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% Encoding: UTF-8 @COMMENT{BibTeX export based on data in FAU CRIS: https://cris.fau.de/} @COMMENT{For any questions please write to firstname.lastname@example.com} @incollection{faucris.115662844, abstract = {This paper presents cutting planes which are useful or potentially useful for solving mixed integer programs that arise in the optimisation of gas networks. We consider polyhedra that are defining essential parts of the model and give a polynomial algorithm for the calculation of the set of vertices of such polyhedra implying a polynomial separation algorithm for the convex hull of the polyhedra can be developed.}, author = {Martin, Alexander and Möller, Markus}, booktitle = {Modeling, Simulation and Optimization of Complex Processes}, editor = {H.G. Bock, E. Kostina, H.X. Phu, R. Rannacher}, faupublication = {no}, keywords = {Mixed Integer Programming; Cutting Planes; Gas Optimisation; Piecewise Linear Functions}, pages = {307 - 330}, peerreviewed = {unknown}, publisher = {Springer, Heidelberg}, title = {{Cutting} {Planes} for the {Optimisation} of {Gas} {Networks}}, year = {2005} } @incollection{faucris.203352087, abstract = {Rail freight traffic in Germany has experienced significant growth rates over the last decade, and recent forecasts expect this tendency to continue over the next 20 years due to the increases in national and international trade. Internal predictions of Deutsche Bahn AG, the most important German railway enterprise, assume a mean increase of 2{%} per year for rail freight traffic until 2030. At this pace, the German railway network in its current state would reach its capacity limit way before this date. As investments into the network infrastructure bear a very high price tag, it is crucial to use the available budget in the most efficient manner. Furthermore, the large size of the networks under consideration warrants the development of efficient algorithms to handle the complex network design problems arising for real-world data. This led us to the development of network aggregation procedures which allow for much shorter solution times by compressing the network information. More exactly, our framework works by clustering the nodes of the underlying graph to components and solving the network design problem over this aggregated graph. This kind of aggregation may either be used as a quick heuristic, or it can be extended to an exact method, e.g. by iterative refinement of the clustering, The latter results in a cutting plane algorithm, which also introduces new variables with each refinement. This idea developed in Bärmann et al. (Math Program Comput 7(2):189--217, 2015) is extended in this chapter such that it is able to incorporate the costs for routing flow through the network via lifted Benders optimality cuts. Altogether, our algorithm can be seen as a novel kind of Benders decomposition which allows to shift variables from the subproblem to the master problem in the process. Computations on several benchmark sets demonstrate the effectiveness of the approach.}, address = {Cham}, author = {Bärmann, Andreas and Liers, Frauke}, booktitle = {Handbook of Optimization in the Railway Industry}, doi = {10.1007/978-3-319-72153-8_3}, editor = {Borndörfer R, Klug T, Lamorgese L, Mannino C, Reuther M, Schlechte T}, faupublication = {yes}, isbn = {978-3-319-72153-8}, pages = {47--72}, peerreviewed = {Yes}, publisher = {Springer International Publishing}, title = {{Aggregation} {Methods} for {Railway} {Network} {Design} {Based} on {Lifted} {Benders} {Cuts}}, year = {2018} } @misc{faucris.112073544, abstract = {Runways are one of the most valuable recourses in Air Traffic Management (ATM) and need to be managed as efficiently as possible. At the airports, usually one planning tool schedules the arrivals (arrival planner), whereas another tool schedules the departures (departure planner). These separate planners are coordinated by some cooperation tool. In this paper, we address the question whether this planning strategy is or could ever be (almost) optimal. In fact, there could be situations in which an integrated planner that schedules both arrivals and departures simultaneously might compute considerably better schedules.
In this work, we study the runway scheduling problem with aircraft precedences and safety distance constraints. We consider two extreme scenarios. In the best-case scenario, the two planners cooperate completely in order to determine optimized schedules. In the worst-case scenario, however, the planning tools compete and act as adversaries. Using techniques from mathematical optimization, we model these two scenarios. We experimentally evaluate the approaches on randomly generated instances with respect to running times for solving the problems to global optimality and with respect to the computed throughput. On small examples, we show that indeed there can be large differences in the runway utilization in the two scenarios. It would be interesting to investigate whether today's real schedules are closer to the best-case or closer to the worst-case scenario in order to understand whether the development, implementation and maintenance of an integrated tool could pay off.}, author = {Liers, Frauke and Martin, Alexander and Peter, Andrea}, faupublication = {yes}, peerreviewed = {automatic}, title = {{Mathematical} {Analysis} of {Runway} {Scheduling} with {Aircraft} {Precedences}}, year = {2017} } @article{faucris.120013784, abstract = {We study the transient optimization of gas transport networks including both discrete controls due to switching of controllable elements and nonlinear fluid dynamics described by the system of isothermal Euler equations, which are partial differential equations in time and 1-dimensional space. This combination leads to mixed-integer optimization problems subject to nonlinear hyperbolic partial differential equations on a graph. We propose an instantaneous control approach in which suitable Euler discretizations yield systems of ordinary differential equations on a graph. This networked system of ordinary differential equations is shown to be well-posed and affine-linear solutions of these systems are derived analytically. As a consequence, finite-dimensional mixed-integer linear optimization problems are obtained for every time step that can be solved to global optimality using general-purpose solvers. We illustrate our approach in practice by presenting numerical results on a realistic gas transport network.}, author = {Gugat, Martin and Leugering, Günter and Martin, Alexander and Schmidt, Martin and Sirvent, Mathias and Wintergerst, David}, doi = {10.1007/s10589-017-9970-1}, faupublication = {yes}, journal = {Computational Optimization and Applications}, keywords = {Mixed-integer optimal control, Instantaneous control, Partial differential equations on graphs, Gas networks, Mixed-integer linear optimization.}, pages = {267-294}, peerreviewed = {Yes}, title = {{MIP}-based instantaneous control of mixed-integer {PDE}-constrained gas transport problems}, volume = {70}, year = {2018} } @inproceedings{faucris.120545084, address = {Darmstadt}, author = {Martin, Alexander}, booktitle = {Suffizienz in der Baukultur: Besser, Anders, Weniger}, editor = {U.~Kunkel}, faupublication = {yes}, pages = {18 -- 19}, peerreviewed = {No}, publisher = {Konradin Medien GmbH}, series = {db-{Kongress} 2014}, title = {{Diskrete} {Optimierung} als {Anregung} für {Suffizienz}-{Strategien}}, year = {2014} } @misc{faucris.205829426, abstract = {In the course of the energy transition, load and supply centers are growing apart in many electricity markets worldwide, rendering regional price signals even more important to provide adequate locational investment incentives. In this context, the establishment of price zones in order to at least partially price grid bottlenecks is under discussion. This paper addresses the key question of how to configure price zones on a network in order to optimally govern investment and production decisions in the long run. We extend the multilevel equilibrium model from Grimm et al. (2017a) to endogenously determine welfare-maximizing price zones for a given electricity market and analyze their impact on market outcomes. This mixed-integer nonlinear model contains a graph partitioning problem on the first level to model the zoning of the network. Using a generalized Benders decomposition and a problem-tailored scenario clustering for reducing the input data size, we are able to solve the model to global optimality even for large instances. We apply the approach to the German electricity market as an example to examine the impact of optimal zoning on key performance indicators such as welfare, generation mix and locations, or electricity prices. It turns out that already a few optimally chosen zones lead to significant welfare gain}, author = {Ambrosius, Mirjam and Grimm, Veronika and Kleinert, Thomas and Liers, Frauke and Schmidt, Martin and Zöttl, Gregor}, faupublication = {yes}, keywords = {Electricity Markets; Price Zones; Investment Incentives; Multilevel Optimization; Graph Partitioning}, peerreviewed = {automatic}, title = {{Endogenous} {Price} {Zones} and {Investment} {Incentives} in {Electricity} {Markets}: {An} {Application} of {Multilevel} {Optimization} with {Graph} {Partitioning}}, url = {http://www.optimization-online.org/DB_HTML/2018/10/6868.html}, year = {2018} } @inproceedings{faucris.108914344, author = {Martin, Alexander and et al.}, author_hint = {U.~Günther, A.~Martin, T.~Shang}, booktitle = {Tagungsband 2. Zwischenkolloqium {SFB} 666}, editor = {P.~Groche}, faupublication = {no}, pages = {29 -- 34}, peerreviewed = {No}, publisher = {Meisenbach Verlag, Bamberg}, support_note = {Author relations incomplete. You may find additional data in field 'author_hint'}, title = {{Integration} von {Fertigungsrestriktionen} - {Ein} {Ansatz} aus der {Graphentheorie}}, year = {2008} } @misc{faucris.122404304, abstract = {In this paper we show how to use an old mathematical concept of diophantine analysis, the approximation theorem of Kronecker, in symmetric cryptography. As a rst practical application we propose and analyze the new symmetric 128-bit block cipher KronCrypt. The cipher is a 4-round Feistel network with a non-bijective round function f made up of a variable number of large key-dependent S-boxes, XORs and modular additions. Its key length is variable but not less than 128 bit. The main innovation of KronCrypt in the area of symmetric cryptography is the fact that the key-dependent S-boxes are based upon a constructive proof of the approximation theorem of Kronecker used as a boolean function. We prove the correctness of our concept in general and show how we designe the new cipher KronCrypt. Furthermore, results concerning statistical behaviour, i.e. confusion, diusion and completeness, and dierential cryptanalysis are presented.}, author = {Elsner, Carsten and Schmidt, Martin}, faupublication = {no}, peerreviewed = {automatic}, title = {{KronCrypt} - {A} {New} {Symmetric} {Cryptosystem} {Based} on {Kronecker}'s {Approximation} {Theorem}}, url = {http://eprint.iacr.org/}, year = {2009} } @incollection{faucris.115669224, author = {Günther, Ute and Martin, Alexander and Ritter, Klaus and Wagner, Tim}, booktitle = {PAMM, Proceedings of Applied Mathematics and Mechanics}, faupublication = {no}, pages = {667 - 668}, peerreviewed = {unknown}, title = {{Cash} {Recycling} {Systems}: {Prediction} and {Optimization}}, volume = {6}, year = {2006} } @article{faucris.120541564, abstract = {In many rural counties pupils on their way to school are a large, if not the largest group of customers for public mass transit. Hence an effective optimization of public mass transit in these regions must include the traffic caused by pupils. Besides a change in the schedules of the buses and the starting times of the trips, the school starting time may become an integral part of the planning process. We discuss the legal framework for this optimization problem in German states and counties and present a multi-objective mixed-integer linear programming formulation for the simultaneous specification of school and trip starting times. For its solution, we develop a two stage decomposition heuristic and apply it to practical data sets from three different rural German counties.}, author = {Fügenschuh, Armin-René and Martin, Alexander}, faupublication = {no}, journal = {Annals of Operations Research}, keywords = {Mixed-integer programming; Multicriteria optimization; Multiple traveling salesman problem; Time windows}, pages = {119 -- 216}, peerreviewed = {Yes}, title = {{A} {Multicriterial} {Approach} for {Optimizing} {Bus} {Schedules} and {School} {Starting} {Times}}, volume = {147}, year = {2006} } @incollection{faucris.117699164, abstract = {Complex real-world optimization tasks often lead to mixed-integer nonlinear problems (MINLPs). However, current MINLP algorithms are not always able to solve the resulting large-scale problems. One remedy is to develop problem specific primal heuristics that quickly deliver feasible solutions. This paper presents such a primal heuristic for a certain class of MINLP models. Our approach features a clear distinction between nonsmooth but continuous and genuinely discrete aspects of the model. The former are handled by suitable smoothing techniques; for the latter we employ reformulations using complementarity constraints. The resulting mathematical programs with equilibrium constraints (MPEC) are finally regularized to obtain MINLP-feasible solutions with general purpose NLP solvers.}, author = {Schmidt, Martin and Steinbach, Marc C. and Willert, Bernhard M.}, booktitle = {Facets of Combinatorial Optimization}, doi = {10.1007/978-3-642-38189-8_13}, editor = {Jünger M, Reinelt G}, faupublication = {no}, isbn = {978-3-642-38188-1}, pages = {295-320}, peerreviewed = {Yes}, publisher = {Springer Berlin Heidelberg}, title = {{A} {Primal} {Heuristic} for {Nonsmooth} {Mixed} {Integer} {Nonlinear} {Optimization}}, year = {2013} } @phdthesis{faucris.106579264, author = {Schmidt, Martin}, faupublication = {no}, peerreviewed = {automatic}, school = {Friedrich-Alexander-Universität Erlangen-Nürnberg}, title = {{A} {Generic} {Interior}-{Point} {Framework} for {Nonsmooth} and {Complementarity} {Constrained} {Nonlinear} {Optimization}}, year = {2013} } @article{faucris.115665924, abstract = {A hierachy of simplified models for traffic flow on networks is derived from continuous traffic flow models based on partial differential equations. The hierachy contains nonlinear and linear combinatorial models with and without dynamics. Optimization problems are treated for all models and numerical results and algorithms are compared.}, author = {Fügenschuh, Armin-René and Herty, Michael and Klar, Axel and Martin, Alexander}, faupublication = {no}, journal = {SIAM Journal on Optimization}, keywords = {Combinatorial methods; Partial differential equations; Traffic networks}, pages = {1155 -- 1176}, peerreviewed = {Yes}, title = {{Combinatorial} and {Continuous} {Models} for the {Optimization} of {Traffic} {Flows} on {Networks}}, volume = {16}, year = {2006} } @article{faucris.122464804, abstract = {In this paper we study the Steiner tree problem with degree constraints. Motivated by an application in computational biology we focus on binary Steiner trees in which all node degrees are required to be at most three. It is shown that finding a binary Steiner tree is NP-complete for arbitrary graphs. We relate the problem to Steiner trees without degree constraints as well as degree-constrained spanning trees by proving approximation ratios. Further, we give integer programming formulations for this problem on undirected and directed graphs and study the associated polytopes for both cases. Some classes of facets are introduced. Based on this study a branch-&-cut approach is developed and evaluated on biological instances coming from the reconstruction of phylogenetic trees. We are able to solve nearly all instances up to 200 nodes to optimality within a limited amount of time. This shows the effectiveness of our approach.}, author = {Liers, Frauke and Martin, Alexander and Pape, Susanne}, doi = {10.1016/j.disopt.2016.05.006}, faupublication = {yes}, journal = {Discrete Optimization}, keywords = {Steiner tree; Degree constraint; Steiner ratio; Integer programming; Polytope; Branch-&-cut}, pages = {85-117}, peerreviewed = {Yes}, title = {{Binary} {Steiner} {Trees}: {Structural} {Results} and an {Exact} {Solution} {Approach}}, volume = {21}, year = {2016} } @incollection{faucris.115686384, author = {Epe, Alexa and Mahlke, Debora and Martin, Alexander and Wagner, Herman-Josef and Weber, Christoph and Woll, Oliver and Zelmer, Andrea}, booktitle = {Innovative Modellierung und Optimierung von Energiesystemen}, editor = {R. Schultz, H.-J. Wagner}, faupublication = {no}, pages = {153 --178}, peerreviewed = {unknown}, publisher = {LIT Verlag}, title = {{Betriebsoptimierung} zur ökonomischen {Bewertung} von {Speichern}}, year = {2009} } @inproceedings{faucris.119108924, address = {Bamberg}, author = {Pruckner, Marco and Thurner, Christoph and Martin, Alexander and German, Reinhard}, booktitle = {MMB & DFT 2014, Proceedings of the International Workshop SOCNET 2014 and FGENET 2014}, editor = {K.~Fischbach, M.~Großmann, U.~Krieger, T.~Staake}, faupublication = {yes}, pages = {97 -- 104}, peerreviewed = {Yes}, title = {{A} {Coupled} {Optimization} and {Simulation} {Model} for the {Energy} {Transition}}, volume = {16}, year = {2014} } @article{faucris.115672084, abstract = {In this paper we present a simulated annealing approach for the gas network optimization problem. A gas network consists of a set of pipes to transport the gas from the sources to the sinks whereby gas pressure gets lost due to friction. Further on there are compressors, which increase gas pressure, and valves. The aim is to minimize fuel gas consumption of the compressors whereas demands of consumers have to be satisfied. The problem of transient (time-dependent) optimization of gas networks results in a highly complex mixed integer nonlinear program. We relax the equations describing the gas dynamic in pipes by adding these constraints combined with appropriate penalty factors to the objective function. A suitable neighborhood structure is developed for the relaxed problem where time steps as well as pressure and flow of the gas are decoupled. Our approach convinces with flexibility and very good computational results.}, author = {Mahlke, Debora and Martin, Alexander and Moritz, Susanne}, faupublication = {no}, journal = {Mathematical Methods of Operations Research}, keywords = {Heuristics; Mixed integer nonlinear programming; Relaxation; Simulated annealing; Transient gas optimization}, pages = {99 -- 116}, peerreviewed = {Yes}, title = {{A} simulated annealing algorithm for transient optimization in gas networks}, volume = {66}, year = {2007} } @article{faucris.119464224, abstract = {We consider optimal control problems for gas flow in pipeline networks. The equations of motion are taken to be represented by a first-order system of hyperbolic semilinear equations derived from the fully nonlinear isothermal Euler gas equations. We formulate an optimal control problem on a network and introduce a tailored time discretization thereof. In order to further reduce the complexity, we consider an instantaneous control strategy. The main part of the paper is concerned with a nonoverlapping domain decomposition of the optimal control problem on the graph into local problems on smaller sub-graphs - ultimately on single edges. We prove convergence of the domain decomposition method on networks and study the wellposedness of the corresponding time-discrete optimal control problems. The point of the paper is that we establish virtual control problems on the decomposed subgraphs such that the corresponding optimality systems are in fact equal to the systems obtained via the domain decomposition of the entire optimality system.}, author = {Leugering, Günter and Martin, Alexander and Schmidt, Martin and Sirvent, Mathias}, faupublication = {yes}, journal = {Control and Cybernetics}, keywords = {Optimal control; Gas networks; Euler's equation; Semilinear PDE; Nonoverlapping domain decomposition}, pages = {191-225}, peerreviewed = {Yes}, title = {{Nonoverlapping} {Domain} {Decomposition} for {Optimal} {Control} {Problems} governed by {Semilinear} {Models} for {Gas} {Flow} in {Networks}}, volume = {46}, year = {2017} } @article{faucris.115672964, abstract = {For a long time product development is trying to break down the design process to single steps that allow for an uninterrupted computer-aided and algorithm-based design process. One goal of the Collaborative Research Centre 666 is the "automated" design of integral, bifurcated sheet metal parts. The final 3D CAD-model is generated based on a mathematically optimized geometry which in turn defined by product-specific individual customer requirements.}, author = {Anderl, Reiner and Kormann, Marco and Rollmann, Thomas and Wu, Zhenyu and Martin, Alexander and Ulbrich, Stefan and Günther, Ute}, faupublication = {no}, journal = {Konstruktion}, pages = {79 -- 82}, peerreviewed = {Yes}, title = {{An} {Approach} to {Algorithm}-{Based} {Design} in {Product} {Development}}, volume = {5}, year = {2007} } @incollection{faucris.110561704, abstract = {
}, author = {Schmidt, Martin and Steinbach, Marc C. and Willert, Bernhard M.}, booktitle = {Evaluating Gas Network Capacities}, doi = {10.1137/1.9781611973693.ch9}, editor = {Koch T, Hiller B, Pfetsch ME, Schewe L}, faupublication = {yes}, pages = {163-180}, peerreviewed = {Yes}, publisher = {SIAM}, series = {SIAM-MOS series on Optimization}, title = {{An} {MPEC} based heuristic}, year = {2015} } @incollection{faucris.119769364, abstract = {In this article, we present a new algorithm for the solution of nonconvex mixed-integer nonlinear optimization problems together with an application from gas network optimization, the gas transport energy cost minimization problem. Here, the aim is to transport gas through the network at minimum operating cost. The proposed algorithm is based on the adaptive refinement of a new class of MIP-relaxations and has been developed within an industry project on gas network optimization. Since therefore the implementation is not as general as it could be, our computational results are restricted to instances from gas network optimization at this point of time. However, as these problems are real-world applications and turn out to be rather hard to solve with the aid of state-of-the-art MINLP-solvers we believe that our computational results reveal the potential of this new approach and motivate further research on the presented techniques.}, address = {Berlin Heidelberg}, author = {Geißler, Björn and Morsi, Antonio and Schewe, Lars}, booktitle = {Facets of Combinatorial Optimization}, doi = {10.1007/978-3-642-38189-8_14}, editor = {Jünger M, Reinelt G}, faupublication = {yes}, isbn = {9783642381881}, pages = {321-353}, peerreviewed = {unknown}, publisher = {Springer-Verlag}, title = {{A} new algorithm for {MINLP} applied to gas transport energy cost minimization}, year = {2013} } @article{faucris.115667024, abstract = {This paper reports on the fourth version of the Mixed Integer Programming Library. Since MIPLIB is to provide a concise set of challenging problems, it became necessary to purge instances that became too easy. We present an overview of the 27 new problems and statistical data for all 60 instances.}, author = {Achterberg, Tobias and Koch, Thorsten and Martin, Alexander}, doi = {10.1016/j.orl.2005.07.009}, faupublication = {no}, journal = {Operations Research Letters}, keywords = {IP; MIP; MIPLIB; Mixed Integer Programming; Problem instances}, pages = {1--12}, peerreviewed = {Yes}, title = {{MIPLIB} 2003}, volume = {34}, year = {2006} } @misc{faucris.202208666, abstract = {We consider an extended version of the classical Max-k-Cut problem in which we additionally require that the parts of the graph partition are connected. For this problem we study two alternative mixed-integer linear formulations and review existing as well as develop new branch-and-cut techniques like cuts, branching rules, propagation, primal heuristics, and symmetry breaking. The main focus of this paper is an extensive numerical study in which we analyze the impact of the different techniques for various test sets. It turns out that the techniques from the existing literature are not sufficient to solve an adequate fraction of the test sets. However, our novel techniques significantly outperform the existing ones both in terms of running times and the overall number of instances that can be solved}, author = {Hojny, Christopher and Joormann, Imke and Lüthen, Hendrik and Schmidt, Martin}, faupublication = {yes}, keywords = {Max-cut; Connectivity; Branch-and-cut; Mixed-integer programming}, peerreviewed = {automatic}, title = {{Mixed}-{Integer} {Programming} {Techniques} for the {Connected} {Max}-k-{Cut} {Problem}}, url = {http://www.optimization-online.org/DB_HTML/2018/07/6738.html}, year = {2018} } @incollection{faucris.110458964, abstract = {Efficient planning of runway utilization is one of the main challenges in Air Traffic Management (ATM). In a previous paper, we developed a specific optimization approach for the pre-tactical planning phase that reduces complexity by omitting unnecessary information. Further, we investigated the impact of disturbances on our solutions, since in reality uncertainty and inaccuracy almost always lead to deviations from actual plans. In this paper, we now present approaches to incorporate uncertainty directly in our model in order to achieve a stabilization with respect to changes in the data. Namely, we use techniques from robust optimization and stochastic optimization. Further, we analyze real-world data from a large German airport to obtain realistic delay distributions, which turn out to be two-parametric Γ-distributions. We describe a simulation environment and test our new solution methods against standard algorithms (e.g., First-Come-First-Serve). The encouraging results show that our approaches significantly reduce the number of necessary replan nings.}, author = {Fürstenau, Norbert and Heidt, Andreas and Kapolke, Manu and Liers, Frauke and Mittendorf, Monika and Weiß, Christian}, booktitle = {Proceedings of the SESAR Innovations Days 2015}, editor = {Dirk Schäfer}, faupublication = {yes}, keywords = {runway utilization; planning,pre-tactical; optimization; uncertainties; stochastic; robust; algorithms; models; validation; Monte Carlo simulation}, peerreviewed = {unknown}, publisher = {Eurocontrol}, title = {{Pre}-{Tactical} {Planning} of {Runway} {Utilization} {Under} {Uncertainty}: {Optimization} and {Validation}}, year = {2015} } @article{faucris.117575744, abstract = {In this paper we investigate whether matrices arising from linear or integer programming problems can be decomposed into so-called bordered block diagonal form. More precisely, given some matrix A, we try to assign as many rows as possible to some number β of blocks of size script K such that no two rows as signed to different blocks intersect in a common column. Bordered block diagonal form is desirable because it can guide and speed up the solution process for linear and integer programming problems. We show that various matrices from the linear programming and mixed integer programming libraries Netlib and Miplib can indeed be decomposed into this form by computing optimal decompositions or decompositions with proven quality. These computations are done with a branch-and-cut algorithm based on polyhedral investigations of the matrix decomposition problem. In practice, however, one would use heuristics to find a good decomposition. We present several heuristic ideas and test their performance. Finally, we investigate the usefulness of optimal matrix decompositions into bordered block diagonal form for integer programming by using such decompositions to guide the branching process in a branch-and-cut code for general mixed integer programs.}, author = {Borndörfer, Ralf and E. Ferreira, Carlos and Martin, Alexander}, faupublication = {no}, journal = {SIAM Journal on Optimization}, keywords = {Block structure of a sparse matrix; Cutting planes; Integer programming; Matrix decomposition; Polyhedral combinatorics}, pages = {236 -- 269}, peerreviewed = {Yes}, title = {{Decomposing} {Matrices} into {Blocks}}, volume = {9}, year = {1998} } @article{faucris.115660864, abstract = {We present a new generalization called reliability branching of today's state-of-the-art strong branching and pseudocost branching strategies for linear programming based branch-and-bound algorithms. After reviewing commonly used branching strategies and performing extensive computational studies we compare different parameter settings and show the superiority of our proposed new strategy.}, author = {Achterberg, Tobias and Koch, Thorsten and Martin, Alexander}, faupublication = {no}, journal = {Operations Research Letters}, keywords = {Branch-and-bound; Mixed-integer-programming; Pseudocost-branching; Reliability-branching; Strong-branching; Variable selection}, pages = {42 -- 54}, peerreviewed = {Yes}, title = {{Branching} {Rules} {Revisited}}, volume = {33}, year = {2005} } @article{faucris.117660444, abstract = {Efficient planning of runway utilization is one of the main challenges in Air Traffic Management (ATM). It is important because runway is the combining element between airside and groundside. Furthermore, it is a bottleneck in many cases. In this paper, we develop a specific optimization approach for the pre-tactical planning phase that reduces complexity by omitting unnecessary information. Instead of determining arrival/departure times to the minute in this phase yet, we assign several aircraft to the same time window of a given size. The exact orders within those time windows can be decided later in tactical planning. Mathematically, we solve a generalized assignment problem on a bipartite graph. To know how many aircraft can be assigned to one time window, we consider separation requirements for consecutive aircraft types. In reality, however, uncertainty and inaccuracy almost always lead to deviations from the actual plan or schedule. Thus, we present approaches to incorporate uncertainty directly in our model in order to achieve a stabilization with respect to changes in the data. Namely, we use techniques from robust optimization and stochastic optimization. Further, we analyze real-world data from a large German airport to obtain realistic delay distributions, which turn out to be two-parametric Γ-distributions. Finally, we describe a simulation environment to test our new solution methods.}, author = {Kapolke, Manu and Fürstenau, Norbert and Heidt, Andreas and Liers, Frauke and Mittendorf, Monika and Weiß, Christian}, doi = {10.1016/j.jairtraman.2016.02.004}, faupublication = {yes}, journal = {Journal of Air Transport Management}, keywords = {Pre-tactical planning; Runway; Optimization; Uncertainty; Robustness; Data analysis}, peerreviewed = {Yes}, title = {{Pre}-tactical optimization of runway utilization under uncertainty}, year = {2016} } @incollection{faucris.121811184, abstract = {In this paper we survey the basic features of state-of-the-art branch-and-cut algorithms for the solution of general mixed integer programming problems. In particular we focus on preprocessing techniques, branch-and-bound issues and cutting plane generation.}, author = {Martin, Alexander}, booktitle = {Computational Combinatorial Optimization}, editor = {D. Naddef, M. Jünger}, faupublication = {no}, peerreviewed = {unknown}, publisher = {Springer, Berlin}, title = {{General} {Mixed} {Integer} {Programming}: {Computational} {Issues} for {Branch}-and-{Cut} {Algorithms}}, year = {2001} } @incollection{faucris.122314984, abstract = {
}, author = {Hiller, Benjamin and Humpola, Jesco and Lehmann, Thomas and Lenz, Ralf and Morsi, Antonio and Pfetsch, Marc E. and Schewe, Lars and Schmidt, Martin and Schwarz, Robert and Schweiger, Jonas and Stangl, Claudia and Willert, Bernhard M.}, booktitle = {Evaluating Gas Network Capacities}, doi = {10.1137/1.9781611973693.ch12}, editor = {Koch T, Hiller B, Pfetsch ME, Schewe L}, faupublication = {yes}, pages = {233-270}, peerreviewed = {Yes}, publisher = {SIAM}, series = {SIAM-MOS series on Optimization}, title = {{Computational} results for validation of nominations}, year = {2015} } @incollection{faucris.119107824, abstract = {Steiner trees are constructed to connect a set of terminal nodes in a graph. This basic version of the Steiner tree problem is idealized, but it can effectively guide the search for successful approaches to many relevant variants, from both a theoretical and a computational point of view. This article illustrates the theoretical and algorithmic progress on Steiner tree type problems on two examples, the Steiner connectivity and the Steiner tree packing problem.}, author = {Borndörfer, Ralf and Hoang, Nam Dung and Karbstein, Marika and Koch, Thorsten and Martin, Alexander}, booktitle = {Facets of Combinatorial Optimization}, editor = {Michael JÜnger and Gerhard Reinelt}, faupublication = {yes}, pages = {215--244}, peerreviewed = {Yes}, publisher = {Springer}, title = {{How} {Many} {Steiner} {Terminals} {Can} {You} {Connect} in 20 {Years}?}, year = {2013} } @misc{faucris.115699584, author = {Geißler, Björn and Kolb, Oliver and Lang, Jens and Leugering, Günter and Martin, Alexander and Morsi, Antonio}, faupublication = {yes}, peerreviewed = {automatic}, title = {{Mixed} {Integer} {Linear} {Models} for the {Optimization} of {Dynamical} {Transport} {Networks}}, year = {2010} } @article{faucris.123414324, author = {Gottschalk, Corinna and Koster, Arie and Liers, Frauke and Peis, Britta and Schmand, Daniel and Wierz, Andreas}, doi = {10.1007/s10107-017-1170-3}, faupublication = {yes}, journal = {Mathematical Programming}, keywords = {05C21 Flows in graphs, 90C05 Linear programming, 90C59 Approximation methods and heuristics, 90C46 Optimality conditions, duality}, peerreviewed = {Yes}, title = {{Robust} flows over time: models and complexity results}, year = {2017} } @article{faucris.118421644, abstract = {In this paper, we study the problem of technical transient gas network optimization, which can be considered a minimum cost flow problem with a nonlinear objective function and additional nonlinear constraints on the network arcs. Applying an implicit box scheme to the isothermal Euler equation, we derive a mixed-integer nonlinear program. This is solved by means of a combination of (i) a novel mixed-integer linear programming approach based on piecewise linearization and (ii) a classical sequential quadratic program applied for given combinatorial constraints. Numerical experiments show that better approximations to the optimal control problem can be obtained by using solutions of the sequential quadratic programming algorithm to improve the mixed-integer linear program. Moreover, iteratively applying these two techniques improves the results even further.}, author = {Domschke, Pia and Geißler, Björn and Kolb, Oliver and Lang, Jens and Martin, Alexander and Morsi, Antonio}, doi = {10.1287/ijoc.1100.0429}, faupublication = {yes}, journal = {Informs Journal on Computing}, keywords = {gas networks; optimal control; mixed-integer programming; nonlinear programming; sequential quadratic programming}, pages = {605-617}, peerreviewed = {Yes}, title = {{Combination} of {Nonlinear} and {Linear} {Optimization} of {Transient} {Gas} {Networks}}, volume = {23}, year = {2011} } @article{faucris.111112144, abstract = {Nonconvex mixed-binary nonlinear optimization problems frequently appear in practice and are typically extremely hard to solve. In this paper we discuss a class of primal heuristics that are based on a reformulation of the problem as a mathematical program with equilibrium constraints. We then use different regularization schemes for this class of problems and use an iterative solution procedure for solving series of regularized problems. In the case of success, these procedures result in a feasible solution of the original mixed-binary nonlinear problem. Since we rely on local nonlinear programming solvers the resulting method is fast and we further improve its reliability by additional algorithmic techniques. We show the strength of our method by an extensive computational study on 662 MINLPLib2 instances, where our methods are able to produce feasible solutions for 60% of all instances in at most 10s.}, author = {Schewe, Lars and Schmidt, Martin}, doi = {10.1007/s12532-018-0141-x}, faupublication = {yes}, journal = {Mathematical Programming Computation}, keywords = {Mixed-Integer Nonlinear Optimization, MINLP, MPEC, Complementarity Constraints, Primal Heuristic.}, peerreviewed = {unknown}, title = {{Computing} {Feasible} {Points} for {Binary} {MINLPs} with {MPECs}}, url = {http://www.optimization-online.org/DB_HTML/2016/12/5778.html}, year = {2018} } @incollection{faucris.123585484, author = {Handschin, Edmund and Waniek, Daniel and Martin, Alexander and Mahlke, Debora and Zelmer, Andrea}, booktitle = {Optimierung in der Energiewirtschaft, VDI-Berichte Nr. 2018}, faupublication = {no}, pages = {133 -- 146}, peerreviewed = {Yes}, title = {{Gekoppelte} optimale {Auslegung} von {Strom}-, {Gas}- und {Wärmenetzen}}, year = {2007} } @article{faucris.106529764, abstract = {The development of mathematical simulation and optimization models and algorithms for solving gas transport problems is an active field of research. In order to test and compare these models and algorithms, gas network instances together with demand data are needed. The goal of GasLib is to provide a set of publicly available gas network instances that can be used by researchers in the field of gas transport. The advantages are that researchers save time by using these instances and that different models and algorithms can be compared on the same specified test sets. The library instances are encoded in an XML format. In this paper, we explain this format and present the instances that are available in the library.}, author = {Schmidt, Martin and Aßmann, Denis and Burlacu, Robert and Humpola, Jesco and Joormann, Imke and Kanelakis, Nikolaos and Koch, Thorsten and Oucherif, Djamal and Pfetsch, Marc E. and Schewe, Lars and Schwarz, Robert and Sirvent, Mathias}, doi = {10.3390/data2040040}, faupublication = {yes}, journal = {Data}, keywords = {Gas Transport; Networks; Problem Instances; Mixed-Integer Nonlinear Optimization; GasLib}, peerreviewed = {Yes}, title = {{GasLib} - {A} {Library} of {Gas} {Network} {Instances}}, url = {http://www.optimization-online.org/DB_HTML/2015/11/5216.html}, volume = {2}, year = {2017} } @article{faucris.122769284, abstract = {Economic reasons and the regulation of gas markets create a growing need for mathematical optimization of natural gas networks. Real life planning tasks often lead to highly complex and extremely challenging optimization problems whose numerical treatment requires a breakdown into several simplified problems to be solved by carefully chosen hierarchies of models and algorithms. This paper presents stationary NLP type models of gas networks that are primarily designed to include detailed nonlinear physics in the final optimization steps for mid term planning problems after fixing discrete decisions with coarsely approximated physics.}, author = {Schmidt, Martin and Steinbach, Marc C. and Willert, Bernhard M.}, doi = {10.1007/s11081-014-9246-x}, faupublication = {yes}, journal = {Optimization and Engineering}, keywords = {Gas networks; Stationary flow; High-detail modeling; Nonsmooth nonlinear discrete-continuous optimization; Smoothing techniques}, pages = {131-164}, peerreviewed = {Yes}, title = {{High} detail stationary optimization models for gas networks}, volume = {16}, year = {2015} } @incollection{faucris.115646564, author = {Martin, Alexander}, booktitle = {Encyclopedia of Life Support Systems (EOLSS)}, faupublication = {no}, pages = {411 -- 428}, peerreviewed = {No}, publisher = {UNESCO}, title = {{Large} {Scale} {Optimization}}, year = {2002} } @article{faucris.121780824, abstract = {Potential-based flows are an extension of classical network flows in which the flow on an arc is determined by the difference of the potentials of its incident nodes. Such flows are unique and arise, for example, in energy networks. Two important algorithmic problems are to determine whether there exists a feasible flow and to maximize the flow between two designated nodes. We show that these problems can be solved for the single source and sink case by reducing the network to a single arc. However, if we additionally consider switches that allow to force the flow to 0 and decouple the potentials, these problems are NP-hard. Nevertheless, for particular series-parallel networks, one can use algorithms for the subset sum problem. Moreover, applying network presolving based on generalized series-parallel structures allows to significantly reduce the size of realistic energy network}, author = {Groß, Martin and Pfetsch, Marc E. and Schewe, Lars and Schmidt, Martin and Skutella, Martin}, doi = {10.1002/net.21865}, faupublication = {yes}, journal = {Networks}, keywords = {Maximum flow problem, Network reduction, Potential networks, Potential-based flows, Series-parallel graphs.}, peerreviewed = {Yes}, title = {{Algorithmic} {Results} for {Potential}-{Based} {Flows}: {Easy} and {Hard} {Cases}}, url = {http://www.optimization-online.org/DB_HTML/2017/08/6185.html}, year = {2018} } @article{faucris.106159284, abstract = {In this paper a combined optimization of a coupled electricity and gas system is presented. For the electricity network a unit commitment problem with optimization of energy and reserves under a power pool, considering all system operational and unit technical constraints is solved. The gas network subproblem is a medium-scale mixed-integer nonconvex and nonlinear programming problem. The coupling constraints between the two networks are nonlinear as well. The resulting mixed-integer nonlinear program is linearized with the extended incremental method and an outer approximation technique. The resulting model is evaluated using the Greek power and gas system comprising fourteen gas-fired units under four different approximation accuracy levels. The results indicate the efficiency of the proposed mixed-integer linear program model and the interplay between computational requirements and accuracy.}, author = {Sirvent, Mathias and Kanelakis, Nikolaos and Geißler, Björn and Biskas, Pandelis}, doi = {10.1007/s40565-017-0275-2}, faupublication = {yes}, journal = {Journal of Modern Power Systems and Clean Energy}, pages = {364 - 374}, peerreviewed = {Yes}, title = {{A} {Linearized} {Model} for the {Optimization} of the {Coupled} {Electricity} and {Natural} {Gas} {System}}, url = {https://link.springer.com/article/10.1007%2Fs40565-017-0275-2}, volume = {5}, year = {2017} } @article{faucris.119101664, abstract = {A gas network consists of pipes to transport the gas from the suppliers to the consumers. Due to friction with the pipe walls, gas pressure gets lost. Compressors compensate this pressure loss at the cost of consuming fuel gas. The aim of gas network optimization is to minimize the fuel gas consumption of the compressors in such a way that the contracts with consumers and suppliers are fulfilled. This problem leads to a very complex mixed integer nonlinear optimization problem. We present a linear approach which concentrates on time-dependent and discrete aspects. The nonlinearities are approximated by piece-wise linear functions using the concept of SOS constraints. We develop a branch-and-cut algorithm which has the potential to guarantee global optimality of the linearized problem where the nonlinearities are approximated within a given accuracy. We include an adequate handling of the SOS conditions and a separation algorithm for switching processes of compressors. A simulated annealing algorithm is included yielding feasible solutions. Our computational results show the success of our approach in this challenging field of gas network optimization.}, author = {Mahlke, D. and Martin, Alexander and Moritz, S.}, doi = {10.1080/10556780903270886}, faupublication = {no}, journal = {Optimization Methods and Software}, keywords = {mixed integer programming; transient gas optimization; piece-wise linear approximation; SOS condition; branch-and-cut}, pages = {625 -- 644}, peerreviewed = {Yes}, title = {{A} {Mixed} {Integer} {Approach} for {Time}-{Dependent} {Gas} {Network} {Optimization}}, volume = {25}, year = {2010} } @article{faucris.122465684, abstract = {
The runway is the main element that combines airside and groundside of the ATM System. Thus, it is crucial to develop efficient models and planning algorithms for its effective usage. The best planning algorithm, however, is useless if the resulting plans cannot be implemented in the real world. This often happens because the input data of the planning algorithms face disturbances or changes over time, respectively. For example, an estimated time of arrival/departure of an aircraft may be changed. It is usually not certain for the next ten hours.
In this work, we study the runway scheduling problem under uncertain conditions. First, we present mathematical optimization models that ignore uncertainties. In the most effective approach, we compute for every discretized point in time whether an aircraft is scheduled and if so, which one is. Then, in each planning step we take uncertainties into account. We then apply different robust optimization methods in order to devise solution approaches that lead to stable plans. These optimization approaches are integrated into a simulation tool and evaluated in different traffic scenarios.
The Monte-Carlo simulations for a mixed-mode runway system show that our robust approaches result in fewer sequence changes and target time updates, when compared to the usual approach in which the plan is simply updated in case of infeasibility. Thus, we show that protection against uncertainties by using robust optimization indeed leads to considerably more stable plans.
}, author = {Heidt, Andreas and Helmke, Hartmut and Kapolke, Manu and Liers, Frauke and Martin, Alexander}, doi = {10.1016/j.jairtraman.2016.02.009}, faupublication = {yes}, journal = {Journal of Air Transport Management}, keywords = {Scheduling; Uncertainty; Time-indexed model; MIP; Mixed-integer programming; Dynamic time-indexed model; Strict robustness; Light robustness}, pages = {28-37}, peerreviewed = {Yes}, title = {{Robust} runway scheduling under uncertain conditions}, volume = {56}, year = {2016} } @article{faucris.118144224, abstract = {In this work, we report about the results of a joint research project between Friedrich–Alexander–Universität Erlangen–Nürnberg and Deutsche Bahn AG on the optimal expansion of the German railway network until 2030. The need to increase the throughput of the network is given by company-internal demand forecasts that indicate an increase in rail freight traffic of about 50% over the next two decades. Our focus is to compute an optimal investment strategy into line capacities given an available annual budget, i.e., we are to choose the most profitable lines to upgrade with respect to the demand scenario under consideration and to provide a schedule according to which the chosen measures are implemented. This leads to a multiperiod network design problem—a class of problems that has received increasing interest over the past decade. We develop a mixed-integer programming formulation to model the situation and solve it via a novel decomposition approach that we call multiple-knapsack decomposition. The method can both be used as a quick heuristic and allows for the extension to an exact algorithm for the problem. We demonstrate its potential by solving a real-world problem instance provided by Deutsche Bahn AG and use the results as the basis for a broad case study for the expansion of the German railway network until 2030.}, author = {Bärmann, Andreas and Martin, Alexander and Schuelldorf, Hanno}, doi = {10.1287/trsc.2017.0747}, faupublication = {yes}, journal = {Transportation Science}, keywords = {railway transport; multiperiod network design; decomposition; infrastructure planning; mixed-integer programming}, peerreviewed = {Yes}, title = {{A} {Decomposition} {Method} for {Multiperiod} {Railway} {Network} {Expansion} - {With} a {Case} {Study} for {Germany}}, year = {2017} } @misc{faucris.213204500, abstract = {Bilevel problems are highly challenging optimization problems that appear in many applications of energy market design, critical infrastructure defense, transportation, pricing, etc. Often, these bilevel models are equipped with integer decisions, which makes the problems even harder to solve. Typically, in such a setting in mathematical optimization one develops primal heuristics in order to obtain feasible points of good quality quickly or to enhance the search process of exact global methods. However, there are comparably few heuristics for bilevel problems. In this paper we develop such a primal heuristic for bilevel problems with mixed-integer linear or quadratic upper level and linear or quadratic lower level. The heuristic is based on a penalty alternating direction method, which also allows for a theoretical analysis. We derive a convergence theory stating that the method converges to a stationary point of an equivalent single-level reformulation of the bilevel problem. Finally, we extensively test the method on a large instance set and illustrate its good performance both in terms of running times and solution qualit}, author = {Kleinert, Thomas and Schmidt, Martin}, faupublication = {yes}, peerreviewed = {automatic}, title = {{Computing} {Stationary} {Points} of {Bilevel} {Problems} with a {Penalty} {Alternating} {Direction} {Method}}, url = {http://www.optimization-online.org/DB_HTML/2019/03/7117.html}, year = {2019} } @article{faucris.110059444, abstract = {In 2005 the European Union liberalized the gas market with a disruptive change and decoupled trading of natural gas from its transport. The gas is now transported by independent so-called transmissions system operators or TSOs. The market model established by the European Union views the gas transmission network as a black box, providing shippers (gas traders and consumers) the opportunity to transport gas from any entry to any exit. TSOs are required to offer the maximum possible capacities at each entry and exit such that any resulting gas flow can be realized by the network. The revenue from selling these capacities more than one billion Euro in Germany alone, but overestimating the capacity might compromise the security of supply. Therefore, evaluating the available transport capacities is extremely important to the TSOs.
The runway system is the main element that combines airside and groundside of the ATM System. Efficient models and planning algorithms are required. The best planning algorithm, however, is useless if the resulting plans cannot be implemented in the real word. This often happens because the input data of the planning algorithms is disturbed respectively it changes. For example, an estimated time of an aircraft is not stable for the next ten hours. These disturbances are not deterministic, but often their stochastic distributions with mean values and standard deviations are known. We present a robust model together with an optimization algorithm which explicitly incorporates the knowledge of uncertainty into each planning step. Our approach transforms the planning problem into an assignment problem with side constraints. We compute for every discretized point in time whether an aircraft is scheduled and if so, which one is. Experimentally, we show that running times are better than when using a different non-linear integer optimization model. Our Monte-Carlo simulation for a mixed-mode runway system shows that our approach results in fewer sequence changes and target time updates compared to the usual approach of just updating the plan if the actual plan is not feasible any more.}, author = {Heidt, Andreas and Helmke, Hartmut and Liers, Frauke and Martin, Alexander}, booktitle = {Proceedings of the SESAR Innovation Days 2014}, editor = {D.~Schäfer}, faupublication = {yes}, isbn = {978-2-87497-077-1}, keywords = {scheduling, uncertainty, time-indexed model, MIP, mixed-integer programming, dynamic time-indexed model, mixed mode runway scheduling}, peerreviewed = {unknown}, title = {{Robust} {Runway} {Scheduling} using a time-indexed model}, year = {2014} } @article{faucris.204075926, author = {Grimm, Veronika and Schewe, Lars and Schmidt, Martin and Zöttl, Gregor}, doi = {10.1007/s00186-018-0647-z}, faupublication = {yes}, journal = {Mathematical Methods of Operations Research}, peerreviewed = {Yes}, title = {{A} multilevel model of the {European} entry-exit gas market}, year = {2018} } @inproceedings{faucris.119872104, address = {Düsseldorf}, author = {Steber, David and Seifert, Gaby and Thurner, Christoph and Pruckner, Marco and Luther, Matthias and Martin, Alexander and German, Reinhard}, booktitle = {VDI-Berichte 2303}, date = {2017-11-08/2017-11-09}, editor = {VDI Wissensforum GmbH}, faupublication = {yes}, isbn = {978-3-18-092303-1}, pages = {3-16}, peerreviewed = {No}, publisher = {VDI Verlag GmbH}, title = {{KOSiNeK} - {Kombinierte} {Optimierung}, {Simulation} und {Netzanalyse} des elektrischen {Energiesystems} {Deutschlands} im europäischen {Kontext} - {Projektvorstellung} und erste {Ergebnisse}}, venue = {Würzburg}, year = {2017} } @misc{faucris.121873444, author = {Martin, Alexander}, faupublication = {no}, peerreviewed = {automatic}, title = {{Integer} programs with block structure}, year = {1999} } @inproceedings{faucris.203351150, abstract = {In this paper, we demonstrate how to learn the objective function of a decision maker while only observing the problem input data and the decision maker's corresponding decisions over multiple rounds. Our approach is based on online learning techniques and works for linear objectives over arbitrary sets for which we have a linear optimization oracle and as such generalizes previous work based on KKT-system decomposition and dualization approaches. The applicability of our framework for learning linear constraints is also discussed briefly. Our algorithm converges at a rate of O(1/sqrt(T)), and we demonstrate its effectiveness and applications in preliminary computational results.}, address = {International Convention Centre, Sydney, Australia}, author = {Bärmann, Andreas and Pokutta, Sebastian and Schneider, Oskar}, booktitle = {Proceedings of the 34th International Conference on Machine Learning (ICML)}, editor = {Precup D, Teh YW}, faupublication = {yes}, pages = {400--410}, peerreviewed = {Yes}, publisher = {PMLR}, series = {Proceedings of Machine Learning Research}, title = {{Emulating} the {Expert}: {Inverse} {Optimization} through {Online} {Learning}}, url = {http://proceedings.mlr.press/v70/barmann17a.html}, volume = {70}, year = {2017} } @article{faucris.123844644, author = {Hübner, Jens and Steinbach, Marc C. and Schmidt, Martin}, doi = {10.1287/ijoc.2017.0748}, faupublication = {yes}, journal = {Informs Journal on Computing}, pages = {612-630}, peerreviewed = {Yes}, title = {{A} {Distributed} {Interior}-{Point} {KKT}-{Solver} for {Multistage} {Stochastic} {Problems}}, url = {http://www.optimization-online.org/DB_HTML/2016/02/5318.html}, volume = {29}, year = {2017} } @incollection{faucris.108907964, author = {Fügenschuh, Armin-René and Hess, Wolfgang and Martin, Alexander and Ulbrich, Stefan}, booktitle = {Tagungsband 1. Zwischenkolloqium SFB 666}, editor = {P. Groche}, faupublication = {no}, pages = {37 -- 47}, peerreviewed = {unknown}, publisher = {Meisenbach Verlag, Bamberg}, title = {{Diskrete} und kontinuierliche {Modelle} zur {Topologie}- und {Geometrie}-{Optimierung} von {Blechprofilen}}, year = {2007} } @article{faucris.119135324, abstract = {We show that the edge graph of a 6-dimensional polytope with 12 facets has diameter at most 6, thus verifying the d-step conjecture of Klee and Walkup in the case d = 6. This implies that for all pairs (d, n) with n - d ≤ 6, the diameter of the edge graph of a d-polytope with n facets is bounded by 6, which proves the Hirsch conjecture for all n - d ≤ 6. We prove this result by establishing this bound for a more general structure, so-called matroid polytopes, by reduction to a small number of satisfiability problems. © Taylor & Francis Group, LLC.}, author = {Bremner, David and Schewe, Lars}, doi = {10.1080/10586458.2011.564965}, faupublication = {yes}, journal = {Experimental Mathematics}, keywords = {Diameter; Hirsh conjecture; Oriented matroids; Polytopes; Satisfiability}, pages = {229-237}, peerreviewed = {Yes}, title = {{Edge}-graph diameter bounds for convex polytopes with few facets}, volume = {20}, year = {2011} } @article{faucris.123587684, abstract = {We consider a flow network where the flow of parts can be controlled at the vertices of the network. Based on a modified coarse grid discretization presented in Fügenschuh et al. (SIAM J Scientific Comput 30(3):1490-1507, 2008) we derive a mixed-integer program (MIP). Under suitable assumptions on the cost functional we prove that there exists an equivalent linear program (LP). We present numerical results concerning validity of our result and show the improvement of the computing times using the equivalent LP over the MIP.}, author = {Fügenschuh, Armin-René and Goettlich, S. and Herty, Michael and Kirchner, C. and Martin, Alexander}, doi = {10.1007/s00607-009-0038-7}, faupublication = {no}, journal = {Computing}, keywords = {Adjoint calculus; Conservation laws; Flow networks; Networks}, pages = {245 -- 265}, peerreviewed = {Yes}, title = {{Efficient} {Reformulation} and {Solution} of a {Nonlinear} {PDE}-{Controlled} {Flow} {Network} {Model}}, volume = {85}, year = {2009} } @article{faucris.108901584, abstract = {This survey presents cutting planes that are useful or potentially useful in solving mixed integer programs. Valid inequalities for (i) general integer programs, (ii) problems with local structure such as knapsack constraints, and (iii) problems with 0-1 coefficient matrices, such as set packing, are examined in turn. Finally, the use of valid inequalities for classes of problems with structure, such as network design, is explored.}, author = {Martin, Alexander and et al.}, author_hint = {H.~Marchand, A.~Martin, R.~Weismantel, L.A.~Wolsey}, doi = {10.1016/S0166-218X(01)00348-1}, faupublication = {no}, journal = {Discrete Applied Mathematics}, keywords = {Cutting planes; Mixed integer programming}, pages = {391 -- 440}, peerreviewed = {Yes}, support_note = {Author relations incomplete. You may find additional data in field 'author_hint'}, title = {{Cutting} {Planes} in {Integer} and {Mixed} {Integer} {Programming}}, volume = {123/124}, year = {2002} } @incollection{faucris.120542664, author = {Günther, Ute and Martin, Alexander}, booktitle = {Tagungsband 1. Zwischenkolloqium SFB 666}, editor = {P. Groche}, faupublication = {no}, pages = {47 -- 53}, peerreviewed = {No}, publisher = {Meisenbach Verlag, Bamberg}, title = {{Modellierung} von {Fertigungsrestriktionen} bei der {Herstellung} von verzweigten {Blechbauteilen}}, year = {2007} } @article{faucris.117696964, author = {Domschke, Pia and Groß, Martin and Hante, Falk and Hiller, Benjamin and Schewe, Lars and Schmidt, Martin}, faupublication = {yes}, journal = {Gas und Wasserfach, Gas, Erdgas}, pages = {880-885}, peerreviewed = {No}, title = {{Mathematische} {Modellierung}, {Simulation} und {Optimierung} von {Gastransportnetzwerken}}, url = {https://www.di-verlag.de/de/Zeitschriften/gwf-Gas-Erdgas/2015/11/Mathematische-Modellierung-Simulation-und-Optimierung-von-Gastransportnetzwerken}, volume = {156}, year = {2015} } @article{faucris.117696524, abstract = {When considering cost-optimal operation of gas transport networks, compressor stations play the most important role. Proper modeling of these stations leads to nonconvex mixed-integer nonlinear optimization problems. In this article, we give an isothermal and stationary description of compressor stations, state MINLP and GDP models for operating a single station, and discuss several continuous reformulations of the problem. The applicability and relevance of different model formulations, especially of those without discrete variables, is demonstrated by a computational study on both academic examples and real-world instances. In addition, we provide preliminary computational results for an entire network.}, author = {Rose, Daniel and Schmidt, Martin and Steinbach, Marc C. and Willert, Bernhard M.}, doi = {10.1007/s00186-016-0533-5}, faupublication = {yes}, journal = {Mathematical Methods of Operations Research}, keywords = {Discrete-continuous nonlinear optimization; Gas networks; Gas compressor stations; Mixed-integer optimization; Continuous reformulations}, pages = {409--444}, peerreviewed = {Yes}, title = {{Computational} optimization of gas compressor stations: {MINLP} models versus continuous reformulations}, url = {http://www.optimization-online.org/DB_HTML/2h015/02/4793.html}, volume = {83}, year = {2016} } @article{faucris.120544204, abstract = {We deal with the optimization of the production of branched sheet metal products. New forming techniques for sheet metal give rise to a wide variety of possible profiles and possible ways of production. In particular, we show how the problem of producing a given profile geometry can be modeled as a discrete optimization problem. We provide a theoretical analysis of the model in order to improve its solution time. In this context we give the complete convex hull description of some substructures of the underlying polyhedron. Moreover, we introduce a new class of facet-defining inequalities that represent connectivity constraints for the profile and show how these inequalities can be separated in polynomial time. Finally, we present numerical results for various test instances, both real-world and academic examples.


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'Go Clean Label certified' scheme rolls out, but what does it mean?
from Food Navigator-USA
A new "clean label" certification scheme has been launched in the U.S. market as the concept of "clean" eating continues to gain traction. But will consumer packaged goods brands embrace the "Go Clean Label Certified" logo, and are there risks to using a term that lacks a clear legal definition on food packaging?
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Addicts should also be aware that while dating someone else in recovery can be a great support system, it can also lead to being triggered to relapse by your partners behavior. You can talk about who you really are and what you really want instead of your drinking habits or, more appropriately, lack thereof. You can watch thousands of Italian dating personal ads and get in touch with them all. If you are not ready for dating then please wait until you are. If so, then you came to the right place! Going to the bar to meet someone is out of the question, and even the mainstream dating sites are likely to garner suggestions to meet for drinks after work. The site is free as well, and allows you to connect with over 11,000 sober singles across the country. People are searching for a partner who corresponds to their preferences and desires.
Let Sober Singles Connect You With Others Who are Living Sober Lives The Dating World Can Be Difficult to Navigate When You're Sober. It starts with cost recovery. Keep Your Sobriety Intact at Sober-Dating If you're like most people, it took you a while to finally get sober. Plus, there are no set up fees, monthly fees, device fees, or cancellation fees or contracts. Instead Connect With Sober Singles From the Comfort of Your Own Home and See Who You Could Date Today! This site offered the basic. Without our sobriety, we have nothing! And would it not be wise to date a sober person? I enjoy walking by the bay or the beach and even some.
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Thirty years ago, brainstorming sessions were much in vogue. A group of people would gather in a room to create solutions to problems by throwing out their ideas willy-nilly, feeding off each other's thoughts.
It remains a useful technique today and is no doubt still widely used. Now, with the help of your personal computer, you can hold a one-person brainstorming session. It's done with a program called the Idea Generator ($195), published by Experience in Software Inc., 2039 Shattuck Ave., Suite 401, Berkeley, Calif. 94704, telephone (415) 644-0694.
The software costs $195 and runs on IBM PC and compatible computers with 256 kilobytes of random access memory (RAM) and either two floppy disk drives or a hard disk. It is the work of author and attorney Gerard I. Nierenberg and is based on his book, "The Art of Creative Thinking."
Nierenberg's approach is to stimulate creative problem solving by forcing one to think in new ways and from new perspectives.
By using the computer, Nierenberg makes it easy for users to follow his step-by-step methods. The program does this by asking the user questions, the answers to which generate new questions.
Three Stages
There are three stages to the process: (1) describing the problem or situation, (2) finding possible solutions, and (3) evaluating the solutions. It's not necessarily a simple, straightforward process, however, since you may find in your evaluations that the problem was not adequately defined or that possible solutions were overlooked.
A useful feature allows you to transfer your ideas back and forth from either of two outlining programs, ThinkTank or Ready!, or a word processing program.
You begin by describing the situation you want to solve. Let's say you want a substantially higher income in 1986, so you type in: "I want to earn more money this year."
Next you have to list your goals, one per line on the screen, such as:
- Avoid loss of present fringe and retirement benefits.
- Avoid taking a second job.
- Avoid relocating.
- Be able to take more exotic vacations.
Then it's time to list the people involved in the situation, which includes those who will be affected by the change, those who can help bring it about and those whose approval must be obtained. In this case, the list would include yourself, family members, your boss, business contacts and so on.
Now you have to generate ideas that may solve your problem. Here, the program forces you to look at things from various points of view. It asks you to list similar situations and then to find a metaphor for your situation and think of different ways to approach that metaphorical problem. The program gives you some examples of how to do this.
You are asked then to apply those metaphorical approaches to your own situation and list any new ideas that are generated. Another technique is to ask you to look at the situation from the perspective of someone else--perhaps someone involved whom you listed earlier or some other person, real or imagined.
For instance, you might want to look at your situation the way you imagine a rich uncle would approach it.
Yet another technique used by the program is to ask you for ideas based on satisfying each of your goals singly, as if each were your only goal. That prevents you from discarding ideas just because they don't meet all of your goals.
A more exotic technique employed in the program is called double reversal. First you list the direct opposite of each of your goals and then think of ways to reach those reversed goals. Then you reverse those ideas, and the final result should be a new approach to a familiar situation.
The opposite of not taking a second job, for instance, could be starting a new business of your own on the side. One way to start would be to take a community college course in small business. The reverse of that idea could be to teach a course using your expertise in your present field of endeavor.
Focusing on the people involved in your situation is another way the program forces you to look at the problem, listing the positive and negative factors associated with both those who seem to be blocking your way and those who can help you attain your goals.
Ultimately you will end up with a list of ideas. Then it is time to summarize and finally evaluate them.
You decide whether to evaluate the single best idea, several ideas or even all of your ideas, giving each a rating between 1 and 9, corresponding to lowest and highest on the rating scale. The criteria upon which you base such ratings is how well the idea meets each of your listed goals.
Assessing Ideas
A final evaluation method remains, and that is to assess your ideas in terms of their costs, benefits and effects on people.
As you can probably guess from the description of the idea-generation process, it is not simple and straightforward. You should expect to work backward and forward through the various elements of the program as discoveries in one section cause you to refine previous goals and idea descriptions. You may even have to revise your original statement of the problem.
What the Idea Generator really does is force you to think systematically. The ideas that result are yours, not the computer's.
As with any computerized system, however, what you get out of it can be no better that what you put into it. You may conclude, for instance, that the best way to make more money in 1986, within the confines of the goals that you have set for yourself, is to play the Lottery more often. Good luck.
If you like the Idea Generator, you may also like its predecessor program, the Art of Negotiating, also by Nierenberg, which sells for $495 and is based on his book of the same title.


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This is a Jupiter 846RL intermediate flugelhorn. It features a .433" bore, a yellow brass tunable leadpipe, a rose brass 6" bell, monel piston valves, a third valve trigger and a lacquer finish. This was made in Taiwan. The instrument plays great. The horn looks almost brand new. There are just a few very minor surface scratches and one spot were there might have been a very minor dent that was sm ...
One of the nicest flugelhorns we've had in a while. This Artist model has a beautiful tone and resonates as a flugelhorn should. The silver plating has wear in some places but hasn't affected the playability of the horn. All pistons and slides have been checked out by our on-site technician and the instrument comes with a hard shell case.
Up for sale is a single French horn under the Holton name. Typical of a student French horn, this horn has some wear issues. Underneath the hand hold for the left hand at the keys, there is some lacquer wear as well as several small dents. These will in no way affect the playability of this instrument. The lacquer wear continues down the instrument towards the bell. No dents can be found ...
This student model Bach FH200 Flugelhorn is the perfect first flugel for any trumpet player. It's built with strong durability and, like all Bach products, offers a wide array of tones, such as the warm lower register you hear in most flugelhorns and the ability to play brightly in the higher register. This horn is in very good condition, only showing a little bit of oxidation on the 3rd valve sli ...
This Grand Prix Flugelhorn has a clear, smooth, mellow sound. Made by Antoine Courtois in Paris this is a vintage horn with a Raw Brass finish which gives it a distinctive antique look. As with any horn of this age, there are cosmetic flaws such as scratches, dents and wear on the finish which do not detract from the playability or sound of the instrument. There are signs of soldering and repairs ...
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By Juliet Delorme. Contemporary. Published at Thursday, January 17th, 2019 - 16:39:57 PM.
Think twice before you buy or create an open floor plan, as there are some things that may not work as well as you think.
If you're the type of person that likes to host some entertaining dinners or evenings in general, this could be the best way to do it – you can place much more people by having larger living spaces. The traffic and airiness of the room is maintained, allowing a more communicative vibe.
For the types that want a satisfying view of a wide and open space, an open floor plan is the ideal setting as it adds to the aesthetic and gives a warmer feeling because of the shared space. It enhances communication and brings families closer. There is a wide range of benefits to consider when thinking about an open floor plan.
The best way to do this is by decorating with colors that match the ones on the art piece.
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Characteristics to Help You Get to Choose a Perfect Fun.
Everyone wants to have that excellent hobby to get to spur his/her life. Getting to choose a perfect hobby for yourself is a factor to consider for having a perfect hobby is an essential factor to your happiness. Choose your hobby intentional to see it has a remarkable impact on your life.There are aspects to consider for you to come up with a perfect hobby for yourself. Selecting arts one should get to choose the right one for they are crucial. Hobbies get to have different impacts some will generate money, others will cost you and others will be neutral. Selecting hobbies depends on the person choosing, and the aims he/she has other will choose a hobby that will generate additional money like singing in weddings. Know the type of hobby you want to engage in for there are hobbies that will bring about money generation and can be a perfect choice to that individual looking forward to earning from his/her hobby.
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Paddling Film Festival
Spring rivers are flowing! Get inspired for the season ahead with two and a half hours of short films that... View ArticleApril 25, 2019
Spring rivers are flowing! Get inspired for the season ahead with two and a half hours of short films that... View ArticleApril 25, 2019
What are the impacts of the tree canopy in the National Capital Region? Learn more on the findings of a... View ArticleApril 24, 2019
The Adirondacks, though not technically in Ottawa, are a popular go-to for local skiers, paddlers, mountain bikers, and hikers. With... View ArticleApril 14, 2019
Camp Fortune has been granted permission to build a summer luge run.April 12, 2019
Did Ottawa beat the record for most-days-with-snow-on-the-ground? Unclear...April 12, 2019
Mackfest 2019 planning has started, this year's lead is Eric Chaplin, KWP's club president. Kawartha Whitewater Paddlers club hosts and organizes... View ArticleApril 12, 2019
Join us for our last Cafe scientifique of the season! Donna Dubreuil, from the Ottawa-Carleton Wildlife Centre will be our... View ArticleApril 8, 2019
Hawaiian Hula Beach Party this Saturday April 6th! The first true Spring Skiing weather forecast is looking perfect for this... View ArticleApril 7, 2019
When day becomes night, when the sun gives way to the moon and stars, when nocturnal animals wake … it's... View ArticleApril 5, 2019
Local mountain bike trail builders TerraScult are hiring for the summer!April 2, 2019


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Popular stories, page 10
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Hannah has always seen things. Since she turned fifteen she has been stalked by a ghost. When she moves to San Diego from LA she expects a fresh start. But they get worse and Vic Fuentes has something to do with it.
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Perrentes! Sequel to Skin and Bones! <3
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Words: Josh Millar
Images: Offside Sports Photgraphy (Main) / Sky Sports (Body)
Man United and Man City fans tend to argue a lot on the internet. One of their main gripes is Who Has The Best Goalkeeper In The Premier League out of Ederson and David de Gea. The answer is neither. Apparently.
Stats from Sky Sports and World In Motion show that, over all competitions in 2018–19, Liverpool's Alisson Becker has stopped the most shots in the Premier League, with Spurs' Hugo Lloris behind him in second, while Arsenal's Bernd Leno is in third.
Among the top 6 goalkeepers, Lloris ranks highest in that reliable old xG column, for expected goals saved. Of the 104 shots he's faced this season, he's conceded just 27 goals despite the stats showing he apparently should have conceded 33. Although those statistics can be misleading due to the form of the rest of their team, the Spurs man has saved nearly two more goals than his nearest rival, Allison, who has saved nearly five more goals than expected.
Down in the bottom half of the mini-table of top 6 'keepers, Ederson hasn't excelled in keeping out shots that were expected to go in, and has conceded exactly as many goals as he should have. While Chelsea's Kepa Arrizabalaga has let in two more goals than he should have, David de Gea has conceded over half-a-goal(?) more.
In terms of errors leading directly to goals, The Premier League reports that Lloris hasn't made a single error that lead to one in the Premier League, Allison and Leno have made three each, while de Gea has made two.
Who has the best keeper in the league? Martin Dúbravka is statistically the most consistent, so maybe Newcastle can claim victory. That's the real quiz.
For more great football writing about stuff you actually care about, you can buy our magazine or subscribe for a year here.


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