PhD Defense Henrik Carøe Bylling

Title: Bilevel Optimization with Application in Energy

In mathematics, optimization is the process of selecting a best element (or decision) in a set with regard to a specified criterion. This is a widely used and applied discipline with examples of optimization models in route planning, shipping, scheduling, production planning etc. The optimization problems are classified by the objective function, i.e. the function you want to maximize or minimize, and the constraints. To find a solution to an optimization model, various solution methods exists depending on the classification. The various classes of optimization models also imply different difficulties in solving them computationally.

Usually, there is only one perspective in an optimization model but in bilevel optimization models, there are two perspectives: a leader who makes a decision first, and a follower who subsequently makes a decision based on the leader’s decision. This structure allows the leader to make a strategic decision based on the follower’s reaction. Bilevel optimization models can be applied to strategic decision in energy markets, where the leader decides on e.g. investments and the follower clears the market and finds production levels and prices.

This thesis is based on four papers. The first proposed a novel, general solution method to bilevel optimization problems using off-the-shelf optimization software. Extensive numerical studies using random generated problems show the effectiveness of the proposed solution. The second paper investigates the issue of long-term planning problems in energy. Such planning problems include data representing the entire planning horizon and can thus easily be intractable. The paper investigates aggregation methods of this data in order to make the problems tractable while still finding the best possible solutions. The third paper introduces a solution method to bilevel optimization problems where the models are complicated by the inclusion of prices from the subsequent market clearing. The novel method is shown to solve previous unsolvable problems and to be numerically efficient, even for large models. The final paper applies the method proposed in the third paper to an electricity transmission expansion problem with numerical studies showing the effectiveness.

Ass. Prof. Trine Krogh Boomsma, MATH, University of Copenhagen

Assessment Committee:
Associate Professor. (Chairman), Giovanni Pantuso, University of Copenhagen
Prof. Asgeir Thomasgard, Norwegian University of Science and Technology
Associate Professor, Sonja Wogrin, Comillas Pontifical University