Assistant Professor of Operations Ward Romeijnders was awarded a Veni grant  for his project, “Planning for the unknown. Towards optimal decisions under uncertainty.” These personal Veni grants are worth up to a maximum of €250,000 and enable talented researchers who have just completed a PhD to conduct research of their own choice. They are part of the Innovational Research Incentives Scheme run by the Netherlands Organisation for Scientific Research (NWO).  

Q. Tell us about your research.  

A. Many practical decisions have to be made before key information is known. For example, network operators have to make investments in the electricity grid while future costs of capital and future supply in renewable energy are uncertain. Decision support is required for such problems -- also in healthcare, logistics and engineering. However, this support is only available to a limited degree because of the high complexity of the underlying mathematical optimisation problems.  

Such so-called stochastic mixed-integer optimisation problems are extremely difficult to solve since they combine the difficulties of having integer decision variables (i.e., discrete or yes/no decisions) and uncertainty in the parameters of the problem. Traditional solution methods combine solution approaches from deterministic mixed-integer and stochastic continuous optimisation, but are generally unable to solve practical problems of realistic sizes.

Even simplified, deterministic versions of these problems are challenging since they are not convex, and thus efficient solution methods from the well-developed field of convex optimisation cannot be used to solve them.   Interestingly, however, my recent work has shown that stochastic mixed-integer optimisation problems are (approximately) convex. Thus, from a “convex” perspective, these stochastic problems are easier to solve than their deterministic counterparts. In this sense, the introduction of uncertainty to mixed-integer optimisation problems overcomes the difficulty of having integer decision variables.  

The aim of this project is to design fast solution methods for stochastic mixed-integer optimisation problems, exploiting this new and exciting perspective and building on my previous work. The newly developed solution methodology will be validated by applying the developed method.  

Q. What’s the biggest challenge of this research?  

A. Designing fast and efficient solution methods that are able to solve multistage stochastic mixed-integer recourse models in which decisions have to be made in multiple time stages and information only becomes available gradually over time.