Miguel Anjos

Students Harry Shaw and Freya Whittaker have worked together to produce this article as part of our series of Academic Interviews; featuring Miguel Anjos!

Prof. Miguel Anjos is the Chair, and a Professor, of Operational Research at the School of Mathematics, having previously worked as an academic in the Engineering department of two Canadian institutions.

Miguel's passion for optimization 

Optimization is a topic that first struck him during his undergraduate degree, after taking a course on Mathematical Programming, before he proceeded to pursue a career in operational research. This focuses on the use of tools, like optimization, to improve efficiency in a large variety of areas. These areas really interested him, as he could use mathematics to solve real world problems. Optimization is a topic which is rarely present early into an undergraduate degree – he just happened to take an advanced course in his final years and since then, it’s been clear that it is his area for research. In fact, Miguel gave us advice for students unsure on their options: "at least take a look at operational research, see if it’s something that you like. This is an area that has a lot of opportunity, and it needs mathematicians – and not just for academia, but also outside of it; within the government and private companies." Similarly to his own reasons for picking it, it can be a rewarding subject for students as they can make a difference using maths in so many different areas. Although operational research is only really seen towards the end of a student’s studies, he recommends taking a course in optimization or simulation, much like he himself did, and see what you think; “if nothing else, you’ll learn something new,” is his advice.

Miguel's current work; mathematics vs engineering

We spoke to him about his current work; firstly, what does he enjoy about real-world applications of optimization? Like most academics, he enjoys both theoretical and practical work; the first few years of his PhD were theoretical. In his final year however, he took a course on optimization in engineering, which focussed on the optimization of circuit boards. Taking this course made him realise that all the theoretical work he had done could be applied to practical engineering projects, and he has since worked with engineers focussing on these practical problems. What is a big benefit of mathematicians and engineers working together? He finds mathematicians think differently about problems from engineers, which is a huge advantage as they can learn from each other, and so when working in sync they often produce a better solution then they would have if they’d have done it separately.

Since he has ended up working largely in engineering, would he have rather done an engineering degree or maths degree, in hindsight? He tells us he would have still chosen a maths degree, the main reason is that it is easier to understand the theory and then learn how to use it for practical applications, than to learn the applications and translate this into theory. In addition, once you understand the mathematical theory of a topic, in Miguel’s case optimization, then the theory can be applied to so many different areas, like circuit design, logistics and electricity. After all, Miguel told us, “that’s the point of maths; generalising and abstracting and being as encompassing as you possibly can.”

President of INFORMS

As part of his career in operational research, Miguel has been involved with INFORMS, the American society for operations research. They are very influential in this area and, as such, have ended up with members all over the world. Their conferences have such a large international attendance rate that they have reached the point where INFORMS has become a major gathering point for researchers interested in energy problems. Miguel has found that it’s the best place to be to discuss energy applications and electrical engineering with other likeminded individuals. Within the society, Miguel has recently been appoint President for the INFORMS Section on Energy, Natural Resources, and the Environment; between 2018 and 2020 he was President-Elect.

Miguel's Academic Research

Following on from his work with INFORMS, we ask about his academic research. Was there a particular issue he’s ever been stuck on, and does he remember how he overcame that challenge? He says there’s been a few times, but remembers one during his PhD, where he had this idea which he was doing computational experiments for, but he couldn’t put his finger on what was going on with the results. He ended up spending a large chunk of time looking at the figures and trying to pin it down to a statement that he could prove formally; he did eventually figure out what was going on by simply going over the data so often trying to find out what was occurring. It so happened that someone else in operational research also produced a very similar idea – they both proved it differently and expressed it differently; because it was an area that was so active at the time it was just "one of those things" that happens. There’s also the times when he deals with the applications of theoretical optimization and spends a lot of time trying different ideas in order to solve the issue that an engineer is trying to solve; the main way to get past those roadblocks is to go into as much detail as much as possible in order to understand how to translate it into mathematics.

We then asked, what drew him specifically to power systems management and smart grid design? He recalls the story, calling it serendipitous. It started when he was an academic at the University of Waterloo, working with colleagues involved in circuit design, when a PhD thesis (about electrical engineering and equilibrium models for electricity markets) came across his desk. He read it and realised it was basically optimization from start to finish, detailing how to balance the demands and offers to find the market equilibrium. In Canada, a PhD defence is different to the UK viva model, in that it is an open public event, and so Miguel went to the defence and ended up speaking to the person who authored the thesis, which led to a 2-year long collaboration together. Over the topic, Miguel recalls how once he started digging, he kept learning more and more, realising that there’s a tremendous amount of maths underlying a lot of the work.

Finally, we ask out all of his research, what stands out as something he’s loved? He talks about a problem to do with power flow, which relates to how electricity is actually going to flow on the wires, and how it is related again to a theoretical problem he worked on during his PhD, called Semi-Definite Optimization. This issue with power flow highlights how it is, working as a mathematician in operational research, because he got to take this theoretical point he worked on during his doctorate and apply it to a challenging practical problem. Being able to put two things together, theory he’s passionate about and a problem that needs a solution, has taken things beyond what had been done in that area so far. This is what optimization and operational research can be for mathematicians – using theory you’re passionate about and using it to make a difference in nearly all areas possible.