@misc{Werger2021, type = {Master Thesis}, author = {Werger, Tabea}, title = {Instandhaltungsprogramm - NH90 : ein ganzzahliger Ansatz zur Optimierung des Instandhaltungsprogramms eines milit{\"a}rischen Luftfahrzeugs}, doi = {10.26127/BTUOpen-5872}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-58724}, school = {BTU Cottbus - Senftenberg}, year = {2021}, abstract = {Die vorliegende Arbeit untersucht die Instandhaltungsplanung eines milit{\"a}rischen Luftfahrzeugs. Das Ziel ist die Eingliederung aller Instandhaltungsaufgaben des Luftfahrzeugs in Wartungsintervalle, die durch das aktuelle Instandhaltungsprogramm festgelegt sind. Dieses besteht aus bereits gem{\"a}ß ihrer Frist paketierten Instandhaltungsaufgaben und aus nicht zugeordneten Aufgaben, welche im Folgenden betrachtet werden. Gegenstand der Untersuchung sind die Arbeitsdauer und die Frist der Instandhaltungsaufgaben. Die nicht paketierten Instandhaltungsaufgaben sollen so zugeordnet werden, dass der Arbeitsaufwand und die verlorenen Tage, die durch das Vorziehen von Instandhaltungsaufgaben entstehen, auf ein Minimum reduziert werden. Daf{\"u}r wird ein multikriterielles, ganzzahliges Optimierungsmodell entwickelt. Zum L{\"o}sen wird der Solver IBM ILOG CPLEX Optimization Studio (V 20.1.0.0) verwendet. In der Auswertung wird zus{\"a}tzlich zu den Ergebnissen der Optimierung die Auswirkung von aggregierten und disaggregierten Formulierungen untersucht sowie der Effekt von Ver{\"a}nderungen der Aggressivit{\"a}t von Schnittebenenverfahren.}, subject = {Gemischt-ganzzahlige Optimierung; Hubschrauber; Instandhaltung; Planung; Schnittebenenverfahren; Mixed-integer optimization; Helicopter; Maintenance; Planning; Cutting plane method; Gemischt-ganzzahlige Optimierung; Schnittebenenverfahren; Instandhaltungsplanung}, language = {de} } @techreport{BeisegelBuhlIsraretal.2021, type = {Working Paper}, author = {Beisegel, Jesse and Buhl, Johannes and Israr, Rameez and Schmidt, Johannes and Bambach, Markus and F{\"u}genschuh, Armin}, title = {Mixed-integer programming for additive manufacturing}, doi = {10.26127/BTUOpen-5731}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-57317}, year = {2021}, abstract = {Since the beginning of its development in the 1950s, mixed integer programming (MIP) has been used for a variety of practical application problems, such as sequence optimization. Exact solution techniques for MIPs, most prominently branch-and-cut techniques, have the advantage (compared to heuristics such as genetic algorithms) that they can generate solutions with optimality certificates. The novel process of additive manufacturing opens up a further perspective for their use. With the two common techniques, Wire Arc Additive Manufacturing (WAAM) and Laser Powder Bed Fusion (LPBD), the sequence in which a given component geometry must be manufactured can be planned. In particular, the heat transfer within the component must be taken into account here, since excessive temperature gradients can lead to internal stresses and warpage after cooling. In order to integrate the temperature, heat transfer models (heat conduction, heat radiation) are integrated into a sequencing model. This leads to the problem class of MIPDECO: MIPs with partial differential equations (PDEs) as further constraints. We present these model approaches for both manufacturing techniques and carry out test calculations for sample geometries in order to demonstrate the feasibility of the approach.}, subject = {Wire arc additive manufacturing; Laser powder bed fusion; Mixed-integer programming; Partial differential equations; Finite element method; Additive Fertigung mit Drahtlichtbogen; Laser-Pulverbett-Schmelzen; Gemischt-ganzzahlige Programmierung; Partielle Differenzialgleichungen; Finite-Elemente-Methode; Rapid Prototyping ; Ganzzahlige Optimierung; Finite-Elemente-Methode; Partielle Differentialgleichung}, language = {en} } @techreport{DeeFuegenschuhKaimakamis2021, type = {Working Paper}, author = {Dee, Robin and F{\"u}genschuh, Armin and Kaimakamis, George}, title = {The unit re-balancing problem}, doi = {10.26127/BTUOpen-5658}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-56587}, year = {2021}, abstract = {We describe the problem of re-balancing a number of units distributed over a geographic area. Each unit consists of a number of components. A value between 0 and 1 describes the current rating of each component. By a piecewise linear function this value is converted into a nominal status assessment. The lowest of the statuses determines the efficiency of a unit, and the highest status its cost. An unbalanced unit has a gap between these two. To re-balance the units, components can be transferred. The goal is to maximize the efficiency of all units. On a secondary level, the cost for the re-balancing should be minimal. We present a mixed-integer nonlinear programming formulation for this problem, which describes the potential movement of components as a multi-commodity flow. The piecewise linear functions needed to obtain the status values are reformulated using inequalities and binary variables. This results in a mixed-integer linear program, and numerical standard solvers are able to compute proven optimal solutions for instances with up to 100 units. We present numerical solutions for a set of test instances and a bi-criteria objective function, and discuss the trade-off between cost and efficiency.}, subject = {Re-balancing problem; Efficiency; Mixed-integer linear programming; Bi-criteria optimization; Umverteilungsproblem; Effizienz; Gemischt-ganzzahlige Programmierung; Bikriterielle Optimierung; Ganzzahlige Optimierung; Optimierungsproblem; Effizienz}, language = {en} } @masterthesis{Roman2021, type = {Bachelor Thesis}, author = {Roman, Anschel Julio}, title = {K{\"u}nstliche neuronale Netze in biomedizinischen Anwendungen}, editor = {F{\"u}genschuh, Armin}, doi = {10.26127/BTUOpen-5630}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-56309}, school = {BTU Cottbus - Senftenberg}, year = {2021}, abstract = {Die Bachelorarbeit besch{\"a}ftigt sich mit der Entwicklung effizienter Methoden f{\"u}r die Klassifizierung der Stadien von Zellen. Hierbei liegt der Fokus auf sogenannten Deep-Learning-Algorithmen. Diese haben sich unter anderem in der Bilderkennung als sehr leistungsf{\"a}hig erwiesen und k{\"o}nnen genutzt werden, um große Mengen von mikroskopischen Zellbildern in kurzer Zeit zu klassifizieren. Aufgezeigt werden M{\"o}glichkeiten zur Optimierung solcher Algorithmen mit dem Ziel, Genauigkeit und Speichergr{\"o}ße zu verbessern. Es wurden hierbei der Einfluss von verschiedenen Parametern auf die Performance eines Algorithmus untersucht und gegen{\"u}bergestellt, verschiedene etablierte Modelle miteinander verglichen und eine Auswahl g{\"a}ngiger Methoden zur Modell-Optimierung getestet. Genutzt wurde die Software-Bibliothek TensorFlow, welche {\"u}ber die Programmiersprache Python angesprochen wird. Reale Anwendungsdaten wurden von der Firma Medipan zur Verf{\"u}gung gestellt.}, subject = {K{\"u}nstliche neuronale Netze; Tiefes Lernen; Nichtlineare Optimierung; Bilderkennung; Bildklassifizierung; Artificial neuronal networks; Deep learning; Nonlinear optimization; Image recognition; Image classification; Neuronales Netz; Mustererkennung; Deep learning; Nichtlineare Optimierung}, language = {de} } @techreport{SchmidtFuegenschuh2021, type = {Working Paper}, author = {Schmidt, Johannes and F{\"u}genschuh, Armin}, title = {Planning inspection flights with an inhomogeneous fleet of micro aerial vehicles}, doi = {10.26127/BTUOpen-5656}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-56569}, year = {2021}, abstract = {We consider the problem of planning an inspection flight to a given set of waypo- ints using an inhomogeneous fleet of multirotor, battery-driven micro aerial vehicles (MAVs). Therein, two subproblems must be solved. On the one side, the detailed trajectories of all MAVs must be planned, taking technical and environmental restrictions into account and on the other side, the MAVs must be assigned to the waypoints considering their installed equipment. The goal is to visit all waypoints in minimal time. The strong interaction of the two subproblems makes it necessary to tackle them simultaneously. Several aspects are taken into account to allow realistic solutions. A two-level time grid approach is applied to achieve smooth trajectories, while the flight dynamics of the MAVs are modeled in great detail. Safety distances must be maintained between them and they can recharge at charging stations located within the mission area. There can be polyhedral restricted air spaces that must be avoided. Furthermore, weather conditions are incorporated by polyhedral wind zones affecting the drones and each waypoint has a time window within it must be visited. We formulate this problem as a mixed-integer linear program and show whether the state-of-the-art numerical solver Gurobi is applicable to solve model instances.}, subject = {Mixed integer linear programming; Inspection path planning; Trajectory planning; Micro aerial vehicles; Gemischt-ganzzahlige Programmierung; Inspektionspfadplanung; Trajektorienplanung; Kleinstdrohnen; Ganzzahlige Optimierung; Tourenplanung; Drohne }, language = {en} } @masterthesis{Flister2021, type = {Bachelor Thesis}, author = {Flister, Tobias}, title = {Eine Heuristik zur L{\"o}sung ganzzahliger Programme mit quadratischen Nebenbedingungen}, editor = {F{\"u}genschuh, Armin}, doi = {10.26127/BTUOpen-5617}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-56175}, school = {BTU Cottbus - Senftenberg}, year = {2021}, abstract = {Die Frage nach dem L{\"o}sen von ganzzahligen Programmen mit quadratischen Nebenbedingungen spielt beim Aufbau multistatischer Sonar-Netze eine Rolle. Hierbei werden Schall-Sender und -Empf{\"a}nger in einem Ozeanabschnitt so platziert, dass m{\"o}glichst jeder Bereich durch mindestens ein Sender-Empf{\"a}nger-Paar {\"u}berwacht werden kann. Diskretisiert man den Abschnitt r{\"a}umlich, so kann die Frage nach der Platzierung durch bin{\"a}re Entscheidungsvariablen beschrieben werden. Da es auf die paarweise Platzierung ankommt, werden in den Modellen die Bin{\"a}rvariablen multipliziert, was einem logischen „Und" entspricht. Um die Modelle halbwegs schnell numerisch zu l{\"o}sen, wurden in der Literatur zahlreiche Linearisierungstechniken entwickelt und erprobt. Trotz allem Fortschritt ist man weit davon entfernt, Instanzen mit deutlich mehr als 100 Diskretisierungspunkten in annehmbarer Zeit zur Optimalit{\"a}t zu l{\"o}sen. In dieser Bachelorarbeit werden heuristische L{\"o}sungsverfahren entwickelt, welche in der Lage sind, innerhalb k{\"u}rzester Zeit gute (aber nicht beweisbar optimale) L{\"o}sungen zu liefern. Ausgangspunkt war die Grundidee, Sender und Empf{\"a}nger abwechselnd zu optimieren, bis keine weitere Verbesserung mehr eintritt. Numerische Ergebnisse werden anhand von Testinstanzen pr{\"a}sentiert und mit einem exakten Ansatz verglichen.}, subject = {Heuristiken; Ganzzahlige Programmierung; Quadratische Nebenbedingungen; Multistatisches Sonar; Netzplanung; Heuristics; Integer programming; Quadratic constraints; Multi-static sonar; Network planning; Ganzzahlige Optimierung; Heuristik; Netzplanung}, language = {de} } @techreport{SchmidtBuhlFuegenschuh2021, type = {Working Paper}, author = {Schmidt, Johannes and Buhl, Johannes and F{\"u}genschuh, Armin}, title = {A finite element approach for trajectory optimization in Wire-Arc Additive Manufacturing}, editor = {F{\"u}genschuh, Armin}, doi = {10.26127/BTUOpen-5575}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-55753}, year = {2021}, abstract = {In wire-arc additive manufacturing (WAAM), the desired workpiece is built layerwise by a moving heat source depositing droplets of molten wire on a substrate plate. To reduce material accumulations, the trajectory of the weld source should be continuous, but transit moves without welding, called deadheading, are possible. The enormous heat of the weld source causes large temperature gradients, leading to a strain distribution in the welded material which can lead even to cracks. In summary, it can be concluded that the temperature gradient reduce the quality of the workpiece. We consider the problem of finding a trajectory of the weld source with minimal temperature deviation from a given target temperature for one layer of a workpiece with welding segments broader than the width of the weld pool. The temperature distribution is modeled using the finite element method. We formulate this problem as a mixed-integer linear programming model and demonstrate its solvability by a standard mixed-integer solver.}, subject = {Additive manufacturing; Heat equation; Path optimization; Finite element method; Mixed-integer linear programming; Additive Fertigung; Pfadoptimierung; W{\"a}rmeleitungsgleichung; Finite-Elemente-Methode; Gemischt-ganzzahlige lineare Programmierung; Rapid Prototyping ; W{\"a}rmeleitungsgleichung; Bahnplanung; Ganzzahlige lineare Optimierung; Finite-Elemente-Methode}, language = {en} } @techreport{GnegelSchaudtClausenetal.2021, type = {Working Paper}, author = {Gnegel, Fabian and Schaudt, Stefan and Clausen, Uwe and F{\"u}genschuh, Armin}, title = {A 2D layered graph approach for scheduling delivery robots}, editor = {F{\"u}genschuh, Armin}, issn = {2627-6100}, doi = {10.26127/BTUOpen-5493}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-54931}, year = {2021}, abstract = {In recent years parcel volumes reached record highs. The logistics industry is seeking new innovative concepts to keep pace. For densely populated areas delivery robots are a promising alternative to conventional trucking. These electric robots drive autonomously on sidewalks and deliver urgent goods, such as express parcels, medicine, or meals. The limited cargo space and battery capacity of these vehicles necessitates a depot visit after each customer served. The problem can be formulated as an electric vehicle routing problem with soft time windows and a single unit capacity. The goal is to serve all customers such that the quadratic sum of delays is minimized and each vehicle operates within its battery bounds. To solve this problem, we formulate an MIQP and present an expanded formulation based on a layered graph. For this layered graph we derive two solution approaches based on relaxations, which use less nodes and arcs. The first, Iterative Refinement, always solves the current relaxation to optimality and refines the graph if the solution is not feasible for the expanded formulation. This is repeated until a proven optimal solution is found. The second, Branch and Refine, integrates the graph refinement into a branch and bound framework avoiding restarts. Computational experiments performed on modified Solomon instances demonstrate the advantage of using our solution approaches and show that Branch and Refine outperforms Iterative Refinement in all studied parameter configurations.}, subject = {Delivery robots; Electric vehicle routing problem; Graph refinement; Layered graphs; Partial recharging; Lieferroboter; Streckenplanung f{\"u}r elektrische Fahrzeuge; Graphenverfeinerung; Geschichtete Graphen; Partielles Aufladen; Mobiler Roboter; Tourenplanung; Optimierung}, language = {en} } @techreport{SchmidtFuegenschuh2021, type = {Working Paper}, author = {Schmidt, Johannes and F{\"u}genschuh, Armin}, title = {A two-time-level model for mission and flight planning of an inhomogeneous fleet of unmanned aerial vehicles}, editor = {F{\"u}genschuh, Armin}, doi = {10.26127/BTUOpen-5461}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-54619}, year = {2021}, abstract = {We consider the mission and flight planning problem for an inhomogeneous fleet of unmanned aerial vehicles (UAVs). Therein, the mission planning problem of assigning targets to a fleet of UAVs and the flight planning problem of finding optimal flight trajectories between a given set of waypoints are combined into one model and solved simultaneously. Thus, trajectories of an inhomogeneous fleet of UAVs have to be specified such that the sum of waypoint-related scores is maximized, considering technical and environmental constraints. Several aspects of an existing basic model are expanded to achieve a more detailed solution. A two-level time grid approach is presented to smooth the computed trajectories. The three-dimensional mission area can contain convex-shaped restricted airspaces and convex subareas where wind affects the flight trajectories. Furthermore, the flight dynamics are related to the mass change, due to fuel consumption, and the operating range of every UAV is altitude-dependent. A class of benchmark instances for collision avoidance is adapted and expanded to fit our model and we prove an upper bound on its objective value. Finally, the presented features and results are tested and discussed on several test instances using GUROBI as a state-of-the-art numerical solver.}, subject = {Mixed-integer nonlinear programming; Mission Planning; Inhomogeneous Fleet; Time Windows; Linearization methods; Gemischt-ganzzahlige nichtlineare Programming; Missionsplanung; Inhomogene Flotte; Zeitfenster; Linearisierungsmethoden; Nichtlineare Optimierung; Tourenplanung; Flugk{\"o}rper}, language = {en} } @masterthesis{TchoutoMbatchou2021, type = {Bachelor Thesis}, author = {Tchouto Mbatchou, Thierry}, title = {Training of artificial neuronal networks with nonlinear optimization techniques}, editor = {F{\"u}genschuh, Armin}, doi = {10.26127/BTUOpen-5404}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-54042}, school = {BTU Cottbus - Senftenberg}, year = {2021}, abstract = {Machine learning is a field that has been the object of study of many researchers around the globe during the last decades. Very often to solve machine learning challenges like classification problems for example, one needs to train an artificial neural network. To train this network a certain loss function has to be minimized. There is a ubiquitous approach to achieve this which consists of using variants of the stochastic gradient descent combined with the backpropagation algorithm. In our work, we aimed at testing a rather non-conventional scheme consisting of making use of the solvers a software called AMPL offers.}, subject = {Nonlinear optimization; Artificial neuronal networks; Image recognition; Nichtlineare Optimierung; K{\"u}nstliche Neuronale Netze; Bilderkennung; Bilderkennung; Neuronales Netz; Nichtlineare Optimierung; AMPL}, language = {en} }