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  • 1
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    Supporting Global Numerical Optimization of Rational Functions by Generic Symbolic Convexity Tests (2010)
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    Publication Date: 2020-12-11
    Description: Convexity is an important property in nonlinear optimization since it allows to apply efficient local methods for finding global solutions. We propose to apply symbolic methods to prove or disprove convexity of rational functions over a polyhedral domain. Our algorithms reduce convexity questions to real quantifier elimination problems. Our methods are implemented and publicly available in the open source computer algebra system REDUCE. Our long term goal is to integrate REDUCE as a workhorse'' for symbolic computations into a numerical solver.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Format: application/postscript
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  • 2
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    Large Neighborhood Search beyond MIP (2011)
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    Publication Date: 2022-03-14
    Description: Large neighborhood search (LNS) heuristics are an important component of modern branch-and-cut algorithms for solving mixed-integer linear programs (MIPs). Most of these LNS heuristics use the LP relaxation as the basis for their search, which is a reasonable choice in case of MIPs. However, for more general problem classes, the LP relaxation alone may not contain enough information about the original problem to find feasible solutions with these heuristics, e.g., if the problem is nonlinear or not all constraints are present in the current relaxation. In this paper, we discuss a generic way to extend LNS heuristics that have been developed for MIP to constraint integer programming (CIP), which is a generalization of MIP in the direction of constraint programming (CP). We present computational results of LNS heuristics for three problem classes: mixed-integer quadratically constrained programs, nonlinear pseudo-Boolean optimization instances, and resource-constrained project scheduling problems. Therefore, we have implemented extended versions of the following LNS heuristics in the constraint integer programming framework SCIP: Local Branching, RINS, RENS, Crossover, and DINS. Our results indicate that a generic generalization of LNS heuristics to CIP considerably improves the success rate of these heuristics.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 3
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    Towards globally optimal operation of water supply networks (2012)
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    Publication Date: 2020-08-05
    Description: This paper is concerned with optimal operation of pressurized water supply networks at a fixed point in time. We use a mixed-integer nonlinear programming (MINLP) model incorporating both the nonlinear physical laws and the discrete decisions such as switching pumps on and off. We demonstrate that for instances from our industry partner, these stationary models can be solved to ε-global optimality within small running times using problem-specific presolving and state-of-the-art MINLP algorithms. In our modeling, we emphasize the importance of distinguishing between what we call real and imaginary flow, i.e., taking into account that the law of Darcy-Weisbach correlates pressure difference and flow along a pipe if and only if water is available at the high pressure end of a pipe. Our modeling solution extends to the dynamic operative planning problem.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 4
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    Validation of Nominations in Gas Network Optimization: Models, Methods, and Solutions (2012)
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    Publication Date: 2021-03-16
    Description: 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.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Format: application/pdf
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  • 5
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    Analyzing the computational impact of MIQCP solver components (2013)
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    Publication Date: 2022-03-14
    Description: We provide a computational study of the performance of a state-of-the-art solver for nonconvex mixed-integer quadratically constrained programs (MIQCPs). Since successful general-purpose solvers for large problem classes necessarily comprise a variety of algorithmic techniques, we focus especially on the impact of the individual solver components. The solver SCIP used for the experiments implements a branch-and-cut algorithm based on a linear relaxation to solve MIQCPs to global optimality. Our analysis is based on a set of 86 publicly available test instances.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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    OPUS
  • 6
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    Linear Underestimators for bivariate functions with a fixed convexity behavior (2013)
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    Publication Date: 2020-08-05
    Description: This is a technical report for the SCIP constraint handler cons_bivariate. We describe a cut-generation algorithm for a class of bivariate twice continuously differentiable functions with fixed convexity behavior over a box. Computational results comparing our cut-generation algorithms with state-of-the-art global optimization software on a series of randomly generated test instances are reported and discussed.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Format: application/x-gzip
    Format: application/pdf
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  • 7
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    Mixed-Integer Nonlinear Problems in Transportation Applications (2010)
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    Publication Date: 2020-08-05
    Language: English
    Type: conferenceobject , doc-type:conferenceObject
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  • 8
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    SCIP: Global Optimization of Mixed-Integer Nonlinear Programs in a Branch-and-Cut Framework (2016)
    Details
    Publication Date: 2020-08-05
    Description: This paper describes the extensions that were added to the constraint integer programming framework SCIP in order to enable it to solve convex and nonconvex mixed-integer nonlinear programs (MINLPs) to global optimality. SCIP implements a spatial branch-and-bound algorithm based on a linear outer-approximation, which is computed by convex over- and underestimation of nonconvex functions. An expression graph representation of nonlinear constraints allows for bound tightening, structure analysis, and reformulation. Primal heuristics are employed throughout the solving process to find feasible solutions early. We provide insights into the performance impact of individual MINLP solver components via a detailed computational study over a large and heterogeneous test set.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Format: application/pdf
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  • 9
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    Comparing MIQCP solvers to a specialised algorithm for mine production scheduling (2009)
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    Publication Date: 2020-08-05
    Description: In this paper we investigate the performance of several out-of-the box solvers for mixed-integer quadratically constrained programmes (MIQCPs) on an open pit mine production scheduling problem with mixing constraints. We compare the solvers BARON, Couenne, SBB, and SCIP to a problem-specific algorithm on two different MIQCP formulations. The computational results presented show that general-purpose solvers with no particular knowledge of problem structure are able to nearly match the performance of a hand-crafted algorithm.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Format: application/postscript
    Library Location Call Number Volume/Issue/Year Availability
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    OPUS
  • 10
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    On the computational impact of MIQCP solver components (2011)
    Details
    Publication Date: 2022-03-14
    Description: We provide a computational study of the performance of a state-of-the-art solver for nonconvex mixed-integer quadratically constrained programs (MIQCPs). Since successful general-purpose solvers for large problem classes necessarily comprise a variety of algorithmic techniques, we focus especially on the impact of the individual solver components. The solver SCIP used for the experiments implements a branch-and-cut algorithm based on linear outer approximation to solve MIQCPs to global optimality. Our analysis is based on a set of 86 publicly available test instances.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    OPUS
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