TY - GEN A1 - Bähr, Martin A1 - Buhl, Johannes A1 - Radow, Georg A1 - Schmidt, Johannes A1 - Bambach, Markus A1 - Breuß, Michael A1 - Fügenschuh, Armin T1 - Stable honeycomb structures and temperature based trajectory optimization for wire-arc additive manufacturing T2 - Optimization and Engineering N2 - We consider two mathematical problems that are connected and occur in the layer-wise production process of a workpiece using wire-arc additive manufacturing. As the first task, we consider the automatic construction of a honeycomb structure, given the boundary of a shape of interest. In doing this, we employ Lloyd’s algorithm in two different realizations. For computing the incorporated Voronoi tesselation we consider the use of a Delaunay triangulation or alternatively, the eikonal equation. We compare and modify these approaches with the aim of combining their respective advantages. Then in the second task, to find an optimal tool path guaranteeing minimal production time and high quality of the workpiece, a mixed-integer linear programming problem is derived. The model takes thermal conduction and radiation during the process into account and aims to minimize temperature gradients inside the material. Its solvability for standard mixed-integer solvers is demonstrated on several test-instances. The results are compared with manufactured workpieces. KW - Mixed-integer linear programming KW - Geometric optimization KW - Eikonal equation KW - Heat transmission KW - Additive manufacturing KW - Centroidal Voronoi tesselation Y1 - 2021 U6 - https://doi.org/10.1007/s11081-020-09552-5 SN - 1573-2924 VL - 22 IS - 2 SP - 913 EP - 974 ER - TY - GEN A1 - Khan, Mohammad Faisal A1 - Hasan, Md. Gulzarul A1 - Quddoos, Abdul A1 - Fügenschuh, Armin T1 - Goal Programming Models with Linear and Exponential Fuzzy Preference Relations T2 - Symmetry Y1 - 2020 U6 - https://doi.org/10.3390/sym12060934 SN - 2073-8994 VL - 12 IS - 6 ER - TY - GEN A1 - Ali, Irfan A1 - Fügenschuh, Armin A1 - Gupta, Srikant A1 - Modibbo, Umar Muhammad T1 - The LR-Type Fuzzy Multi-Objective Vendor Selection Problem in Supply Chain Management T2 - Mathematics Y1 - 2020 U6 - https://doi.org/10.3390/math8091621 SN - 2227-7390 VL - 8 IS - 9 ER - TY - GEN A1 - Singham, Dashi I. A1 - Cai, Wenbo A1 - Fügenschuh, Armin T1 - Flexible contracting with heterogeneous agents and stochastic demand T2 - International Journal of Production Economics Y1 - 2021 U6 - https://doi.org/10.1016/j.ijpe.2020.107840 SN - 0925-5273 VL - 231 ER - TY - GEN A1 - Auer, Peter A1 - Dósa, György A1 - Dulai, Tibor A1 - Fügenschuh, Armin A1 - Näser, Peggy A1 - Ortner, Ronald A1 - Werner-Stark, Ágnes T1 - A new heuristic and an exact approach for a production planning problem T2 - Central European Journal of Operations Research Y1 - 2020 U6 - https://doi.org/10.1007/s10100-020-00689-3 SN - 1613-9178 ER - TY - GEN A1 - Zazai, M. Fawad A1 - Fügenschuh, Armin T1 - Computing the trajectories for the development of optimal routes T2 - Optimization and Engineering Y1 - 2020 U6 - https://doi.org/10.1007/s11081-020-09569-w SN - 1573-2924 VL - Vol. 22 (2021) IS - 2 SP - 975 EP - 999 ER - TY - GEN A1 - Moreno, Liana Amaya A1 - Omidi, Maryam A1 - Wurlitzer, Marcus A1 - Luthringer, Bérengère A1 - Helmholz, Heike A1 - Schlüter, Hartmut A1 - Willumeit-Römer, Regine A1 - Fügenschuh, Armin T1 - Understanding Protein Networks Using Vester's Sensitivity Model T2 - IEEE/ACM Transactions on Computational Biology and Bioinformatics Y1 - 2020 U6 - https://doi.org/10.1109/TCBB.2018.2885757 SN - 1545-5963 SN - 1557-9964 VL - 17 IS - 4 SP - 1440 EP - 1450 ER - TY - GEN A1 - Gnegel, Fabian A1 - Fügenschuh, Armin A1 - Hagel, Michael A1 - Leyffer, Sven A1 - Stiemer, Marcus T1 - A Solution Framework for Linear PDE-Constrained Mixed-Integer Problems T2 - Mathematical Programming Y1 - 2021 U6 - https://doi.org/10.1007/s10107-021-01626-1 SN - 0025-5610 SN - 1436-4646 VL - 188 IS - 2 SP - 695 EP - 728 ER - TY - GEN A1 - Fügenschuh, Armin A1 - Müllenstedt, Daniel A1 - Schmdit, Johannes T1 - Flight Planning for Unmanned Aerial Vehicles T2 - Military Operations Research Y1 - 2021 SN - 1082-5983 SN - 2163-2758 VL - 26 IS - 3 SP - 49 EP - 71 ER - TY - GEN A1 - Johannsmann, Leonie M. A1 - Craparo, Emily M. A1 - Dieken, Thor L. A1 - Fügenschuh, Armin A1 - Seitner, Björn O. T1 - Stochastic mixed-integer programming for a spare parts inventory management problem T2 - Computers & Operations Research Y1 - 2022 U6 - https://doi.org/10.1016/j.cor.2021.105568 SN - 1873-765X SN - 0305-0548 VL - 138 SP - 1 EP - 10 ER - TY - GEN A1 - Dee, Robin A1 - Fügenschuh, Armin A1 - Kaimakamis, George T1 - The Unit Re-balancing Problem T2 - Proceedings of the 6th IMA Conference on Mathematics in Defence and Security, Tuesday March 30, 2021 - Wednesday March 31, 2021 Y1 - 2021 UR - https://ima.org.uk/12970/6th-ima-conference-on-mathematics-in-defence-and-security/ SP - 1 EP - 10 ER - TY - BOOK A1 - Schmidt, Johannes A1 - Fügenschuh, Armin T1 - A two-time-level model for mission and flight planning of an inhomogeneous fleet of unmanned aerial vehicles Y1 - 2021 U6 - https://doi.org/10.26127/BTUOpen-5461 CY - Cottbus ER - TY - BOOK A1 - Gnegel, Fabian A1 - Schaudt, Stefan A1 - Clausen, Uwe A1 - Fügenschuh, Armin T1 - A 2D layered graph approach for scheduling delivery robots Y1 - 2021 U6 - https://doi.org/10.26127/BTUOpen-5493 CY - Cottbus ER - TY - BOOK A1 - Gnegel, Fabian A1 - Fügenschuh, Armin A1 - Hagel, Michael A1 - Leyffer, Sven A1 - Stiemer, Marcus T1 - A solution framework for linear PDE-constrained mixed-integer problems Y1 - 2019 U6 - https://doi.org/10.26127/BTUOpen-5045 CY - Cottbus ER - TY - BOOK A1 - Gnegel, Fabian A1 - Fügenschuh, Armin T1 - Branch-and-refine for solving time-dependent problems Y1 - 2020 U6 - https://doi.org/10.26127/BTUOpen-5199 CY - Cottbus ER - TY - BOOK A1 - Bähr, Martin A1 - Buhl, Johannes A1 - Radow, Georg A1 - Schmidt, Johannes A1 - Bambach, Markus A1 - Breuß, Michael A1 - Fügenschuh, Armin T1 - Stable honeycomb structures and temperature based trajectory optimization for wire-arc additive manufacturing Y1 - 2019 U6 - https://doi.org/10.26127/btuopen-5079 CY - Cottbus ER - TY - BOOK A1 - Schmidt, Johannes A1 - Fügenschuh, Armin T1 - Planning inspection flights with an inhomogeneous fleet of micro aerial vehicles Y1 - 2021 U6 - https://doi.org/10.26127/BTUOpen-5656 CY - Cottbus ER - TY - BOOK A1 - Schmidt, Johannes A1 - Buhl, Johannes A1 - Fügenschuh, Armin T1 - A finite element approach for trajectory optimization in Wire-Arc Additive Manufacturing Y1 - 2021 U6 - https://doi.org/10.26127/BTUOpen-5575 CY - Cottbus ER - TY - BOOK A1 - Ocloo, Valentina E. A1 - Fügenschuh, Armin A1 - Menoukeu Pamen, Olivier T1 - A new mathematical model for a 3D container packing problem Y1 - 2020 U6 - https://doi.org/10.26127/BTUOpen-5088 CY - Cottbus ER - TY - BOOK A1 - Johannsmann, Leonie M. A1 - Craparo, Emily M. A1 - Dieken, Thor L. A1 - Fügenschuh, Armin A1 - Seitner, Björn O. T1 - Stochastic mixed-integer programming for a spare parts inventory management problem Y1 - 2020 U6 - https://doi.org/10.26127/BTUOpen-5080 CY - Cottbus ER - TY - RPRT A1 - Zazai, M. Fawad A1 - Fügenschuh, Armin T1 - Computing the trajectories for the development of optimal routes Y1 - 2019 U6 - https://doi.org/10.26127/BTUOpen-5065 CY - Cottbus ER - TY - BOOK A1 - Dee, Robin A1 - Fügenschuh, Armin A1 - Kaimakamis, George T1 - The unit re-balancing problem Y1 - 2021 U6 - https://doi.org/10.26127/BTUOpen-5658 CY - Cottbus ER - TY - GEN A1 - Ghosh, Syamali A1 - Roy, Sankar Kumar A1 - Fügenschuh, Armin T1 - The Multi-Objective Solid Transportation Problem with Preservation Technology Using Pythagorean Fuzzy Sets T2 - International Journal of Fuzzy Systems Y1 - 2022 U6 - https://doi.org/10.1007/s40815-021-01224-5 SN - 2199-3211 SN - 1562-2479 VL - 24 IS - 6 SP - 2687 EP - 2704 ER - TY - GEN A1 - Stieber, Anke A1 - Fügenschuh, Armin T1 - Dealing with Time in the Multiple Traveling Salesmen Problem with Moving Targets T2 - Central European Journal of Operations Research N2 - The multiple traveling salespersons problem with moving targets is a generalization of the classical traveling salespersons problem, where the targets (nodes or objects) are moving over time. Additionally, for each target a visibility time window is given. The task is to find routes for several salespersons so that each target is reached exactly once within its visibility time window and the sum of all traveled distances of all salespersons is minimal. We present different modeling formulations for this TSP variant. The time requirements are modeled differently in each approach. Our goal is to examine what formulation is most suitable in terms of runtime to solve the multiple traveling salespersons problem with moving targets with exact methods. Computational experiments are carried out on randomly generated test instances to compare the different modeling approaches. The results for large-scale instances show, that the best way to model time requirements is to directly insert them into a formulation with discrete time steps. Y1 - 2022 U6 - https://doi.org/10.1007/s10100-020-00712-7 SN - 1613-9178 SN - 1435-246X VL - 30 IS - 3 SP - 991 EP - 1017 ER - TY - GEN A1 - Dee, Robin A1 - Fügenschuh, Armin A1 - Kaimakamis, George T1 - The Unit Re-Balancing Problem T2 - Mathematics Y1 - 2021 U6 - https://doi.org/10.3390/math9243205 SN - 2227-7390 VL - 9 IS - 24 ER - TY - CHAP A1 - Fügenschuh, Armin A1 - Marahrens, Sönke A1 - Johannsmann, Leonie M. A1 - Matuszewski, Sandra A1 - Müllenstedt, Daniel A1 - Schmidt, Johannes ED - Turnitsa, Charles ED - Blais, Curtis Blais ED - Tolk, Andreas T1 - Using Computer-Generated Virtual Realities, Operations Research, and Board Games for Conflict Simulations T2 - Simulation and Wargaming Y1 - 2022 SN - 978-1-119-60478-5 SN - 978-1-119-60479-2 U6 - https://doi.org/10.1002/9781119604815 SP - 273 EP - 287 PB - John Wiley & Sons, Inc. CY - Hoboken, NJ ER - TY - RPRT A1 - Beisegel, Jesse A1 - Buhl, Johannes A1 - Izar, Rameez A1 - Schmidt, Johannes A1 - Bambach, Markus A1 - Fügenschuh, Armin ED - Fügenschuh, Armin T1 - Mixed-integer programming for additive manufacturing Y1 - 2021 U6 - https://doi.org/10.26127/BTUOpen-5731 CY - Cottbus ER - TY - GEN A1 - Schmidt, Johannes A1 - Fügenschuh, Armin T1 - Trajectory optimization for arbitrary layered geometries in wire-arc additive manufacturing T2 - Optimization and Engineering Y1 - 2024 U6 - https://doi.org/10.1007/s11081-023-09813-z SN - 1573-2924 VL - 25 SP - 529 EP - 553 ER - TY - GEN A1 - Gnegel, Fabian A1 - Fügenschuh, Armin T1 - Branch-and-refine for solving time-expanded MILP formulations T2 - Computers & Operations Research Y1 - 2023 U6 - https://doi.org/10.1016/j.cor.2022.106043 SN - 1873-765X SN - 0305-0548 VL - Vol. 149 SP - 1 EP - 15 ER - TY - GEN A1 - Schmidt, Johannes A1 - Fügenschuh, Armin T1 - A two-time-level model for mission and flight planning of an inhomogeneous fleet of unmanned aerial vehicles T2 - Computational Optimization and Applications Y1 - 2023 U6 - https://doi.org/10.1007/s10589-023-00450-x SN - 1573-2894 SN - 1389-4420 VL - 85 IS - 1 SP - 293 EP - 335 ER - TY - GEN A1 - Schmidt, Johannes A1 - Fügenschuh, Armin ED - Grothe, Oliver ED - Nickel, Stefan ED - Rebennack, Steffen ED - Stein, Oliver T1 - Temperature-Based Trajectory Planning for Surfaces in Wire- Arc Additive Manufacturing T2 - Operations Research Proceedings 2022 : Selected Papers of the Annual International Conference of the German Operations Research Society (GOR), Karlsruhe, Germany, September 6-9, 2022 Y1 - 2023 SN - 978-3-031-24906-8 SN - 978-3-031-24907-5 SP - 539 EP - 545 PB - Springer CY - Heidelberg ER - TY - CHAP A1 - Beisegel, Jesse A1 - Buhl, Johannes A1 - Israr, Rameez A1 - Schmidt, Johannes A1 - Bambach, Martin A1 - Fügenschuh, Armin ED - Cristiani, Emiliano ED - Falcone, Maurizio ED - Tozza, Silvia T1 - Mixed-Integer Programming Models for Two Metal Additive Manufacturing Methods T2 - Mathematical Methods for Objects Reconstruction Y1 - 2023 SN - 978-981-9907-75-5 SN - 978-981-9907-76-2 SP - 121 EP - 155 PB - Springer CY - Heidelberg ER - TY - RPRT A1 - Schmidt, Johannes A1 - Fügenschuh, Armin T1 - Trajectory optimization for arbitrary layered geometries in wire-arc additive manufacturing Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:co1-opus4-62678 CY - Cottbus ; Senftenberg ER - TY - GEN A1 - Gnegel, Fabian A1 - Schaudt, Stefan A1 - Clausen, Uwe A1 - Fügenschuh, Armin T1 - A graph-refinement algorithm to minimize squared delivery delays using parcel robots T2 - Mathematics Y1 - 2024 U6 - https://doi.org/10.3390/math12203201 SN - 2227-7390 VL - 12 IS - 20 PB - MDPI AG ER - TY - GEN A1 - Ali, Irfan A1 - Sarkar, Biswajit A1 - Ali, Syed Mithun A1 - Fügenschuh, Armin T1 - Editorial: Environmental waste and renewable energy optimization for the sustainable development goals achievement T2 - Frontiers in Environmental Science KW - environment waste management KW - renewable energy KW - sustainable development goals - SDGs KW - green economy (GE) KW - multi-criteria decision making (MCDM) Y1 - 2023 U6 - https://doi.org/10.3389/fenvs.2023.1167835 SN - 2296-665X VL - 11 ER - TY - GEN A1 - Fügenschuh, Armin A1 - Lorenz, Ulf A1 - Pelz, Peter F. T1 - OPTE special issue on technical operations research (TOR) T2 - Optimization and Engineering KW - Optimization KW - Engineering, general KW - Systems Theory, Control KW - Environmental Management KW - Operations Research/Decision Theory KW - Financial Engineering Y1 - 2021 U6 - https://doi.org/10.1007/s11081-021-09640-0 SN - 1389-4420 SN - 1573-2924 VL - 22 IS - 2 SP - 581 EP - 586 ER - TY - GEN A1 - Rahman, Md Sadikur A1 - Shaikh, Ali Akbar A1 - Ali, Irfan A1 - Bhunia, Asoke Kumar A1 - Fügenschuh, Armin T1 - A Theoretical Framework for Optimality Conditions of Nonlinear Type-2 Interval-Valued Unconstrained and Constrained Optimization Problems Using Type-2 Interval Order Relations T2 - Mathematics KW - type-2 interval KW - type-2 interval order relations KW - type-2 interval-valued function KW - optimality KW - generalized KKT conditions Y1 - 2021 U6 - https://doi.org/10.3390/math9080908 SN - 2227-7390 VL - 9 IS - 8 ER - TY - GEN A1 - Fügenschuh, Armin T1 - MEDEVAC mission planning and decision making with mixed-integer programming and wargaming T2 - Proceedings of the 18th NATO Operations Research and Analysis (OR&A) Conference N2 - In the highly dynamic environment of military operations, efficient medical evacuation (MEDEVAC) of casualties is a critical strategic challenge. This paper presents a method for planning MEDEVAC missions using mathematical optimization and gamification. By applying Mixed-Integer Programming (MIP), a mathematical optimization technique, to solve a MEDEVAC dispatching and routing problem, a structured approach to decision making in emergency situations is presented. Our MIP model enables the detailed consideration of operational conditions and the mission support with combat helicopters as escorts, and thus improves the strategic planning and efficiency of MEDEVAC operations. When it comes to balance mission safety versus execution speed, we will enter the realm of multicriteria optimization models. As a further aspect, the role of gamification is emphasized by developing a board game that simulates the planning task and thus promotes understanding of the planning software. This approach allows planners to compare the quality of their manual planning with the computer-generated solution, improve their own planning skills and realize the benefits of software support for automated, AI- (Artificial Intelligence-) -assisted planning. Y1 - 2025 UR - https://www.sto.nato.int/publications/STO Meeting Proceedings/STO-MP-SAS-192/MP-SAS-192-15.pdf SN - 978-92-837-2580-0 U6 - https://doi.org/10.14339/STO-MP-SAS-192-15-PDF VL - STO-MP-SAS-192 SP - 1 EP - 14 PB - NATO Science and Technology Organization (STO) ER - TY - RPRT A1 - Zell, Sascha A1 - Fügenschuh, Armin T1 - Optimizing autonomous unmanned aircraft system deployment locations for enhanced wildfire detection and monitoring T1 - Standortoptimierung autonomer unbemannter Flugsysteme zur fortgeschrittenen Erkennung und Beobachtung von Waldbränden N2 - The increase in the frequency and severity of wildfires as a symptom of climate change requires innovative methods of wildfire fighting. For this reason, we propose a framework for an autonomous Unmanned Aircraft System (UAS), consisting of a fleet of Micro Air Vehicles (MAVs) stored in purpose-built hangars. The intention is to deploy the UAS as the first responder to an alarm and have the sensor-equipped MAVs monitor the target area even before other standard firefighting vehicles have arrived. The focus of this paper is primarily on the development and application of a location-allocation optimization Mixed-Integer Linear Programming (MILP) model that selects different MAV and hangar types and locates them, with the objective of approaching the target area as quickly as possible while guaranteeing a certain monitoring time at the scene. The model is applied to a large, sparsely populated, rural operational area, around a third of which consists of forest in the South of Brandenburg, Germany. The spatial demand is measured through an easily reproducible and transferable open data approach. Finally, several instances with different fixed numbers of hangars and MAVs to be set up are solved by the commercial state-of-the-art solver CPLEX and analyzed for their computation time. N2 - Die Zunahme der Häufigkeit und Schwere von Waldbränden als Symptom des Klimawandels erfordert innovative Methoden der Waldbrandbekämpfung. Für diesen Zweck nutzen wir ein autonomes unbemanntes Luftfahrtsystem (Unmanned Aricraft System - UAS), das aus einer Flotte von Drohnen besteht, die in eigens dafür errichteten Hangars gelagert werden. Ziel ist, das UAS als Erstreaktion bei einem Alarm einzusetzen und die mit Sensoren ausgestatteten Drohnen das Zielgebiet beobachten zu lassen, noch bevor die ersten Einsatzkräfte vor Ort eintreffen. Der Fokus dieses Papers liegt in erster Linie auf der Entwicklung und Anwendung eines Modells der gemischt-ganzzahligen Programmierung (Mixed-Integer Linear Programming - MILP) zur Optimierung der Standortzuweisung. Es werden verschiedene Drohnen- und Hangartypen auswählt und platziert, mit dem Ziel, die Einsatzbereiche so schnell wie möglich anzufliegen und gleichzeitig eine bestimmte Beobachtungszeit am Einsatzort zu garantieren. Das Modell wird auf ein großes, dünn besiedeltes, ländliches Einsatzgebiet, das zu etwa einem Drittel aus Wald besteht, im Süden von Brandenburg, Deutschland angewendet. Die räumliche Nachfrage wird durch einen leicht reproduzierbaren und übertragbaren Ansatz mittels Open Data gemessen. Schließlich werden mehrere Instanzen mit unterschiedlichen festgelegten Anzahlen von Hangars und aufzustellenden MAVs mit dem kommerziellen State-of-the-Art Solver CPLEX gelöst und auf ihre Rechenzeit hin analysiert. Y1 - 2025 U6 - https://doi.org/10.26127/BTUOpen-6942 SN - 2627-6100 PB - Brandenburgische Technische Universität Cottbus-Senftenberg CY - Cottbus ER - TY - CHAP A1 - Schmidt, Johannes A1 - Fügenschuh, Armin T1 - A column generation approach for weighted set packing problems with forbidden pairs T2 - Operations Research Proceedings 2023 : selected papers of the Annual International Conference of the German Operations Research Society (GOR), Germany, August 29–September 1, 2023 N2 - The weighted set packing problem (WSPP) is a variant of the well-known set packing problem, assigning a weight to every considered subset of a given finite base set. Its solution is a maximum sum-weight, element-disjoint covering of the base set. Using its formulation as a binary linear program (BLP), every column of the constraint matrix describes one of the given subsets. Thus, column generation (CG) provides a good solution method, generating iteratively only promising subsets as candidates for the covering. We consider an extension of the WSPP, where forbidden pairs are taken into consideration, i.e., there can be pairs of subsets that cannot be chosen at the same time, and adapt CG to derive a new solution algorithm to solve the resulting BLP. At each iteration, the optimal solution obtained with CG is checked for potential conflicts and either they are resolved locally without changing the objective function value or a new linear constraint forbidding the conflicting pair of columns is added. Then the CG procedure starts again. The applicability of this approach is shown for a team orienteering problem involving two unmanned aerial vehicles that must maintain safety distances between them. KW - Set packing problem KW - Conflict resolution KW - Column generation Y1 - 2025 SN - 978-3-031-58405-3 U6 - https://doi.org/10.1007/978-3-031-58405-3_14 SN - 2731-040X SP - 107 EP - 113 PB - Springer Nature Switzerland CY - Cham ER - TY - RPRT A1 - Schmidt, Johannes A1 - Fügenschuh, Armin T1 - Inter-sample avoidance in trajectory planning via an integer-polytope formulation for mixed-integer optimization T1 - Vermeidung von Kollisionen zwischen diskreten Zeitpunkten in der Trajektorienplanung mittels eines ganzzahligen Polytops für gemischt-ganzzahlige Optimierungsprobleme N2 - Autonomous vehicles such as drones or mobile robots must plan trajectories that avoid static obstacles. Their dynamics are captured by Newton’s laws and discretized numerically, so the vehicle’s position is tracked only at finitely many sample points. The resulting information gap allows a path to cut through an obstacle while still appearing feasible at all samples, a phenomenon called corner cutting. Finer time grids mitigate but never eliminate this artefact and increase computation time. We propose a new inter-sample avoidance scheme for polyhedral obstacles. The facet-defining half-spaces partition the three-dimensional mission space into sub-domains that we encode with binary sign vectors. Feasible one-step moves correspond to a specific subset of these vectors; we (i) enumerate that set exhaustively and (ii) give an integer-polytope formulation that enforces it without additional state variables or extra time steps. For planar motion with a single triangular no-fly zone we prove that the formulation is tight-the polytope equals the convex hull of its 0/1 points. The method is compared qualitatively with existing inter-sample avoidance techniques and its limitations are discussed. Computational experiments with a mixed-integer linear programming model for UAV mission planning, solved by Gurobi, demonstrate that the new formulation achieves realistic trajectories at competitive, or lower, solution times N2 - Autonome Fahrzeuge wie Drohnen oder mobile Roboter müssen Routen planen, die statische Hindernisse umgehen. Ihre Dynamik wird durch die Newtonschen Gesetze erfasst und numerisch diskretisiert, sodass die Position des Fahrzeugs nur an einer endlichen Anzahl von Zeitpunkten verfolgt wird. Die daraus resultierende Informationslücke ermöglicht es, dass eine Route ein Hindernis durchschneidet und dennoch zu allen Zeitpunkten als machbar erscheint – ein Phänomen, das als „Corner Cutting“ bezeichnet wird. Feinere Zeitraster mildern dieses Artefakt, können es jedoch nie vollständig beseitigen und erhöhen zudem die Rechenzeit. Wir schlagen ein neues Schema zur Vermeidung von Hindernissen zwischen den Zeitpunkten für polyedrische Hindernisse vor. Die facettendefinierenden Halbräume unterteilen den dreidimensionalen Missionsraum in Teilgebiete, die wir mit binären Vorzeichenvektoren kodieren. Machbare Ein-Schritt-Bewegungen entsprechen einer bestimmten Teilmenge dieser Vektoren; wir (i) zählen diese Menge vollständig auf und (ii) geben eine ganzzahlige Polytopformulierung an, die sie ohne zusätzliche Zustandsvariablen oder zusätzliche Zeitschritte sicherstellt. Für planare Bewegungen mit einer einzigen dreieckigen Flugverbotszone beweisen wir, dass die Formulierung effizient ist – das Polytop entspricht der konvexen Hülle seiner 0/1-Punkte. Die Methode wird qualitativ mit bestehenden Techniken zur Vermeidung von Hindernissen zwischen den Zeitpunkten verglichen und ihre Grenzen werden diskutiert. Rechenexperimente mit einem gemischt-ganzzahligen linearen Optimierungsmodell für die Missionsplanung von UAVs, gelöst von Gurobi, zeigen, dass die neue Formulierung realistische Routen bei konkurrenzfähigen oder niedrigeren Rechenzeiten erzielt. KW - Gemischt-ganzzahlige Optimierung KW - Konvexe Hülle KW - Trajektorienplanung KW - Unbemannte Luftfahrzeuge KW - Convex hull KW - Inter-sample avoidance KW - Mixed-integer optimization KW - Trajectory planning KW - Unmanned aerial vehicles Y1 - 2025 U6 - https://doi.org/10.26127/BTUOpen-7169 SN - 2627-6100 PB - Brandenburgische Technische Universität Cottbus-Senftenberg CY - Cottbus ER - TY - RPRT A1 - Schmidt, Johannes A1 - Fügenschuh, Armin A1 - Böschow, Moritz T1 - Sports league scheduling with minitournaments T1 - Planung von Sportligen mit Miniturnieren N2 - In amateur or youth sports leagues, the teams play all matches during their leisure time. Thus, a schedule with a smaller number of game days is preferred and the teams are willing to partly renounce on the fairness for this by playing minitournaments instead of single matches. In this format, multiple teams meet at one of them and play against each other, reducing the number of necessary game days and required referees at the cost of unevenly distributed home field advantages. The travel times of all teams now depend on their assignment to the respective minitournaments and the choice of the home team. We present a binary linear optimization model to schedule a sports league as a double Round Robin tournament with minitournaments and most evenly distributed home field advantages, yielding a feasible league schedule with minimal total traveling distances for all teams. After adjusting orbital shrinking to break the occurring symmetries in the possible assignments, we discuss the computational efficiency and evaluate an existing schedule for the "Basketball Senioren Landesliga Brandenburg" amateur basketball league in Germany. N2 - In Amateur- oder Jugendsportligen tragen die Mannschaften alle Spiele in ihrer Freizeit aus. Daher wird ein Spielplan mit einer geringeren Anzahl von Spieltagen bevorzugt, und die Mannschaften sind bereit, dafür teilweise auf die Fairness zu verzichten, indem sie Miniturniere anstelle von Einzelspielen spielen. Bei diesem Format treffen sich mehrere Mannschaften an einem Spieltag und spielen gegeneinander, wodurch die Anzahl der notwendigen Spieltage und der benötigten Schiedsrichter reduziert wird, allerdings auf Kosten eines ungleich verteilten Heimvorteils. Die Reisezeiten aller Mannschaften hängen nun von ihrer Zuordnung zu den jeweiligen Miniturnieren und der Wahl der Heimmannschaft ab. Wir stellen ein binäres lineares Optimierungsmodell vor, um eine Sportliga als doppeltes Round-Robin-Turnier mit Miniturnieren und möglichst gleichmäßig verteilten Heimvorteilen zu planen. Das Ziel ist ein zulässiger Ligaplan mit minimalen Gesamtreisezeiten für alle Mannschaften. Nach der Anpassung der "orbital shrinking"-Methode, um die auftretenden Symmetrien in den möglichen Zuordnungen zu brechen, diskutieren wir die rechnerische Effizienz und evaluieren einen bestehenden Spielplan für die Basketball Senioren Landesliga Brandenburg in Deutschland. KW - Diskrete Optimierung KW - Lineare Optimierung KW - Sportligenplanung KW - Discrete optimization KW - Linear optimization KW - Orbital shrinking KW - Sport scheduling Y1 - 2025 U6 - https://doi.org/10.26127/BTUOpen-7029 SN - 2627-4019 PB - Brandenburgische Technische Universität Cottbus-Senftenberg CY - Cottbus ER -