My primary area of research is experimental optimization, which is something that I have worked on since 2009, and which was the subject of my four years of PhD study at the Automatic Control Laboratory of the Ecole Polytechnique Fédérale de Lausanne (EPFL). Basically, “optimization” just means “decision making”, where you want to make the best decision possible. The “experimental” part means that the only way for you to find that best decision is by making a chain of subpar decisions, to learn from the experience of each, and then eventually find the best.
If that sounds familiar, then it should, since we all do this, either consciously or subconsciously, pretty much every day. A good layman’s example to illustrate what I mean is cooking. Imagine that you want to make the most delicious soup possible, and you have to make a decision on how much salt and how much pepper to add. A cookbook might give you some guidance, but ultimately the only way to find the most delicious recipe for you and your kitchen is by cooking the soup multiple times, with different quantities of salt and pepper each time, and then finally settling on the recipe you think is best (“optimal”). Thus, each time you cook, you actually perform an “experiment” and, by learning from each one, you gradually refine the recipe until it becomes perfect. Ideally, experimental optimization research should then tell you how to adapt your recipe from one cooking session to the next so as to find the best recipe as quickly as possible. This simple example generalizes to countless practical applications in engineering, science, and medicine.
My research in this area is three-pronged. First, I am interested in developing general theory for experimental-optimization algorithms, as very much is currently absent, and many of the methods that have been developed (many of them in the chemical engineering community) remain largely ad hoc in nature. Specifically, I am interested in developing more theory for problems with “safety constraints”, which limit what experiments may be performed due to safety reasons, as algorithms that routinely violate these limitations essentially become dangerous if applied in real life. My second focus is on developing the actual algorithms and solution methods for solving generalized experimental optimization problems. Here, I have already contributed with the development of my SCFO solver, and am constantly working on improving the solver and making it more efficient. Finally, my third concentration has to do with the empirical testing of different solution methods for many (preferably very, very many) realistic problems, so as to be able to make educated recommendations about which methods may be more suitable for which kinds of problems. To this end, I have created the ExpOpt Test Problem Database, which collects and stores the simulated results of algorithm performance for different algorithms and problems.
My secondary research interest is also in optimization, but is more computational than experimental in nature. Here, I am interested in the fascinating challenge of global optimization (as opposed to local optimization). If local optimization may be likened to finding the peak of the nearest mountain by climbing until you reach the very top, global optimization basically means finding the peak of the highest mountain in the entire mountain range, and is significantly harder. Currently, the majority of the research done in this field is based on branch-and-bound approaches, which are working better and better for an increasing number of problems but may still fall to the curse of dimensionality. My contribution here lies in the development of an alternate method, which iteratively approximates the optimization problem by a set of concave functions, and then applies an enumeration technique. While I myself am not convinced that this may be more efficient than branch and bound, I am curious to study the technique and take it as far as it will go, since I do believe that it has the potential to be competitive with current state-of-the-art methods, but is currently heavily under-researched (having been developed and
essentially abandoned in the 1960s).
Finally, from 2008 onwards, I have been heavily involved – though not in any sort of official capacity – in researching the Uyghur language, as spoken in the Xinjiang autonomous region of China. While the language has over ten million native speakers, they are nevertheless a minority group in China, and few language materials are available to outside learners. My research essentially consists in reviewing everything that has already been published about the different linguistic aspects of Uyghur (grammar, morphology, phonetics, etc.) in the English/Russian/Uyghur/Mandarin literature, mixing and verifying this with my own observations here in Xinjiang, and then combining this into a comprehensive and authoritative website-book of sorts, available for free to anyone with an Internet connection.