4.8 KiB
— title: "Operations Research and Optimisation: where to start?" date: 2020-05-26 —
Operations research (OR) is a vast area comprising a lot of theory, different branches of mathematics, and too many applications to count. In this post, I will try to explain why I find it so fascinating, but also why it can be a little disconcerting to explore at first. Then I will try to ease the newcomer's path in this rich area, by suggesting a very rough "map" of the field and a few references to get started.
Keep in mind that although I studied it during my graduate studies, this is not my primary area of expertise (I'm a data scientist by trade), and I definitely don't pretend to know everything in OR. This is a field too vast for any single person to understand in its entirety, and I talk mostly from a "amateur mathematician and computer scientist" standpoint.
Why is it hard to approach?
Operations research can be difficult to approach, since there are many references and subfields. Compared to machine learning for instance, OR has a slightly longer history (going back to the 17th century, for example with Monge and the optimal transport problem)1. This means that good textbooks and such have existed for a long time, but also that there will be plenty of material to choose from.
Moreover, OR is very close to applications. Sometimes methods may vary a lot in their presentation depending on whether they're applied to train tracks, sudoku, or travelling salesmen. In practice, the terminology and notations are not the same everywhere. This is disconcerting if you are used to "pure" mathematics, where notations evolved over a long time and is pretty much standardised for many areas. In contrast, if you're used to the statistics literature with its strange notations, you will find that OR is actually very well formalized.
There are many subfields of operations research, including all kinds of optimization (constrained and unconstrained), game theory, dynamic programming, stochastic processes, etc.
Where to start
For an overall introduction, I recommend cite:wentzel1988_operat. It is an old book, published by Mir Publications, a Soviet publisher which published many excellent scientific textbooks2. It is out of print, but it is available on Archive.org. The book is quite old, but everything presented is still extremely relevant today. It requires absolutely no background, and covers everything: a general introduction to the field, linear programming, dynamic programming, Markov processes and queues, Monte Carlo methods, and game theory. Even if you already know some of these topics, the presentations is so clear that it is a pleasure to read! (In particular, it is one of the best presentations of dynamic programming that I have ever read. The explanation of the simplex algorithm is also excellent.)
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why it may be more difficult to approach than other, more recent areas like ML and DL
- slightly longer history
- always very close to applications: somehow more "messy" in its notations, vocabulary, standard references, etc, as other "purer" fields of maths (similar to stats in this regard)
- often approached from a applied point of view means that many very different concepts are often mixed together
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why it is interesting and you should pursue it anyway
- history of the field
- examples of applications
- theory perspective, rigorous field
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different subfields
- optimisation: constrained and unconstrained
- game theory
- dynamic programming
- stochastic processes
- simulation
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how to learn and practice
- references
- courses
- computational assets
References
{-} For a very nice introduction (in French) to optimal transport, see these blog posts by Gabriel Peyré, on the CNRS maths blog: Part 1 and Part 2. See also the resources on optimaltransport.github.io (in English).
{-} Mir also published Physics for Everyone by Lev Landau and Alexander Kitaigorodsky, a three-volume introduction to physics that is really accessible. Together with Feynman's famous lectures, I read them (in French) when I was a kid, and it was the best introduction I could possibly have to the subject.