TY - GEN A1 - Steffy, Daniel A1 - Wolter, Kati T1 - Valid Linear Programming Bounds for Exact Mixed-Integer Programming N2 - Fast computation of valid linear programming (LP) bounds serves as an important subroutine for solving mixed-integer programming problems exactly. We introduce a new method for computing valid LP bounds designed for this application. The algorithm corrects approximate LP dual solutions to be exactly feasible, giving a valid bound. Solutions are repaired by performing a projection and a shift to ensure all constraints are satisfied; bound computations are accelerated by reusing structural information through the branch-and-bound tree. We demonstrate this method to be widely applicable and faster than solving a sequence of exact LPs. Several variations of the algorithm are described and computationally evaluated in an exact branch-and-bound algorithm within the mixed-integer programming framework SCIP. T3 - ZIB-Report - 11-08 KW - linear programming bounds KW - mixed integer programming KW - branch-and-bound KW - exact computation Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12332 ER - TY - GEN A1 - Heinz, Stefan A1 - Beck, J. Christopher T1 - Solving Resource Allocation/Scheduling Problems with Constraint Integer Programming N2 - Constraint Integer Programming (CIP) is a generalization of mixed-integer programming (MIP) in the direction of constraint programming (CP) allowing the inference techniques that have traditionally been the core of \P to be integrated with the problem solving techniques that form the core of complete MIP solvers. In this paper, we investigate the application of CIP to scheduling problems that require resource and start-time assignments to satisfy resource capacities. The best current approach to such problems is logic-based Benders decomposition, a manual decomposition method. We present a CIP model and demonstrate that it achieves performance competitive to the decomposition while out-performing the standard MIP and CP formulations. T3 - ZIB-Report - 11-14 KW - constraint integer programming KW - cumulative constraint KW - optional resources KW - mixed integer programming KW - constraint programming Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12691 ER - TY - GEN A1 - Cook, William A1 - Koch, Thorsten A1 - Steffy, Daniel A1 - Wolter, Kati T1 - An Exact Rational Mixed-Integer Programming Solver N2 - We present an exact rational solver for mixed-integer linear programming that avoids the numerical inaccuracies inherent in the floating-point computations used by existing software. This allows the solver to be used for establishing theoretical results and in applications where correct solutions are critical due to legal and financial consequences. Our solver is a hybrid symbolic/numeric implementation of LP-based branch-and-bound, using numerically-safe methods for all binding computations in the search tree. Computing provably accurate solutions by dynamically choosing the fastest of several safe dual bounding methods depending on the structure of the instance, our exact solver is only moderately slower than an inexact floating-point branch-and-bound solver. The software is incorporated into the SCIP optimization framework, using the exact LP solver QSopt_ex and the GMP arithmetic library. Computational results are presented for a suite of test instances taken from the MIPLIB and Mittelmann collections. T3 - ZIB-Report - 11-07 KW - mixed integer programming KW - branch-and-bound KW - exact computation Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12329 ER - TY - GEN A1 - Gottwald, Robert Lion A1 - Maher, Stephen J. A1 - Shinano, Yuji T1 - Distributed domain propagation N2 - Portfolio parallelization is an approach that runs several solver instances in parallel and terminates when one of them succeeds in solving the problem. Despite it's simplicity portfolio parallelization has been shown to perform well for modern mixed-integer programming (MIP) and boolean satisfiability problem (SAT) solvers. Domain propagation has also been shown to be a simple technique in modern MIP and SAT solvers that effectively finds additional domain reductions after a variables domain has been reduced. This paper investigates the impact of distributed domain propagation in modern MIP solvers that employ portfolio parallelization. Computational experiments were conducted for two implementations of this parallelization approach. While both share global variable bounds and solutions they communicate differently. In one implementation the communication is performed only at designated points in the solving process and in the other it is performed completely asynchronously. Computational experiments show a positive performance impact of communicating global variable bounds and provide valuable insights in communication strategies for parallel solvers. T3 - ZIB-Report - 16-71 KW - mixed integer programming KW - parallelization KW - domain propagation KW - portfolio solvers Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-61380 SN - 1438-0064 ER - TY - THES A1 - Berthold, Timo T1 - Heuristic algorithms in global MINLP solvers N2 - In the literature for mixed integer programming, heuristic algorithms (particularly primal heuristics) are often considered as stand-alone procedures; in that context, heuristics are treated as an alternative to solving a problem to proven optimality. This conceals the fact that heuristic algorithms are a fundamental component of state-of-the-art global solvers for mixed integer linear programming (MIP) and mixed integer nonlinear programming (MINLP). In the present thesis, we focus on this latter aspect; we study heuristic algorithms that are tightly integrated within global MINLP solvers and analyze their impact on the overall solution process. Our contributions comprise generalizations of primal heuristics for MIP towards MINLP as well as novel ideas for MINLP primal heuristics and for heuristic algorithms to take branching decisions and to collect global information in MIP. These are: - Shift-and-Propagate, a novel propagation heuristic for MIP that does not require the solution to an LP relaxation, - a generic way to generalize large neighborhood search (LNS) heuristics from MIP to MINLP, - an Objective Feasibility Pump heuristic for nonconvex MINLP that uses second-order information and a dynamic selection of rounding procedures, - RENS, an LNS start heuristic for MINLP that optimizes over the set of feasible roundings of an LP solution, - Undercover, an LNS start heuristic for MINLP that solves a largest sub-MIP of a given MINLP, - Rapid Learning, a heuristic algorithm to generate globally valid conflict constraints for MIPs, - Cloud Branching, a heuristic algorithm that exploits dual degeneracy to reduce the number of candidates for branching variable selection. Additionally, we propose a new performance measure, the primal integral, that captures the benefits of primal heuristics better than traditional methods. In our computational study, we compare the performance of the MIP and MINLP solver SCIP with and without primal heuristics on six test sets with altogether 983 instances from academic and industrial sources, including our project partners ForNe, SAP, and Siemens. We observe that heuristics improve the solver performance regarding all measures that we used - by different orders of magnitude. We further see that the harder a problem is to solve to global optimality, the more important the deployment of primal heuristics becomes. The algorithms presented in this thesis are available in source code as part of the solver SCIP, of which the author has been a main developer for the last years. Methods described in this thesis have also been re-implemented within several commercial and noncommercial MIP and MINLP software packages, including Bonmin, CBC, Cplex, Gams, Sulum, and Xpress. KW - mixed integer nonlinear programming KW - primal heuristic KW - mixed integer programming KW - branching rule KW - large neighborhood search KW - solver software Y1 - 2014 UR - http://www.zib.de/berthold/Berthold2014.pdf SN - 978-3-8439-1931-9 PB - Dr. Hut Verlag 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 - 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 - 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 A1 - Perregaard, Michael A1 - Mészáros, Csaba T1 - Four good reasons to use an Interior Point solver within a MIP solver N2 - "Interior point algorithms are a good choice for solving pure LPs or QPs, but when you solve MIPs, all you need is a dual simplex." This is the common conception which disregards that an interior point solution provides some unique structural insight into the problem at hand. In this paper, we will discuss some of the benefits that an interior point solver brings to the solution of difficult MIPs within FICO Xpress. This includes many different components of the MIP solver such as branching variable selection, primal heuristics, preprocessing, and of course the solution of the LP relaxation. T3 - ZIB-Report - 17-42 KW - mixed integer programming KW - interior point algorithm KW - Newton barrier method KW - analytic center Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64599 SN - 1438-0064 ER - TY - GEN A1 - Achterberg, Tobias A1 - Berthold, Timo A1 - Hendel, Gregor T1 - Rounding and Propagation Heuristics for Mixed Integer Programming N2 - Primal heuristics are an important component of state-of-the-art codes for mixed integer programming. In this paper, we focus on primal heuristics that only employ computationally inexpensive procedures such as rounding and logical deductions (propagation). We give an overview of eight different approaches. To assess the impact of these primal heuristics on the ability to find feasible solutions, in particular early during search, we introduce a new performance measure, the primal integral. Computational experiments evaluate this and other measures on MIPLIB~2010 benchmark instances. T3 - ZIB-Report - 11-29 KW - primal heuristic KW - mixed integer programming KW - domain propagation Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-13255 ER -