Die vorliegende Arbeit beschäftigt sich mit der Erstkoordinierung von Flughafenslots. In Europa unterliegt es der Verantwortung des jeweiligen Flughafenkoordinators zu Beginn einer Saison einen initialen Flugplan zu erstellen. Dies ist... more
Die vorliegende Arbeit beschäftigt sich mit der Erstkoordinierung von Flughafenslots. In Europa unterliegt es der Verantwortung des jeweiligen Flughafenkoordinators zu Beginn einer Saison einen initialen Flugplan zu erstellen. Dies ist eine komplexe Aufgabe und bietet hohes Potential für Optimierungsverfahren. Der Fokus dieser Arbeit liegt in der vollständig automatisierten Erstellung eines initialen Flugplans anhand heuristischer Algorithmen. Diese Arbeit wurde in engem Kontakt mit der Schedule Coordination Austria entwickelt und ein großer Schwerpunkt liegt daher in der praktischen Anwendbarkeit. Aufgrund der großen Menge an Flugdaten wurde ein heuristischer Ansatz gewählt. Erstmals wird eine Konstruktionsheuristik vorgestellt, die die Koordinierung von Flughafenslots in relativ kurzer Laufzeit ermöglicht. Zusätzlich werden heuristische Verbesserungsmethoden vorgestellt, um die Ergebnisse weiter zu optimieren. Die Erstkoordinierung basiert auf initialen Anfragen der Fluglinien für...
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In dieser Arbeit behandeln wir das Intraday Particle Therapy Patient Scheduling Problem (I-PTPSP), ein Planungsproblem für Behandlungstermine von Patienten, das in medizinischen Einrichtungen für Krebstherapien mit Synchrotrons, einem... more
In dieser Arbeit behandeln wir das Intraday Particle Therapy Patient Scheduling Problem (I-PTPSP), ein Planungsproblem für Behandlungstermine von Patienten, das in medizinischen Einrichtungen für Krebstherapien mit Synchrotrons, einem speziellen Typ von Teilchenbeschleunigern für die Strahlentherapie, auftritt. Das Problem beschreibt bevorstehende Behandlungen mit bereits zugewiesenen Terminen auf einen Zeithorizont von maximal einem Tag. Die Problematik liegt darin, dass durch unvorhergesehene Ereignisse diese Behandlungen nicht mehr zu den vorgesehenen Zeitpunkten durchgeführt werden können und deshalb der bestehende Zeitplan an die neue Situation angepasst werden muss. Dieser neue Zeitplan muss möglichst schnell erstellt werden, um negative Auswirkungen auf beispielsweise die Wartezeiten und laufenden Kosten der Einrichtung zu begrenzen. Das I-PTPSP modelliert diese Situation. Eine Besonderheit des I-PTPSP liegt in der Art und Weise wie die Behandlungen durchgeführt werden. Das S...
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Diese Arbeit behandelt eine stochastische Erweiterung des klassischen Routenplanungsproblem, die den Kundenbedarf als Zufallsvariablen betrachtet. Der Schwerpunkt wird auf die Entwicklung eines hybriden evolutionären Algorithmus zur... more
Diese Arbeit behandelt eine stochastische Erweiterung des klassischen Routenplanungsproblem, die den Kundenbedarf als Zufallsvariablen betrachtet. Der Schwerpunkt wird auf die Entwicklung eines hybriden evolutionären Algorithmus zur Lösung dieses sogennanten Vehicle Routing Problems mit stochastischem Bedarf (VRPSD) gelegt. Bei solchen Routenplanungsproblemen verlassen die Fahrzeuge das Depot mit voller Fracht, um Kunden zu bedienen, deren exakte Nachfrage jedoch zur Startzeit unbekannt ist und erst bei Ankunft genau feststeht. Das VRPSD ist ein NP-schweres kombinatorisches Optimierungsproblem. Dies bedeutet, dass es unter der Annahme von P6=NP keine Lösung in Polynomialzeit für dieses Problem gibt. Aus diesem Grund wurde ein genetischer Algorithmus entwickelt, der auf der Permutation von Knotenpunkten als Lösungskandidaten beruht, so dass eine möglichst gute Lösung in einem akzeptablen Zeitrahmen gefunden werden kann. Die Evaluierung einer solchen Permutation, die jene Positionen b...
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This article considers the two-stage fixed-charge transportation problem which models an important transportation application in a supply chain, from manufacturers to customers through distribution centers. For solving this optimization... more
This article considers the two-stage fixed-charge transportation problem which models an important transportation application in a supply chain, from manufacturers to customers through distribution centers. For solving this optimization problem we describe a hybrid algorithm that combines a steady-state genetic algorithm with a local search procedure. The computational results for an often used collection of benchmark instances show that our proposed hybrid method delivers results that are competitive to those of other state-of-the-art algorithms for solving the two-stage fixed-charge transportation problem.
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We present exact mixed integer programming approaches including branch-and-cut and branch-and-cut-and-price for the minimum label spanning tree problem as well as a variant of it having multiple labels assigned to each edge. We compare... more
We present exact mixed integer programming approaches including branch-and-cut and branch-and-cut-and-price for the minimum label spanning tree problem as well as a variant of it having multiple labels assigned to each edge. We compare formulations based on network flows and directed connectivity cuts. Further, we show how to use odd-hole inequalities and additional inequalities to strengthen the formulation. Label variables can be added dynamically to the model in the pricing step. Primal heuristics are incorporated into the framework to speed up the overall solution process. After a polyhedral comparison of the involved formulations, comprehensive computational experiments are presented in order to compare and evaluate the underlying formulations and the particular algorithmic building blocks of the overall branch-and-cut- (and-price) framework.
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Inspired by the recent success of parallelized exact methods to solve difficult scheduling problems, we present preliminary results of a general parallel beam search framework for combinatorial optimization problems. Beam search is a... more
Inspired by the recent success of parallelized exact methods to solve difficult scheduling problems, we present preliminary results of a general parallel beam search framework for combinatorial optimization problems. Beam search is a constructive metaheuristic traversing a search tree layer by layer while keeping in each layer a bounded number of promising nodes to consider many partial solutions in parallel. We propose a variant which is suitable for intra-node parallelization by multithreading with data parallelism. For sufficiently large problem instances and beam widths our work-in-progress implementation in the JIT-compiled Julia language admits promising speed-ups over 30x on 32 cores with uniform memory access for the Permutation Flow Shop Scheduling (PFSP) problem with flowtime objective.
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Optimierungsprobleme in wirklichen Einsatzszenarien bestehen oftmals aus verschiedenen, miteinander verknüpften und sich gegenseitig beeinflussenden NP-schweren Optimierungsproblemen. Daher wird in dieser Diplomarbeit das Travelling Thief... more
Optimierungsprobleme in wirklichen Einsatzszenarien bestehen oftmals aus verschiedenen, miteinander verknüpften und sich gegenseitig beeinflussenden NP-schweren Optimierungsproblemen. Daher wird in dieser Diplomarbeit das Travelling Thief Problem (TTP) näher betrachtet. Das TTP besteht aus dem bereits sehr gut erforschten Knapsack Problem (KP) und dem Travelling Salesman Problem (TSP). Beim TTP versucht ein Dieb, auf seiner Tour, so viele Gegenstände wie möglich, einzusammeln, wobei er die Maximalkapazität seines Rucksacks nicht überschreiten darf. Alle Gegenstände sind sowohl mit einem Gewicht als auch einem Profit verknüpft. Durch das Mitnehmen eines Gegenstandes erhöht der Dieb seinen Profit, aber er reduziert auch seine Reisegeschwindigkeit auf seiner restlichen Tour. Da er für seinen Rucksack eine Miete pro Zeiteinheit bezahlen muss versucht er seine Reisezeiten zu minimieren und den Profit durch eingesammelte Gegenstände zu maximieren. Ein mögliches Anwendungsszenario wäre zum...
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protein identification following deconvolution of multiply charged peaks, isotope clusters, and removal of background noise
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In this paper we present the application of an evolution strategy to the problem of detecting multi-planet transit events in photometric time-data series. Planetary transits occur when a planet regularly eclipses its host star, reducing... more
In this paper we present the application of an evolution strategy to the problem of detecting multi-planet transit events in photometric time-data series. Planetary transits occur when a planet regularly eclipses its host star, reducing stellar luminosity. The transit method is amongst the most successful detection methods for exoplanet and is presently performed by space telescope missions. The goal of
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This paper presents a genetic algorithm (GA) approach to the problem of choosing C disjoint subsets of n items to be packed into distinct containers, such that the total value of the selected items is maximized, without exceeding the... more
This paper presents a genetic algorithm (GA) approach to the problem of choosing C disjoint subsets of n items to be packed into distinct containers, such that the total value of the selected items is maximized, without exceeding the capacity of each of the containers. This so-called multiple container packing problem (MCPP) has applications in naval as well as financial management. It is a hard combinatorial optimization problem comprising similarities to the knapsack problem and the bin packing problem.A novel technique for encoding MCPP solutions is used within the GA: The genotype is a vector of numerical weights associated with the items of the problem. The corresponding phenotype is obtained by temporarily modifying the original problem according to these weights and applying a greedy decoding heuristic for the MCPP to the new problem. This solution is then evaluated using the original problem data again. Two different techniques for biasing the original problem and four decod...
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Abstract. Virtual network mapping considers the problem of fitting multiple virtual networks into one physical network in a cost-optimal way. This problem arises in Future Internet research. One of the core ideas is to utilize different... more
Abstract. Virtual network mapping considers the problem of fitting multiple virtual networks into one physical network in a cost-optimal way. This problem arises in Future Internet research. One of the core ideas is to utilize different virtual networks to cater to different application classes, each with customized protocols that deliver the required Quality-ofService. In this work we introduce a Greedy Randomized Adaptive Search Procedure (GRASP) and Variable Neighborhood Search (VNS) algorithm for solving the Virtual Network Mapping Problem. Both algorithms make use of a Variable Neighborhood Descent with ruin-and-recreate neighborhoods. We show that the VNS approach significantly outperforms the previously best known algorithms for this problem.
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The Bounded Diameter Minimum Spanning Tree problem (BDMST) and the Hop Constrained Minimum Spanning Tree problems (HCMST) are NP-hard combinatorial optimization problems which have their main application in network design. In this thesis... more
The Bounded Diameter Minimum Spanning Tree problem (BDMST) and the Hop Constrained Minimum Spanning Tree problems (HCMST) are NP-hard combinatorial optimization problems which have their main application in network design. In this thesis an existing relax-and-cut approach for finding lower bounds and approximate solutions to those problems is enhanced and extended, and a hybrid algorithm based on the relax-and-cut approach as well as on an existing metaheuristic, namely an ant colony optimization (ACO), is presented. The enhanced relax-and-cut (R&C) approach is based on an integer linear programming (ILP) formulation which relies on so called jump constraints. The number of jump constraints in this formulation is exponential by means of the instance size. Therefore, violated constraints are identified and relaxed on the fly. The enhanced R&C algorithm is a so called non deleayed relax-and-cut algorithm which is based on subgradient optimization. Since the number of separated jump in...
The longest common subsequence (LCS) problem is a prominent NP–hard optimization problem where, given an arbitrary set of input strings, the aim is to find a longest subsequence, which is common to all input strings. This problem has a... more
The longest common subsequence (LCS) problem is a prominent NP–hard optimization problem where, given an arbitrary set of input strings, the aim is to find a longest subsequence, which is common to all input strings. This problem has a variety of applications in bioinformatics, molecular biology and file plagiarism checking, among others. All previous approaches from the literature are dedicated to solving LCS instances sampled from uniform or near-to-uniform probability distributions of letters in the input strings. In this paper, we introduce an approach that is able to effectively deal with more general cases, where the occurrence of letters in the input strings follows a non-uniform distribution such as a multinomial distribution. The proposed approach makes use of a time-restricted beam search, guided by a novel heuristic named Gmpsum. This heuristic combines two complementary scoring functions in the form of a convex combination. Furthermore, apart from the close-to-uniform be...
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Longest common subsequence problems find various applications in bioinformatics, data compression and text editing, just to name a few. Even though numerous heuristic approaches were published in the related literature for many of the... more
Longest common subsequence problems find various applications in bioinformatics, data compression and text editing, just to name a few. Even though numerous heuristic approaches were published in the related literature for many of the considered problem variants during the last decades, solving these problems to optimality remains an important challenge. This is particularly the case when the number and the length of the input strings grows. In this work we define a new way to transform instances of the classical longest common subsequence problem and of some of its variants into instances of the maximum clique problem. Moreover, we propose a technique to reduce the size of the resulting graphs. Finally, a comprehensive experimental evaluation using recent exact and heuristic maximum clique solvers is presented. Numerous, so-far unsolved problem instances from benchmark sets taken from the literature were solved to optimality in this way.
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Electric vehicles represent a promising alternative to traditional internal combustion engine vehicles that might support the attainment of settled climate and energy targets. The widespread adoption of electric vehicles is complicated,... more
Electric vehicles represent a promising alternative to traditional internal combustion engine vehicles that might support the attainment of settled climate and energy targets. The widespread adoption of electric vehicles is complicated, however, by their need for frequent recharging and the rather long charging duration. Moreover, charging facilities are still relatively scarce and power constraints imposed by the electric grid have to be respected. We consider the problem of scheduling the recharging of a fleet of electric vehicles at multiple facilities with limited resources. The goal is to recharge as many vehicles as possible. Every vehicle that is scheduled for charging needs a parking spot during the entire time of its stay and shall be recharged as much as possible before departure. Facilities only have a limited number of parking spots and charging machines and a limited amount of power available for charging. Machines can work at several charging rates, but higher ones sho...
This paper considers the planning of the collection of fresh milk from local farms with a fleet of refrigerated vehicles. The problem is formulated as a version of the Periodic Vehicle Routing Problem with Time Windows. The objective... more
This paper considers the planning of the collection of fresh milk from local farms with a fleet of refrigerated vehicles. The problem is formulated as a version of the Periodic Vehicle Routing Problem with Time Windows. The objective function is oriented to the quality of service by minimizing the service times to the customers within their time windows. We developed a hybrid metaheuristic that combines GRASP and VNS to find solutions. In order to help the hybrid GRASP-VNS find high-quality and feasible solutions, we consider infeasible solutions during the search using different penalty functions.
The well known cycle double cover conjecture in graph theory is strongly related to the compatible circuit decomposition problem. A recent result by Fleischner et al. (2018) gives a sufficient condition for the existence of a compatible... more
The well known cycle double cover conjecture in graph theory is strongly related to the compatible circuit decomposition problem. A recent result by Fleischner et al. (2018) gives a sufficient condition for the existence of a compatible circuit decomposition in a transitioned 2-connected Eulerian graph, which is based on an extension of the definition of K5-minors to transitioned graphs. Graphs satisfying this condition are called SUD-K5-minor-free graphs. In this work we formulate a generalization of this property by replacing the K5 by a 4-regular transitioned graph H, which is part of the input. Furthermore, we consider the decision problem of checking for two given graphs if the extended property holds. We prove that this problem is NPcomplete and fixed parameter tractable with the size of H as parameter. We then formulate an equivalent problem, present a mathematical model for it, and prove its correctness. This mathematical model is then translated into a mixed integer linear ...
The longest common subsequence (LCS) problem is a prominent NP–hard optimization problem where, given an arbitrary set of input strings, the aim is to find a longest subsequence, which is common to all input strings. This problem has a... more
The longest common subsequence (LCS) problem is a prominent NP–hard optimization problem where, given an arbitrary set of input strings, the aim is to find a longest subsequence, which is common to all input strings. This problem has a variety of applications in bioinformatics, molecular biology and file plagiarism checking, among others. All previous approaches from the literature are dedicated to solving LCS instances sampled from uniform or near-to-uniform probability distributions of letters in the input strings. In this paper, we introduce an approach that is able to effectively deal with more general cases, where the occurrence of letters in the input strings follows a non-uniform distribution such as a multinomial distribution. The proposed approach makes use of a time-restricted beam search, guided by a novel heuristic named Gmpsum. This heuristic combines two complementary scoring functions in the form of a convex combination. Furthermore, apart from the close-to-uniform be...
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The aim of this work is to schedule the charging of electric vehicles (EVs) at a single charging station such that the temporal availability of each EV as well as the maximum available power at the station are considered. The total costs... more
The aim of this work is to schedule the charging of electric vehicles (EVs) at a single charging station such that the temporal availability of each EV as well as the maximum available power at the station are considered. The total costs for charging the vehicles should be minimized w.r.t. time-dependent electricity costs. A particular challenge investigated in this work is that the maximum power at which a vehicle can be charged is dependent on the current state of charge (SOC) of the vehicle. Such a consideration is particularly relevant in the case of fast charging. Considering this aspect for a discretized time horizon is not trivial, as the maximum charging power of an EV may also change in between time steps. To deal with this issue, we instead consider the energy by which an EV can be charged within a time step. For this purpose, we show how to derive the maximum charging energy in an exact as well as an approximate way. Moreover, we propose two methods for solving the schedu...
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This article presents a cooperative optimization approach (COA) for distributing service points for mobility applications, which generalizes and refines a previously proposed method. COA is an iterative framework for optimizing service... more
This article presents a cooperative optimization approach (COA) for distributing service points for mobility applications, which generalizes and refines a previously proposed method. COA is an iterative framework for optimizing service point locations, combining an optimization component with user interaction on a large scale and a machine learning component that learns user needs and provides the objective function for the optimization. The previously proposed COA was designed for mobility applications in which single service points are sufficient for satisfying individual user demand. This framework is generalized here for applications in which the satisfaction of demand relies on the existence of two or more suitably located service stations, such as in the case of bike/car sharing systems. A new matrix factorization model is used as surrogate objective function for the optimization, allowing us to learn and exploit similar preferences among users w.r.t. service point locations. ...
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Logic-based Benders decomposition (BD) extends classic BD by allowing more complex subproblems with integral variables. Metaheuristics like variable neighborhood search are becoming useful here for faster solving the subproblems'... more
Logic-based Benders decomposition (BD) extends classic BD by allowing more complex subproblems with integral variables. Metaheuristics like variable neighborhood search are becoming useful here for faster solving the subproblems' inference duals in order to separate approximate Benders cuts. After performing such a purely heuristic BD approach, we continue by exactly verifying and possibly correcting each heuristic cut to finally obtain a proven optimal solution. On a bi-level vehicle routing problem, this new hybrid approach exhibits shorter overall runtimes and yields excellent intermediate solutions much earlier than the classical exact method.
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Abstract In this paper, we present a novel approach towards time-series similarity search. Our technique relies on trends in a curve's movement over time. A trend is characterized by a series', values channeling... more
Abstract In this paper, we present a novel approach towards time-series similarity search. Our technique relies on trends in a curve's movement over time. A trend is characterized by a series', values channeling in a certain direction (up, down, sideways) over a given time period before changing direction. We extract trend-turning points and utilize them for computing the similarity of two series based on the slopes between their turning points. For the turning point extraction, well-known techniques from financial market analysis are ...
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ABSTRACT Free-form deformation is an efficient, intuitive, and elegant method for solid geometric modeling and soft object animation. It is defined via a set of control points initially positioned at a regular user-defined 3D lattice,... more
ABSTRACT Free-form deformation is an efficient, intuitive, and elegant method for solid geometric modeling and soft object animation. It is defined via a set of control points initially positioned at a regular user-defined 3D lattice, which embeds either the whole geometric model or just part of it. By successively deforming the 3D lattice, the model is deformed as well, e.g. into a bent, twisted or tapered model with a rather complex shape. Traditionally, the displacement of the control points is performed interactively until the final model meets the aesthetic requirements of the designer. On the other hand, e.g. in the field of practical engineering, the models have to fulfill physical requirements respectively quality criteria.In this case, the new positions of the control points need to be calculated, which is a very complex optimization task. We propose to use evolution strategies to solve this problem. The advantages and possibilities of this approach are demonstrated with one example, the calorimetric characterization of a scanner, where the results can directly be compared with the results; gained by a standard polynomial regression algorithm.