Conference Agenda

Quantum computation (QC) is an ever more prominent approach to tackling complex optimization problems. In the field of power system engineering, such a challenge is present in the transmission expansion problem (TEP), which gains increasingly interest as the current transmission network urgently needs support in facilitating the growing electricity demand and generation.

TEP involves determining the optimal placement and sizing of new transmission lines to enhance the efficiency and reliability of power grid networks. Currently, the TEP faces a trade-off between reducing the complexity of the model and computational demand. The applied techniques often involve clustering methods to reduce the number of variables of the optimization process, or simplifications in the combinatorics of the selection process for new lines, which QC could address.

There is a lot of ongoing research in TEP and the applicability of quantum computation in the field of power system engineering, but little to no work has been published in terms of QC in TEP. This work consists of a study of the current quantum computation and TEP literature and proposed European TEP projects. The analysis of present TEP methods will enable the identification of use cases and the creation of implementations of QC. The results will be rated based on feasibility, the prediction of computational speed up or allowed increase of complexity through the utilization of quantum properties, or even quantum supremacy.

Decision-making problems can be formalized as a partition of the set of solutions with respect to an order relation. In this work, we will provide a basic overview of decision-making problems focusing on their formalization as optimization problems. In particular, the partitioning process of these problems involves separating raw information from primitives, which are the fundamental building blocks of the decision model. The decision model is constructed by aggregating preferences that may be multiple, redundant, and conflicting. It is proven that if primitives are expressed on a single attribute, any problem statement results in using an optimization procedure for partitioning the solution set. In real-world scenarios, however, primitives are often expressed on multiple attributes, which raises the question of how to handle such cases. This novel perspective suggests that decision-making problems can be formulated as Multi-Objective Optimization (MOO) problems (if the objectives conflict with each other) or potentially as bi-level optimization problems (if the solution for one objective narrows the search space of solutions for another objective). This approach offers a more comprehensive framework for addressing decision-making problems with multiple attributes, providing a richer understanding of the decision-making process and its applications.

We discuss a multi-objective perspective on the concept of loss functions in Neural Network training. Rather than considering a weighted sum of different loss terms such as data loss and regularization terms, or data loss and residual loss in Physics Informed Neural Networks, we consider these loss terms as independent and conflicting training goals. We suggest a dichotomic scheme to approximate the Pareto front that uses bisection steps whenever the training gets stuck in local minima. We present results for classical image classification tasks as well as for the training of Physics Informed Neural Networks.