PhD candidate: Boris Nijhoff
Start: Fall 2025
Many situations can arise in which a decision needs to be taken under uncertainty. For instance, optimising the operation of a renewable power generation system involves uncertain future weather conditions and electricity prices. A common way to account for uncertainty in an optimization model is given by stochastic programming. In this framework, decisions are modelled in two or more stages, and the objective is the expectation of the outcomes under the assumed distribution of the uncertainty.
Computationally, however, computing this expectation, and in particular optimising over it, with decisions conditional on the outcome of the uncertainty, is intractable, if not impossible. Even when the assumed distribution is over an empirical (finite) sample, can the model increase in size so much that it is intractable in any reasonable timeframe.
Given this computational intractability of stochastic programmes, the aim of scenario generation methods are to represent the complicated distribution of uncertainty by a small set of scenarios (outcomes of the uncertainty), so that the resulting stochastic programme over the scenario set closely approximates the computationally intractable problem (in the solution it finds).
Much of the existing literature on scenario generation focuses on approximating the underlying distribution of the uncertainty adequately with a restricted size (distribution based). This project therefore focuses on using the specific problem in generating scenarios (problem based), so that the resulting problem is a close approximation of the original problem, instead of a close approximation of the underlying uncertainty distribution.
These methods will allow for faster computations of stochastic programmes, while maintaining a higher solution quality. This will help, for example, decision making in the transition to more renewable energy sources.
When making longterm decisions, one might want to account additionally for risk. Following this, the first part of this project particularly focuses on scenario generation for risk-averse stochastic programmes
