arXiv subjects

Léonard von Niederhäusern

Publications and source records attributed to Léonard von Niederhäusern.

3 recordsLinked to original sources

arXiv2023

The value of Shared Information for allocation of drivers in ride-hailing: a proof-of-concept study

For drivers in ride-hailing companies, allocation within the city is paramount to get matched with rides. This decision depends on many factors, where some of them (such as demand and allocation of others) are unknown for the drivers, but are available for the company. In this work, we investigate whether it is beneficial or not for the ride-hailing company to share this information with their drivers. To do so, we study the problem through the lens of Stackelberg games, and we propose a new indicator called the Expected Value of Shared Information. We present a simplified model to conduct a proof-of-concept study: we provide explicit single-level reformulations of the bilevel programming problems derived from the model, and perform several simulations with randomly generated data. Our preliminary results suggest that sharing information could be beneficial and deserves to be further studied.

math.OC↗

arXiv2021

On the geometry of symmetry breaking inequalities

Breaking symmetries is a popular way of speeding up the branch-and-bound method for symmetric integer programs. We study fundamental domains, which are minimal and closed symmetry breaking polyhedra. Our long-term goal is to understand the relationship between the complexity of such polyhedra and their symmetry breaking capability. Borrowing ideas from geometric group theory, we provide structural properties that relate the action of the group with the geometry of the facets of fundamental domains. Inspired by these insights, we provide a new generalized construction for fundamental domains, which we call generalized Dirichlet domain (GDD). Our construction is recursive and exploits the coset decomposition of the subgroups that fix given vectors in $\mathbb{R}^n$. We use this construction to analyze a recently introduced set of symmetry breaking inequalities by Salvagnin (2018) and Liberti and Ostrowski (2014), called Schreier-Sims inequalities. In particular, this shows that every permutation group admits a fundamental domain with less than $n$ facets. We also show that this bound is tight. Finally, we prove that the Schreier-Sims inequalities can contain an exponential number of isomorphic binary vectors for a given permutation group $G$, which provides evidence of the lack of symmetry breaking effectiveness of this fundamental domain. Conversely, a suitably constructed GDD for this $G$ has linearly many inequalities and contains unique representatives for isomorphic binary vectors.

cs.DM↗

arXiv2021

A Rolling Horizon Approach for a Bilevel Stochastic Pricing Problem for Demand-Side Management

To guarantee the well-functioning of electricity distribution networks, it is crucial to constantly ensure the demand-supply balance. To do this, one can control the means of production, but also influence the demand: demand-side management becomes more and more popular as the demand keeps increasing and getting more chaotic. In this work, we propose a bilevel model involving an energy supplier and a smart grid operator (SGO): the supplier induces shifts of the load controlled by the SGO by offering time-dependent prices. We assume that the SGO has contracts with consumers and decides their consumption schedule, guaranteeing that the inconvenience induced by the load shifts will not overcome the related financial benefits. Furthermore, we assume that the SGO manages a source of renewable energy (RE), which leads us to consider a stochastic bilevel model, as the generation of RE is by nature highly unpredictable. To cope with the issue of large problem sizes, we design a rolling horizon algorithm that can be applied in a real context.

math.OC↗