Mathematical Optimization: What’s in a Name?

Edward Rothberg is CEO and co-founder of Gurobi optimizationwhich produces one of the fastest math optimization solvers in the world.

As the great William Shakespeare once wrote, “What’s in a name? What we call a rose by any other name would smell so sweet.” Unfortunately for those unfortunate lovers in Romeo and Julietnames He does matter. They are important to the Capulets and Montecchios, and they are important to us in the real world.

As such, I find myself at a challenging point. My company lives in a space that doesn’t know what to call itself. We call what we do “mathematical optimization,” but unless you already know what that means, your eyes are probably already glazed over.

To make matters more complex, our industry overlaps with many others. So it’s reasonable to say that we’re in the business of artificial intelligence (AI), prescriptive analytics, operations research, and mathematical programming — and the list goes on. While each of these terms has its merits, each seems to miss the mark in important ways. We need simple, straightforward terminology, but as the bard would say, “Ah, there’s the problem.” If it’s too simple, it doesn’t communicate the transformative power of technology. If we manage to package it all up, it becomes a salad of inaccessible technical words.

How did our industry get to this point and how did we get to “mathematical optimization” in the first place? Here’s a little bit of history.

Operations Research and Mathematical Programming

The original name of our field was “operations research” and “mathematical programming” was a lot of what we did. In today’s context, however, these terms are less clear: “Research” evokes the scientific method, and “programming” makes many people think of computer science.

When the field was founded in the 1940s, “programming” implied “establishing a plan or course of action” – similar to how a theater program describes the acts in a play. The term “mathematical programming” was intended to convey “using mathematics to develop a plan of action”.

Likewise, “operations research” was intended to describe “a rigorous approach to improving the operation of some organization.” I suspect that, nowadays, people are more inclined to see “research” as a precursor to “practice”.

optimization

This term is widely used in the field, but it is a very broad term and has been co-opted several times. Within our field, we use “optimization” to refer to the “process of finding values ​​that optimize a mathematical function”. Outside of our field, however, people hear “optimization” and think of search engine optimization or code optimization. While they are useful tools in their own right, they are relegated to very narrow segments of business practices, and these segments are often not essential to the company’s mission.

the science of the best

In the early 2000s, the professional society in this field (INFORMS) decided to devote significant attention to marketing the profession. This was a multifaceted effort, but the main result was a term that should be appropriate for people in the field and also informative and intuitive for people outside the field.

The term they chose was “The Science of the Best”. Although many have debated the reasons why, unfortunately, the term has not been successful in its goal of attracting new people.

Prescriptive Analysis

Analytics is, by definition, “using data to reach a conclusion”. While it’s a commonly understood term, our industry is divided over whether “analytics” is the proper umbrella for us to live under. Analysis is the journey to reach a conclusion, but mathematical optimization identifies the best way to act based on that conclusion. In other words, analysis focuses on the before and mathematical optimization focuses on the after.

In the 2010s, Tom Davenport popularized the notion of an analytics maturity model, which showed organizations progressing through three levels of sophistication: descriptive, predictive, and prescriptive analytics. While “descriptive” and “predictive” have very intuitive meanings, “prescriptive analysis,” which should cover our area, does not evoke similar intuition. “Prescriptive” implies that we are imposing rules or courses of action on people when mathematical optimization is really aimed at helping people make complex decisions. It provides people with recommendations on the optimal way to proceed – not rigid rules to follow.

Artificial Intelligence (AI)

While AI has come a long way over the past 20 years and continues to do so, it essentially means “a computer performing tasks that would otherwise require human intelligence.” Is that what we do? Technically, yes, but “AI” also applies to self-driving cars, speech recognition, and a host of other topics that are unrelated to what we do. While it appeals to people, it’s too broad to give a good sense of the types of problems we solve.

The search continues

At Gurobi, we currently use the term “mathematical optimization”. Our competitors use different terminology. I suspect we all see the need to find a more accessible name. At the very least, it should capture a few key points:

1. Complexity: This technology can help companies function more efficiently in complex and dynamic environments where activities can have significant interdependencies.

2. Data: This technology can extract (usually significant) value from business data.

3. Decisions: This technology can help support or automate the process of making better decisions.

Also, the terminology needs to be easily understood by non-practitioners who may not have mathematicians on staff or understand what a mathematician can offer their business. The typical prospect doesn’t look at a problem and think, “I need mathematical optimization to solve this.” How can we give them the words they need to accurately identify their needs and solutions?

Once again, I invoke Shakespeare’s words: “O to a fiery muse who would ascend to the brightest sky of invention.” Or, to put it another way, does anyone have any good ideas for a better name?


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