TY - GEN A1 - Burgschweiger, Jens A1 - Gnädig, Bernd A1 - Steinbach, Marc T1 - Nonlinear Programming Techniques for Operative Planning in Large Drinking Water Networks N2 - Mathematical decision support for operative planning in water supply systems is highly desirable but leads to very difficult optimization problems. We propose a nonlinear programming approach that yields practically satisfactory operating schedules in acceptable computing time even for large networks. Based on a carefully designed model supporting gradient-based optimization algorithms, this approach employs a special initialization strategy for convergence acceleration, special minimum up and down time constraints together with pump aggregation to handle switching decisions, and several network reduction techniques for further speed-up. Results for selected application scenarios at Berliner Wasserbetriebe demonstrate the success of the approach. T3 - ZIB-Report - 05-31 KW - Water supply KW - large-scale nonlinear programming KW - convergence enhancement KW - discrete decisions KW - network reduction Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8657 ER - TY - GEN A1 - Burgschweiger, Jens A1 - Gnädig, Bernd A1 - Steinbach, Marc T1 - Optimierte Tagesplanung im Berliner Trinkwassernetz N2 - Der Artikel beschreibt ein mathematisches Optimierungssystem zur Betriebsplanung in großen Wassernetzen, das bei den Berliner Wasserbetrieben eingesetzt wird. Für das Berliner Versorgungsnetz werden Optimierungsergebnisse vorgestellt. T3 - ZIB-Report - 05-32 KW - Trinkwasserversorgung KW - kostenminimale Betriebsplanung KW - nichtlineare Optimierung KW - diskrete Entscheidungen Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8668 ER - TY - GEN A1 - Steinbach, Marc T1 - On PDE Solution in Transient Optimization of Gas Networks N2 - Operative planning in gas distribution networks leads to large-scale mixed-integer optimization problems involving a hyperbolic PDE defined on a graph. We consider the NLP obtained under prescribed combinatorial decisions---or as relaxation in a branch and bound framework, addressing in particular the KKT systems arising in primal-dual interior methods. We propose a custom solution algorithm using sparse local projections, based on the KKT systems' structual properties induced by the discretized gas flow equations in combination with the underlying network topology. The numerical efficiency and accuracy of the algorithm are investigated, and detailed computational comparisons with a control space method and with the multifrontal solver MA27 are provided. T3 - ZIB-Report - 04-46 KW - Gas network KW - operative planning KW - PDE constrained optimization KW - KKT system factorization KW - sparse projection method Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8215 ER - TY - GEN A1 - Burgschweiger, Jens A1 - Gnädig, Bernd A1 - Steinbach, Marc T1 - Optimization Models for Operative Planning in Drinking Water Networks N2 - The topic of this paper is minimum cost operative planning of pressurized water supply networks over a finite horizon and under reliable demand forecast. Since this is a very hard problem, it is desirable to employ sophisticated mathematical algorithms, which in turn calls for carefully designed models with suitable properties. The paper develops a nonlinear mixed integer model and a nonlinear programming model with favorable properties for gradient-based optimization methods, based on smooth component models for the network elements. In combination with further nonlinear programming techniques (to be reported elsewhere), practically satisfactory near-optimum solutions even for large networks can be generated in acceptable time using standard optimization software on a PC workstation. Such an optimization system is in operation at Berliner Wasserbetriebe. T3 - ZIB-Report - 04-48 KW - Drinking water supply KW - distribution network KW - minimum cost operative planning KW - continuous time model KW - mixed integer model KW - nonlinear programming m Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8237 ER - TY - GEN A1 - Berthold, Timo A1 - Gleixner, Ambros T1 - Undercover: a primal MINLP heuristic exploring a largest sub-MIP N2 - We present Undercover, a primal heuristic for nonconvex mixed-integer nonlinear programming (MINLP) that explores a mixed-integer linear subproblem (sub-MIP) of a given MINLP. We solve a vertex covering problem to identify a minimal set of variables that need to be fixed in order to linearize each constraint, a so-called cover. Subsequently, these variables are fixed to values obtained from a reference point, e.g., an optimal solution of a linear relaxation. We apply domain propagation and conflict analysis to try to avoid infeasibilities and learn from them, respectively. Each feasible solution of the sub-MIP corresponds to a feasible solution of the original problem. We present computational results on a test set of mixed-integer quadratically constrained programs (MIQCPs) and general MINLPs from MINLPLib. It turns out that the majority of these instances allow for small covers. Although general in nature, the heuristic appears most promising for MIQCPs, and complements nicely with existing root node heuristics in different state-of-the-art solvers. T3 - ZIB-Report - 12-07 KW - Primal Heuristic KW - Mixed-Integer Nonlinear Programming KW - Large Neighborhood Search KW - Mixed-Integer Quadratically Constrained Programming KW - Nonconvex Optimization Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14631 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Gleixner, Ambros T1 - Undercover – a primal heuristic for MINLP based on sub-MIPs generated by set covering N2 - We present Undercover, a primal heuristic for mixed-integer nonlinear programming (MINLP). The heuristic constructs a mixed-integer linear subproblem (sub-MIP) of a given MINLP by fixing a subset of the variables. We solve a set covering problem to identify a minimal set of variables which need to be fixed in order to linearise each constraint. Subsequently, these variables are fixed to approximate values, e.g. obtained from a linear outer approximation. The resulting sub-MIP is solved by a mixed-integer linear programming solver. Each feasible solution of the sub-MIP corresponds to a feasible solution of the original problem. Although general in nature, the heuristic seems most promising for mixed-integer quadratically constrained programmes (MIQCPs). We present computational results on a general test set of MIQCPs selected from the MINLPLib. T3 - ZIB-Report - 09-40 KW - MINLP KW - MIQCP KW - Primalheuristik KW - Nachbarschaftssuche KW - Mengenüberdeckung KW - mixed-integer nonlinear programming KW - MIQCP KW - primal heuristic KW - large neighborhood search KW - set covering Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11632 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Gleixner, Ambros A1 - Heinz, Stefan A1 - Vigerske, Stefan T1 - Analyzing the computational impact of MIQCP solver components N2 - 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. T3 - ZIB-Report - 13-08 KW - mixed-integer quadratically constrained programming KW - mixed-integer programming KW - branch-and-cut KW - nonconvex KW - global optimization Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17754 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Gleixner, Ambros A1 - Heinz, Stefan A1 - Vigerske, Stefan T1 - On the computational impact of MIQCP solver components N2 - 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. T3 - ZIB-Report - 11-01 KW - MIQCP KW - MIP KW - mixed-integer quadratically constrained programming KW - computational KW - nonconvex Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11998 ER - TY - GEN A1 - Bestuzheva, Ksenia A1 - Gleixner, Ambros A1 - Völker, Helena T1 - Strengthening SONC Relaxations with Constraints Derived from Variable Bounds N2 - Certificates of polynomial nonnegativity can be used to obtain tight dual bounds for polynomial optimization problems. We consider Sums of Nonnegative Circuit (SONC) polynomials certificates, which are well suited for sparse problems since the computational cost depends only on the number of terms in the polynomials and does not depend on the degrees of the polynomials. This work is a first step to integrating SONC-based relaxations of polynomial problems into a branch-and-bound algorithm. To this end, the SONC relaxation for constrained optimization problems is extended in order to better utilize variable bounds, since this property is key for the success of a relaxation in the context of branch-and-bound. Computational experiments show that the proposed extension is crucial for making the SONC relaxations applicable to most constrained polynomial optimization problems and for integrating the two approaches. T3 - ZIB-Report - 22-23 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-88306 SN - 1438-0064 ER - TY - GEN A1 - Vu, Thi Huong A1 - Litzel, Ida A1 - Koch, Thorsten T1 - Similarity-based fuzzy clustering scientific articles: potentials and challenges from mathematical and computational perspectives N2 - Fuzzy clustering, which allows an article to belong to multiple clusters with soft membership degrees, plays a vital role in analyzing publication data. This problem can be formulated as a constrained optimization model, where the goal is to minimize the discrepancy between the similarity observed from data and the similarity derived from a predicted distribution. While this approach benefits from leveraging state-of-the-art optimization algorithms, tailoring them to work with real, massive databases like OpenAlex or Web of Science -- containing about 70 million articles and a billion citations -- poses significant challenges. We analyze potentials and challenges of the approach from both mathematical and computational perspectives. Among other things, second-order optimality conditions are established, providing new theoretical insights, and practical solution methods are proposed by exploiting the problem’s structure. Specifically, we accelerate the gradient projection method using GPU-based parallel computing to efficiently handle large-scale data. T3 - ZIB-Report - 25-09 KW - bibliometrics KW - fuzzy clustering KW - large-scale publication data KW - non-convex optimization KW - second-order optimality KW - gradient projection methods KW - Nesterov acceleration KW - GPU-based parallel computing Y1 - 2025 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/10036 ER - TY - GEN A1 - Ehrhardt, Klaus A1 - Steinbach, Marc T1 - Nonlinear Optimization in Gas Networks N2 - The operative planning problem in natural gas distribution networks is addressed. An optimization model focusing on the governing PDE and other nonlinear aspects is presented together with a suitable discretization for transient optimization in large networks by SQP methods. Computational results for a range of related dynamic test problems demonstrate the viability of the approach. T3 - ZIB-Report - 03-46 KW - Gas networks KW - operative planning KW - large-scale optimization Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7687 ER - TY - GEN A1 - Henrion, Rene A1 - Li, Pu A1 - Möller, Andris A1 - Steinbach, Marc A1 - Wendt, Moritz A1 - Wozny, Günter T1 - Stochastic Optimization for Operating Chemical Processes Under Uncertainty N2 - Mathematical optimization techniques are on their way to becoming a standard tool in chemical process engineering. While such approaches are usually based on deterministic models, uncertainties such as external disturbances play a significant role in many real-life applications. The present article gives an introduction to practical issues of process operation and to basic mathematical concepts required for the explicit treatment of uncertainties by stochastic optimization. T3 - ZIB-Report - 01-04 KW - Uncertainty KW - Chemical Processes KW - Multistage Stochastic Programs KW - Probabilistic Constraints Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6304 ER - TY - GEN A1 - Bestuzheva, Ksenia A1 - Gleixner, Ambros A1 - Vigerske, Stefan T1 - A Computational Study of Perspective Cuts N2 - The benefits of cutting planes based on the perspective function are well known for many specific classes of mixed-integer nonlinear programs with on/off structures. However, we are not aware of any empirical studies that evaluate their applicability and computational impact over large, heterogeneous test sets in general-purpose solvers. This paper provides a detailed computational study of perspective cuts within a linear programming based branch-and-cut solver for general mixed-integer nonlinear programs. Within this study, we extend the applicability of perspective cuts from convex to nonconvex nonlinearities. This generalization is achieved by applying a perspective strengthening to valid linear inequalities which separate solutions of linear relaxations. The resulting method can be applied to any constraint where all variables appearing in nonlinear terms are semi-continuous and depend on at least one common indicator variable. Our computational experiments show that adding perspective cuts for convex constraints yields a consistent improvement of performance, and adding perspective cuts for nonconvex constraints reduces branch-and-bound tree sizes and strengthens the root node relaxation, but has no significant impact on the overall mean time. T3 - ZIB-Report - 21-07 KW - perspective cuts, mixed-integer nonlinear programming, nonconvex optimization, computational study Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-81821 SN - 1438-0064 ER -