPU implementing a Java Virtual Machine.

But for developers who need to squeeze every bit of performance out of their applications, that's not enough. Since the dawn of computing, performance-minded programmers have used insights about hardware to fine tune their code.

Let's say you're working on code for which speed is paramount, perhaps a new video codec or a library to process tensors. There are individual instructions that will dramatically improve performance, like fused multiply-add, as well as entire instruction sets like SSE2 and AVX, that can give the critical portions of your code a speed boost.
Photo by Andrew Dunn, licensed CC-BY-SA-2.0.

Here's the problem: there's no way to know a priori which instructions your CPU supports. Identifying the CPU manufacturer isn't sufficient. For instance, Intel’s Haswell architecture supports the AVX2 instruction set, while Sandy Bridge doesn't. Some developers resort to desperate measures like reading /proc/cpuinfo to identify the CPU and then consulting hardcoded mappings of CPU IDs to instructions.

Enter cpu_features, a small, fast, and simple open source library to report CPU features at runtime. Written in C99 for maximum portability, it allocates no memory and is suitable for implementing fundamental functions and running in sandboxed environments.

The library currently supports x86, ARM/AArch64, and MIPS processors, and we'll be adding to it as the need arises. We also welcome contributions from others interested in making programs “write once, run fast everywhere.”

By Guillaume Chatelet, Google Compiler Research Team
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