TY - GEN A1 - Weismantel, Robert A1 - Ferreira, Carlos E. A1 - Martin, Alexander T1 - A Cutting Plane Based Algorithm for the Multiple Knapsack Problem. N2 - In this paper we describe a cutting plane based algorithm for the multiple knapsack problem. We use our algorithm to solve some practical problem instances arising in the layout of electronic circuits and in the design of main frame computers, and we report on our computational experience. This includes a discussion and evaluation of separation algorithms, an LP-based primal heuristic and some implementation details. The paper is based on the polyhedral theory for the multiple knapsack polytope developed in our companion paper SC 93-04 and meant to turn this theory into an algorithmic tool for the solution of practical problems. T3 - ZIB-Report - SC-93-07 Y1 - 1993 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1031 ER - TY - CHAP A1 - Schewe, Lars A1 - Koch, Thorsten A1 - Martin, Alexander A1 - Pfetsch, Marc T1 - Mathematical optimization for evaluating gas network capacities T2 - Evaluating Gas Network Capacities Y1 - 2015 SN - 9781611973686 SP - 87 EP - 102 PB - Society for Industrial and Applied Mathematics ER - TY - JOUR A1 - Pfetsch, Marc A1 - Fügenschuh, Armin A1 - Geißler, Björn A1 - Geißler, Nina A1 - Gollmer, Ralf A1 - Hiller, Benjamin A1 - Humpola, Jesco A1 - Koch, Thorsten A1 - Lehmann, Thomas A1 - Martin, Alexander A1 - Morsi, Antonio A1 - Rövekamp, Jessica A1 - Schewe, Lars A1 - Schmidt, Martin A1 - Schultz, Rüdiger A1 - Schwarz, Robert A1 - Schweiger, Jonas A1 - Stangl, Claudia A1 - Steinbach, Marc A1 - Vigerske, Stefan A1 - Willert, Bernhard T1 - Validation of Nominations in Gas Network Optimization: Models, Methods, and Solutions JF - Optimization Methods and Software N2 - In this article we investigate methods to solve a fundamental task in gas transportation, namely the validation of nomination problem: Given a gas transmission network consisting of passive pipelines and active, controllable elements and given an amount of gas at every entry and exit point of the network, find operational settings for all active elements such that there exists a network state meeting all physical, technical, and legal constraints. We describe a two-stage approach to solve the resulting complex and numerically difficult feasibility problem. The first phase consists of four distinct algorithms applying linear, and methods for complementarity constraints to compute possible settings for the discrete decisions. The second phase employs a precise continuous programming model of the gas network. Using this setup, we are able to compute high quality solutions to real-world industrial instances that are significantly larger than networks that have appeared in the mathematical programming literature before. Y1 - 2014 U6 - https://doi.org/10.1080/10556788.2014.888426 PB - Taylor & Francis ER - TY - GEN A1 - Pfetsch, Marc A1 - Fügenschuh, Armin A1 - Geißler, Björn A1 - Geißler, Nina A1 - Gollmer, Ralf A1 - Hiller, Benjamin A1 - Humpola, Jesco A1 - Koch, Thorsten A1 - Lehmann, Thomas A1 - Martin, Alexander A1 - Morsi, Antonio A1 - Rövekamp, Jessica A1 - Schewe, Lars A1 - Schmidt, Martin A1 - Schultz, Rüdiger A1 - Schwarz, Robert A1 - Schweiger, Jonas A1 - Stangl, Claudia A1 - Steinbach, Marc A1 - Vigerske, Stefan A1 - Willert, Bernhard T1 - Validation of Nominations in Gas Network Optimization: Models, Methods, and Solutions N2 - In this article we investigate methods to solve a fundamental task in gas transportation, namely the validation of nomination problem: Given a gas transmission network consisting of passive pipelines and active, controllable elements and given an amount of gas at every entry and exit point of the network, find operational settings for all active elements such that there exists a network state meeting all physical, technical, and legal constraints. We describe a two-stage approach to solve the resulting complex and numerically difficult mixed-integer non-convex nonlinear feasibility problem. The first phase consists of four distinct algorithms facilitating mixed-integer linear, mixed-integer nonlinear, reduced nonlinear, and complementarity constrained methods to compute possible settings for the discrete decisions. The second phase employs a precise continuous nonlinear programming model of the gas network. Using this setup, we are able to compute high quality solutions to real-world industrial instances whose size is significantly larger than networks that have appeared in the literature previously. T3 - ZIB-Report - 12-41 Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16531 SN - 1438-0064 ER - TY - GEN A1 - Martin, Alexander A1 - Weismantel, Robert T1 - Conjunctive Cuts for Integer Programs N2 - This paper deals with a family of conjunctive inequalities. Such inequalities are needed to describe the polyhedron associated with all the integer points that satisfy several knapsack constraints simultaneously. Here we demonstrate the strength and potential of conjunctive inequalities in connection with lifting from a computational point of view. T3 - ZIB-Report - SC-98-18 KW - Polyhedral Combinatorics KW - Integer Programming KW - Separation Algorithm Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3618 ER - TY - GEN A1 - Martin, Alexander A1 - Weismantel, Robert T1 - Contributions to General Mixed Integer Knapsack Problems N2 - This paper deals with a general mixed integer knapsack polyhedron for which we introduce and analyze a new family of inequalities. We discuss the value of this family both from a theoretic and a computational point of view. T3 - ZIB-Report - SC-97-38 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3075 ER - TY - GEN A1 - Martin, Alexander A1 - Weismantel, Robert T1 - Packing Paths and Steiner Trees: Routing of Electronic Circuits. N2 - One of the challenging problems in the design of electronic circuits is the so-called routing problem. Roughly speaking, the task is to connect so-called terminal sets via wires on a predefined area. In addition, certain design rules are to be taken into account and an objective function such as the wiring length must be minimized. The routing problem in general is too complex to be solved in one step. Depending on the user's choice of decomposing the chip design problem into a hierarchy of stages, on the underlying technology, and on the given design rules, various subproblems arise. We discuss several variants of practically relevant routing problems and give a short overview on the underlying technologies and design rules. Many of the routing problems that come up this way can be formulated as the problem of packing so-called Steiner trees in certain graphs. We consider the Steiner tree packing problem from a polyhedral point of view and present three possibilities to define an appropriate polyhedron. Weighing their pros and cons we decide for one of these polytopes and sketch some of our investigations. T3 - ZIB-Report - SC-93-15 Y1 - 1993 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1113 ER - TY - GEN A1 - Martin, Alexander A1 - Weismantel, Robert T1 - The Intersection of Knapsack Polyhedra and Extensions N2 - This paper introduces a scheme of deriving strong cutting planes for a general integer programming problem. The scheme is related to Chvatal-Gomory cutting planes and important special cases such as odd hole and clique inequalities for the stable set polyhedron or families of inequalities for the knapsack polyhedron. We analyze how relations between covering and incomparability numbers associated with the matrix can be used to bound coefficients in these inequalities. For the intersection of several knapsack polyhedra, incomparabilities between the column vectors of the associated matrix will be shown to transfer into inequalities of the associated polyhedron. Our scheme has been incorporated into the mixed integer programming code SIP. About experimental results will be reported. T3 - ZIB-Report - SC-97-61 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3300 ER - TY - CHAP A1 - Martin, Alexander A1 - Müller, J. A1 - Pokutta, Sebastian T1 - On clearing coupled day-ahead electricity markets T2 - Proceedings of 23rd Australasian Finance and Banking Conference Y1 - 2010 UR - http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1660528 N1 - Additional Note: doi:10.1080/10556788.2013.823544 ER - TY - JOUR A1 - Martin, Alexander A1 - Müller, J. A1 - Pokutta, Sebastian T1 - Strict linear prices in non-convex European day-ahead electricity markets JF - Optimization Methods and Software Y1 - 2014 UR - http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1660528 N1 - Additional Note: 10.1080/10556788.2013.823544 N1 - URL of the PDF: http://dx.doi.org/10.1080/10556788.2013.823544 VL - 29 IS - 1 SP - 189 EP - 221 ER -