arXiv subjects

Julia Sudhoff Santos

Publications and source records attributed to Julia Sudhoff Santos.

4 recordsLinked to original sources

arXiv2026

Consistent Path Selection for Bi-objective Median Location Problems on Graphs

We consider single-facility median location problems on graphs where two conflicting cost values are associated with the edges. As an example, suppose that a decision maker wants to locate one new facility, e. g., a pizza delivery place, which uses bicycles for delivery. The two objective functions could then be the total traveling time and the total number of left turns, as the latter are very risky. Path choices then depend on the preferences of the decision maker, and in general, there may not exist a unique optimal path between a customer and a new facility location. In this paper, we consider the location decision and the routing decision in a coupled problem, i. e., we search for an optimal location and for consistent delivery paths simultaneously. We introduce the concept of consistent paths, where we assume that the choice of a path from the facility to a demand node implies certain preferences. All paths of a solution are consistent if the preferences of all paths do not contradict each other. We present an algorithm that computes a minimum complete set of efficient solutions with consistent path choices and illustrate the results at example instances in the city of Wuppertal in Germany.

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arXiv2026

Adapting Polyhedral Dominance Cones to Ordinal Preference Structures

In combinatorial optimization, ordinal costs can be used to model the quality of elements whenever numerical values are not available. When considering, for example, routing problems for cyclists, the safety of a street can be ranked in ordered categories like safe (separate bike lane), medium safe (street with a bike lane) and unsafe (street without a bike lane). However, ordinal optimization may suggest unrealistic solutions with huge detours to avoid unsafe street segments. In this paper, we investigate how partial preference information regarding the relative quality of the ordinal categories can be used to improve the relevance of the computed solutions. By introducing preference weights which describe how much better a category is at least or at most, compared to the subsequent category, we enlarge the ordinal dominance cone. This leads to a smaller set of alternatives, i. e., of ordinally efficient solutions. We show that the corresponding weighted ordinal ordering cone is a polyhedral cone and provide descriptions via its extreme rays and via its facets. The latter implies a linear transformation to an associated multi-objective optimization problem. This paves the way for the application of standard multi-objective solution approaches. We demonstrate the usefulness of the weighted ordinal ordering cone by investigating a safest path problem with different preference weights. Moreover, we investigate the interrelation between the weighted ordering cone to standard dominance concepts of multi-objective optimization, like, e.g., Pareto dominance, lexicographic dominance and weighted sum dominance.

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arXiv2024

On the Computational Complexity of Multi-Objective Ordinal Unconstrained Combinatorial Optimization

Multi-objective unconstrained combinatorial optimization problems (MUCO) are in general hard to solve, i.e., the corresponding decision problem is NP-hard and the outcome set is intractable. In this paper we explore special cases of MUCO problems that are actually easy, i.e., solvable in polynomial time. More precisely, we show that MUCO problems with up to two ordinal objective functions plus one real-valued objective function are tractable, and that their complete nondominated set can be computed in polynomial time. For MUCO problems with one ordinal and a second ordinal or real-valued objective function we present an even more efficient algorithm that applies a greedy strategy multiple times.

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arXiv2024

Computing safe bicycle routes -- Berechnung sicherer Fahrradwege

The safety of streets is difficult to quantify numerically. However, it is possible to sort streets regarding their safety into ordered categories, like safe, neutral and unsafe. In this paper we model the computation of safe bicycle routes as an optimization problem with ordinal coefficients. We describe an appropriate optimality concept for ordinal optimization problems and introduce a solution strategy for ordinal routing problems. Furthermore, we introduce a concept to incorporate safety preferences by introducing weights such that longer path with a higher safety rating are preferred. We apply the concept of ordinal routing to compute safe bicycle routes in Stuttgart, Germany, based on dates from OpenStreetMaps. We show that the choice of the weights does not only represent the trade-off of safety vs. path length, but has also an impact on the number of alternative solutions and thus on the computation time. -- Die Sicherheit von Wegen ist nur eingeschränkt messbar und daher schwierig zu quantifizieren. Dahingegen ist es verhältnismäßig leicht Wege bezüglich ihrer Sicherheit in geordnete Kategorien, wie beispielsweise sicher, neutral und gefährlich einzuordnen. In diesem Beitrag werden Optimierungsprobleme mit geordneten Kategorien formuliert und Optimalität für diese definiert. Daraus wird eine Lösungsstrategie für solche Probleme abgeleitet. Darüber hinaus wird erklärt, wie die Abgrenzung zwischen den Kategorien erhöht werden kann, sodass längere aber dafür sicherere Wege mit Hilfe von Gewichten berechnet werden können. Diese theoretischen Ergebnisse werden in der Praxis angewendet und es werden auf Grundlage von Daten von OpenStreetMaps sichere Fahrradwege in Stuttgart berechnet. Dabei zeigt sich, dass eine gute Wahl der Gewichte zu weniger Lösungen und kürzeren Rechenzeiten führt.

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