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 = {

In this chapter we discuss the problem of validation of nominations as a nonsmooth and nonconvex mixed-integer nonlinear feasibility problem. For this problem we present a primal heuristic that is based on reformulation techniques that smooth the appearing nonsmooth aspects and that reformulate discrete aspects with complementarity constraints and problem specific relaxations. The resulting mathematical program with equilibrium constraints (MPEC) model can be regularized by standard techniques leading to a nonlinear program (NLP) type model. Solutions to the latter can finally be used as approximative solutions to the underlying feasibility problem.

}, 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

The different approaches to solve the validation of nomination problem presented in the previous chapters are evaluated computationally in this chapter. Each approach is analyzed individually, as well as the complete solvers for these problems. We demonstrate that the presented approaches can successfully solve large-scale real-world instances.

}, 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-call

This is a report on a large project in mathematical optimization, set out to develop a new toolset for evaluating gas network capacities. The goals and the challenges as they occurred in the project are described, as well as the developments and design decisions taken to meet the requirements.

}, author = {Hiller, Benjamin and Koch, Thorsten and Schewe, Lars and Schwarz, Robert and Schweiger, Jonas}, doi = {10.1016/j.ejor.2018.02.035}, faupublication = {yes}, journal = {European Journal of Operational Research}, keywords = {OR in energy; Natural gas network optimization; Entry-exit model; Transport network capacity; Large-scale mixed-integer nonlinear programming}, pages = {797-808}, peerreviewed = {Yes}, title = {{A} {System} to {Evaluate} {Gas} {Network} {Capacities}: {Concepts} and {Implementation}}, volume = {270}, year = {2018} } @article{faucris.115641064, author = {Martin, Alexander}, faupublication = {no}, journal = {Mathematical Methods of Operations Research}, pages = {277 -- 284}, peerreviewed = {Yes}, title = {{A} polynomially solvable case of the separation problem for the {Steiner} partition inequalities}, volume = {62}, year = {1990} } @incollection{faucris.108905104, abstract = {We develop a primal heuristic based on a genetic algorithm for the minimum graph bisection problem and incorporate it in a branch-and-cut framework. The problem concerns partitioning the nodes of a weighted graph into two subsets such that the total weight of each set is within some lower and upper bounds. The objective is to minimize the total cost of the edges between both subsets of the partition. We formulate the problem as an integer program. In the genetic algorithm the LP-relaxation of the IP-formulation is exploited. We present several ways of using LP information and demonstrate the computational success.}, author = {Armbruster, Michael and Fügenschuh, Marzena and Helmberg, Christoph and Jetchev, Nikolay and Martin, Alexander}, booktitle = {Proceedings of 6th European Conference, EvoCOP 2006, Budapest, Hungary, April 10-12, 2006}, doi = {10.1007/11730095_1}, faupublication = {no}, pages = {1-12}, peerreviewed = {unknown}, publisher = {Springer, Berlin}, series = {Lecture Notes in Computer Science}, title = {{Hybrid} {Genetic} {Algorithm} {Within} {Branch}-and-{Cut} for the {Minimum} {Graph} {Bisection} {Problem}}, volume = {3906}, year = {2006} } @incollection{faucris.115675384, address = {Dresden}, author = {Wäldele, Martin and Fügenschuh, Armin-René and Birkhofer, Herbert and Martin, Alexander}, booktitle = {5. Gemeinsames Kolloquium Konstruktionstechnik 2007}, faupublication = {no}, pages = {73 - 82}, peerreviewed = {unknown}, title = {{Algorithmenbasierte} {Produktentwicklung} für integrale {Blechbauweisen} höherer {Verzweigungsordnung}}, year = {2007} } @article{faucris.124196424, abstract = {We introduce a mixed integer linear modeling approach for the optimization of dynamic transport networks based on the piecewise linearization of nonlinear constraints and we show how to apply this method by two examples, transient gas and water supply network optimization. We state the mixed integer linear programs for both cases and provide numerical evidence for their suitability.}, author = {Geißler, Björn and Kolb, Oliver and Lang, Jens and Leugering, Günter and Martin, Alexander and Morsi, Antonio}, doi = {10.1007/s00186-011-0354-5}, faupublication = {yes}, journal = {Mathematical Methods of Operations Research}, keywords = {Mixed integer linear programming;Piecewise linear approximation;Gas network optimization;Water network optimization}, pages = {339-362}, peerreviewed = {Yes}, title = {{Mixed} integer linear models for the optimization of dynamical transport networks}, volume = {73}, year = {2011} } @misc{faucris.119599304, abstract = {We consider the optimization of a gas network that is described by a coupled system of parabolic partial differential equations. Energy and mass balance at network junctions and active elements, like compressors or valves, are modeled as additional algebraic equations. The resulting optimal control problem is discretized in space and time by a particular finite volume method, which can be shown to be well-posed under rather general assumptions. This discretize-first-then-optimize

procedure yields a mixed-integer nonlinear problem (MINLP) that can be solved to global optimality.

For the numerical solution of the MINLP, we consider a relaxation approach allowing to solve the problem globally by a sequence of mixed-integer problems (MIPs) with any required accuracy. The relaxation is based on piecewise linearization of the nonlinear constraints modeling the gas dynamics on the pipelines. Due to the particular discretization of the state equations, only univariate nonlinearities have to be approximated. This substantially facilitates the numerical treatment of the nonlinear constraints. To illustrate the efficiency of the proposed approach, we present numerical tests for typical benchmark problems.}, author = {Burlacu, Robert and Egger, Herbert and Gross, Martin and Martin, Alexander and Pfetsch, Marc E. and Schewe, Lars and Sirvent, Mathias and Skutella, Martin}, faupublication = {yes}, keywords = {Discretization; Instationary Gas Transport Optimization; Mixed-Integer Nonlinear Programming}, peerreviewed = {automatic}, title = {{A} {Global} {Optimization} {Approach} for {Instationary} {Gas} {Transport} in {Pipeline} {Networks}}, url = {https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/221}, year = {2017} } @article{faucris.115708824, abstract = {While semidefinite relaxations are known to deliver good approximations for combinatorial optimization problems like graph bisection, their practical scope is mostly associated with small dense instances. For large sparse instances, cutting plane techniques are considered the method of choice. These are also applicable for semi- definite relaxations via the spectral bundle method, which allows to exploit structural properties like sparsity. In order to evaluate the relative strengths of linear and semi- definite approaches for large sparse instances, we set up a common branch and-cut framework for linear and semidefinite relaxations of the minimum graph bisection problem. It incorporates separation algorithms for valid inequalities of the bisection cut polytope described in a recent study by the authors. While the problem specific cuts help to strengthen the linear relaxation significantly, the semidefinite bound prof- its much more from separating the cycle inequalities of the cut polytope on a slightly enlarged support. Extensive numerical experiments show that this semidefinite branch- and-cut approach without problem specific cuts is a superior choice to the classical simplex approach exploiting bisection specific inequalities on a clear majority of our large sparse test instances from VLSI design and numerical optimization.}, author = {Armbruster, Michael and Fügenschuh, Marzena and Helmberg, Christoph and Martin, Alexander}, faupublication = {yes}, journal = {Mathematical Programming Computation}, keywords = {Branch and cut algorithms; Cutting plane algorithms; Polyhedral combinatorics; Semidefinite programs; Graph bisection}, pages = {275 -- 306}, peerreviewed = {Yes}, title = {{LP} and {SDP} {Branch}-and-{Cut} {Algorithms} for the {Minimum} {Graph} {Bisection} {Problem}: {A} {Computational} {Comparison}}, volume = {4}, year = {2012} } @book{faucris.122269004, address = {Philadelphia}, editor = {Koch, Thorsten and Hiller, Benjamin and Pfetsch, Marc E. and Schewe, Lars}, faupublication = {yes}, isbn = {978-1-611973-68-6}, peerreviewed = {automatic}, publisher = {SIAM}, series = {SIAM-MOS Series on Optimization}, title = {{Evaluating} {Gas} {Network} {Capacities}}, year = {2015} } @article{faucris.124029664, abstract = {

In this work we study polyhedra in the context of network flow problems, in which the flow value on each arc lies in one of several predefined intervals. This is motivated by nonlinear problems on transportation networks, where nonlinearities are handled by piecewise linear approximation or relaxation—a common and established approach in many applications. Several methods for modeling piecewise linear functions which provide a complete description for a single network arc are known. However, in general this property is lost when considering multiple arcs. We show how to strengthen the formulation for specific substructures consisting of multiple arcs by linear inequalities. For the case of paths of degree-two nodes we give a complete description of the polyhedron projected to the integer variables. Our model is based on—but not limited to—the connection between binary variables and flow variables that is used in the multiple choice method or the convex combination method; we also show how to transfer our results to a formulation based on the incremental method. Computational results show that a state-of-the-art mixed-integer program solver greatly benefits from using our cutting planes for random and realistic network topologies.

},
author = {Liers, Frauke and Merkert, Maximilian},
doi = {10.1137/15M1006751},
faupublication = {yes},
journal = {SIAM Journal on Optimization},
keywords = {combinatorial optimization, complete description, network flow problems, piecewise linear functions},
pages = {2863-2886},
peerreviewed = {Yes},
title = {{Structural} {Investigation} of {Piecewise} {Linearized} {Network} {Flow} {Problems}},
volume = {26},
year = {2016}
}
@misc{faucris.119276344,
abstract = {In this paper we present a four-level market model that accounts for airport capacity extension, fleet investment, aircraft scheduling, and ticket trade. In particular, budget-constrained airports decide on the first level on their optimal runway capacity extension and on a corresponding airport charge. Airports anticipate optimal long-term fleet investment of airlines on the second level, optimal medium-term aircraft scheduling on the third level, and short-term outcomes of a competitive ticket market on the fourth level. We compare this market model with an integrated single-level benchmark model that simultaneousely accounts for all investment, scheduling, and market clearing constraints. As we show, our four-level market model may result in inefficient long-run investments in both runway capacity and new aircraft. In addition, we identify policy regulations that may have the potential to reduce inefficiencies of the market model relative to the integrated benchmark model.},
author = {Sirvent, Mathias and Weibelzahl, Martin},
faupublication = {yes},
peerreviewed = {automatic},
title = {{Airport} {Capacity} {Extension}, {Fleet} {Investment}, and {Optimal} {Aircraft} {Scheduling} in a {Four}-{Level} {Market} {Model}: {On} the {Effects} of {Market} {Regulations}},
url = {http://www.optimization-online.org/DB_HTML/2017/05/5989.html},
year = {2017}
}
@inproceedings{faucris.203404200,
author = {Steber, David and Pruckner, Marco and Thurner, Christoph and Burlacu, Robert and Graber, Thomas and Deß, Tobias and Luther, Matthias and Martin, Alexander and German, Reinhard},
booktitle = {Integration of Sustainable Energy Conference (ISEneC) 2018},
faupublication = {yes},
peerreviewed = {unknown},
title = {{Combined} {Optimization}, {Simulation} and {Grid} {Analysis} of the {German} {Electrical} {Power} {System} in an {European} {Context} ({KOSiNeK}) - {Presentation} of the research project and first results},
venue = {Nürnberg},
year = {2018}
}
@article{faucris.108900484,
abstract = {We investigate the problem of partitioning the nodes of a graph under capacity restriction on the sum of the node weights in each subset of the partition. The objective is to minimize the sum of the costs of the edges between the subsets of the partition. This problem has a variety of applications, for instance in the design of electronic circuits and devices. We present alternative integer programming formulations for this problem and discuss the links between these formulations. Having chosen to work in the space of edges of the multicut, we investigate the convex hull of incidence vectors of feasible multicuts. In particular, several classes of inequalities are introduced, and their strength and robustness are analyzed as various problem parameters change.},
author = {E. Ferreira, Carlos and Martin, Alexander and de Souza, Cid C. and Weismantel, Robert and Wolsey, Laurence},
faupublication = {no},
journal = {Mathematical Programming},
keywords = {Clustering; Ear decomposition; Equipartition; Graph partitioning; Integer programming; Knapsack},
pages = {247 - 266},
peerreviewed = {Yes},
title = {{Formulations} and valid inequalities for the node capacitated graph partitioning problem},
volume = {74},
year = {1996}
}
@inproceedings{faucris.121872124,
abstract = {We show that no minimal vertex triangulation of a closed, connected, orientable 2-manifold of genus 6 admits a polyhedral embedding in R3. We also provide examples of minimal vertex triangulations of closed, connected, orientable 2-manifolds of genus 5 that do not admit any polyhedral embeddings. We construct a new infinite family of non-realizable triangula tions of surfaces. These results were achieved by transforming the problem of finding suitable oriented matroids into a satisfiability problem. This method can be applied to other geometric realizability problems, e.g. for face lattices of polytopes.},
author = {Schewe, Lars},
booktitle = {Discrete Differential Geometry: Abstracts from the workshop},
date = {2006-03-05/2006-03-11},
faupublication = {no},
pages = {707-708},
peerreviewed = {unknown},
series = {Oberwolfach Reports},
title = {{Nonrealizable} minimal triangulations of surfaces},
volume = {3},
year = {2006}
}
@article{faucris.119629444,
abstract = {The minimization of operation costs for natural gas transport networks is studied. Based on a recently developed model hierarchy ranging from detailed models of instationary partial differential equations with temperature dependence to highly simplified algebraic equations, modeling and discretization error estimates are presented to control the overall error in an optimization method for stationary and isothermal gas flows. The error control is realized by switching to more detailed models or finer discretizations if necessary to guarantee that a prescribed model and discretization error tolerance is satisfied in the end. We prove convergence of the adaptively controlled optimization method and illustrate the new approach with numerical example},
author = {Mehrmann, Volker and Schmidt, Martin and Stolwijk, Jeroen},
doi = {10.1007/s10013-018-0303-1},
faupublication = {yes},
journal = {Vietnam Journal of Mathematics},
keywords = {Gas transport optimization; Isothermal stationary Euler equations; Model hierarchy; Adaptive error control; Marking strategy},
peerreviewed = {Yes},
title = {{Model} and {Discretization} {Error} {Adaptivity} within {Stationary} {Gas} {Transport} {Optimization}},
url = {http://www.optimization-online.org/DB_HTML/2017/12/6365.html},
year = {2018}
}
@inproceedings{faucris.108694564,
author = {Sieh, Volkmar and Burlacu, Robert and Hönig, Timo and Janker, Heiko and Raffeck, Phillip and Wägemann, Peter and Schröder-Preikschat, Wolfgang},
booktitle = {Proceedings of the 20th International Symposium on Real-Time Distributed Computing (ISORC 2017)},
date = {2017-05-16/2017-05-18},
doi = {10.1109/ISORC.2017.10},
faupublication = {yes},
isbn = {9781538615744},
keywords = {energy-model generation; static analysis; timing-model generation; WCEC; WCET},
note = {UnivIS-Import:2017-12-18:Pub.2017.tech.IMMD.IMMD4.anendt},
pages = {158--167},
peerreviewed = {Yes},
publisher = {Institute of Electrical and Electronics Engineers Inc.},
title = {{An} {End}-{To}-{End} {Toolchain}: {From} {Automated} {Cost} {Modeling} to {Static} {WCET} and {WCEC} {Analysis}},
url = {https://www4.cs.fau.de/Publications/2017/sieh_17_isorc.pdf},
venue = {Toronto, Canada},
year = {2017}
}
@article{faucris.117698284,
abstract = {Many real-world optimization models comprise nonconvex and nonsmooth functions leading to very hard classes of optimization models. In this article, a new interior-point method for the special, but practically relevant class of optimization problems with locatable and separable nonsmooth aspects is presented. After motivating and formalizing the problems under consideration, modifications and extensions to a standard interior-point method for nonlinear programming are investigated to solve the introduced problem class. First theoretical results are given and a numerical study is presented that shows the applicability of the new method for real-world instances from gas network optimization.},
author = {Schmidt, Martin},
doi = {10.1007/s13675-015-0039-6},
faupublication = {yes},
journal = {EURO Journal on Computational Optimization},
keywords = {Interior-point methods; Barrier methods; Line-search methods; Nonlinear and nonsmooth optimization; Classification of optimization models; Gas network optimization; 90C30; 90C51; 90C90; 90C35; 90C56; 90B10},
pages = {309-348},
peerreviewed = {No},
title = {{An} interior-point method for nonlinear optimization problems with locatable and separable nonsmoothness},
volume = {3},
year = {2015}
}
@book{faucris.115716084,
abstract = {Water supply- and drainage systems and mixed water channel systems are networks whose high dynamic is determined and/or affected by consumer habits on drinking water on the one hand and by climate conditions, in particular rainfall, on the other hand. According to their size, water networks consist of hundreds or thousands of system elements. Moreover, different types of decisions (continuous and discrete) have to be taken in the water management. The networks have to be optimized in terms of topology and operation by targeting a variety of criteria. Criteria may for example be economic, social or ecological ones and may compete with each other. The development of complex model systems and their use for deriving optimal decisions in water management is taking place at a rapid pace. Simulation and optimization methods originating in Operations Research have been used for several decades; usually with very limited direct cooperation with applied mathematics. The research presented here aims at bridging this gap, thereby opening up space for synergies and innovation. It is directly applicable for relevant practical problems and has been carried out in cooperation with utility and dumping companies, infrastructure providers and planning offices. A close and direct connection to the practice of water management has been established by involving application-oriented know-how from the field of civil engineering. On the mathematical side all necessary disciplines were involved, including mixed-integer optimization, multi-objective and facility location optimization, numerics for cross-linked dynamic transportation systems and optimization as well as control of hybrid systems. Most of the presented research has been supported by the joint project "Discret continuous optimization of dynamic water systems" of the federal ministry of education and research (BMBF).},
author = {Martin, Alexander and Klamroth, Kathrin and Lang, Jens and Leugering, Günter and Morsi, Antonio and Oberlack, Martin and Ostrowski, Manfred and Rosen, Roland},
faupublication = {yes},
peerreviewed = {Yes},
publisher = {Birkhäuser},
series = {International Series of Numerical Mathematics},
title = {{Mathematical} {Optimization} of {Water} {Networks}},
volume = {162},
year = {2012}
}
@inproceedings{faucris.120590404,
abstract = {Mixed integer programming has become a very powerful tool for modeling and solving real-world planning and scheduling problems, with the breadth of applications appearing to be almost unlimited. A critical component in the solution of these mixed-integer programs is a set of routines commonly referred to as presolve. Presolve can be viewed as a collection of preprocessing techniques that reduce the size of and, more importantly, improve the “strength” of the given model formulation, that is, the degree to which the constraints of the formulation accurately describe the underlying polyhedron of integer-feasible solutions. In the Gurobi commercial mixed-integer solver, the presolve functionality has been steadily enhanced over time, now including a number of so-called multi-row reductions. These are reductions that simultaneously consider multiple constraints to derive improvements in the model formulation. In this paper we give an overview of such multi-row techniques and present computational results to assess their impact on overall solver performance.},
author = {Achterberg, Tobias and Bixby, Robert E. and Gu, Zonghao and Rothberg, Edward and Weninger, Dieter},
booktitle = {Proceedings of the Twenty-Sixth RAMP Symposium},
date = {2014-10-16/2014-10-17},
editor = {Hosei University, Tokyo},
faupublication = {yes},
keywords = {Mixed Integer Programming, Presolving, Gurobi},
pages = {181-196},
peerreviewed = {unknown},
title = {{Multi}-{Row} {Presolve} {Reductions} in {Mixed} {Integer} {Programming}},
url = {http://www.orsj.or.jp/ramp/2014/paper/4-4.pdf},
venue = {Tokyo},
year = {2014}
}
@incollection{faucris.115668124,
abstract = {We investigate the minimum graph bisection problem concerning partitioning the nodes of a graph into two subsets such that the total weight of each set is within some lower and upper limits. The objective is to minimize the total cost of edges between both subsets of the partition. This problem has a variety of applications, for instance in the design of electronic circuits and in parallel computing. We present an integer linear programming formulation for this problem. We develop a primal heuristic based on a genetic algorithm, incorporate it in a branch-and-cut framework and present some computational results.},
author = {Armbruster, Michael and Fügenschuh, Marzena and Helmberg, Christoph and Jetchev, Nikolay and Martin, Alexander},
booktitle = {Operations Research Proceedings 2005, Bremen, September 7-9, 2005},
faupublication = {no},
pages = {315-320},
peerreviewed = {unknown},
publisher = {Springer, Berlin},
title = {{LP}-based {Genetic} {Algorithm} for the {Minimum} {Graph} {Bisection} {Problem}},
year = {2005}
}
@incollection{faucris.115453184,
author = {Schewe, Lars and Koch, Thorsten and Martin, Alexander and Pfetsch, Marc E.},
booktitle = {Evaluating Gas Network Capacities},
doi = {10.1137/1.9781611973696},
editor = {Koch T, Hiller B, Pfetsch ME, Schewe L},
faupublication = {yes},
isbn = {9781611973686},
pages = {87--102},
peerreviewed = {unknown},
publisher = {SIAM},
series = {SIAM-MOS series on Optimization},
title = {{Mathematical} optimization for evaluating gas network capacities},
year = {2015}
}
@incollection{faucris.115696504,
author = {Göllner, Thea and Günther, Ute and Hess, Wolfgang and Martin, Alexander and Ulbrich, Stefan},
booktitle = {Tagungsband 3. Zwischenkolloqium SFB 666},
editor = {P. Groche},
faupublication = {yes},
pages = {25 -- 32},
peerreviewed = {No},
publisher = {Meisenbach Verlag, Bamberg},
title = {{Form}- und {Topologieoptimierung} verzweigter {Blechbauteile}},
year = {2010}
}
@misc{faucris.113664584,
author = {Hiller, Benjamin and Koch, Thorsten and Pfetsch, Marc E. and Schmidt, Martin and Geißler, Björn and Henrion, René and Joormann, Imke and Martin, Alexander and Morsi, Antonio and Römisch, Werner and Schewe, Lars and Schultz, Rüdiger and Steinbach, Marc C.},
faupublication = {yes},
peerreviewed = {automatic},
title = {{Capacity} {Evaluation} for {Large}-{Scale} {Gas} {Networks}},
url = {http://www.mso.math.fau.de/fileadmin/wima/data_members/schmidt/forne-komso.pdf},
year = {2017}
}
@article{faucris.108434744,
abstract = {We show that no minimal vertex triangulation of a closed, connected, orientable 2-manifold of genus 6 admits a polyhedral embedding in ℝ. We also provide examples of minimal vertex triangulations of closed, connected, orientable 2-manifolds of genus 5 that do not admit any polyhedral embeddings. Correcting a previous error in the literature, we construct the first infinite family of such nonrealizable triangulations of surfaces. These results were achieved by transforming the problem of finding suitable oriented matroids into a satisfiability problem. This method can be applied to other geometric realizability problems, e. g., for face lattices of polytopes. © 2009 Springer Science+Business Media, LLC.},
author = {Schewe, Lars},
doi = {10.1007/s00454-009-9222-y},
faupublication = {no},
journal = {Discrete & Computational Geometry},
keywords = {Embeddings; Oriented matroids; Polyhedral surfaces; Satisfiability},
pages = {289-302},
peerreviewed = {Yes},
title = {{Nonrealizable} minimal vertex triangulations of surfaces: {Showing} nonrealizability using oriented matroids and satisfiability solvers},
volume = {43},
year = {2010}
}
@article{faucris.108957244,
abstract = {Mathematical modeling of market design issues in liberalized electricity markets often leads to mixed-integer nonlinear multilevel optimization problems for which no general-purpose solvers exist and which are intractable in general. In this work, we consider the problem of splitting a market area into a given number of price zones such that the resulting market design yields welfare-optimal outcomes. This problem leads to a challenging multilevel model that contains a graph-partitioning problem with multi-commodity flow connectivity constraints and nonlinearities due to proper economic modeling. Furthermore, it has highly symmetric solutions. We develop different problem-tailored solution approaches. In particular, we present an extended KKT transformation approach as well as a generalized Benders approach that both yield globally optimal solutions. These methods, enhanced with techniques such as symmetry breaking and primal heuristics, are evaluated in detail on academic as well as on realistic instances. It turns out that our approaches lead to effective solution methods for the difficult optimization tasks presented here, where the problem-specific generalized Benders approach performs considerably better than the methods based on KKT transformatio},
author = {Grimm, Veronika and Kleinert, Thomas and Liers, Frauke and Schmidt, Martin and Zöttl, Gregor},
doi = {10.1080/10556788.2017.1401069},
faupublication = {yes},
journal = {Optimization Methods & Software},
keywords = {Multilevel Optimization; Mixed-Integer Nonlinear Optimization; Graph Partitioning; Generalized Benders Decomposition; Electricity Market Design},
pages = {406-436},
peerreviewed = {Yes},
title = {{Optimal} price zones in electricity markets: a mixed-integer multilevel model and global solution approaches},
url = {http://www.optimization-online.org/DB_HTML/2017/01/5799.html},
volume = {34},
year = {2019}
}
@article{faucris.112089384,
abstract = {We investigate the problem of designing energy-efficient timetables for railway traffic. More precisely, we slightly adapt a given timetable draft before it is published by moderately shifting the departure times of the trains at the stations. To this end, we propose a mixed-integer programming model for feasible adaptations of the timetable draft and investigate its behaviour under different objective functions which fall into two classes: reducing the energy cost and increasing the stability of the power supply system. These tests are performed on real-world problem instances from our industry partner Deutsche Bahn AG. They show a significant potential for improvements in the existing railway timetables.},
author = {Bärmann, Andreas and Martin, Alexander and Schneider, Oskar},
doi = {10.1007/s12469-017-0160-4},
faupublication = {yes},
journal = {Public Transport},
keywords = {Railway timetabling; Power peak reduction; Mixed-integer programming},
pages = {95-113},
peerreviewed = {unknown},
title = {{A} comparison of performance metrics for balancing the power consumption of trains in a railway network by slight timetable adaptation},
volume = {9},
year = {2017}
}
@incollection{faucris.115720924,
abstract = {We introduce a mixed integer linear modeling approach for the optimization of dynamic water supply networks based on the piecewise linearization of nonlinear constraints. One advantage of applying mixed integer linear techniques is that these methods are nowadays very mature, that is, they are fast, robust, and are able to solve problems with up to a huge number of variables. The other major point is that these methods have the potential of finding globally optimal solutions or at least to provide guarantees of the solution quality. We demonstrate the applicability of our approach on examples networks.},
author = {Morsi, Antonio and Geißler, Björn and Martin, Alexander},
booktitle = {Mathematical Optimization of Water Networks},
faupublication = {yes},
pages = {35 -- 54},
peerreviewed = {Yes},
publisher = {Birkhäuser},
series = {International Series of Numerical Mathematics},
title = {{Mixed} {Integer} {Optimization} of {Water} {Supply} {Networks}},
volume = {162},
year = {2012}
}
@article{faucris.123677664,
abstract = {Many mixed-integer optimization problems are constrained by nonlinear functions that do not possess desirable analytical properties like convexity or factorability or cannot even be evaluated exactly. This is, e.g., the case for problems constrained by differential equations or for models that rely on black-box simulation runs. For these problem classes, we present, analyze, and test algorithms that solve mixed-integer problems with only Lipschitz continuous nonlinearities. Our theoretical results depend on the assumptions made on the (in)exactness of function evaluations and on the knowledge of Lipschitz constants. If Lipschitz constants are known, we prove finite termination at approximate globally optimal points both for the case of exact and inexact function evaluations. If only approximate Lipschitz constants are known, we prove finite termination and derive additional conditions under which infeasibility can be detected. A computational study for gas transport problems and an academic case study show the applicability of our algorithms to real-world problems and how different assumptions on the constraint functions up- or downgrade the practical performance of the method},
author = {Schmidt, Martin and Sirvent, Mathias and Wollner, Winnifried},
doi = {10.1007/s10107-018-1309-x},
faupublication = {yes},
journal = {Mathematical Programming},
keywords = {Mixed-Integer Nonlinear Optimization, Lipschitz Optimization, Inexact Function Evaluations, Decomposition Methods, Gas Networks.},
peerreviewed = {Yes},
title = {{A} {Decomposition} {Method} for {MINLPs} with {Lipschitz} {Continuous} {Nonlinearities}},
url = {http://www.optimization-online.org/DB_HTML/2017/07/6130.html},
year = {2018}
}
@incollection{faucris.115669664,
abstract = {A new technique for forming sheet metal makes it possible to construct branched sheet metal products out of one piece of sheet metal. Since the number of potential ways to produce one and the same component increases exponentially with every additional branch, appropriate tools for handling the large number of possibilities are necessary. In this paper we give a Mixed Integer Program that models the different ways of producing branched profiles and show how to incorporate manufacturing constraints into the model.},
author = {Günther, Ute and Martin, Alexander},
booktitle = {PAMM, Proceedings of Applied Mathematics and Mechanics},
faupublication = {no},
pages = {697 -- 698},
peerreviewed = {unknown},
title = {{Mixed} {Integer} {Models} for {Branched} {Sheet} {Metal} {Products}},
volume = {6},
year = {2006}
}
@incollection{faucris.111139424,
abstract = {We consider optimal control problems for the flow of gas or fresh water in pipe networks as well as drainage or sewer systems in open canals. The equations of motion are taken to be represented by the nonlinear isothermal Euler gas equations, the water hammer equations, or the St. Venant equations for flow. We formulate model hierarchies and derive an abstract model for such network flow problems including pipes, junctions, and controllable elements such as valves, weirs, pumps, as well as compressors. We use the abstract model to give an overview of the known results and challenges concerning equilibria, well-posedness, controllability, and optimal control. A major challenge concerning the optimization is to deal with switching on-off states that are inherent to controllable devices in such applications combined with continuous simulation and optimization of the gas flow. We formulate the corresponding mixed-integer nonlinear optimal control problems and outline a decomposition approach as a solution technique.},
address = {Singapore},
author = {Hante, Falk and Leugering, Günter and Martin, Alexander and Schewe, Lars and Schmidt, Martin},
booktitle = {Industrial Mathematics and Complex Systems: Emerging Mathematical Models, Methods and Algorithms},
doi = {10.1007/978-981-10-3758-0_5},
editor = {Manchanda, Pammy; Lozi, René; Siddiqi, Abul Hasan},
faupublication = {yes},
isbn = {978-981-10-3758-0},
keywords = {Networks, pipes, canals, Euler and St. Venant equations, hierarchy of models, domain decomposition, controllability, optimal control.},
pages = {77-122},
peerreviewed = {unknown},
publisher = {Springer Singapore},
series = {Industrial and Applied Mathematics},
title = {{Challenges} in {Optimal} {Control} {Problems} for {Gas} and {Fluid} {Flow} in {Networks} of {Pipes} and {Canals}: {From} {Modeling} to {Industrial} {Applications}},
url = {https://opus4.kobv.de/opus4-trr154/files/121/isiam-paper.pdf},
year = {2017}
}
@incollection{faucris.123294864,
abstract = {In many rural areas, the public bus service is demand-oriented: By far the biggest group of customers are pupils who are transported to their schools within certain strict time limits. Usually, all schools start around the same time, which causes a morning peak in the number of deployed buses. However, schools are allowed to change their starting times within some interval. The question is, how to simultanenously rectify the starting times for all schools and bus trips in a certain county so that the number of scheduled buses is minimal. This problem can be formulated as a vehicle routing problem with coupled time windows (VRP-CTW), which is an extension of the vehicle routing problem with time windows (VRP-TW), where additional coupling constraints on the time windows are introduced. We give a mixed-integer programming formulation for VRP-CTW, and present solutions and lower bounds for randomly generated and real-world instances.},
author = {Fügenschuh, Armin-René and Martin, Alexander and et al.},
author_hint = {A.~Fügenschuh, A.~Martin, P.~Stöveken},
booktitle = {Operations Research Proceedings 2004},
editor = {H. Fleuren; D. den Hertog; P. Kort},
faupublication = {no},
pages = {150 -- 157},
peerreviewed = {unknown},
publisher = {Springer, Berlin},
support_note = {Author relations incomplete. You may find additional data in field 'author_hint'},
title = {{Integrated} {Optimization} of {School} {Starting} {Times} and {Public} {Bus} {Services}},
year = {2005}
}
@incollection{faucris.123286284,
abstract = {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.
Moreover, we introduce a new class of facet-defining inequalities that

Read More: http://epubs.siam.org/doi/abs/10.1137/110853248

Read More: http://epubs.siam.org/doi/abs/10.1137/110853248

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.

Read More: http://epubs.siam.org/doi/abs/10.1137/110853248

Read More: http://epubs.siam.org/doi/abs/10.1137/110853248

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.

Read More: http://epubs.siam.org/doi/abs/10.1137/110853248*n* . They have been used to study various problems in discrete and computational geometry (for more material on oriented matroids, see [1,2]). A number of methods to generate oriented matroids have been proposed (for instance in [4,8-10]) as these methods can be used as a building block for the algorithmic treatment of some hard problems: Algorithms to generate oriented matroids have for instance been used to decide whether certain 4-polytopes exist [6,10,14]. For these questions it is important to have effective algorithms for the generation of oriented matroids. We propose to use satisfiability solvers to generate oriented matroids. We have adapted this approach to generate oriented matroids that satisfy certain geometric constraints. Even though one can use the generated oriented matroids as a first step to find realizations (see for instance [2,6]), we will only focus on non-realizability results.},
address = {Berlin, Heidelberg},
author = {Schewe, Lars},
booktitle = {Mathematical Software - ICMS 2006},
doi = {10.1007/11832225_19},
editor = {Andrés Iglesias, Nobuki Takayama},
faupublication = {no},
isbn = {9783540380849},
pages = {216-218},
peerreviewed = {unknown},
publisher = {Springer},
series = {Lecture Notes in Computer Science},
title = {{Generation} of oriented matroids using satisfiability solvers},
volume = {4151},
year = {2006}
}
@incollection{faucris.108917204,
abstract = {In this chapter we compare continuous nonlinear optimization with mixed integer optimization of water supply networks by means of a meso scaled network instance. We introduce a heuristic approach, which handles discrete decisions arising in water supply network optimization through penalization using nonlinear programming. We combine the continuous nonlinear and the mixed integer approach introduced in Chap. 3 to incorporate the solution quality. Finally, we show results for a real municipal water supply network.},
author = {Kolb, Oliver and Morsi, Antonio and Lang, Jens and Martin, Alexander},
booktitle = {Mathematical Optimization of Water Networks},
editor = {A. Martin; K. Klamroth; J. Lang; G. Leugering; A. Morsi; M. Oberlack; M. Ostrowski; R. Rosen},
faupublication = {yes},
pages = {55 -- 65},
peerreviewed = {Yes},
publisher = {Birkhäuser},
series = {International Series of Numerical Mathematics},
title = {{Nonlinear} and {Mixed} {Integer} {Linear} {Programming}},
volume = {162},
year = {2012}
}
@incollection{faucris.108909064,
author = {Fügenschuh, Armin-René and Martin, Alexander},
booktitle = {PAMM, Proceedings of Applied Mathematics and Mechanics},
faupublication = {no},
pages = {2060049-2060050},
peerreviewed = {No},
title = {{Mixed}-{Integer} {Models} for {Topology} {Optimization} in {Sheet} {Metal} {Design}},
volume = {7},
year = {2007}
}
@article{faucris.115723344,
abstract = {In this work, we present an exact approach for solving network design problems that is based on an iterative graph aggregation procedure. The scheme allows existing preinstalled capacities. Starting with an initial aggregation, we solve a sequence of network design master problems over increasingly fine-grained representations of the original network. In each step, a subproblem is solved that either proves optimality of the solution or gives a directive where to refine the representation of the network in the subsequent iteration. The algorithm terminates with a globally optimal solution to the original problem. Our implementation uses a standard integer programming solver for solving the master problems as well as the subproblems. The computational results on random and realistic instances confirm the profitable use of the iterative aggregation technique. The computing time often reduces drastically when our method is compared to solving the original problem from scratch.},
author = {Bärmann, Andreas and Liers, Frauke and Martin, Alexander and Merkert, Maximilian and Thurner, Christoph and Weninger, Dieter},
doi = {10.1007/s12532-015-0079-1},
faupublication = {yes},
journal = {Mathematical Programming Computation},
pages = {189-217},
peerreviewed = {unknown},
title = {{Solving} {Network} {Design} {Problems} via {Iterative} {Aggregation}},
volume = {7},
year = {2015}
}
@article{faucris.120380524,
abstract = {A gas network basically consists of a set of compressors and valves that are connected by pipes. The problem of gas network optimization deals with the question of how to optimize the flow of the gas and to use the compressors cost-efficiently such that all demands of the gas network are satisfied. This problem leads to a complex mixed integer nonlinear optimization problem. We describe techniques for a piece-wise linear approximation of the nonlinearities in this model resulting in a large mixed integer linear program. We study sub-polyhedra linking these piece wise linear approximations and show that the number of vertices is computationally tractable yielding exact separation algorithms. Suitable branching strategies complementing the separation algorithms are also presented. Our computational results demonstrate the success of this approach.},
author = {Martin, Alexander and Möller, Markus and Moritz, Susanne},
doi = {10.1007/s10107-005-0665-5},
faupublication = {no},
journal = {Mathematical Programming},
keywords = {Branch-and-Bound; Cutting planes; Gas optimization; Mixed integer programming; Piece-wise linear functions; SOS constraints},
pages = {563 - 582},
peerreviewed = {Yes},
title = {{Mixed} {Integer} {Models} for the {Stationary} {Case} of {Gas} {Network} {Optimization}},
volume = {105},
year = {2006}
}
@misc{faucris.108959004,
abstract = {In this paper we analyze a uniform price electricity spot market that is
followed by redispatch in the case of network congestion. We assume
that the transmission system operator is incentivized to minimize
redispatch cost and compare a cost-based redispatch to a market-based
redispatch mechanism. For networks with at least three nodes we show
that in contrast to cost-based redispatch, in the case of market-based
redispatch the cost-minimizing allocation may not be short-run
efficient. As we demonstrate, the possibility of the transmission system
operator to reduce market-based redispatch cost at the expense of a
reduced welfare may be driven by the electricity supply side or the
electricity demand side. Based on these results, we propose a new hybrid
approach where the transmission system operator implements the
efficient (instead of the cost minimizing) dispatch and uses
market-based redispatch compensations},
author = {Grimm, Veronika and Martin, Alexander and Sölch, Christian and Weibelzahl, Martin and Zöttl, Gregor},
doi = {10.2139/ssrn.3120403},
faupublication = {yes},
keywords = {Electricity Markets; Redispatch; Congestion Management; Computational Equilibrium Models},
peerreviewed = {automatic},
title = {{Market}-based {Redispatch} {May} {Result} in {Inefficient} {Dispatch}},
url = {https://ssrn.com/abstract=3120403},
year = {2018}
}
@inproceedings{faucris.115685504,
author = {Waniek, Daniel and Rehtanz, Christian and Handschin, Edmund and Martin, Alexander and Mahlke, Debora and Zelmer, Andrea},
booktitle = {Innovative Modellierung und Optimierung von Energiesystemen},
editor = {R.~Schultz, H.-J-~Wagner},
faupublication = {no},
pages = {9 -- 38},
peerreviewed = {Yes},
publisher = {LIT Verlag},
title = {{Kostenoptimierte} {Planung} gekoppelter {Strom}-, {Gas}- und {Wärmenetze}},
year = {2009}
}
@incollection{faucris.115682204,
abstract = {Semidefinite relaxations are known to deliver good approximations for combinatorial optimization problems like graph bisection. Using the spectral bundle method it is possible to exploit structural properties of the underlying problem and to apply, even to sparse large scale instances, cutting plane methods, probably the most successful technique in linear programming. We set up a common branch-and-cut framework for linear and semidefinite relaxations of the minimum graph bisection problem. It incorporates separation algorithms for valid inequalities presented in the recent study [2] of the facial structure of the associated polytope. Extensive numerical experiments show that the semidefinite branch-and-cut approach outperforms the classical simplex approach on a clear majority of the sparse large scale test instances. On instances from compiler design the simplex approach is faster.},
author = {Armbruster, Michael and Helmberg, Christoph and Fügenschuh, Marzena and Martin, Alexander},
booktitle = {Integer Programming and Combinatorial Optimization},
editor = {A. Lodi, A. Panconesi, G. Renaldi},
faupublication = {no},
keywords = {Branch and cut algorithms; Cutting plane algorithms; Polyhedral combinatorics; Semidefinite programs},
pages = {112 -- 124},
peerreviewed = {Yes},
series = {Proceedings of the IPCO 2008 Conference, LNCS 5035},
title = {{A} {Comparative} {Study} of {Linear} and {Semidefinite} {Branch}-and-{Cut} {Methods} for {Solving} the {Minimum} {Graph} {Bisection} {Problem}},
year = {2008}
}
@incollection{faucris.117399964,
abstract = {Efficient planning of runway utilisation 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. However, uncertainty and inaccuracy almost always lead to deviations from the actual plan or schedule. In this paper, we develop an optimization approach for the pre-tactical planning phase that provides some flexibility in the face of small disturbances in the input data, so that we need to change our plans less frequently. Instead of determining arrival/departure times to the minute in this phase yet, we assign several aircraft to the same time slot of a given size. The exact orders within those time windows can be decided later in tactical planning. Mathematically, this leads to a generalised assignment problem on a bipartite graph. We develop an integer program (IP), which can be solved very fast but may provide unnecessary large time buffers, and extend it to a mixed integer program (MIP) that solves the problem to global optimality. We present computational results concerning the abovementioned optimization approach and investigate the impact of disturbances on our deterministic solutions. As a next step, we will incorporate uncertainties directly in our model. Therefore, we analyse real-world data from a large German airport in order to obtain realistic delay distributions and describe a simulation environment to test current and future solution methods.},
author = {Heidt, Andreas and Kapolke, Manu and Liers, Frauke and Fürstenau, Norbert and Helmke, Hartmut},
booktitle = {Proceedings of the SESAR Innovation Days 2014},
editor = {Dirk Schaefer, Javier Saez},
faupublication = {yes},
isbn = {978-2-87497-077-1},
keywords = {arrival / departure scheduling; stochastic optimization; robustness; delay statistics; modeling},
peerreviewed = {unknown},
title = {{Pre}-tactical {Time} {Window} assignment: {Runway} {Utilization} and the {Impact} of {Uncertainties}},
url = {http://www.sesarinnovationdays.eu},
year = {2014}
}
@article{faucris.106309324,
abstract = {We consider the combination of a network design and graph partitioning model in a multilevel framework for determining the optimal design of zonal pricing electricity markets. This together with nonlinearities due to economic modeling yields extremely challenging mixed-integer nonlinear multilevel models for which we develop two problem-tailored solution techniques. The first approach relies on an equivalent bilevel formulation and a standard KKT transformation thereof, whereas the second is a tailored generalized Benders decomposition. We prove for both methods that they yield global optimal solutions. Finally, we compare the approaches in a numerical study and show that the tailored Benders approach clearly outperforms the standard KKT transformatio},
author = {Kleinert, Thomas and Schmidt, Martin},
doi = {10.1016/j.disopt.2019.02.002},
faupublication = {yes},
journal = {Discrete Optimization},
keywords = {Electricity market design; Graph partitioning; Mixed-integer optimization; Multilevel optimization; Network design},
peerreviewed = {Yes},
title = {{Global} {Optimization} of {Multilevel} {Electricity} {Market} {Models} {Including} {Network} {Design} and {Graph} {Partitioning}},
year = {2019}
}
@article{faucris.118445404,
abstract = {Let Δ(d, n) be the maximum possible diameter of the vertex-edge graph over all d-dimensional polytopes defined by n inequalities. The Hirsch bound holds for particular n and d if Δ(d, n)≤n-d. Francisco Santos recently resolved a question open for more than five decades by showing that Δ(d, 2d)≥d+1 for d=43; the dimension was then lowered to 20 by Matschke, Santos and Weibel. This progress has stimulated interest in related questions. The existence of a polynomial upper bound for Δ(d, n) is still an open question, the best bound being the quasi-polynomial one due to Kalai and Kleitman in 1992. Another natural question is for how large n and d the Hirsch bound holds. Goodey showed in 1972 that Δ(4, 10)=5 and Δ(5, 11)=6, and more recently, Bremner and Schewe showed that Δ(4, 11)=Δ(6, 12)=6. Here, we show that Δ(4, 12)=Δ(5, 12)=7. © 2013 Copyright Taylor and Francis Group, LLC.},
author = {Bremner, David and Deza, Antoine and Hua, William and Schewe, Lars},
doi = {10.1080/10556788.2012.668906},
faupublication = {yes},
journal = {Optimization Methods & Software},
keywords = {combinatorics; convex polytopes; discrete geometry; linear optimization; pivoting methods},
pages = {442-450},
peerreviewed = {Yes},
title = {{More} bounds on the diameters of convex polytopes},
volume = {28},
year = {2013}
}
@incollection{faucris.115647224,
abstract = {The study and solution of mixed-integer programming problems is of great interest, because they arise in a variety of mathematical and practical applications. Today's state-of-art software packages for solving mixed-integer programs based on linear programming include preprocessing, branch-and-bound, and cutting planes techniques. The main purpose of this article is to describe these components and recent developments that can be found in many solvers. Besides linear programming based relaxation methods we also discuss Langrangean, Dantzig-Wolfe and Benders' decomposition and their interrelations.},
author = {Fügenschuh, Armin-René and Martin, Alexander},
booktitle = {Handbooks in Operations Research and Management Science},
editor = {K.~Aardal, G.~Nemhauser, R.~Weismantel},
faupublication = {no},
pages = {69 -- 122},
peerreviewed = {unknown},
publisher = {Kluwer},
title = {{Computational} {Integer} {Programming} and {Cutting} {Planes}},
volume = {12},
year = {2005}
}
@misc{faucris.214630022,
author = {Bärmann, Andreas and Büsing, Christina and Liers, Frauke},
faupublication = {yes},
keywords = {Globalized Robust Optimization; Gamma-Uncertainties; Mixed-Integer Programming; Combinatorial Optimization},
peerreviewed = {automatic},
title = {{Globalized} {Robust} {Optimization} with {Gamma}-{Uncertainties}},
year = {2019}
}
@article{faucris.115677804,
abstract = {We introduce a continuous optimal control problem governed by ordinary and partial differential equations for supply chains on networks. We derive a mixed-integer model by discretization of the dynamics of the partial differential equations and by approximations to the cost functional. Finally, we investigate numerically properties of the derived mixed-integer model and present numerical results for a real-world example.},
author = {Fuegenschuh, A. and Goettlich, S. and Herty, Michael and Klar, Axel and Martin, Alexander},
doi = {10.1137/060663799},
faupublication = {no},
journal = {SIAM Journal on Scientific Computing},
keywords = {Supply chains; Conservation laws; Networks; Optimization},
pages = {1490 -- 1507},
peerreviewed = {Yes},
title = {{A} {Discrete} {Optimization} {Approach} to {Large} {Scale} {Supply} {Networks} {Based} on {Partial} {Differential} {Equations}},
volume = {30},
year = {2008}
}
@misc{faucris.122817024,
author = {Bokowski, Jürgen and Martin, Alexander},
faupublication = {no},
peerreviewed = {automatic},
title = {{Egoisten} schaden sich selbst},
year = {2002}
}
@article{faucris.106480484,
abstract = {This paper provides a first approach to assess gas market interaction on a network with nonconvex flow models. In the simplest possible setup that adequately reflects gas transport and market interaction, we elaborate on the relation of the solution of a simultaneous competitive gas market game, its corresponding mixed nonlinear complementarity problem (MNCP), and a first best benchmark. We provide conditions under which the solution of the simultaneous game is also the solution of the corresponding MNCP. However, equilibria cannot be determined by the MNCP as the transmission system operator's (TSO’s) first-order conditions are insufficient, which goes back to nonconvexities of the gas flow model. This also implies that the welfare maximization problem may have multiple solutions that sometimes do not even coincide with any of the market equilibria. Our analysis shows that, even in the absence of strategic firms, market interaction fails to implement desirable outcomes from a welfare perspective due to the TSO’s incentive structure. We conclude that the technical environment calls for a market design that commits the TSO to a welfare objective through regulation and propose a design where the market solution corresponds to a welfare maximum and vice vers},
author = {Grimm, Veronika and Grübel, Julia and Schewe, Lars and Schmidt, Martin and Zöttl, Gregor},
doi = {10.1016/j.ejor.2018.09.016},
faupublication = {yes},
journal = {European Journal of Operational Research},
keywords = {Fundamental Welfare Theorems; Multiplicity; Natural Gas Markets; Nonconvex Equilibrium Models; Uniqueness},
peerreviewed = {Yes},
title = {{Nonconvex} {Equilibrium} {Models} for {Gas} {Market} {Analysis}: {Failure} of {Standard} {Techniques} and {Alternative} {Modeling} {Approaches}},
url = {https://www.sciencedirect.com/science/article/abs/pii/S0377221718307768},
year = {2018}
}
@article{faucris.122777864,
abstract = {Due to strict regulatory rules in combination with complex nonlinear physics, major gas network operators in Germany and Europe face hard planning problems that call for optimization. In part 1 of this paper we have developed a suitable model hierarchy for that purpose. Here we consider the more practical aspects of modeling. We validate individual model components against a trusted simulation tool, give a structural overview of the model hierarchy, and use its large variety of approximations to devise robust and efficient solution techniques. An extensive computational study demonstrates the suitability of our models and techniques for previously unsolvable problems in gas network planning.},
author = {Schmidt, Martin and Steinbach, Marc C. and Willert, Bernhard M.},
doi = {10.1007/s11081-015-9300-3},
faupublication = {yes},
journal = {Optimization and Engineering},
keywords = {Gas networks; Stationary flow; High-detail modeling; Nonsmooth nonlinear discrete-continuous optimization; Smoothing techniques; 90B10; 90C06; 90C30; 90C90},
pages = {437-472},
peerreviewed = {Yes},
title = {{High} detail stationary optimization models for gas networks: validation and results},
url = {http://www.optimization-online.org/DB_HTML/2014/10/4602.html},
volume = {17},
year = {2016}
}
@article{faucris.115721144,
abstract = {The recently imposed new gas market liberalization rules in Germany lead to a change of business of gas network operators. While previously network operator and gas vendor were united, they were forced to split up into independent companies. The network has to be open to any other gas trader at the same conditions, and free network capacities have to be identified and publicly offered in a non-discriminatory way. We discuss how these changing paradigms lead to new and challenging mathematical optimization problems. This includes the validation of nominations, that asks for the decision if the network’s capacity is sufficient to transport a specific amount of flow, the verification of booked capacities and the detection of available freely allocable capacities, and the topological extension of the network with new pipelines or compressors in order to increase its capacity. In order to solve each of these problems and to provide meaningful results for the practice, a mixture of different mathematical aspects have to be addressed, such as combinatorics, stochasticity, uncertainty, and nonlinearity. Currently, no numerical solver is available that can deal with such blended problems out-of-the-box. The main goal of our research is to develop such a solver, that moreover is able to solve instances of realistic size. In this article, we describe the main ingredients of our prototypical software implementations.},
author = {Fügenschuh, Armin and Geißler, Björn and Gollmer, Ralf and Hayn, Christine and Henrion, René and Hiller, Benjamin and Humpola, Jesco and Koch, Thorsten and Lehmann, Thomas and Martin, Alexander and Mirkov, Radoslava and Morsi, Antonio and Rövekamp, Jessica and Schewe, Lars and Schmidt, Martin and Schultz, Rüdiger and Schwarz, Robert and Schweiger, Jonas and Stangl, Claudia and Steinbach, Marc C. and Willert, Bernhard M.},
doi = {10.1007/s12667-013-0099-8},
faupublication = {yes},
journal = {Energy Systems},
keywords = {Gas market liberalization; Entry / exit model; Gas network access regulation; Mixed-integer nonlinear nonconvex stochastic optimization; 90B10; 90C11; 90C30; 90C90},
pages = {449-473},
peerreviewed = {Yes},
title = {{Mathematical} optimization for challenging network planning problems in unbundled liberalized gas markets},
volume = {5},
year = {2014}
}
@inproceedings{faucris.203351645,
abstract = {This article summarizes the findings of my Ph.D. thesis finished in 2015, whose topic are algorithmic approaches for the solution of network design problems. I focus on the results of a joint project with Deutsche Bahn AG on developing an optimal expansion strategy for the German railway network until 2030 to meet future demands. I have modelled this task as a multi-period network design problem and have derived an efficient decomposition approach to solve it. In a case study on real-world data on the German railway network, I demonstrate both the efficiency of by method as well as the high quality of the solutions it computes.},
address = {Cham},
author = {Bärmann, Andreas},
booktitle = {Operations Research Proceedings 2016},
editor = {Fink A, Fügenschuh A, Geiger MJ},
faupublication = {yes},
isbn = {978-3-319-55702-1},
pages = {3--8},
peerreviewed = {unknown},
publisher = {Springer International Publishing},
title = {{An} {Optimal} {Expansion} {Strategy} for the {German} {Railway} {Network} {Until} 2030},
year = {2018}
}

Read More: http://epubs.siam.org/doi/abs/10.1137/110853248