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 - Heinz, Stefan A1 - Vigerske, Stefan T1 - Extending a CIP framework to solve MIQCPs N2 - This paper discusses how to build a solver for mixed integer quadratically constrained programs (MIQCPs) by extending a framework for constraint integer programming (CIP). The advantage of this approach is that we can utilize the full power of advanced MIP and CP technologies. In particular, this addresses the linear relaxation and the discrete components of the problem. For relaxation, we use an outer approximation generated by linearization of convex constraints and linear underestimation of nonconvex constraints. Further, we give an overview of the reformulation, separation, and propagation techniques that are used to handle the quadratic constraints efficiently. We implemented these methods in the branch-cut-and-price framework SCIP. Computational experiments indicates the potential of the approach. T3 - ZIB-Report - 09-23 KW - mixed integer quadratically constrained programming KW - constraint integer programming KW - convex relaxation KW - nonconvex Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11371 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Pfetsch, Marc T1 - Nonlinear pseudo-Boolean optimization: relaxation or propagation? N2 - Pseudo-Boolean problems lie on the border between satisfiability problems, constraint programming, and integer programming. In particular, nonlinear constraints in pseudo-Boolean optimization can be handled by methods arising in these different fields: One can either linearize them and work on a linear programming relaxation or one can treat them directly by propagation. In this paper, we investigate the individual strengths of these approaches and compare their computational performance. Furthermore, we integrate these techniques into a branch-and-cut-and-propagate framework, resulting in an efficient nonlinear pseudo-Boolean solver. T3 - ZIB-Report - 09-11 KW - Pseudo-Boolean KW - constraint integer programming KW - linear relaxation KW - separation algorithm KW - domain propagation Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11232 SN - 1438-0064 ER - TY - GEN A1 - Achterberg, Tobias A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Koch, Thorsten A1 - Wolter, Kati T1 - Constraint Integer Programming: Techniques and Applications N2 - This article introduces constraint integer programming (CIP), which is a novel way to combine constraint programming (CP) and mixed integer programming (MIP) methodologies. CIP is a generalization of MIP that supports the notion of general constraints as in CP. This approach is supported by the CIP framework SCIP, which also integrates techniques for solving satisfiability problems. SCIP is available in source code and free for noncommercial use. We demonstrate the usefulness of CIP on three tasks. First, we apply the constraint integer programming approach to pure mixed integer programs. Computational experiments show that SCIP is almost competitive to current state-of-the-art commercial MIP solvers. Second, we demonstrate how to use CIP techniques to compute the number of optimal solutions of integer programs. Third, we employ the CIP framework to solve chip design verification problems, which involve some highly nonlinear constraint types that are very hard to handle by pure MIP solvers. The CIP approach is very effective here: it can apply the full sophisticated MIP machinery to the linear part of the problem, while dealing with the nonlinear constraints by employing constraint programming techniques. T3 - ZIB-Report - 08-43 KW - constraint programming KW - mixed integer programming KW - branch-and-cut KW - optimization software KW - chip verification Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10950 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Pfetsch, Marc T1 - Detecting Orbitopal Symmetries N2 - Orbitopes can be used to handle symmetries which arise in integer programming formulations with an inherent assignment structure. We investigate the detection of symmetries appearing in this approach. We show that detecting so-called orbitopal symmetries is graph-isomorphism hard in general, but can be performed in linear time if the assignment structure is known. T3 - ZIB-Report - 08-33 KW - Symmetrie-Erkennung KW - Orbitope KW - Ganzzahlige Programmierung KW - Symmetrie-Brechung KW - Graphenisomorphie KW - symmetry detection KW - orbitopes KW - integer programming KW - symmetry breaking KW - graph ismorphism Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10842 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Pfetsch, Marc T1 - Solving Pseudo-Boolean Problems with SCIP N2 - Pseudo-Boolean problems generalize SAT problems by allowing linear constraints and a linear objective function. Different solvers, mainly having their roots in the SAT domain, have been proposed and compared,for instance, in Pseudo-Boolean evaluations. One can also formulate Pseudo-Boolean models as integer programming models. That is,Pseudo-Boolean problems lie on the border between the SAT domain and the integer programming field. In this paper, we approach Pseudo-Boolean problems from the integer programming side. We introduce the framework SCIP that implements constraint integer programming techniques. It integrates methods from constraint programming, integer programming, and SAT-solving: the solution of linear programming relaxations, propagation of linear as well as nonlinear constraints, and conflict analysis. We argue that this approach is suitable for Pseudo-Boolean instances containing general linear constraints, while it is less efficient for pure SAT problems. We present extensive computational experiments on the test set used for the Pseudo-Boolean evaluation 2007. We show that our approach is very efficient for optimization instances and competitive for feasibility problems. For the nonlinear parts, we also investigate the influence of linear programming relaxations and propagation methods on the performance. It turns out that both techniques are helpful for obtaining an efficient solution method. T3 - ZIB-Report - 08-12 KW - Pseudo-Boolean KW - Constraint Programming KW - Ganzzahlige Programmierung KW - Branch-And-Cut KW - Optimierungssoftware KW - Pseudo-Boolean KW - constraint integer programming KW - integer programming KW - branch-and-cut KW - optimization software Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10671 SN - 1438-0064 ER - TY - GEN A1 - Achterberg, Tobias A1 - Berthold, Timo A1 - Koch, Thorsten A1 - Wolter, Kati T1 - Constraint Integer Programming: a New Approach to Integrate CP and MIP N2 - This article introduces constraint integer programming (CIP), which is a novel way to combine constraint programming (CP) and mixed integer programming (MIP) methodologies. CIP is a generalization of MIP that supports the notion of general constraints as in CP. This approach is supported by the CIP framework SCIP, which also integrates techniques from SAT solving. SCIP is available in source code and free for non-commercial use. We demonstrate the usefulness of CIP on two tasks. First, we apply the constraint integer programming approach to pure mixed integer programs. Computational experiments show that SCIP is almost competitive to current state-of-the-art commercial MIP solvers. Second, we employ the CIP framework to solve chip design verification problems, which involve some highly non-linear constraint types that are very hard to handle by pure MIP solvers. The CIP approach is very effective here: it can apply the full sophisticated MIP machinery to the linear part of the problem, while dealing with the non-linear constraints by employing constraint programming techniques. T3 - ZIB-Report - 08-01 KW - Constraint Programming KW - Ganzzahlige Programmierung KW - Branch-And-Cut KW - Optimierungssoftware KW - Chipverifikation KW - constraint programming KW - mixed integer programming KW - branch-and-cut KW - optimization software KW - chip verification Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10520 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo T1 - Heuristics of the Branch-Cut-and-Price-Framework SCIP N2 - In this paper we give an overview of the heuristics which are integrated into the open source branch-cut-and-price-framework SCIP. We briefly describe the fundamental ideas of different categories of heuristics and present some computational results which demonstrate the impact of heuristics on the overall solving process of SCIP. T3 - ZIB-Report - 07-30 KW - Primalheuristiken KW - Gemischt-Ganzzahlige Programmierung KW - Branch and Cut KW - SCIP KW - mixed integer programming KW - primal heuristics KW - branch and cut KW - SCIP Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10280 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo T1 - RENS - Relaxation Enforced Neighborhood Search N2 - In the recent years, a couple of quite successful large neighborhood search heuristics for mixed integer programs has been published. Up to our knowledge, all of them are improvement heuristics. We present a new start heuristic for general MIPs working in the spirit of large neighborhood search. It constructs a sub-MIP which represents the space of all feasible roundings of some fractional point - normally the optimum of the LP-relaxation of the original MIP. Thereby, one is able to determine whether a point can be rounded to a feasible solution and which is the best possible rounding. Furthermore, a slightly modified version of RENS proves to be a well-performing heuristic inside the branch-cut-and-price-framework SCIP. T3 - ZIB-Report - 07-28 KW - Primalheuristiken KW - Gemischt-Ganzzahlige Programmierung KW - Nachbarschaftssuche KW - mixed integer programming KW - primal heuristics KW - large neighborhood search Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4264 SN - 1438-0064 ER - TY - GEN A1 - Achterberg, Tobias A1 - Berthold, Timo T1 - Improving the Feasibility Pump N2 - The Feasibility Pump of Fischetti, Glover, Lodi, and Bertacco has proved to be a very successful heuristic for finding feasible solutions of mixed integer programs. The quality of the solutions in terms of the objective value, however, tends to be poor. This paper proposes a slight modification of the algorithm in order to find better solutions. Extensive computational results show the success of this variant: in 89 out of 121 MIP instances the modified version produces improved solutions in comparison to the original Feasibility Pump. T3 - ZIB-Report - 05-42 KW - mixed integer programming KW - primal heuristics KW - feasibility pump Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8754 ER - TY - GEN A1 - Shinano, Yuji A1 - Achterberg, Tobias A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Koch, Thorsten A1 - Winkler, Michael T1 - Solving hard MIPLIB2003 problems with ParaSCIP on Supercomputers: An update N2 - Contemporary supercomputers can easily provide years of CPU time per wall-clock hour. One challenge of today's software development is how to harness this wast computing power in order to solve really hard mixed integer programming instances. In 2010, two out of six open MIPLIB2003 instances could be solved by ParaSCIP in more than ten consecutive runs, restarting from checkpointing files. The contribution of this paper is threefold: For the first time, we present computational results of single runs for those two instances. Secondly, we provide new improved upper and lower bounds for all of the remaining four open MIPLIB2003 instances. Finally, we explain which new developments led to these results and discuss the current progress of ParaSCIP. Experiments were conducted on HLRNII, on HLRN III, and on the Titan supercomputer, using up to 35,200 cores. T3 - ZIB-Report - 13-66 KW - Mixed Integer Programming KW - MIPLIB2003 KW - ParaSCIP KW - Ubiquity Generator Framework KW - Supercomputer Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42888 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo T1 - Primal MINLP Heuristics in a nutshell N2 - Primal heuristics are an important component of state-of-the-art codes for mixed integer nonlinear programming (MINLP). In this article we give a compact overview of primal heuristics for MINLP that have been suggested in the literature of recent years. We sketch the fundamental concepts of different classes of heuristics and discuss specific implementations. A brief computational experiment shows that primal heuristics play a key role in achieving feasibility and finding good primal bounds within a global MINLP solver. T3 - ZIB-Report - 13-42 KW - Primal Heuristic KW - MINLP KW - Mixed Integer Nonlinear Programming KW - Feasibility Pump KW - Large Neighborhood Search Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42170 SN - 1438-0064 ER -