arXiv subjects

Anita Schöbel

Publications and source records attributed to Anita Schöbel.

At least 19 recordsLinked to original sources

arXiv2026

Optimizing Travel Time and Regenerative Energy for Periodic Timetables

Regenerating braking energy is one major pathway to make rail traffic energy-efficient. It is therefore desirable to design timetables that exploit this feature. However, timetables that allow to regenerate energy are often bad for the passengers. We hence formulate and analyze a bicriteria optimization problem (PESP-Passenger-Energy) to find periodic railway timetables that maximize the regenerated energy in terms of the brake-traction overlap time and minimize the travel time of the passengers. Our model extends the Periodic Event Scheduling Problem (PESP) and offers a rich combinatorial theory. We investigate its computational complexity on one-station networks, building on matchings and Hamiltonian paths. Besides showing its NP-hardness even for a single objective, we identify several polynomial-time solvable special cases. Finally, we provide two case studies, underlining the practicability of our model, and analyzing the Pareto front.

math.OC↗

arXiv2025

Benders Decomposition for Passenger-Oriented Train Timetabling with Hybrid Periodicity

Periodic timetables are widely adopted in passenger railway operations due to their regular service patterns and well-coordinated train connections. However, fluctuations in passenger demand require varying train services across different periods, necessitating adjustments to the periodic timetable. This study addresses a hybrid periodic train timetabling problem, which enhances the flexibility and demand responsiveness of a given periodic timetable through schedule adjustments and aperiodic train insertions, taking into account the rolling stock circulation. Since timetable modifications may affect initial passenger routes, passenger routing is incorporated into the problem to guide planning decisions towards a passenger-oriented objective. Using a time-space network representation, the problem is formulated as a dynamic railway service network design model with resource constraints. To handle the complexity of real-world instances, we propose a decomposition-based algorithm integrating Benders decomposition and column generation, enhanced with multiple preprocessing and accelerating techniques. Numerical experiments demonstrate the effectiveness of the algorithm and highlight the advantage of hybrid periodic timetables in reducing passenger travel costs.

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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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arXiv2025

Fare Structure Design in Public Transport

Fare planning is one among several steps in public transport planning. Fares are relevant for the covering of costs of the public transport operator, but also affect the ridership and the passenger satisfaction. A fare structure is the assignment of prices to all paths in a network. In practice, often a given fare structure shall be changed to fulfill new requirements, meaning that a new fare strategy is desired. This motivates the usage of prices of the former fare structure or other desirable prices as reference prices. In this paper, we investigate the fare structure design problem that aims to determine fares such that the sum of absolute deviations between the new fares and the reference prices is minimized. Fare strategies that are considered here are flat tariffs, affine distance tariffs and zone tariffs. Additionally, we regard constraints that ensure that it is not beneficial to buy a ticket for a longer journey than actually traveled (no-elongation property) or to split a ticket into several sub-tickets to cover a journey (no-stopover property). Our literature review provides an overview of the research on fare planning. We analyze the fare structure design problem for flat, distance and zone tariffs, pointing out connections to median problems. Further, we study its complexity which ranges from linear-time solvability to NP-complete cases.

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arXiv2024

Risk management in multi-objective portfolio optimization under uncertainty

In portfolio optimization, decision makers face difficulties from uncertainties inherent in real-world scenarios. These uncertainties significantly influence portfolio outcomes in both classical and multi-objective Markowitz models. To address these challenges, our research explores the power of robust multi-objective optimization. Since portfolio managers frequently measure their solutions against benchmarks, we enhance the multi-objective min-regret robustness concept by incorporating these benchmark comparisons. This approach bridges the gap between theoretical models and real-world investment scenarios, offering portfolio managers more reliable and adaptable strategies for navigating market uncertainties. Our framework provides a more nuanced and practical approach to portfolio optimization under real-world conditions.

q-fin.PM↗

arXiv2024

Planning and Optimizing Transit Lines

For all line-based transit systems like bus, metro and tram, the routes of the lines and the frequencies at which they are operated are determining for the operational performance of the system. However, as transit line planning happens early in the planning process, it is not straightforward to predict the effects of line planning decisions on relevant performance indicators. This challenge has in more than 40 years of research on transit line planning let to many different models. In this chapter, we concentrate on models for transit line planning including transit line planning under uncertainty. We pay particular attention to the interplay of passenger routes, frequency and capacity, and specify three different levels of aggregation at which these can be modeled. Transit line planning has been studied in different communities under different names.The problem can be decomposed into the components line generation, line selection, and frequency setting. We include publications that regard one of these individual steps as well as publications that combine two or all of them. We do not restrict to models build with a certain solution approach in mind, but do have a focus on models expressed in the language of mathematical programming.

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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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arXiv2023

Approaches for Biobjective Integer Linear Robust Optimization

Real-world optimization problems often do not just involve multiple objectives but also uncertain parameters. In this case, the goal is to find Pareto-optimal solutions that are robust, i.e., reasonably good under all possible realizations of the uncertain data. Such solutions have been studied in many papers within the last ten years and are called robust efficient. However, solution methods for finding robust efficient solutions are scarce. In this paper, we develop three algorithms for determining robust efficient solutions to biobjective mixed-integer linear robust optimization problems. To this end, we draw from methods for both multiobjective optimization and robust optimization: dichotomic search for biobjective mixed-integer optimization problems and an optimization-pessimization approach from (single-objective) robust optimization, which iteratively adds scenarios and thereby increases the uncertainty set. We propose two algorithms that combine dichotomic search with the optimization-pessimization method as well as a dichotomic search method for biobjective linear robust optimization that exploits duality. On the way we derive some other results: We extend dichotomic search from biobjective linear problems to biobjective linear minmax problems and generalize the optimization-pessimization method from single-objective to multi-objective robust optimization problems. We implemented and tested the three algorithms on linear and integer linear instances and discuss their respective strengths and weaknesses.

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arXiv2022

Location problems with cutoff

In this paper we study a generalized version of the Weber problem of finding a point that minimizes the sum of its distances to a finite number of given points. In our setting these distances may be $cut$ $off$ at a given value $C > 0$, and we allow for the option of an $empty$ solution at a fixed cost $C'$. We analyze under which circumstances these problems can be reduced to the simpler Weber problem, and also when we definitely have to solve the more complex problem with cutoff. We furthermore present adaptions of the algorithm of [Drezner et al., 1991, $Transportation$ $Science$ 25(3), 183--187] to our setting, which in certain situations are able to substantially reduce computation times as demonstrated in a simulation study. The sensitivity with respect to the cutoff value is also studied, which allows us to provide an algorithm that efficiently solves the problem simultaneously for all $C>0$.

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arXiv2022

The Cheapest Ticket Problem in Public Transport

Route choice models in public transport have been discussed for a long time. The main factor why a passenger chooses a specific path is usually based on its length or travel time. However, also the ticket price that passengers have to pay may influence their decision since passengers prefer cheaper paths over more expensive ones. In this paper, we deal with the cheapest ticket problem which asks for a cheapest ticket to travel between a pair of stations. The complexity and the algorithmic approach to solve this problem depend crucially on the underlying fare structure, e.g., it is easy if the ticket prices are proportional to the distance traveled (as in distance tariff fare structures), but may become NP-complete in zone tariff fare structures. We hence discuss the cheapest ticket problem for different variations of distance- and zone-based fare structures. We start by modeling the respective fare structure mathematically, identify its main properties, and finally provide a polynomial algorithm, or prove NP-completeness of the cheapest ticket problem. We also provide general results on the combination of two fare structures, which is often observed in practice.

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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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arXiv2021

Nachhaltige Strategien gegen die COVID-19-Pandemie in Deutschland im Winter 2021/2022

In this position paper, a large group of interdisciplinary experts outlines response strategies against the spread of SARS-CoV-2 in the winter of 2021/2022 in Germany. We review the current state of the COVID-19 pandemic, from incidence and vaccination efficacy to hospital capacity. Building on this situation assessment, we illustrate various possible scenarios for the winter, and detail the mechanisms and effectiveness of the non-pharmaceutical interventions, vaccination, and booster. With this assessment, we want to provide orientation for decision makers about the progress and mitigation of COVID-19.

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arXiv2021

Estimating the Robustness of Public Transport Systems Using Machine Learning

The planning of attractive and cost efficient public transport systems is a highly complex optimization process involving many steps. Integrating robustness from a passenger's point of view makes the task even more challenging. With numerous different definitions of robustness in literature, a real-world acceptable evaluation of the robustness of a public transport system is to simulate its performance under a large number of possible scenarios. Unfortunately, this is computationally very expensive. In this paper, we therefore explore a new way of such a scenario-based robustness approximation by using methods from machine learning. We achieve a fast approach with a very high accuracy by gathering a subset of key features of a public transport system and its passenger demand and training an artificial neural network to learn the outcome of a given set of robustness tests. The network is then able to predict the robustness of untrained instances with high accuracy using only its key features, allowing for a robustness oracle for transport planners that approximates the robustness in constant time. Such an oracle can be used as black box to increase the robustness within a local search framework for integrated public transportation planning. In computational experiments with different benchmark instances we demonstrate an excellent quality of our predictions.

cs.LG↗

arXiv2020

The foreshadow of a second wave: An analysis of current COVID-19 fatalities in Germany

A second wave of SARS-CoV-2 is unfolding in dozens of countries. However, this second wave manifests itself strongly in new reported cases, but less in death counts compared to the first wave. Over the past three months in Germany, the reported cases increased by a factor five or more, whereas the death counts hardly grew. This discrepancy fueled speculations that the rise of reported cases would not reflect a second wave but only wider testing. We find that this apparent discrepancy can be explained to a large extent by the age structure of the infected, and predict a pronounced increase of death counts in the near future, as the spread once again expands into older age groups. To re-establish control, and to avoid the tipping point when TTI capacity is exceeded, case numbers have to be lowered. Otherwise the control of the spread and the protection of vulnerable people will require more restrictive measures latest when the hospital capacity is reached.

q-bio.PE↗

arXiv2017

Multi-objective minmax robust combinatorial optimization with cardinality-constrained uncertainty

In this paper we develop two approaches to find minmax robust efficient solutions for multi-objective combinatorial optimization problems with cardinality-constrained uncertainty. First, we extend an algorithm of Bertsimas and Sim (2003) for the single-objective problem to multi-objective optimization. We propose also an enhancement to accelerate the algorithm, even for the single-objective case, and we develop a faster version for special multi-objective instances. Second, we introduce a deterministic multi-objective problem with sum and bottleneck functions, which provides a superset of the robust efficient solutions. Based on this, we develop a label setting algorithm to solve the multi-objective uncertain shortest path problem. We compare both approaches on instances of the multi-objective uncertain shortest path problem originating from hazardous material transportation.

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arXiv2016

Improvable Knapsack Problems

We consider a variant of the knapsack problem, where items are available with different possible weights. Using a separate budget for these item improvements, the question is: Which items should be improved to which degree such that the resulting classic knapsack problem yields maximum profit? We present a detailed analysis for several cases of improvable knapsack problems, presenting constant factor approximation algorithms and two PTAS.

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arXiv2016

A biobjective approach to robustness based on location planning

Finding robust solutions of an optimization problem is an important issue in practice, and various concepts on how to define the robustness of a solution have been suggested. The idea of recoverable robustness requires that a solution can be recovered to a feasible one as soon as the realized scenario becomes known. The usual approach in the literature is to minimize the objective function value of the recovered solution in the nominal or in the worst case. As the recovery itself is also costly, there is a trade-off between the recovery costs and the solution value obtained; we study both, the recovery costs and the solution value in the worst case in a biobjective setting. To this end, we assume that the recovery costs can be described by a metric. We demonstrate that this leads to a location planning problem, bringing together two fields of research which have been considered separate so far. We show how weakly Pareto efficient solutions to this biobjective problem can be computed by minimizing the recovery costs for a fixed worst-case objective function value and present approaches for the case of linear and quasiconvex problems for finite uncertainty sets. We furthermore derive cases in which the size of the uncertainty set can be reduced without changing the set of Pareto efficient solutions.

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arXiv2016

Algorithm Engineering in Robust Optimization

Robust optimization is a young and emerging field of research having received a considerable increase of interest over the last decade. In this paper, we argue that the the algorithm engineering methodology fits very well to the field of robust optimization and yields a rewarding new perspective on both the current state of research and open research directions. To this end we go through the algorithm engineering cycle of design and analysis of concepts, development and implementation of algorithms, and theoretical and experimental evaluation. We show that many ideas of algorithm engineering have already been applied in publications on robust optimization. Most work on robust optimization is devoted to analysis of the concepts and the development of algorithms, some papers deal with the evaluation of a particular concept in case studies, and work on comparison of concepts just starts. What is still a drawback in many papers on robustness is the missing link to include the results of the experiments again in the design.

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