@techreport{GnegelFuegenschuhHageletal.2019, author = {Gnegel, Fabian and F{\"u}genschuh, Armin and Hagel, Michael and Leyffer, Sven and Stiemer, Marcus}, title = {A solution framework for linear PDE-constrained mixed-integer problems}, editor = {F{\"u}genschuh, Armin}, issn = {2627-6100}, doi = {10.26127/BTUOpen-5045}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-50453}, year = {2019}, abstract = {We present a general numerical solution method for control problems with PDE-defined state variables over a finite set of binary or continuous control variables. We show empirically that a naive approach that applies a numerical discretization scheme to the PDEs (and if necessary a linearization scheme) to derive constraints for a mixed-integer linear program (MILP) leads to systems that are too large to be solved with state-of-the-art solvers for MILPs, especially if we desire an accurate approximation of the state variables. Our framework comprises two techniques to mitigate the rise of computation times with increasing discretization level parameters: First, the linear system is solved for a basis of the control space in a preprocessing step. Second, certain constraints are just imposed on demand via the IBM ILOG CPLEX feature of a lazy constraint callback. These techniques are compared with an approach where the relations obtained by the discretization of the continuous constraints are directly included in the MILP. We demonstrate our approach on two examples: modeling of the spread of wildfire and the mitigation of water contamination. In both examples the computational results demonstrate that the solution time is significantly reduced by our methods. In particular, the dependence of the computation time on the size of the spatial discretization of the PDE is significantly reduced.}, subject = {Mixed-integer linear programming; Partial differential equations; Finite-element methods; Convection-diffusion equation; Global optimal control; Gemischt-ganzzahlige lineare Programmierung; Globale Optimalsteuerung; Konvektions-Diffusions-Gleichung; Finite-Elemente-Methode; Partielle Differentialgleichungen; Optimale Kontrolle; Finite-Elemente-Methode; Lineare Optimierung; Konvektions-Diffusionsgleichung}, language = {en} } @techreport{SchmidtFuegenschuhBoeschow2025, type = {Working Paper}, author = {Schmidt, Johannes and F{\"u}genschuh, Armin and B{\"o}schow, Moritz M.}, title = {Sports league scheduling with minitournaments}, doi = {10.26127/BTUOpen-7029}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-70293}, year = {2025}, abstract = {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.}, subject = {Discrete optimization; Linear optimization; Orbital shrinking; Sport scheduling; Diskrete Optimierung; Lineare Optimierung; Sportligenplanung; Lineare Optimierung; Diskrete Optimierung; Wettkampfklasse; Amateursport; Jugendsport; Spielplan }, language = {en} } @techreport{OclooFuegenschuhPamen2020, type = {Working Paper}, author = {Ocloo, Valentina E. and F{\"u}genschuh, Armin and Pamen, Olivier M.}, title = {A new mathematical model for a 3D container packing problem}, editor = {F{\"u}genschuh, Armin}, issn = {2627-6100}, doi = {10.26127/BTUOpen-5088}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-50880}, year = {2020}, abstract = {Wir betrachten das Problem der Einzelcontainerpackung eines Unternehmens, das seine Kunden bedienen muss, indem es zuerst die Produkte in Kartons legt und diese dann in einen Container l{\"a}dt. F{\"u}r dieses Problem entwickeln und l{\"o}sen wir ein lineares gemischt-ganzzahliges Modell. Unser Modell ber{\"u}cksichtigt geometrische Randbedingungen, beispielsweise {\"U}berlappungsverbote, Orientierungs-Bedingungen und Randbedingungen f{\"u}r die relative Positionierung der Kartons. Wir betrachten auch die Erweiterung des Modells durch die Integration der Schwerpunktsabweichung der Packung vom Containermittelpunkt. Das Modell wurde an einer großen Anzahl von realen Instanzen getestet, die bis zu 41 Kartons enthalten. In den meisten F{\"a}llen wurden optimale L{\"o}sungen erzielt bzw. nah-optimale L{\"o}sungen mit beweisbar kleiner Optimalit{\"a}tsl{\"u}cke.}, subject = {Container packing problem; Mixed-integer programming; Box orientation; Non-overlapping; Center of gravity deviation; Optimierungsproblem; Container; Lineare Optimierung; Logistik}, language = {en} } @techreport{ZellSchneidereitFuegenschuhetal.2024, type = {Working Paper}, author = {Zell, Sascha and Schneidereit, Toni and F{\"u}genschuh, Armin and Breuß, Michael}, title = {Advanced search and rescue operations for drowning swimmers using autonomous unmanned aircraft systems : location optimization, flight trajectory planning and image-based localization}, doi = {10.26127/BTUOpen-6866}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-68669}, year = {2024}, abstract = {Drowning is among the most prevalent causes of death from unintentional injuries worldwide. Because of the time-sensitive nature of swimming accidents and the shortage of lifeguard staff resulting in unsupervised swimming areas, interest in supportive rescue methods increases. In this paper, we propose an autonomous Unmanned Aircraft System (UAS) usable by Emergency Medical Service (EMS) providers in swimmer rescue scenarios additionally to Standard Rescue Operation (SRO) equipment. The UAS consists of Unmanned Aerial Vehicles (UAVs) and purpose-built hangars located near the swimming area to store the UAVs. When receiving an alert, the UAVs autonomously navigate to the emergency site to conduct a Search and Rescue (S\&R) operation for the drowning person. We introduce a Mixed-Integer Linear Programming (MILP) model to address the Facility Location Problem (FLP), assisting with identification of accessibility-optimal UAV hangar placements near the swimming area. Additionally, we present a MILP model to optimize the UAV flight trajectories in advance of the operation, allowing for efficient coordination of a heterogeneous UAV fleet. We apply the presented MILP models to a real-world scenario in the Lusatian Lake District using the state-of-the-art commercial solver CPLEX to solve the instances. Furthermore, we present a method for automated image-based swimmer localization using the state-of-the-art neural network You Only Look Once (YOLO). Finally, we use a Discrete-Event Simulation (DES) approach to quantify how much time is saved by using additional resources.}, subject = {Unmanned Aerial Vehicle; Unmanned Aircraft System; Water Rescue; Mixed-Integer Linear Programming; You Only Look Once; Drohne; Drohnenhangar; Wasserrettung; Gemischt-ganzzahlige Programmierung; Standortoptimierung; Drohne ; Wasserrettung; Lineare Optimierung}, language = {en} } @techreport{ZellFuegenschuh2025, type = {Working Paper}, author = {Zell, Sascha and F{\"u}genschuh, Armin}, title = {Optimizing autonomous unmanned aircraft system deployment locations for enhanced wildfire detection and monitoring}, doi = {10.26127/BTUOpen-6942}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-69422}, year = {2025}, abstract = {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.}, subject = {Mixed-lnteger linear programming; Unmanned aircraft systems; Micro air vehicles; Autonomous wildfire monitoring; Location-allocation optimization; Gemischt-ganzzahlige Programmierung; Drohnen; Drohnenhangar; Standortproblem; Autonome Waldbrandbek{\"a}mpfung; Waldbrand; {\"U}berwachung; Drohne (Flugk{\"o}rper); Autonomes System; Standortproblem; Lineare Optimierung}, language = {en} }