Reddit reviews Introduction to Linear Optimization (Athena Scientific Series in Optimization and Neural Computation, 6)

Sure, there are a few directions you could go:

Algorithms: A basic understanding of how to think about and analyze algorithms is pretty necessary if you were to go into combinatorial optimization and is a generally useful topic to know in general. CLRS is the most famous introductory book on algorithms, and it gets the job done. It's long, but I thought it was decent enough. There are also plenty of video lectures on algorithms online; I liked the MIT OpenCourseWare of this class.

Graph Theory: Many combinatorial optimization problems involve graphs, so you would definitely want to know some graph theory. It's also super interesting, and definitely worth learning regardless! West is a good book with lots of exercises. Bondy and Murty and Diestel also have good books, which are freely available in PDF if you do a google search. Since you're doing a project on traffic optimization, you might find network flows interesting. Networks are directed graphs, where you think about moving "flow" across the edges of the graph, so they are useful for modelling a lot of real-life problems, including traffic. Ahuja is the best book I know on network flows.

Linear and Integer Programming: Many optimization problems can be described as maximizing (or minimizing) some linear function subject to a set of linear constraints. These are linear programs (LPs). If the variables need to take on integer values, then you have an integer program (IP). Most combinatorial optimization problems can be formulated as integer programs. Integer programming is NP-hard, but in practice there are methods that can solve most IPs , even very large ones, relatively quickly. So, if you actually want to optimize things in real-life this is a very useful thing to know. There's also a mathematically rich field of developing methods to solve IPs. It's a bit of a different flavor than the rest of this stuff, but it's definitely a fertile area of research. Bertsimas is good for learning linear programming. Unfortunately, I don't have a good recommendation for learning integer programming from scratch. Perhaps the chapters in Papadimitriou - Combinatorial Optimization would be a good introduction.

Approximation Algorithms: This is about algorithms which quickly (in polynomial time) find provably good but not necessarily optimal solutions to NP-hard problems. Williamson and Shmoys have a great book that is freely available here.

The last book I'd recommend is Schrijver. This is the bible for the field. I put it here at the end because it's more of a reference book rather than something you could read cover to cover, but it's REALLY good.

Lastly, if you like traffic optimization, maybe look up what people are doing in operations research departments. A lot of OR is about modelling real problems with math and analyzing the models, so this would include things like traffic optimization, vehicle routing problems, designing smart electric grids, financial engineering, etc.

Edit: Not sure why my links aren't all formatting correctly... sorry!

OK, well, that's a pretty wide range, and completely different types of books and authors to read, but, I can take a crack at about a quarter of it.

Consilience by E.O. Wilson to start, I suppose, for interdisciplinary linkages.

The early (and by that, I mean 60s-70s) ecology textbooks were actually far more devoted to modeling systems than they are today. The neat color graphics and technology we currently use to do so are not going to be there, but the underlying concepts they were obsessed with then are actually being used by other disciplines, currently.

And, you need to start reading more micro- and macro- economics basics. They don't realize it, but they use the same models (and wind up drawing completely different conclusions than the environmental scientists. Ha!). Any intro textbook (they're basically all the same) and then the intermediate textbooks if you've done the intros courses, in that field will do. Get one that's one edition earlier than the current, it's cheaper and they revise them so often, it doesn't matter. The basics aren't going to change; unless you're looking into international economics/trade issues, then stick with the most current.

Find Tufte's The Visual Display of Quantitative Information, at some point. It's not directly about it, but it will help enormously when you inevitably have to write some papers or proposals about it. You'll see why when you get your hands on it. It's the most cross-disciplinary book ever.

I would consider this nearly a must to work your way though: Introduction to Linear Optimization. Normally, I'd not recommend that kind of 'light reading' (/s), but since you're a math major, you should be able to pull it off. It's hard to predict where within this you're going to end up, but that one, at least, is going to be a huge tool in working through things more quickly than your peers, if you can master it. Applicable to almost every discipline.

Anything in engineering that covers "control systems" is going to end up talking about this, and having to explain the models first, before it launches into strategies, whether it's mechanical, electrical, environmental, etc. And risk management specific books. Not in their beginnings, that's just all basic probability stuff, but the back half will get interesting in that direction. Actually, since most engineering risk management books are written more generically to accommodate most of the sub-disciplines of engineering, those might be the best to seek out if the ones in mechanical/electrical control systems are requiring too much subdiscipline basics knowledge. Just the other day I was looking through one that was about factory line design specifics I thought would be applicable to so many other processes and fields than just what it was covering, including what business majors would call "logistics".

Tons of computer science books cover this from their own take on what that term means, and none I can remember off the top of my head. Here's hoping we'll have a more programmer-type person stop by and recommend specifics in those.