arXiv subjects

Philine Schiewe

Publications and source records attributed to Philine Schiewe.

6 recordsLinked to original sources

arXiv2026

A robust optimization approach to flow decomposition

In this paper, we generalize the minimum flow decomposition problem (MFD) to incorporate uncertain edge capacities and tackle it from the perspective of robust optimization. In the classical flow decomposition problem, a network flow is decomposed into a set of weighted paths from a fixed source node to a fixed sink node that precisely represents the flow distribution across all edges. MFD problems permeate multiple important applications, including reconstructing genomic sequences to representing the flow of goods or passengers in distribution networks. Inspired by these applications, we generalize the MFD to an inexact case with bounded flow values, provide a detailed analysis, and explore different variants that are solvable in polynomial time. Moreover, we introduce the concept of robust flow decomposition by incorporating uncertain bounds and applying different robustness concepts to handle the uncertainty. Finally, we present two different adjustably robust problem formulations and perform computational experiments illustrating the benefit of adjustability.

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arXiv2025

An Equilibrium Model for Schedule-Based Transit Networks with Hard Vehicle Capacities

Modelling passenger assignments in public transport networks is a fundamental task for city planners, especially when deliberating network infrastructure decisions. A key aspect of a realistic model is to integrate passengers' selfish routing behaviour under limited vehicle capacities. We formulate a side-constrained user equilibrium model in a schedule-based transit network, where passengers are modelled via a continuum of non-atomic agents that travel from their origin to their destination. An agent's route may comprise several rides along given lines, each using vehicles with hard loading capacities. We give a characterization of (side-constrained) user equilibria via a quasi-variational inequality and prove their existence for fixed departure times by generalizing a well-known result of Bernstein and Smith (Transp. Sci., 1994). We further derive a polynomial time algorithm for single-commodity instances with fixed departure times. For the multi-commodity case with departure time choice, we show that deciding whether an equilibrium exists is NP-hard, and we devise an exponential-time algorithm that computes an equilibrium if it exists, and signals non-existence otherwise. Using our quasi-variational characterization, we formulate a heuristic for computing multi-commodity user equilibria in practice, which is tested on multiple real-world instances. In terms of social cost, the computed user-equilibria are quite efficient compared to a system optimum.

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arXiv2025

Quantum Computing for Discrete Optimization: A Highlight of Three Technologies

Quantum optimization has emerged as a promising frontier of quantum computing, providing novel numerical approaches to mathematical optimization problems. The main goal of this paper is to facilitate interdisciplinary research between the Operations Research (OR) and Quantum Computing communities by helping OR scientists to build initial intuition for-, and offering them a hands-on gateway to quantum-powered methods in the context of discrete optimization. To this end, we consider three quantum-powered optimization approaches that make use of different types of quantum hardware available on the market. To illustrate these approaches, we solve three classical optimization problems: the Traveling Salesperson Problem, Weighted Maximum Cut, and Maximum Independent Set. With a general OR audience in mind, we attempt to provide an intuition behind each approach along with key references, describe the corresponding high-level workflow, and highlight crucial practical considerations. In particular, we emphasize the importance of problem formulations and device-specific configurations, and their impact on the amount of resources required for computation (where we focus on the number of qubits). These points are illustrated with a series of experiments on three types of quantum computers: a neutral atom machine from QuEra, a quantum annealer from D-Wave, and gate-based devices from IBM.

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arXiv2024

The Bus Rapid Transit Investment Problem

Bus Rapid Transit (BRT) systems can provide a fast and reliable service to passengers at low investment costs compared to tram, metro and train systems. Therefore, they can be of great value to attract more passengers to use public transport. This paper thus focuses on the BRT investment problem: Which segments of a single bus line should be upgraded such that the number of newly attracted passengers is maximized? Motivated by the construction of a new BRT line around Copenhagen, we consider a setting in which multiple parties are responsible for the financing of different segments of the line. As each party has a limited willingness to invest, we solve a bi-objective problem to quantify the trade-off between the number of attracted passengers and the investment budget. We model different problem variants: First, we consider two potential passenger responses to upgrades on the line. Second, to prevent scattered upgrades along the line, we consider different restrictions on the number of upgraded connected components on the line. We propose an epsilon-constraint-based algorithm to enumerate the complete set of non-dominated points and investigate the complexity of this problem. Moreover, we perform extensive numerical experiments on artificial instances and a case study based on the BRT line around Copenhagen. Our results show that we can generate the full Pareto front for real-life instances and that the resulting trade-off between investment budget and attracted passengers depends both on the origin-destination demand and on the passenger response to upgrades. Moreover, we illustrate how the generated Pareto plots can assist decision makers in selecting from a set of geographical route alternatives in our case study.

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arXiv2022

Line Planning in Public Transport: Bypassing Line Pool Generation

Line planning, i.e. choosing paths which are operated by one vehicle end-to-end, is an important aspect of public transport planning. While there exists heuristic procedures for generating lines from scratch, most theoretical observations consider the problem of choosing lines from a predefined line pool. In this paper, we consider the complexity of the line planning problem when all simple paths can be used as lines. Depending on the cost structure, we show that the problem can be NP-hard even for paths and stars and that no polynomial time approximation of sub-linear performance is possible. Additionally, we identify polynomially solvable cases and present a pseudo-polynomial solution approach for trees.

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arXiv2021

Integrated Optimization of Sequential Processes: General Analysis and Application to Public Transport

Planning in public transportation is traditionally done in a sequential process: After the network design process, the lines and their frequencies are planned. When these are fixed, a timetable is determined and based on the timetable, the vehicle and crew schedules are optimized. After each step, passenger routes are adapted to model the behavior of the passengers as realistically as possible. It has been mentioned in many publications that such a sequential process is sub-optimal, and integrated approaches, mainly heuristics, are under consideration. Sequential planning is not only common in public transportation planning but also in many other applied problems, among others in supply chain management, or in organizing hospitals efficiently. The contribution of this paper hence is two-fold: on the one hand, we develop an integrated integer programming formulation for the three planning stages line planning, (periodic) timetabling, and vehicle scheduling which also includes the integrated optimization of the passenger routes. This gives us an exact formulation rewriting the sequential approach as an integrated problem. We discuss properties of the integrated formulation and apply it experimentally to data sets from the LinTim library. On the other hand, we propose a mathematical formulation for general sequential processes which can be used to build integrated formulations. For comparing sequential processes with their integrated counterparts we analyze the price of sequentiality, i.e., the ratio between the solution obtained by the sequential process and an integrated solution. We also experiment with different possibilities for partial integration of a subset of the sequential problems and again illustrate our results using the case of public transportation. The obtained results may be useful for other sequential processes.

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